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rspa_1915_0006 | 0950-1207 | Electromagnetic waves in a perfectly conducting tube. | 170 | 179 | 1,915 | 91 | Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character | L. Silberstein, Ph. D.|Prof. A. W. Porter, F. R. S. | article | 6.0.4 | http://dx.doi.org/10.1098/rspa.1915.0006 | en | rspa | 1,910 | 1,900 | 1,900 | 1 | 17 | 268 | http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1915_0006 | 10.1098/rspa.1915.0006 | null | null | null | Fluid Dynamics | 32.013246 | Tables | 24.300019 | Fluid Dynamics | [
42.87064743041992,
-45.77571487426758
] | ]\gt ; Electromagnetic in Perfectly Conducting Tube .
By L. SILBERSTEIN , Ph. D. , Lecturer in Natural Philosophy at the University of Bome .
Communicated by Prof. A. W. Porter , F.R.S. Received December 5 , 1914 .
) The problem of waves in conducting tubes has already been treated by various authors .
* Nevertheless , the solutions here proposed , offering certain peculiarities with respect to the velocity of the corresponding waves , and partly also with respect to the shape .
and distribution of the lines of orce , seemed worthy of notice .
Let be measured along the axis of an infinite right cylindrical tube of circular section .
The material of the tube is assumed to be a perfect conductor , its interior being empty or filled with air .
The electromagnetic waves will be assumed throughout to be axially symmetrical and of permanent type , i.e. to conserve all their features while proceeding along the tube .
If be the distance of a point from the axis , further , and the * J. J. Thomson , 'Recent Researches in Electricity and Mgnetism , ' 1893 ; Lord Bayleigh , 'Phil .
Mag vol. 43 , p. 125 ( 1897 ) ; R. H. Weber , 'Ann .
der Phyffi , ' vol. 8 , p. 721 ( 1902 ) .
An account of the experimental investigations by .
Lang , Drude und Becker will be found in a paper by A. Kalahne , 'Ann .
PhySik ' ) .
Kalahne 's theoretical investigations concern only a ] tube .
:
|
rspa_1915_0007 | 0950-1207 | The analysis of gases after passage of electric discharge. | 180 | 189 | 1,915 | 91 | Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character | A. C. G. Egerton|Prof. J. N. Collie, F. R. S. | article | 6.0.4 | http://dx.doi.org/10.1098/rspa.1915.0007 | en | rspa | 1,910 | 1,900 | 1,900 | 1 | 128 | 2,860 | http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1915_0007 | 10.1098/rspa.1915.0007 | null | null | null | Thermodynamics | 36.073759 | Atomic Physics | 30.61428 | Thermodynamics | [
-0.20577555894851685,
-50.78888702392578
] | ]\gt ; the onter air during the experiment or the subsequent analysis , or ( iii ) be case tutation process detion o the above authors appear to show that : because tases oution aubsequent analysis o the ases .
( ii ) The gases did llot enter from the outer air , because similar effects were btain e the tube was jacketed by another tube , the space between the two evacuated .
Sometimes , also .
only helium was obtained , whereas neon would be expected if air had leaked in .
( iii ) gas was not formed by some change at the electrodes , as similar effects were obtained ( though to a lesser extent ) by means of an electrodeless discharge .
The result of the work indicated , then , that the hydrogen ( or possibly the glass tube ) had in some way been affected by the discharge , so as to obtain helium or neon .
It is noteworthy that positive results of the production of He or No are only sometimes obtained .
J. J. Thomson .
had noticed that helium lines were always very marked in the positive ray spectrum produced the } ) ombardlnent of metallic substances by cathode is , when only pure hydrogen had been allowed to enter the tube .
He favoured the view that the metallic electrodes were responsible for the production of the helium , and that it might have been formed by slow radioactive processes and only liberated by the cathodic bombardment .
Subsequently the Hon. R. Chem. Trans. ; and ' Chem. Soc. Proc. , ' vol. 29 , p. 217 ( 1913 ) .
neon ( trutt mshort investigation obtained nisch and the residual by means of cooled charcoal ) .
He held that the gases could not be safely transferred by means of small inverted tubes over mercury , without the possibility of a trace of air entering the process : and this led him to construct an apparatus which was entire ] self-contained , and by means of which all external transference the tube to the analysis atus w entirely avoided .
The work of these investigators has not , therefore , led to similar results , and the following questions present themselves :Firstly , were the electrical conditions of Strutt 's experiments unfavourable to the formation of rare rases ?
Secondly , was the method of analysis less irdly , is it possible to prevent access of air into the apparatus during the experiment and analysis , and to entirely free the electrodes of all detectable traces of rare gases ?
In the work to be described , which was carried out in continuation of some other work along similar lines , special attention has been paid to these points : the electrical conditions were varied considerably by altering the apparatus and the shape of the tubes ; the method of analysis was made as sensitive as possible and blank tests were frequently applied .
The result , unfortunately , has not thrown any light on the production of the rare gases , as these gases were not obtained when the tube and electrodes had been evacuated as far as possible , and when there was no detectable leakage of air in the apparatus .
Experimental .
In continuation of some former work the depicted was built .
It has been found that when the gases were pumped out of the lube and transferred by means .
small tubes to the analysing burettes , as often as not , traces of argon could be detected .
This argon was traced to some mercury ; by means of tube , this difficulty was overcome and the gases could be directly and completely into the analysing burette from the discharge tube without coming into contact with ercury , which stands in the presence of air .
The presence of about of cu .
mm. of air can be detected by the argon .
The nitrogen is often not found unless larger quantities of air are present , as ozone is formed during the analysis and combines with the nitrogen and mercury ; phosphorus , too , absorbs 'Roy .
Soc. Proc , vol. 89 , p. 499 ( 1914 ) .
a small cup of liquid air , and the discharge is passed ; water and ozone are formed and a high vacuum is obtained ozone partly condensing and partly combining with the mercury ) .
The tube and the mercury are then warmed and absorbed by opening to the phosphorus or charcoal .
Sometimes Analysis of Gases after Passage of Electric .
183 a small quantity of oxygen and carbon oxides remain unabsorbed , t , hese disappear on passing the discharge the capillary jacketed by liquid air , owing to the formation of ozone ; any small residual quantities of nitrogen or of hydrogen also disappear to this .
In order to be sure that none of the rare ases are hidden , the mercury is warmed , the process of analysis repeated .
and the spectrum of the residual ases carefully examined .
In the final experiment the hydrogen and were sparked at ordinary pressure by means of two platinum wires sealed in the burette .
The following experiments are some of those that have been made with this apparatus:\mdash ; ( a ) The discharge tube was a cylindrical tube with two disc electrodes placed opposite each other .
A 6-inch coil with hammer break was used .
Gas analysed by phosphorus\mdash ; No No or He found .
( b ) Another similar tube .
A 9-inch coil with a long spring hanumer break .
Gas analysed by phosphorus\mdash ; No , no He , no No found .
( c ) A similar tube but with both anti-cathode and anode .
A large -inch coil , Caldwell electrolytic break , plate and point rectifier in the circuit .
Gas analysed similarly\mdash ; Trace , no No , no He .
( This merest trace of argon came from the oxygen used.for the analysis .
) ( d ) A tube with spiral aluminium wire as cathode , anode in a small side bulb connected with the narrow tube , the tube acting in some measure as a rectifier .
A 20-inch coil , electrolytic break and rectifier , also a 9-inch coil and two types of hammer break .
Analysed by No or He ( experiment lasted lours ) .
( e ) A tube with two platinunl electrodes 12 cm .
by mm. in two lass bulbs ( 4 cm .
) connected by a narrow tube .
Gas analysed by charcoal:\mdash ; 1 .
A 9-inch coil , hammer breaks and rectifier\mdash ; No No or He .
2 .
A 20-inch coil , hammer break in No or He .
3 .
A 20-inch coil , electrolytic break and rectifier\mdash ; No No or He .
In this experiment there was much " " .
\ldquo ; from the cathode ; in the last part of the experiment the cathode was olten red hot .
( f ) Similar tube , aluminium anodes , platinum cathodes .
-inch coil , electrolytic break and rectifier .
Very much ' splashing Gas analysed by charcoal\mdash ; No No or He .
( g ) Spectrum-shaped tube ; palladium rod anode , palladium plate cathodes , a 9-inch coil and a hammer break .
There was so much ' splashing\ldquo ; that a larger coil could not be used .
Gas analysed by charcoal\mdash ; No No or He .
( h ) One cubic centimetre was pumped out of a llontgen tube , through which the heaviest obtainable unidirectional discharge had been passed for 2 .
A20-inch coil , electrolytic break and rectifier ( five hours , cathode that its presence was doubtful .
iven oathode Tashed outwas ranode wtogether arWIn aents theated a with pure hydrogen .
The duration of each experiment was about eight : hours , unless otherwise stated .
At a certain of exhaustion the hydrogen is shot very easily into walls of the tube , provided the latter does not become too hot or the vacuum too low .
Charges of hydrogen are let in , when necessary , from the place between the two taps provided for that purpose .
amount of absorbed by the walls appears to depend on the temperature , the shape of the tube , the pressure of the gas , and the potential of the cathode during exhaustion .
A long time is equired to entirely rid the walls and electrodes of gases ; if a stronger cathode discharge is passed through the tube it is generally possible to tain more gas ( hydrogen and a little oxygen ) .
However , with small tubes and many washes with pure hydrogen , it is certainly quite possible to get rid of all detectable traces of air .
Once , when a minute leak was present , it was noticed that the spectrum of nitrogen was not given for some minutes , but only that of oxygen ; the tube had dium electrodes .
It would seem that very small quantities of nitrogen had been made active , and were absorbed by metal deposited on the walls of the tube .
of Experiments.\mdash ; In the above experiments electric has been passed with three different sized coils , three different types of interrupters , tJrrough various sized and shaped tubes , with palladium , platinum , !
osed ihang eectrodes oarious shapes ayses oarried ovaysIt wnteresti and to calculate approximately the amount of that would be needed .
In the first place , suppose one assumes an association process , and let the helium be formed from a certain quantity of .
It is a consequence of relativity theory that the variation of the mass of a is connected with the variation of the internal energy by the , where is the square of the velocity of , and the last term merely depends on the movement of the system relative to the observer , and can be ected in this case .
* ergs per gramme-molecule of ] ) elium formed , ergs per atom of helium .
1/ 100 .
mm. of helium formed ( a detectable quantity ) would therefore need elgs .
An induction coil certainly might supply this total energy in am hour , but there are two important considerations .
First , the energy is only conveyed in the form of charged particles , and there can hardly be particles possessing energy of the order of ergs within a discharge tube ; the energy of the hydrogen ion in the dark space being of order ergs , and that of the cathode particles on the average ergs , ( a cathode particle would have to move in.a field of over 30 million volts to possess ergs ) .
Many particles would therefore have to act simultaneously or their effects be additive ; this would increase enormously the time required to produce a detectable quantity of helium .
The second consideration is that four hydrogen atoms or possibly two hydrogen lnolecules must lneet in order to form helium , and the energy must either be supplied at the moment of encounter , or they must be altered previously in such a way that they will associate on encounter and form helium .
It is possible to calculate the probability of the occurrence of such a collision .
'Jahrb .
der Radioakt p. 636 1912 ) .
Mr. A. C. G. Egerton .
of two or ?
in a time is where is the duration of the collision , the time between two ] But , to kinetic theory , ' the diameter of an atom , pressure , 11 number of atoms per unit volume at normal pressure and temperature , mean velocity ; and where is the fraction of the diameter to which distance the atoms interrate ; will be a maximum when in molecules per cubic centimetre , mm. , cm .
, The frequency of collision is , ?
times per second .
The number of atoms per centimetre at 1 .
pressure is atoms .
total number of collisions in a tube of 100 .
is per second The probability that during a collision lasting secs .
( at the colliding atoms will be struck other ato1ns is or for a i.ourfold collision ; and the number of collisions per second in a tube of 100 .
will become per sec. That helium can be produced by a fourfold collision of hydrogen atoms .
* J. H. Jeans , 'Dynamic Theory of Gases , ' p. 205 .
ains troduced fheAnalysis o see what those conditions in an electric discharge tube could be , other than the effect of an electron upon them .
So it is necessary to calculate the chance of a collision of a cathode particle with the molecules of hydrogen .
The probability of an electron colliding with an atom or molecule would be where number of times an electron collides with an atom per second .
where current in anlperes , distance between electrodes , free path of electrons , number of atoms in discharge tube .
The maximum value of is , where velocity of electrons , diameter of atom .
But , potential between electrodes in E.S. units .
But and , where is volume ; therefore Putting milliampere .
cm .
, mm. , volts , The probability that an electron should strike a simple collision of two hydrogen molecules , which lasts secs .
, is therefore , or as collisions take place per second , atoms of helium might be formed per second , which would mean a detectable quantity in about 6 years .
Thus even a collision of an electron with two in the gases within discharge tube , unless the conditions within a tube are very different what are taken to be and are such as to increase enormously the nulnber of collisions of electrons , atoms , ions or molecules .
This result is arrived at both from considerations of the energy needed to effect a change and also from considerations of the possible a Vexed , let some disi eration process be could the helium be formed by the ration of the metallic electrodes or of the oxygen , silica , and other constituents of the glass or oxygen , the discharge tube The atomic weight of llercury is and if the atoms were entirely split up into helium atoms , energy of order of 10 would be required per ( this follows as before from Einstein 's theory ) .
For or carbon the quantity might be somewhat less than ergs but for most elements it would be considerably more .
The chances of finding in a discharge tube particles possessing sufficient to bring about such complete disintegration is small ; the -particle possesses energy ergs but even this does not seem to ppreciably drate the atoms it meets with .
* However , there is no reason to suppose that the atonls must be completely clisintegrated .
It is onceivable that a partial disintegration and libel.ation of a helium atom from certain less stable atoms might arise under conditions of electric stress such as are obtained in a tube .
Snch effects should be most likely to occur with the heaviest elements or possibly with rare earths or potassium .
From the above considerations it is more probable that the production of rare gases would arise from a process of disintegration of association .
Although it is not possible to make these calculations without certain It is possible the -particle docs possess sufficient energy to disintegrale some of atoms it ( see Ramsay and Cameroll , Chem. Soc. Trans vol. 91 , p. 1605 1907 ) ) .
eases aobtained bvidence oenergy othatassumptions which atten)radioactivityEl ?
with t of Collie and Patterson , by the of an electric has not been successful .
Both from theoretical and experimental standpoints , it is held that if such a production has an origin other than from atmospheric contaminatioL1 , the source must be looked for in some action on the solids which compose the tube ( electrodes ) rather than from gases .
I am greatly indebted to lnv friend , .
] .
A. indemann , the method of calculating the probability of collision of electron .
and and of some of the samples gas analysed .
I have also to thank Prof. Nernst for his interest in these experiments carried out in his laboratory in Berlin .
The experiments were conducted in continuation of work carried out with Sir William amsay on other lines but with somewhat similar apparatns , and to him and Prof. Collie I am grateful for the generous permission to the work .
|
rspa_1915_0008 | 0950-1207 | An electrically heated full radiator. | 190 | 197 | 1,915 | 91 | Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character | H. B. Keene, D. Sc.|Sir Oliver Lodge, F. R. S. | article | 6.0.4 | http://dx.doi.org/10.1098/rspa.1915.0008 | en | rspa | 1,910 | 1,900 | 1,900 | 9 | 138 | 3,000 | http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1915_0008 | 10.1098/rspa.1915.0008 | null | null | null | Thermodynamics | 39.473607 | Electricity | 31.125962 | Thermodynamics | [
0.3873116374015808,
-24.69448471069336
] | 190 An Electrically Heated Full Radiator .
By H. B. Keen , D.Sc .
, Assistant Lecturer in Physics at the University of Birmingham .
( Communicated by Sir Oliver Lodge , F.R.S. Received December 10 , 1914 .
) In a previous paper by the author* the value of the " radiation constant " of the Stefan-Boltzmann law was obtained , using an apparatus which fulfilled the condition of a full receiver ; all previous determinations being open to objection on the ground that this condition was not attained .
The " emitter " used in that investigation and maintained at a temperature of 1100 ' C. was of the usual type\#151 ; a modified form of Heroeus furnace ; but it was pointed out at the time that such a radiator is by no means a uniform temperature enclosure , and that the author intended to construct such an enclosure which would approximate more nearly to the ideal full radiator .
The value of the radiation constant is open ttf criticism until it has been determined with apparatus in which both " emitter " and " receiver " fulfil " black body " conditions .
The present paper describes an electrically heated high temperature full radiator , for which there is such a pressing need in full radiation measurements .
The Form of the Radiator.\#151 ; The radiator consists of a bottle-shaped crucible of alumina with a cylindrical body 8 inches in diameter , and with conical ends and circular aperture B ( fig. 1 ) .
The crucible was wound with platinum strip for electrical heating in a manner to be described later .
This form of radiator is preferable to the sphere , as it somewhat simplifies the difficulty of the electrical winding , although considerable difficulty was experienced in winding the conical ends .
A further advantage consists in the fact that the region A , which will be " visible " from the receiver , loses less radiation to the cold aperture B than it would do were that surface parallel to B. This principle is utilised in the receiver previously described .
Method of Electrical Winding.\#151 ; It was desired to attain a temperature of at least 1000-1100 ' C. , and for this purpose platinum strip was used .
Experiments seem to show that alumina is not the ideal material for the crucible , on account of the fact that in the earlier experiments the platinum winding invariably broke down on cooling after maintaining the radiator for some hours at 1000 ' C. , and after switching off the heating current .
It * " A Determination of the Radiation Constant , " 4 Roy .
Soc. Proe .
, ' A , vol. 88 , p. 49 ( 1913 ) . .
An Electrically Heated Radiator .
appeared that the platinum adhered to the crucible , and on cooling the expansion of the alumina fractured the platinum strip .
In view of this property of the clays at high temperatures it is probable that porcelain would be preferable .
It was desirable that the strip should be held in position in some manner , KIESELCUHR ALUMINA ALUMINA APERTURE FOR THERMOCOUPLE ALUMINA IRON TUBE UNIFORM TEMPERATURE ENCLOSURE Fig. 1 .
particularly on the cones .
The dental cements tried for this purpose proved to be unsatisfactory\#151 ; breakdowns continued to occur , and on examination the strip seemed to show that electrolysis was taking place with the cement .
The two main difficulties to be overcome were ( 1 ) the expansion of the crucible on cooling , ( 2 ) electrolysis .
The first was solved by " crimping " the platinum strip between two cogDr .
H. B. Keen .
wheels , and winding it so as to be separated from the crucible by a pliable mica bed .
This prevented the strip adhering to the crucible and allowed of considerable movement .
The electrolysis difficulty was overcome by removing all traces of dental cement and replacing it by pure aluminium oxide .
Since the adoption of this method of winding no further difficulty has been experienced .
These practical points are recorded as they may be of interest to others concerned in high temperature furnace work .
Some 30 metres of platinum strip 042 cm .
wide and 0'012 cm .
thick were used .
This thickness was chosen for strength to minimise the risk of mechanical fracture .
Before winding , the whole crucible was encased in mica to prevent the strip adhering to the alumina .
Winding the Cylinder.\#151 ; The crimped platinum strip was wound over the mica jacket of the alumina cylinder with a spacing of approximately 1 cm .
between the windings .
The platinum was now interlaced with narrow mica strips to keep it in position and so prevent short-circuiting .
This was covered with another mica jacket to prevent contact between the conductor and the kieselguhr .
Although mica provides an excellent insulating medium which is chemically inactive , it becomes friable and powdery at 1000 ' C. , and it was therefore necessary to provide an additional strengthening jacket which remains hard at high temperatures .
This was attained by covering the whole with pure asbestos cloth and pasting the outside of this with asbestos cement .
Fig. 2 shows the winding in section .
On examination this was found to be in very good condition both mechanically and electrically after running on several occasions at 1100 ' C. Winding the Cones.\#151 ; Owing to the stiffness of the platinum strip it was impossible to make it lie flat on the conical surface .
Further , some means had to be devised whereby the strip could be held in position during the process of winding and the spacing maintained during the heating so that there was no possibility of short-circuiting .
The platinum strip was formed into a conical cage using stout mica strip as the spacing and supporting material .
Equally spaced saw cuts were made in the mica , these served to grip the platinum and give the necessary spacing .
The principle of the arrangement is shown in fig. 3 .
Two platinum coils and a few of the mica strips are illustrated on an enlarged scale .
A strengthening matrix was provided by pouring into the interspaces a thick paste of pure aluminium oxide and water .
The water was driven off ' by heating electrically , leaving a compact mass giving excellent insulation and support .
The ends of the platinum winding were brought out through the kieselguhr and connected to a row of six binding screws on the outside of the case .
For the purpose of economy , heavy copper leads were used ; but , owing to oxidation An Electrically Heated , Full Radiator .
of the copper-platinum joint at this high temperature , the copper had to be discarded .
To avoid further difficulty , the platinum strip was made continuous to the binding screws , so that the only " contact " in the circuit was cool and visible .
Supporting and Lagging the Crucible.\#151 ; The crucible was supported by means of two blocks of alumina which rested in the collars of the two circular end castings , as shown in fig. 1 .
These castings were rigidly attached to each other by means of a steel cylindrical jacket , the intervening spaces being filled with kieselguhr .
The apparatus rested on a V-bloek casting and weighed approximately 130 kgm .
A covered " band-hole " was cut in the steel cylinder to facilitate the removal of moisture when drying out and also the examination of the interior when necessary .
Arrangements for Temperature Measurement.\#151 ; Owing to the possible inconvenience in introducing a thermocouple through the aperture B ( fig. 1 ) during radiation measurements , a side hole was provided as shown .
The direction of this inlet allowed of the couple being moved parallel to the radiating surface and any differences of temperature determined .
Further , the position of the hole is such that it will not be " visible " from the aperture of the receiving apparatus to be used in future experiments .
The temperature was measured by a platinum platinum-rhodium thermocouple which had been calibrated at the National Physical Laboratory for the earlier experiments on the radiation constant .
The temperature was observed by means of the deflection of a calibrated moving-coil galvanometer .
This method is of sufficient accuracy for the present purpose of obtaining uniformity , since an absolute value of the temperature is not Fig. 2 .
Fig. 3 .
required .
Dr. H. B. Keen .
In order to determine whether the galvanometer was indicating temperatures of the right order , a modification of the " hot-wire " method was used to check the indications of the thermocouple .
While the furnace was slowly heating up , an additional couple of nickel-nichrome , joined by a short silver wire , was inserted and connected to a galvanometer , which served to indicate the time at which the silver melted .
At this instant the scale reading of the Pt-PtRh couple was observed and was found to agree with the melting point of silver ( 961 ' C. ) to within a few degrees .
Adjustment of the Heating Current to give a Uniform Temperature.\#151 ; Let the winding on the back cone A = Circuit 1 .
" " cylinder = Circuit 2 .
" " front cone = Circuit 3 .
The resistances of the three circuits were measured at room temperature .
Since the heat insulation of each of the three sections is not equally efficient , then it is obvious that an equal consumption of energy in each circuit will not provide a uniform temperature within the enclosure .
The simplest plan is to allow each winding to act as its own thermometer by arranging that the increase in resistance is ' in the same ratio in each case .
Usually the three circuits were put in series and a suitable current left running overnight .
When the temperature reached 700-800 ' C. the circuits were arranged in parallel , so that the energy consumption of each could be controlled and measured from time to time .
At 1100 ' C. , the temperature at which uniformity was required , the energy consumed in each circuit was measured and then so adjusted that the resistance of each coil had increased in the same ratio .
As will be seen later , this gave the required conditions .
The following is characteristic of a set of observations :\#151 ; Let CiVi , C2V2 , C3V3 , represent the current and potential for circuits 1 , 2 , and 3 respectively .
Resist , at 1100 ' C. Resist , at 12 ' O. ' Energy consumption in watts .
Total energy consumption .
Circuit 1 Cj = 9 *0 amps .
Vj = 70 -0 volts } 4-2(0 ) 630 Circuit 2 Co = 6 *9 amps .
Yo = 67 *9 volts | 4-2(0 ) 468 Y 1743 watts Circuit 3 ^ C3 \#151 ; 8 *7 amps .
V3 \#151 ; 74 0 volts .
| 4-2(0 ) 645 J Temperature = 1150 ' C. An Electrically Heated Full Radiator .
Assuming the previously determined value of the radiation constant = 5-89 x 10-5 ergs/ sec. cm.2 deg.4 , the rate of emission of energy through the aperture B at 1100 ' C. \#151 ; 508 watts .
" Ti'ffi ' r " \#151 ; Energy appearing as radiation from aperture _ 508 J eienc^ \#151 ; Total energy consumption 1743 = 0-29 , that is to say 29 per cent , of the energy put in appears as radiation .
Making a similar calculation for the Herseus furnace used in the earlier experiments and assuming that it emits full radiation it can be shown that the " efficiency " in this case is only about 25 per cent. .
Note.\#151 ; The energy was supplied by a direct current machine capable of giving 50 amperes at any potential from 20 to 160 volts .
By this means the potential could be varied and the necessity for resistances variable over large ranges avoided .
One small variable resistance in each circuit was provided and adjusted such that the machine was running at 110 volts when the temperature required was obtained .
To avoid fluctuations in the dynamo potential the machine was now switched in parallel with the departmental 110 volt battery .
When perfectly steady conditions of temperature were desired the machine was thrown out of circuit , leaving the radiator running off the battery alone .
The electrical connections are shown in fig. 4 .
\lt ; Z\gt ; K , \#151 ; k2 K3 ~Ti- c2* i WW\AJ CIRCUIT Al ?
l \lt ; *\gt ; WVVvAj C3+ CIRCUIT N'2 1/ WVV^ CIRCUIT N'3 .
/ WWVWWV .
_____J 0- / WWW^ __T / yv^wyu A/ v/ v^vy .
rn s $ Fig. 4 .
Electrical connections for constant-temperature enclosure .
For u parallel " close PP and K4 .
For series close SS and open K4 .
Dr. H. B. Keen .
Exploration of Temperature Distribution.\#151 ; This was most conveniently carried out by inserting the thermocouple through the aperture B. In order to place the junction at different points within the radiator the length of the couple immersed must vary if used in the ordinary way .
Unless the wires of the couple are chemically pure and physically uniform the electromotive force will depend upon the length immersed .
It was known from previous investigation that the couple used was defective in this respect .
It was therefore necessary to devise some means of reaching different parts of the radiator , keeping the length of the couple immersed constant .
The couple was insulated by means of twin-bore fireclay tubing which was supported in a porcelain tube so that the break K in the twin fireclay ( see fig. 5 ) was Fig. 5 .
approximately at the centre of the enclosure .
Another porcelain tube was attached alongside and carried a loosely fitting fused silica tube provided with a platinum wire loop W. This loop encircled the loose end of the thermocouple so that the junction could be brought to any position within the enclosure by sliding the silica tube S in its porcelain guide .
In this manner the temperature distribution was determined .
For the values of the energy consumption given above the temperatures at the various points were as follows:\#151 ; A series of observations of the temperature at the various positions shown in fig. 6 were taken in the following order :\#151 ; Position of junction .
Temperature .
Position of junction .
Temperature .
( 2 ) .
1150 ' C. ( 5 ) 1154 ' C. ( 1 ) 1151 ( 3 ) 1155 ( 3 ) 1153 ( 1 ) 1154 Fig. 6.\#151 ; Vertical Section of Radiator .
An Electrically Heated Full Radiator .
It will be seen that the temperature was rising .
After waiting for steadier conditions the following series were taken :\#151 ; Position of junction .
Temperature .
Position of junction .
Temperature .
( 3 ) 1149 ' C. ( 3 ) 1150 ' C. ( 4 ) 1147 ( 1 ) 1149 ( 1 ) 1149 ( 4 ) 1150 There is evidence here of a slight rise of temperature and the maximum difference of 3 ' C. occurs at the same place ( position 4 ) .
It is quite useless to attempt further refinements at the present stage , since it is intended to determine the radiation constant for various temperature distributions within the enclosure .
The results so obtained will determine the degree of uniformity which is necessary .
If for instance the temperature of the cone opposite A is reduced by 100 ' C. and the value of the radiation constant obtained remained unaltered then the uniformity described above is sufficiently good .
For this reason it is proposed to proceed with the radiation experiment without further delay .
The Quality of the Radiation emitted.\#151 ; There is no satisfactory means of determining the diffusing power of a sample of the alumina at the temperature of the radiator ( 1100 ' 0 .
) , owing to the difficulty of obtaining the actual temperature of the radiating surface of an exposed sample .
It is highly probable that a porous clay is an exceedingly good radiator on account of the pores providing a surface of minute full radiators .
Such was the surface of the crucible .
As a further precaution this surface was covered with a dull black coating ( by Messrs. Morgan , of Battersea , London , S.W. ) which would withstand 1100 ' C. My colleague , Dr. Guy Barlow , has shown that the radiation passing through a circular aperture of area a in a spherical uniform temperature cavity of cross-section A departs from the full radiation at that temperature by approximately are / A per cent. , where R is the percentage of the radiation diffusely reflected by the material .
If we assume that the black alumina surface diffusely reflects as much as 5 per cent. , then the radiation from the aperture B departs from the full radiation at that temperature by only about 0*2 per cent. I am indebted to the late Prof. J. H. Pointing , F.R.S. , for granting the funds which enabled me to carry out this investigation , and also to Mr. G. O. Harrison , of the Physics Workshop , for the valuable assistance he has rendered .
|
rspa_1915_0009 | 0950-1207 | On the spectra of ordinary lead and lead of radioactive origin. | 198 | 201 | 1,915 | 91 | Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character | Thomas R. Merton, B. Sc. (Oxon.)|A. Fowler, F. R. S. | article | 6.0.4 | http://dx.doi.org/10.1098/rspa.1915.0009 | en | rspa | 1,910 | 1,900 | 1,900 | 2 | 82 | 1,927 | http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1915_0009 | 10.1098/rspa.1915.0009 | null | null | null | Atomic Physics | 66.40816 | Thermodynamics | 15.031532 | Atomic Physics | [
13.233471870422363,
-50.268184661865234
] | 198 On the Spectra of Ordinary Lead and Lead of Radioactive Origin .
% By Thomas B. Merton , B.Sc. ( Oxon .
) .
( Communicated by A. Fowler , F.R.S. Received December 21 , 1914 .
) The view that the spectra of isotopes are identical was first put to the test by Bussell and Rossi* and Exner and Haschek , f who examined the spectra of thorium and ionium preparations .
The former of these observers worked with a mixture containing at least 10 per cent , of ionium , but no lines were found which were not present in the spectrum of pure thoria .
AstonJ has submitted neon to fractional diffusion , by which a partial separation was effected , as shown by the change of density , but no change in the spectrum was observed .
More recently Soddy and HymanS and Richards and LembertH have compared the spectrum of lead of radioactive origin with that of ordinary lead .
The former of these investigators , who worked with lead from thorite , found that the line \ = 4760T was stronger in ordinary lead than in the thorite lead , but that the spectra in other respects appeared to be identical .
Richards and Lembert also found that the spectra were identical .
In both of these investigations , the Fery spectrograph was used for the photography of the spectra ; no details are given , but it is presumed that in both cases the spectra of the radioactive and ordinary lead were photographed in juxtaposition on the same plate .
This method is admirably suited to a general comparison , but it gives no numerical data as to the exact degree of identity of the wave-lengths in the two spectra .
It might reasonably be expected that in the spectra of isotopes small differences of wave-length would occur , though the character and distribution of the lines were the same .
According to the recent views of Prof. Hicks , an atomic weight term enters exactly into the separations of doublets and triplets in series spectra .
Ho series have yet been found for the spectrum of lead , but Kayser and Bunge 1T * * * S * 4 Roy .
Soc. Proc./ vol. 87 , p. 478 ( 1912 ) .
t 4 Sitzungsber .
K. Akad .
Wiss .
Wien/ vol. 121 ( 2 Abth .
) , p. 175 ( 1912 ) .
X British Association Meeting , 1913 .
S ' Cheni .
Soc. Trans./ vol. 105 , p. 1402 ( 1914 ) .
|| 4 Amer .
Chem. Soc. Journ./ vol. 36 , p. 1329 ( 1914 ) .
H 4 Wied .
Ann./ vol. 52 , p. 93 ( 1894 ) .
Spectra of Ordinary Lead and Lead of Radioactive Origin .
199 have found that a group of ten lines repeats itself three times with constant frequency differences .
It seems probable , however , that doublet or triplet series exist in the lead spectrum , and for the lines which fall into such series there should , according to the views of Prof. Hicks , be differences of wavelength in the two isotopes corresponding with the difference of atomic weight .
In the present investigation , I have made a comparison of the wave-lengths of some of the most prominent lines in the spectrum of ordinary lead and of the lead in Joachimsthal pitchblende .
The spectra were photographed with a concave grating spectrograph , mounted according to the arrangement of Eagle* and provided with a concave grating of 4 feet radius of curvature having 20,000 lines to the inch .
The plates were measured on a Hilger micrometer .
The spectra were produced in the carbon arc , the carbons being cored , as the case might be , with the pitchblende residues or with iron oxide containing a small proportion of ordinary lead .
The residues contained a considerable quantity of iron which served as a comparison spectrum .
A number of plates were taken , in which the two spectra were in juxtaposition , and the lines due to lead were found to be identical in the two spectra .
The object of the present investigation , however , is to set some superior limit to any wave-length differences that might occur .
The wave-lengths of the principal lead lines between X = 3500 and X = 4100 have therefore been independently measured in the ordinary and radioactive lead spectra , the iron lines being used as standards .
The values obtained are given in the following table :\#151 ; A , ordinary lead .
A , lead from residues .
A , ordinary lead \#151 ; A , lead from residues .
A , Kayser .
*3572 -88 3572 -88 \#177 ; 0*00 3572 -88 3639 -72 3639 *69 + 0 *03 3639 -71 *3671 -66 3671 *64 + 0 *02 3671 -65 3683 -59 3(583 *60 -0*01 3683 -60 *3740 -08 3740 06 + 0 *02 3740 -10 4057 -98 4057 *99 -0*01 4057 -97 4062 -31 4062 *33 -0 *02 4062 -30 The dispersion was about 10 A.U. per millimetre and the differences observed , which are not systematic , are within the experimental error , and it may therefore be concluded that no differences greater than '03 A.U. occur in these lines .
The three lines marked with an asterisk are members of the groups of ten , discovered by Kayser and Rung { Joe .
cit. ) .
* ' Astrophys .
Journ. , ' vol. 31 , 2 , p. 120 ( 1910 ) .
200 Spectra of Ordinary Lead and Lead of Radioactive Origin .
The atomic weight determinations of Richards and Lembert ( loc. cit.\ Honigschmid and Horovitz* and Curief show that the atomic weight of lead from the pitchblende residues is somewhat greater than the value predicted by theory , this being no doubt due to the presence of a small'quantity of ordinary lead in the pitchblende .
If the spectrum lines in the two leads differed in wave-length by a small amount , the lines from the pitchblende residues would be double .
If the components were not resolved in the spectroscope , the doubling should nevertheless make itself felt as an apparent shift or an asymmetric broadening of the line .
On the assumption that the lead in my residues has an atomic weight about *5 unit less than ordinary lead , Prof. J. W. Nicholson has very kindly calculated for me the order of the change of wave-length to be expected according to Prof. Hicks ' theory , in the case of lines belonging to series , doublets or triplets .
If the separation of two such lines in a doublet were 50 A.U. at X = 4000 A.U. ( an order of separation which might reasonably be expected to occur in the case of lead doublets ) , then a change of atomic weight of 0*5 unit should alter the separation of the lines by about 0*3 A.U. , or if each of the lines were shifted by an equal amount , a change of wave-length of the order of 0*15 A.U. in each line would result .
It may be stated with certainty that in the lead lines , which are not given in the above list but which were observed in the photographs of the spectra taken in juxtaposition , no change of wave-length of this order occurs .
A special examination has been made of the line X = 4058 .
This line is by far the strongest line which can be photographed through glass lenses and prisms .
The comparison has been made of this line in the two lead spectra by photographing the ring systems produced by means of a Fabry and Perot etalon .
The line X = 4058 .
when produced in the carbon arc at atmospheric pressure , is too broad for the production of interference rings of sufficiently good definition .
The spectrum was therefore produced in a glass globe of about 1 litre in capacity , exhausted by means of a Fleuss pump to a pressure of a few millimetres of mercury , between carbon rods , cored with small quantities of the two leads as carbonates or oxides .
Under these conditions sharp definition could be obtained .
The convergent beam of light from a lens placed at a suitable distance from the arc passed through the Etalon , and an achromatic lens of 6 inches focal length brought the ring system to a focus on the slit of a large Hilger constant-deviation spectroscope provided with a camera attachment .
The etalon consisted of two half-silvered plane parallel glass plates separated by three glass studs , the distance between the * 4 Comptes Rendus/ vol. 158 , p. 1796 ( 1914 ) .
^ t 'Comptes Rendus , ' vol. 158 , p. 1676 ( 1914 ) .
On the Viscosity of the Vapour of Iodine .
plates being 6*50 mm. The exposures were made within two or three minutes of one another , to avoid variations due to changes of temperature .
Photographs taken in this way showed that the interference rings are identical for the two* lead spectra , and measurements of the diameters of the rings agree within the limits of experimental error , the calculated results showing that there is certainly no difference of wave-length for the line \ = 4058 as great as 0*003 A.U. in the spectrum of ordinary lead and of the lead from pitchblende .
In conclusion , I should like to thank Prof. Nicholson for the calculation which he has made for me .
On the Viscosity of the Vapour of Iodine .
By A. O. Rankine , D.Sc .
, Fellow of and Assistant in the Department of Physics in University College , London . .
( Communicated by Prof. A. W. Porter , F.R.S. Received January 15 , 1915 .
) In a previous communication* I have described the measurements I have made of the viscosity of bromine vapour .
The method used for this purpose involved the distillation of bromine from one vessel to another through a capillary tube .
The pressure difference between the two ends of the capillary was established by maintaining the two vessels at suitable different temperatures , and the rate of transpiration of the bromine vapour was estimated by observing the volume of the liquid bromine which evaporated in a *given time .
It was hoped that the same method could be applied to iodine by adjusting the temperatures of evaporation and condensation to values above the melting point of iodine ( 113 ' C. ) , and measuring the transpiration rate by means of the disappearance of liquid from the evaporation vessel .
Preliminary experiments , however , soon revealed the fact that the liquid iodine was not sufficiently mobile , and its surface was too indefinite and variable in shape to allow small changes of volume to be observed .
It was , therefore , found necessary to modify in several respects the method used with bromine .
The present paper describes the modified method , which was found to work extremely well and to give very consistent results .
Values of the viscosity of * 4 Roy .
Soc. Proc. , ' A , vol. 88 , pp. 575-588 ( 1913 ) .
|
rspa_1915_0010 | 0950-1207 | On the viscosity of the vapour of iodine. | 201 | 208 | 1,915 | 91 | Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character | A. O. Rankine, D. Sc.|Prof. A. W. Porter, F. R. S. | article | 6.0.4 | http://dx.doi.org/10.1098/rspa.1915.0010 | en | rspa | 1,910 | 1,900 | 1,900 | 1 | 18 | 388 | http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1915_0010 | 10.1098/rspa.1915.0010 | null | null | null | Thermodynamics | 42.813482 | Tables | 38.085043 | Thermodynamics | [
-8.502452850341797,
-36.310333251953125
] | ]\gt ; By A. O. RANKINE , D.Sc .
, Fellow of and Assistant in the Department of Physics in University College , London .
( Communicated by Prof. A. W. Porter , F.R.S. Received January 16 , 1916 .
) In a previous communioation*I have described the measurements I have made of the viscosity of bromiue vapour .
The method used for this purpose involved the distillation of bromine from one vessel to another through a capillary tube .
The pressure difference between the two ends of the capillary was established by maintaining the two vessels at suitable different temperatures , and the rate of transpiration of the bromine vapour was estimated by observing the volume of the liquid bromine which evaporated in a , given time .
It was hoped that the same method could be applied to iodine by adjusting the temperatures of evaporation and condensation to values above the melting point of iodine and measuring the transpiration rate by means of the disappearance of liquid from the evaporation vessel .
Preliminary experiments , however , soon revealed the fact that the liquid iodine was not sufficiently mobile , and its surface was too indefinite and variable in shape to allow small changes of volume to be served .
It was , ffierefore , found .
neoessar ) to modify in several respects the method used with We may now test how far the results for iodine fall into line with the empirical laws which I have shown to hold for bromine and chlorine .
The critical temperature of iodine is or 78 absolute .
The ratio is therefore .
This compares with for the same : ratio in the case of chlorine and for bromine .
the difficulties .
of accurately the critical temperatures of these gases , and also the value of Sutherland 's constant , these three ratios equal within the accuracy of the experiments .
Further , if we calculate by extrapolation of Sutherland 's equation the viscosity of iodine vapour at the critical temperature , we obtain the value , and the value of A is the atomic weight , is , which is practically equal to the same ratio for chlorine and From LandoIt and Bornstein 's Tables .
Phii .
Mag vol. 36 , ) 1893 ) .
|
rspa_1915_0011 | 0950-1207 | A new type of series in the band spectrum associated with helium. | 208 | 216 | 1,915 | 91 | Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character | A. Fowler, F. R. S. | article | 6.0.4 | http://dx.doi.org/10.1098/rspa.1915.0011 | en | rspa | 1,910 | 1,900 | 1,900 | 7 | 100 | 2,803 | http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1915_0011 | 10.1098/rspa.1915.0011 | null | null | null | Atomic Physics | 59.418222 | Tables | 35.483218 | Atomic Physics | [
13.555238723754883,
-49.88517761230469
] | ]\gt ; It will be seen that this group of gases in the periodic Table obey laws similar to those which hold for the inert A New Type of Series in the Band Spectrum Associated with Helium .
By A. FOWLER , F.R.S. , Assistan ProfeF ; sor of Physics , Imperial College , South Kensington .
( Received January 19 , 1915 .
) A previously unknown band spectrum noticed in the course of experiments on bydrogen and helium made at the Imperial College in 1912 , and was further ated and described by W. E. Curtis in the year following An independent account of this spectrum was also br ; iven , almost at the same time , by Dr. E. Goldstein .
In each case , some hesitation was felt in attributing the new spectrum solely to helium , in consequence of the persistence of traces of in the helium tubes employed . .
Curtis found that the band spectrum was best developed , in the wider parts of the tubes , when a with small capacity and a small air-gap was passed helium at a pressure rather than that which is usual in sealed tubes of the gas .
The discharge is then quite brilliant , and by giving long exposures , amounting in some cases to seven or eight hours , 'Phil .
Mag January , 1911 , p. 45 . .
Soc. Proc , vol. 89 , p. 146 ( 1913 ) . .
Deutsch .
Phys. Gesell vol. 15 , p. 402 ( 1913 ) .
Band Spectrum with Curtis obtained an excellent series of photographs of the spectrum with concave grating of 10 feet radius , some of were in the second and orders .
with other instruments were also taken by Curtis , but he has been unable to continue the investigation in conseof his temporary enlistment .
Under these circumstances it has been desirable to make a preliminary analysis of the bands , so that might be drawn to any points of special interest without undue As previously described and illustrated by Curtis and Goldstein , the pectrum includes some conspicuous bands with heads , others with Louble heads , and a number of complex ions in which no heads ecognisable at .
A prominent fluting with a single head , beginning at 5733 , degrades to the violet , but otherwise all the which have been recognised as such are vraded to the red .
The first result of the investigation was the unexpected discovery that the double-headed bands are not arranged according to the usual of band spectra , but closely follow the law of line series .
The structure of the individual bands , vever , is essentially the same as that of bands which are distributed in the more usual way ; that is , the distances between successive lines of a series form an approximately arithmetical progression .
Mr. Cnrtis 's plates show five bands of the main doublet series , and four additional bands in the ultra-violet which plainly belong to it have since been on a small scale .
A fairly conspicuous doublet in the green , 5133 , , was not included in the main series , and it therefore became important to search for additional bands , in order to determine if there were other series which might be related to the first .
Only one other doublet , a faint one at 3634 , 3620- , was at first recognised by inspection , and it remained to be seen if others could be picked out in the more complex regions where bands of different types might be superposed .
For this purpose , all the individual lines composing the bands between and were measured , so that the special istics of the different types of bands could be ascertained , About 1300 lines in all have been measured , but the final determinations of the wavelengths , with the necessary corrections for temperature and other sources of error , will occupy a great deal of time , and it is not considered desirable to give so long a list until the wavo-lengths have been freed from systematic errors .
The provisional wave-lengths , however , are adequate for a first discussion .
As a general statement , it may be remarked that the lines composing single-headed bands show a smaller second difference than those Mr. A. Fowler .
A New Type of in the to the doublets , but in each case the second difference increases in passin from bands in the red to those in the violet part of the spectrum .
many of the band lines can be arranged in series , but comparativel few have been traced or suspected .
Two doublets are related to those about 5133 and 3634 , vever , have been identified also a few -headed bands in addition to those tabulated rtis .
No regularity in the arrangement of the single bands has been recognised , and present paper is restricted to consideration of the doublets .
Structur of Doublets .
structure of the double band , at , is illustrated in , where the intensities of the component lines are represented by the ths of the lines in diagram .
In this case , the more rible , and weaker , component of the doublet includes seven strong lines , and the less ible component at least eight .
In each case the lines to the observed heads .
The " " tail\ldquo ; of the band consists of a numbet of , of which the brightest form the obvious series which is shown in the diagram ; the calculated convergence point this series lies considerably on .
violet side of the two observed heads , and the lines cease to be visible before the convergence point is reached .
eries of the latter type are very numerous throughout the spectrum ; they appear to accompany all the bands , whether or double , and the second diHerence is apparently dependent on that in the band with which it is connected .
The provisional wave-lengths of the lines mapped in fig. 1 are given in Table I , which also shows the corresponding wave-numbers ( reduced to vacuum ) , and the first and second differences .
It will be seen that the second differences are approximately constant .
Band Spectrum with Helium .
TABLE I.\mdash ; Details of the Donblet 4625 , The Scrics of Do The bands belonging to the main series of doublets are readily nised pection of the photographs .
They all occur in regions which are free from complication by the superposition of other bands , and the last seven are apparently the only bands which ] 0CCU in the ultra-violet between 3450 and , beyond which the spectrum has not yet been examined .
The intensities of the bands decrease gradually passing along the series .
The wave-lengths ( International scale ) and wave-numbers ( corrected to vacuum ) of the heads of these bands are given in II ; the first three have been derived from rating plates , but the remainder are only approximate values obtained from taken with slmaller dispersion .
* Calculations soon confirmed the suspicion that the series of the chal.acter hitherto exclusively yarded as belonging to line spectra .
The * The instruments which would ordinarily have been used for oving on the wavelengths are detained in Russia , where they were for ervations of the eclipse of 1914 , August 21 .
VOL. XCI.\mdash ; A. .
A. Fowler .
A Type of in the series may , in fact , be represented in the usual way by the formulae 1iydberg or Hicks .
For the less ible components of the which are the stronger , the following formulae have been calculated:\mdash ; ' The adopted value of the ydberg constant is that given by Curtis for International scale .
derived from his measurements of lines of hydrogen .
The differences between the observed and calculated wave-numbers shown under I and II in Table II , and will be seen that the bands represented with quite an ordinary degree of accuracy .
The wave-number intervals between the two components of the diminish in passing to the ultra-violet , but the convergence is less rapid would be the case if they corresponded with the components of doublets the Principal se1ies of a line spectrum .
Attempts to unite the more refrangible coulponents of the doublets formulae have been less successful .
The simple Rydberg formula residuals , and even the Hicks formula with four constants is not entirely satisfactory .
following formulae have been calculated:\mdash ; - , The observed minus calculated values are shown under III , Table II , from which it will be seen that there are considerable residuals in each case .
A Ritz formula , with three constants , has been calculated ; it gives.residuals slightly larger than those iven formula In view of the observed rate of contraction of the doublets , the iven by formulae III and appear to be too high as compared with linlit 34295 for the series of less ngible heads , which is probably far from correct .
From this point of view , the limit given by formula would seem to be ] correct , relatively to that of the less heads .
OIL the other hand , the position of the band in the .
Soc. , vol. 90 , p. 605 ( 1914 ) .
Band Table II.\mdash ; The bIain Series of Doublets .
to given by is very discordant with that indicated the less refrangible band by I and II ,4711 , respectively ) , and a closer agreement in this respect is shown by III and respectively ) .
The difficulty in a satisfactory formula for the more refrangible components is doubtless associated with the unusual character of the doublet separations , wlrich resemble neither nor Subordinate series in the case of line spectra .
It may be remarked , however , that some of the known line series are not satisfactorily represented by any of the recognised f.ormulae .
There is at all events no escape from the conclusion that the doublet bands in question are arranged substantially in the same way as the lines in an ordinary line serieH .
Second of Doublets .
The first doublet of the second series is quite a conspicuous feature in the preen of the visible spectrum , and the third can be recognised without Mr. A. Fowl A New Type of Series in the difficulty on the large scale photographs .
The heads of the second however , occur among other band lines , and were only identified measurement of the individual lines ; the fourth band is very faint , prolonged exposures would evidently be required to bring out members of this series .
The positions of these bands are indicated Table III .
The less refrangible heads of the four ) served bands are represented by the following Rydberg formula , as will be seen under Table The more refrangible heads , as in the case of the main series , are not well represented by a Bydberg formula , and it is probable that even the Hicks formula would be unsatisfactory if a greater number of bands were available to test its applicability .
The values of nnder and VIlI in Table III refer to the following formulae : Corresponding to , formula gives as the wave-number of the less refrangible component of a possible infra-red member of the series , and formulae and VIII give 3721 and 3382 respectively for the more refrangible head .
Band Spectrum Associated with Helium .
nparison of Two Series .
It is remarkable that , although the two series of doublets follow the law of line spectra individually , no relation between them to any which exists between the different members of a system of line series is cerCainly indicated .
The series which has been described as the " " nain series\ldquo ; of doublets , in consideration of its brightness and extent , would probably correspond with the Principal series in the case of a line spectrun ) if it had any equivalent .
The second series would similarly correspo1ld to one of the subordinate series , and the fact that the first ternl of the occurs with a positive sign may be taken to indicate it would be equivalent to a Diffuse series .
A third series , which would corresl ) to the series in a line spectrum , has not yet been identified .
accordance with vell k ) rinciples , however , an approximate formula for the Sharp tlay be derived that for the Principal , bnt neither of Lwo or additional doublets which'n have been pected o positions so calculated .
In a of line , as expressed by the tster law , the common limit of the 1)iffuse and Sharp series fro1ll of tho set.ies by an anount equal to the wave-number of first Principal line .
In the present case the diHerence between the of the two doublet series is about , while the wave-number of the first lnembe of the main series calculated by the for1nulae I and II is betn 4700 and .
The differe t ce appears to be too great to be accounted for by the character of the formlae enJployed , ind , if so , the doublet series cannot stand in the relation of Principal Diffuse The same conclusion is ested by the fact the less of the doublets are .
in both series .
Thus , although there can be no doubt that the heads of ublet bands are according to the law of line spectra , other relations shown by the different series of a line systenl do not appear to band spectrutl associated with helium , as previonsly described Curtis oldstein , includes with single heads and bands heads .
A preliminary of this spectrum has led ) the foll o conclusions:\mdash ; ( 1 ) doublets do llot ordinary law of } ) ectra , but can be arranged ill two sel.ies of the type hitherto tSHociated with line , and call be ately represented by the ustlal Mr. A. E. Oxley .
fuence of involving the Rydberg constant .
Nine bands of the main series and four of the fainter second series have been identified .
The two series may be likened to the Principal and Diffuse series in the case of line spectra , but the usual relation between such series is not certainly indicated , and no equivalent of the Sharp series has yet been traced .
( 3 ) The doublet separations are not in accordance with those associated with line spectra ; they diminish in passing along the series , but do not vanish at the limit .
No regularity in the arrangement of the single bands has been recognised .
The author is indebted to Mr. F. S. Phillips and to Major-General du Guard Gray , C.B. , for photographs of the new band spectrum supplementing those obtained by Mr. Curtis .
The Influence of Constitution on gnetic ASusceptibility .
Part III.\mdash ; On the Molecular Field in nagnetic S By A. E. OXLEY , M.A. , M.Sc .
, Coutts Trotter Student , Trinity College , , Mackinnoll Student of the Royal Society .
Commnnicated by Prof. J. J. Thomson , O.M. , F.R.S. Received Jmle 24 , 1914 .
) ( Abstract .
) The work is a continuation of in ns , vol. 214 , .
, which co1ltains Parts and II .
The suggestion made at the end of Part II , p. 143 , that the local molecular field in diamagnetic crystalline substances may be comparable with the ferronetic molecular field , has been justified .
Estimates of the order of magnitude of this field have been obtained from the following sources:\mdash ; ( a ) Th. change of spccific susceptibilit , ?
accompanying crystallisation .
The extent of this change may be interpreted , on Langevin 's theory of diamagnetism , as produced by a local molecular field of the order of intensity gauss , which comes into operation on crystallisation S4 ) .
This intense local field distorts the molecules and alters the periods of vibration of the contained electrons .
From the nature of the structure which has been postulated for a netic molecule , this field is of an alternating character , the distance over which it is unidirectional comparable with the
|
rspa_1915_0012 | 0950-1207 | The influence of molecular constitution and temperature on magnetic susceptibility. Part III.\#x2014;On the molecular field in diamagnetic substances. | 216 | 218 | 1,915 | 91 | Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character | A. E. Oxley, M. A., M. Sc.|Prof. Sir. J. J. Thomson, O. M., F. R. S. | abstract | 6.0.4 | http://dx.doi.org/10.1098/rspa.1915.0012 | en | rspa | 1,910 | 1,900 | 1,900 | 1 | 55 | 1,328 | http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1915_0012 | 10.1098/rspa.1915.0012 | null | null | null | Atomic Physics | 37.387354 | Fluid Dynamics | 25.19291 | Atomic Physics | [
29.221132278442383,
-76.31464385986328
] | 216 Mr. A. E. Oxley .
The Influence of Molecular involving the Rydberg constant .
Nine bands of the main series and four of the fainter second series have been identified .
( 2 ) The two series may be likened to the Principal and Diffuse series in the case of line spectra , but the usual relation between such series is not certainly indicated , and no equivalent of the Sharp series has yet been traced .
( 3 ) The doublet separations are not in accordance with those associated with line spectra ; they diminish in passing along the series , but do not vanish at the limit .
No regularity in the arrangement of the single bands has been recognised .
The author is indebted to Mr. F. S. Phillips and to Major-General du Guard Gray , C.B. , for photographs of the new band spectrum supplementing those previously obtained by Mr. Curtis .
The Influence of Molecular Constitution and Temperature on Magnetic Susceptibility .
Part III.\#151 ; On the Molecular Field in Diamagnetic Substances .
By A. E. Oxley , M.A. , M.Sc .
, Coutts Trotter Student , Trinity College , Cambridge , Mackinnou Student of the Royal Society .
( Communicated by Prof. Sir J. J. Thomson , O.M. , F.R.S. Received June 24 , 1914 .
) ( Abstract .
) The work is a continuation of that in ' Phil. Trans. , ' A , vol. 214 , pp. 109-146 , which contains Parts T and II .
The suggestion made at the end of Part II , p. 143 , that the local molecular field in diamagnetic crystalline substances may be comparable with the ferromagnetic molecular field , has been justified .
Estimates of the order of magnitude of this field have been obtained from the following sources:\#151 ; ( a ) The change of specific susceptibility accompanying crystallisation .
The extent of this change may be interpreted , on Langevin 's theory of diamagnetism , as produced by a local molecular field of the order of intensity 107 gauss , which comes into operation on crystallisation ( S 4 ) .
This intense local field distorts the molecules and alters the periods of vibration of the contained electrons .
From the nature of the structure which has been postulated for a diamagnetic molecule , this field is of an alternating character , the distance over which it is unidirectional being comparable with the Constitution and Temperature on Magnetic Susceptibility .
217 distance between the molecules .
When a substance crystallises , the periods of the vibrating electrons will be changed and the extent of this change is the Zeeman effect of the local molecular field .
In general we shall get a simple displacement of the line , corresponding to a particular vibration , and not a doubling .
This effect is a consequence of the peculiar structure of the diamagnetic molecule and its magnitude is a measure of the shift of an absorption band owing to crystallisation .
( Cf .
the pressure-shift of spectrum lines .
) ( b ) The large value of the natural double refraction of crystalline , as compared , with the artificially induced double refraction in corresponding liquids when subjected to the largest magnetic field , at our disposal .
It is at once seen that the local molecular field must be large compared with the largest field obtainable in the laboratory ( \lt ; 105 gauss ) in order to account for the augmented double refraction of the crystalline state .
The value of the local molecular field deduced is of the order 107 gauss ( S 4 ) .
( c ) The potential energy associated with the local molecular field .
The intense local molecular field which ( a ) and ( b ) disclose implies that the potential energy ( magnetic ) associated with a diamagnetic crystalline structure is very large .
This energy , expressed in thermal units per gramme of the substance , is a measure of the latent heat of fusion ( S 5 ) .
The values so obtained are of the right order of magnitude .
If , as the fusion point is approached , the molecules assume rotational vibrations , then we should expect that the specific heat of the substance would be abnormally high over such a critical region of temperature .
Abundant experimental evidence shows that such is the case .
( d ) The change of volume on crystallisation may be as a magnetostriction effect of the molecular field , providing this field has an intensity of the order 107 gauss locally .
These results are sufficient to establish the magnitude of the local molecular field in crystalline diamagnetic substances and show that it is of the same order of intensity as the ferro-magnetic molecular field .
As stated above , this field in diamagnetics is of an alternating character , the distance over which it is unidirectional being comparable with the distance between the molecules .
Nevertheless , it produces a definite distortion in every molecule of the crystalline structure .
This is in accordance with the hypothesis of molecular distortion , which forms the starting-point of the present work ( see the Introduction to Part I ) .
It is this intense mutual action between the molecules which gives rise to the rigidity of crystalline media .
As the molecules will exert different mutual influences in different directions , 218 Molecular Constitution and Magnetic Susceptibility .
according to their particular structure , the rigidity will be greater in some directions than in others .
This accounts for the existence of planes of cleavage in crystalline media ( S 5 ) .
The experimental evidence for the change of susceptibility on crystallisation , from which the theory of the molecular field in diamagnetic substances has developed , is contained in Part I. About 25 aromatic substances were investigated altogether , and for these the conclusions stated above hold good in so far as the data for individual cases are obtainable .
Aliphatic substances , however , show an almost inappreciable change of susceptibility on crystallisation , and the object of the additional experiments of S 6 , together with the " parallelism between the magnetic double refraction of liquids and the change of susceptibility due to crystallisation , " developed in S 7 , is to show that these conclusions may be extended to diamagnetic crystalline media in general .
The extent of the induced magnetic double refraction depends upon the degree of dissymmetry and unsaturation of the molecule .
As the induced double refraction in aliphatics is inappreciable ( Cotton and Mon ton ) , we may conclude that these factors are small for such substances .
In the most favourable cases of unsaturation and dissymmetry the value of amounts to a few per cent. only .
It is , therefore , probable that with aliphatic substances the value of 3y would not be detectable , even though the molecular field is comparable with 107 gauss .
The source of the local molecular field in diamagnetic substances must be located in the individual atoms .
The molecular field is then a result of the co-operation of these atomic fields when the molecules become related to one another in a definite way in the crystalline structure .
It is pointed out that such fields residing within the atoms are identical with the magnetic atom fields of Ritz and Humphreys , and probably also with the field of the magneton .
In conclusion , a discussion of the nature of the molecular field is given ( S 8 ) .
This field must be localised to a large extent in all substances in order to satisfy the condition of continuity of magnetic induction .
I hope to publish further extensions of this work in a future communication .
|
rspa_1915_0013 | 0950-1207 | The transmission of electric waves over the surface of the Earth. | 219 | 219 | 1,915 | 91 | Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character | A. E. H. Love, F. R. S. | abstract | 6.0.4 | http://dx.doi.org/10.1098/rspa.1915.0013 | en | rspa | 1,910 | 1,900 | 1,900 | 1 | 14 | 307 | http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1915_0013 | 10.1098/rspa.1915.0013 | null | null | null | Fluid Dynamics | 49.068274 | Tables | 36.199167 | Fluid Dynamics | [
42.53339385986328,
-44.24042892456055
] | 219 The Transmission of Electric Waves over the Surface of the Earth .
By A. E. H. Love , F.E.S. ( Received December 19 , 1914 .
) ( Abstract .
) An analytical solution of the general equations of electrodynamics is obtained for the case of waves generated by a vibrating doublet in presence of a conducting sphere , and is adapted to obtain the known solution for perfect conduction , and the correction for moderate resistance , such as that of sea-water .
The known solution is expressed by the sum of a series involving zonal harmonics , and the correction by a similar series .
Different results have been obtained by different writers who have investigated the numerical value of the former sum .
In the paper a new method of summing the series is explained , and worked out in detail for the wave-length 5 km .
In the case of perfect conduction the result confirms that found by H. M. Macdonald.* The effect of resistance is found to be a slight increase of the strength of the signals at considerable distances , counteracting to some small extent the enfeebling effect of the curvature of the surface .
A comparison is instituted between the results of the theory and those of recorded experiments .
From these it had previously been inferred that the diffraction theory fails to account for the facts ; but , after a discussion of the experimental evidence , it appears that the observations may admit of a different interpretation , according to which the results of the diffraction theory would be in good agreement with those of daylight observations at great distances .
* ' Proc. Roy .
Soc. , ' A , vol. 90 , p. 50 ( 1914 ) .
VOL. XCI .
\#151 ; A T
|
rspa_1915_0014 | 0950-1207 | On the origin of the Indo-Gangetic trough, commonly called the Himalayan foredeep. | 220 | 238 | 1,915 | 91 | Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character | Colonel Sir Sidney Burrard, K. C. S. I., R. E., F. R. S. | article | 6.0.4 | http://dx.doi.org/10.1098/rspa.1915.0014 | en | rspa | 1,910 | 1,900 | 1,900 | 11 | 306 | 8,729 | http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1915_0014 | 10.1098/rspa.1915.0014 | null | null | null | Geography | 68.64868 | Fluid Dynamics | 14.625575 | Geography | [
-28.384601593017578,
19.130035400390625
] | 220 On the Origin of the Indo-Gangetic , commonly called 1 the Himalayan Foredeep .
By Colonel Sir Sidney Burrard , K.C.S.L , R.E. , F.R.S. , Surveyor-General j of India .
( Received July 31 , 1914 .
) 1 .
The Question under Discussion .
The plains of Northern India consist of alluvial deposits brought down by I the Rivers Indus and Ganges .
These plains conceal from our view a deep 1 trough that has been formed in the solid rock of the Earth 's crust .
The 1 trough is bounded on the north by mountains of the tertiary age and on the I south by an ancient pre-tertiary tableland .
North of the trough the Earth 's crust has undergone continual compression , disturbance , and uplift since the , beginning of the tertiary age ; south of the trough it has remained undis-J turbed since the close of the palaeozoic era.* On fig. 1 are shown the !
Indo-Gangetic trough , the mountainous area on its north , and the tableland .
on its south .
From the writings of Suess , the Indo-Gangetic trough has come to be j called the Himalayan foredeep .
In this paper I am proposing to consider I one question only , namely , the origin of the Himalayan foredeep .
S* .
2 .
The Zone of Low Density in the Crust .
In 1912 I published a paper in which I endeavoured to show that a zone 1 of low density underlies the Indo-Gangetic alluvium and skirts the southern 1 foot of the Himalaya Mountain s.f The existence of this line of low density in the crust has not been disputed .
1 Its significance lies in the fact that it furnishes an argument against I Prof. Suess 's theory of Himalayan formation .
Prof. Suess held that the 1 mountains of Tibet and Persia are advancing southwards in a great series of | folds .
} : Mr. Hayden , Director of the Geological Survey of India , writes that the | great series of folds in Central Asia are supposed to have been caused by a 1 horizontal thrust from the north .
S * ' Geology of India , ' p. 2 , R. D. Oldham .
+ Survey of India Professional Paper No. 12 , 'On the Origin of the Himalayan 1 Mountains .
' f The Face of the Earth , ' vol. 1 , p. 596 .
S ' Sketch of Geography and Geology , ' p. 48 .
Bi On the Origin of the Indo-Gangetic Trough .
222 Sir S. Burrard .
Mr. Middlemiss speaks of " the well-established forward march " of the Himalaya range.* Mr. Oldham states that there has been a southerly advance of the margin of the hills since the Upper Siwalik age.f It will thus be seen that geological authorities have adopted the theory that the Himalayas are advancing southwards towards the foredeep .
The discovery of a zone of deficient density in the crust skirting the Himalayan foot led me to ask this question : Is the existence of this long line of deficient density lying south of the Himalayas compatible with the view that the crust of Asia is being pushed southwards by a tangential force from the north ?
My conclusion was that the existence of this deficiency of matter throughout the northern zone of the Indo-Gangetic alluvium was a strong argument against the theory that the Himalaya Mountains are moving southwards .
The Himalayas are a portion of the plateau of Perso-Tibet , and this plateau appears to me to owe its elevation partly to direct vertical uplift and partly to horizontal thrusts .
Horizontal forces from the north and the south seem to have squeezed the plateau between them ; on the north side of the plateau the horizontal thrust seems to have emanated from the low-lying plains of the Oxus and from the deserts of Tarim*(fig .
1 ) , and to have acted in a southerly direction ; on the south side the horizontal thrust seems to have emanated from the low-lying plains of the Euphrates , Indus , and Ganges , and to have acted in a northerly direction .
I closed my paper of 1912 by suggesting that the Himalayan foredeep had been caused by a tension in the crust and that it was , in fact , a crustal opening or rift .
I made use in places of the word " crack .
" The objection has since been raised that the sub-crust of the Earth is in too viscous a state to " crack .
" It has been stated that by the use of the word " crack " I have assumed that the sub-crust is solid , and behaves like a solid .
I do not , however , wish to make any such assumption , nor do I wish to insist on any particular word .
Here , in front of the Himalayas is a deep trough ; this trough has been attributed by some authorities to horizontal " compression " of the Earth's1 crust ; it has been attributed by others to " depression " of the crust by the weight of alluvial deposits .
I ask that the hypothesis of an " opening " of the crust may be considered side by side with these hypotheses of " compression " and " depression .
" 11 the sub-crust is regarded as solid , the word * .
crack " will define my meaning ; * ' The Kangra Earthquake , ' p. 340 .
% + ' Geology of India , ' p. 470 , K. D. Oldham .
On the Origin of the In Trough .
223 if the sub-crust is regarded as viscous , the words " tension " or " stretching " or " opening " can be substituted for the word " crack .
" 3 .
The SiwalikFoot-hills .
Wedged in between the Himalaya Mountains and the Indo-Gangetic trough is a narrow zone of low foot-hills called the Siwalik Hills .
It is open to question whether these hills ought to be classed with the mountains or with the " foredeep .
" The materials composing the Siwalik Hills are so similar to the recent alluvial deposits that they are regarded as an elevated portion of the Indo-Gangetic plains .
Compared with the great ranges of the Himalaya and Tibet , the Siwalik range is insignificant ; compared with the alluvial deposits filling the Indo-Gangetic depression , the Siwalik masses are small .
In discussions of Himalayan questions , the Siwalik Hills assume importance , because they are always before our eyes .
Popular and crowded European stations are situated in the outer hills , and we are apt to attach undue importance to our surroundings .
But in the formation of the Himalaya Mountains on the one side and of the Himalayan foredeep on the other , these small intermediate Siwalik Hills are mere secondary effects .
The strata of which the Siwaliks are composed date back to early tertiary times , and throughout this period have been subjected to horizontal compression and to disturbance .
Although they have undergone long-continued tangential compression , these hills have not been elevated into mountains like the neighbouring Himalaya .
The explanation of this difference is , I think , that the Himalaya Mountains have been upraised by forces acting at great depths in the Earth 's sub-crust , whilst the Siwalik Hills have been formed out of the outer crust .
The foundations of the Himalaya Mountains extend downwards to depths perhaps of 50 miles or more ; the Siwalik Hills are wholly superficial .
I attribute the compression of the Siwalik strata to the opening of the Himalayan foredeep ; as the foredeep opens , the superficial strata along its northern edge are squeezed against the Himalayan Mountains .
4 .
Mr. Oldham 's Explanation of the Himalayan Foredeep .
The explanation of the origin of the Himalaya Mountains given in Mr. Oldham 's ' Geology of India , ' pages 471-474 , is based upon the Rev. 0 .
Fisher 's theory that the crust of the Earth is floating upon a fluid magma .
It would be beyond the scope of this paper to enter into the details of the Sir S. Burrard .
Fisher-Oldham theory of mountains , as I wish to confine myself to Mr.-Oldham 's recent paper in these 'Proceedings , ' vol. 90 .
The main feature of that paper is his discussion of the Indo-Gangetic trough .
In his opinion this trough has been created by the sinking of the crust under the weight of the alluvial deposits brought down from the mountains by the rivers .
To quote his own words :\#151 ; " The load thrown on D ( the alluvial plains ) will cause it to sink specially in the neighbourhood of A ( the Himalayas ) where the load is greatest , till the magma displaced by the lower surface of the crust is sufficient to float the load."* Mr. Oldham 's explanation of the Indo-Gangetic trough is that it is a \#171 ; depression " due to the sinking of strata under their own weight .
Prof. Suess 's explanation is that this trough is a downward bend of the crust of the Earth in front of the advancing Himalayan wave .
Mr. Oldham attributes the trough to vertical subsidence and " depression " ; Prof. Suess attributes the trough to horizontal " compression " from the north.f I have ventured to suggest that the trough has been due neither to \#171 ; depression " under weight of load , nor to " compression " by horizontal force , but to the opening of the sub-crust under " tension .
" Three different hypotheses have thus been submitted for consideration .
Of these Suess 's hypothesis of " compression " has been severely criticised by Prof. James Geikie in Chapter XI of his recent work , ' Mountains\#151 ; their Origin , Growth , and Decay .
' In this paper I propose to consider the two hypotheses of " depression " and of " tension " and to explain my reasons for thinking that the hypothesis of a sub-crust opening under tension is more in accordance with observed facts than the idea of strata being depressed under their own weight .
Mr. Oldham accepts the existence of the geodetic line of low density , and his explanation of that line , i.e. of the Himalayan foredeep , is this : 15,000 to 30,000 feet of sediment have been deposited by the Himalayan rivers at the foot of the mountains ; the Earth 's crust has been insufficiently rigid to support these deposits , and the latter have continued to sink deeper and deeper into the solid crust .
With reference to this theory of strata sinking und6r their own weight I beg to invite the attention of geologists to the following considerations:\#151 ; * ' Geology of India , ' p. 474 , It .
D. Oldham .
t Mr. Oldham sees evidence of compression in the Siwalik Hills , but he thinks that the compression caused by the advance of the Himalayas " will elevate the marginal deposits " ; he does not attribute the trough-like form of the Himalayan foredeep to ' ' compression ?
; " On the Origin of the Indo-Gangetic Trough .
225 5 .
First Consideration : The Weight of the Load .
If alluvium of density 2*1 is resting in rock of density 2*7 , as Mr. Oldham assumes , like an iceberg rests upon water , the portion above sea-level will be il two-sevenths of that below sea-level ; if alluvium has been pressed down by r its own weight to a depth of 20,000 feet , displacing a denser substance , we i ought to see 5700 feet of it standing above sea-level ; if it has been pressed 0 down by superincumbent weight to 30,000 feet , there should be 8600 feet above sea-level .
The actual height of Jalpaiguri , Mr. Oldham 's station on the alluvium , is , however , only 280 feet above sea-level .
Mr. Oldham 's assumed sub-crustal magma is denser than the crust floating j upon it .
If my calculations are to be made rigorous , we must compare the weight of the alluvium with the weight , not of displaced rock , but of displaced ; magtna ; and the alluvium will then be computed to be standing at a greater height even than I have deduced above .
The fact that it does not stand at any such height is a strong argument against the hypothesis of a quasi- ' liquid interior for the Earth as well as against the general idea of sinking \#171 ; strata .
6 .
Second Consideration : The Tuscarora Deep .
The Himalayan foredeep resembles the Japanese foredeep , commonly known 1 as the Tuscarora Deep ; these two foredeeps , though differing in certain I particulars , have so many features in common that they are believed to have I originated from similar causes .
The Himalayan foredeep is now filled with j alluvium , the Japanese foredeep is still filled with sea-water .
The Japanese foredeep will possibly be filled with sedimentary deposits in time , but its I existing trough-like form cannot be attributed now to the weight of deposits .
The existence of a long trough , between 5 and 6 miles deep , that has obviously not been caused by deposits , is a strong proof that the Himalayan foredeep has also originated independently of the.deposits which now fill it .
7 .
Third Consideration : The Submarine Swatches .
To the best of my belief the Indo-Gangetic trough is continued out to sea , both on the east and on the west .
I attach two small charts ( figs. 2 and 3 ) , | which show the submarine troughs extending seawards from the deltas of I the Ganges and of the Indus.* These troughs have not yet been filled with alluvial deposits , they are antecedent to the deposits .
It is a significant fact that in Indian waters the only rivers that are continued seawards by submarine troughs are the Ganges and the Indus .
The Godaveri , the Caveri , the Kistna , have no such troughs extending beyond * ' Geological Magazine , ' vol. 10 , No. 591 , p. 387 , September , 1913 .
Sir S. Burrard .
their deltas .
The submarine troughs of the Ganges and Indus will doubtless be filled with deposits in time , and our successors may then be led to believe that the troughs were created by the weight of these deposits .
In early tertiary times , before the existing loads of silt had been brought CALCUTTA .SWATCH ' OF. .
.NO GROUND False P* The dotted line is the 100 fathom ( 600feet ) contour .
Depths in feet .
Scale 1 inch = about 46 miles Fig. 2 .
down from the mountains by the rivers , the Indo-Gangetic trough had already been formed and was a narrow arm of the sea.* 8 .
Fourth Consideration : How Rivers Deposit their Loads .
Mr. Oldham writes that the load of silt thrown on to the plains will cause them to sink , " especially in the neighbourhood of the Himalayas where the * H. H. Hayden , ' Sketch of Geography and Geology of the Himalayas , ' p. 255 .
See so charts in McCabe 's 'Story of Evolution .
' On the Origin of the Indo-Gangetic Trough .
227 \gt ; 5 load is greatest .
" He assumes , therefore , that a river debouching from \#169 ; the Himalayas will deposit the greatest portion of its load near the point where it leaves the hills , and that as the load of silt sinks into the crust the amount of crustal subsidence along the course of the river will be \#169 ; greatest where the river leaves the hills .
Let us take two contiguous Himalayan rivers , the Ganges and the Jumna ; the Ganges leaves the mountains at Rikkikesh , the Jumna leaves them at Depths In teet Scale 1 Inch m 21 Miles The dotted time is the 100 fathom ( 600 feet ) contour Fig. 3 .
Kalsi .
Rikkikesh is 45 miles from Kalsi .
The great load of silt brought down by the Ganges will ( according to the theory of " depression by weight " ) cause a sinking of the crust near Rikkikesh , whilst the load brought down by the Jumna will cause a subsidence near Kalsi .
But why should these silt-loads of the Ganges and Jumna cause subsidence of the crust throughout the 45 miles that intervene between Rikkikesh and Kalsi ?
The geodetic observations have led us to believe that there is a deep invisible trough skirting the foot of the mountains ; we have no geodetic data in support of the view that the depth of this trough increases at Sir S. Burrard .
points where rivers emerge from the hills and decreases at intermediate points .
The geological theory demands not a continuous trough in the crust , but a series of basins under Hurdwar , Kalsi , and similar riverain points.* .
| ' 9 .
Fifth Consideration : The Hidden Troughs of the Punjab .
Mr. Oldham , dealing only with the eastern half of the Indo-Gangetic trough ( see fig. 1 ) , shows in his diagram that the alluvial deposits of a river are a maximum at the foot of the mountains and decrease gradually as the river recedes from the mountains .
On its northern margin , he writes , the depth of the alluvium is great , on its southern margin its thickness is small ; the depth , he assumes , " decreases gradually from north to south .
" But let us apply this hypothesis to North-Western India , to the plains of the Indus and Sutlej ( see fig. 1 ) .
The Punjab is bounded on the north-west by the Sulaiman range and on the north-east by the Himalayas ( fig. 1 ) .
We have reason to believe , though the evidence is not yet complete , that a trough filled with alluvium skirts the feet of both ranges ; this deficiency of matter runs round the edge of the Punjab plains ; in the centre of the Punjab is an excess of matter .
The alluvial deposits over the Punjab have , however , been brought down from the Himalayas by the Indus , Jhelum , Chenab , Eavee , Beas , and Sutlej ( fig. 1 ) .
Where the Ravee leaves the Himalayas , near Pathankot , a deep hidden trough exists ; this trough should , according to the " depression by weight " theory , become shallower as the Eavee crosses the Punjab ; it does become shallower for a certain distance , but on the west of the Punjab becomes deeper again , namely , along the foot of the Sulaiman Mountains ; f this deepening demands , according to Mr. Oldham 's theory , a new source of alluvial deposit , and as we found the source of the eastern deposits in the Himalayas so we naturally turn to the Sulaiman Range to supply the western ones ; but the rivers of the Sulaiman have always been insignificant , compared with those of the Himalaya , and their alluvial deposits have been trifling compared with those of the Indus ; and we find that whereas the association of a trough of deficient density with the foot of a mountain range holds good on both sides of the Punjab , the association of this trough with sources of alluvial deposit holds good only on one side ; if , therefore , the weight of the alluvium was not the cause of the trough below the Sulaiman Mountains , it is difficult to argue that it must have been the cause of the trough below the Himalaya .
* This theory will be tested geodetically .
t See Plate 5 of Lenox-Conyngham 's 'Pendulum Operations in India .
' On the Origin of the In Trough .
10 .
Sixth Consideration : The Bore-Holes .
The plains of Northern India are deposits of silt brought down by rivers from the Himalayas .
Bore-holes have been sunk and remains of organic life found buried at great depths in the silt ; it has been assumed that the rock-floors underlying the Indus-Ganges valleys have been continually sinking under the increasing weight of the deposits .
Both on the west and on the east , long , deep , narrow , submarine troughs extend out into the oceans in continuation of the Indus and Ganges valleys .
The waters of the Indus and Ganges are continually pouring silt into these troughs ; amongst the silt are remains of organic life that once flourished at sea-level\#151 ; plants , shells , bones\#151 ; and these are being deposited at great depths in the troughs .
The assumption that organic remains found at depths in bore-holes must have been originally deposited at sea-level is thus not justified .
The simplest explanation is that the plains of Northern India are concealing a sub-crustal crack , that the submarine troughs are continuations of the crack , and that as the crack has opened and grown deeper , the deposits filling it up have been continually sinking to lower levels .
11 .
The Subterranean Form of the Indo- , the Slope of its Bock-walls , the Depth of its Rock-floor .
In my original paper on this subject I emphasised the fact that a band of low density exists in the crust along the northern border of the Indo-Gangetic trough .
I thought that this band of low density indicated an opening in the Earth 's crust , and this view was strengthened by the topographical appearance of the Indo-Gangetic trough , the parallel sides of which give the idea of a crack in our planet ( see fig. 1 ) .
But I did not presume to deduce any value for the depth of the trough from the geodetic results .
It is true that I did refer on one occasion to a possible depth of 20 miles , but this figure was independent of the geodetic results : I suggested 20 miles for the depth of the crack , because that is the depth at which earthquakes have their origin in our time .
The geodetic results justify the conclusion that a line of low density exists ; Mr. Hayford writes to me from America :\#151 ; " Your present work is certainly very effective in showing clearly the existence of a belt of defective density and a belt of excessive density each crossing India .
No future investigation will contradict those two conclusions .
" The line of low density is proved , but we cannot determine the exact form | of the trough .
I admire the skill with which Mr. Oldham has grappled with Sir S. Burrard .
the geodetic problem , but still the figures in his paper , published by the Royal Society , have all been based on three uncertain assumptions:\#151 ; Firstly , he has had to assume that the Himalaya Mountains are*everywhere in complete local isostatic equilibrium ; secondly , he has had to assume certain values for the densities of alluvium and rocks at great depths ; and , thirdly , he has had to assume an intimate knowledge of deep-seated geological formations in a foredeep , the origin of which is unknown .
There is evidence to show that the Himalayan mass is largely compensated , as a whole , but when we come to numerical calculations it is unsafe to assume that the compensation is locally effective.* Mr. Oldham has told us that 15,000 to 30,000 feet of sediment have been deposited along the foot of the Himalayas , and that these deposits have sunk into the Earth 's crust , and created a trough by their weight .
These deposits , lying in their self-made trough , he calls the " invisible topography , " and he tells geodesists that they must make allowance in their calculations for the invisible as well as for the visible topography .
But what happens when these deposits are disturbed ?
Geologists have found that these deep deposits have in places been elevated above sea-level .
Mr. Oldham himself writes in the ' Geology of India , ' p. 470 : " The Siwaliks now form low hills , in which these once horizontal deposits have been disturbed , elevated , and exposed to denudation .
" Where , then , is his invisible topography ?
Is it lying in its bed undisturbed , or has it been uplifted ?
If it has been uplifted , has the old rock which the alluvium depressed been uplifted also .
In his calculations Mr. Oldham has assumed the existence of undisturbed deposits , when the latter are known to have been elevated .
On p. 40 , ' Proceedings of the Royal Society , ' vol. 90 , Mr. Oldham draws the deepest part of his undisturbed trough exactly under the zone where the deposits have been elevated .
If we observe the plumb-line or pendulum at the Earth 's surface , we constantly obtain results that have no apparent topographical or geological explanation ; we find the plumb-line deflected away from visible mountains , we find it deflected towards oceanic hollows , we even obtain abnormal results when observing upon desert plains .
It is evident that there exist invisible deep-seated causes .
The calculation of the depth at which these invisible causes are situated is a complicated problem .
If we make different assump* A large floating iceberg is in equilibrium a whole ; its visible masses above sea-level are compensated by invisible masses below sea-level as a whole .
But every ice pinnacle of the berg is not individually and locally compensated by a corresponding root of ice .
Tender the Himalayan station , Mussooree , height 6924 feet , the compensation appears to amount only to three-fourths of the visible mountain .
On the Origin of the InTrough .
231 1 tions concerning the dimensions and densities of a hidden disturbing cause , \ aUy number of different values of the depth can be found to satisfy the ) geodetic results .
Mr. Oldham has taken the plumb-line observations of a few stations and 1 has endeavoured to show that these observations can be explained on the I hypothesis that the Gangetic trough is 3\#163 ; miles deep .
It is easy , however , by slight changes in the assumptions to obtain greater I values for the depth of the foredeep than 3| miles , and I do not know why | the smaller value should be preferred to the greater .
Mr. Oldham , wishing then to show that a rift would not produce effects in I accordance with geodetic results , assumes a rift of symmetrical section , I 17 miles deep , 5 miles wide* I agree that this assumed rift does not accord I in any way with the geodetic results .
The only references that I made in j my memoir to the form of the Indo-Gangetic rift were as follows :\#151 ; ( i ) " The Himalayan side of the rift appears to be a steep wall , the southern j side has a gentle slope " ( p. 3 ) .
( ii ) " There has been a succession of cracks in successive sub-crustal shells .
On each occasion that the rift has become deeper , it has opened further north than before .
Only by such an hypothesis am I able to explain the steepness of the wall on the north side of the rift and the gentleness of the slope on the I south side " ( p. 7 ) .
The above extracts will show that the idea of a symmetrical rift , 17 miles by 5 miles , has not been derived from my paper .
The Himalayan foredeep has , I think , the same form as the great deeps off .the coast of Asia ; the following extracts are borrowed from Prof. James Geikie 's recent work on ' Mountains : their Origin , Growth , and Decay *:\#151 ; " On the accompanying map , a section across the Pacific from Japan to North America shows the Tuscarora deep of the great Japanese trough .
It will be observed that the sea-floor descends from the coast at a somewhat high angle to the depth of 4600 fathoms , after which it rises with a much gentler gradient , until the level floor of the ocean is reached at a depth of a little over 2000 fathoms .
The deepest part of the trough , therefore , lies relatively close in shore or at the foot of the continental escarpment .
" The bottom of the Aleutian trough is somewhat irregular , varying in depth from 3000 to 4000 fathoms .
It extends from the Alaskan Peninsula along the whole front of the arc of islands , and is almost continuous \*ith the enormous Japanese depression .
The latter skirts the outer coasts of the Kurile Islands , Japan , and the Bonin Islands , with a depth ranging between * Such dimensions as 17 miles by 5 miles were not mentioned in my paper .
232 Sir S. Burrard .
3000 and 4000 fathoms , the deepest part of the trough throughout its whole extent lying nearest the land .
" The Philippine trough begins opposite the Riu Kiu Islands , and extends along the whole eastern margin of the Philippines to Tulur Island , at a depth of 3000 to 4700 fathoms , the greatest depths , as in all other cases , lying closest in shore .
" Geodetic observations have led us to infer that the rock-floor of the Himalayan foredeep has a steep slope on the side of the mountains and a gentle slope on the opposite side .
It would , however , be unsafe to assume that these surface forms are the results of superficial causes .
The compensation of mountains and continents extends , according to Mr. Hayford , to a depth of 70 miles ; the Himalayan and Japanese foredeeps are both lines of constant seismic activity , and the earthquakes are believed to occur at depths exceeding 20 miles .
The forms of the Himalayan and Japanese foredeeps are possibly the effects at the Earth 's surface of deep-seated sub-crustal movements.* The idea I have formed of the Indo-Gangetic trough and of the Tuscarora deep is that sub-crustal shells have been cracking under tension , and that the cracks have been followed by sub-crustal movements ( due to shrinkage at considerable depths ) towards the side of the mountains .
The cracks may have become filled , partly by lava flows from below , partly by slow rock-flows from the sides , and partly by debris from above .
All that we know of the materials filling the trough is that they are abnormally light .
Before I leave the question of the form of the trough , I must refer for one moment to the position of that point at which the depth is a maximum .
Mr. Oldham makes this point actually under the Siwalik Hills ( see his diagram on p. 233 ) .
The geodetic observations lead me to place the greatest depth of the trough altogether south of the Siwalik Hills , and many miles south of Mr. Oldham 's position .
In the ' Geological Magazine , ' vol. 10 , Ho. 594 , pp. 532-536 ( December , 1913 ) , Mr. Oldham wrote as follows :\#151 ; " Every observer , in every part of the range which has been visited , has found evidence of compression in precisely that zone where * Colonel Burrard 's postulate demands extension .
" Geologists have , it is true , found evidence of compression in the mountains , * The width of the Himalayan foredeep varies from 350 miles in North-West India to 100 miles south of Nepal .
Captain Couchman , in charge of the pendulum observations , is of opinion that the deepest part of the Himalayan foredeep is not where the alluvial deposits sl'and highest above sea-level , but is opposite to Eastern Nepal , where the Himalayan range is at its highest .
On the Origin of the Indo-Gangetic Trough .
but not in the " foredeep " ; my postulate demands extension in the foredeep only , not in the mountains .
I submit that the yielding to tension under the foredeep has been the cause of the compression in the mountains .
Whilst I have no means of determining either the depth of the Himalayan foredeep , or the densities of the rocks and debris that are filling it , I give in fig. 4 ( b ) a rough diagram to illustrate my idea of the form of the trough .
The figure 4 ( a ) is copied from Mr. Oldham 's paper , p. 40 , ' Proceedings of ' the Royal Society , 'vol .
90 ( 1914 ) .
M and N represent the Himalayas , R to S % represents the Siwalik foot-hills .
This figure 4 ( a ) illustrates Mr. Oldham 's # 10000 5000 BJt , 0 ft Surface of Ground Miles 40 \#151 ; 4a -20----- -"B it ioooo 5000 1L 0 ft Surface of Ground c , IO Fia .
4 .
explanation of the foredeep .
The bottom of his foredeep is shown by means of the dotted line AB .
His idea of the form of the foredeep is RAB .
According to his explanation river deposits have sunk by their weight to the depth of the line AB , and RAB is the " invisible topography .
" He believes that the Himalayas , NM , have moved southwards and have crumpled up the Siwalik foot-hills at R and S. He places the deepest point of the foredeep at A , i.e. at the northern edge of the Siwalik foot-hills .
Fig. 4 ( \amp ; ) illustrates my idea of the form of the foredeep , which I have drawn with a dotted line .
I place the deepest point of the foredeep at D , i.e. : south of the Siwalik foot-hills .
The depth of D is unknown .
South South Sir S. Burrard .
The explanation which I beg to offer is that the Earth 's figure and out\#174 ; shells have been under tensile strain and that the foredeep has opened from E to C. As the sub-crust at C has been forced to move northwards , the Himalayas at M and N have been uplifted vertically , and the Siwalik deposits at S and E , after sinking into the rift , have been uplifted and pressed against the Himalayas .
12 .
The Hypothesis of Rift .
I am indebted to Mr. J. de Graaff Hunter , M.A. , Mathematical Adviser to the Survey of India , for the following note upon the cooling of the Earth and upon cracks in the sub-crust .
Note on Cooling of the Earth and Cracks Sub-crust .
By J. de Graaff Hunter , M.A. It appears to me that the early state of the Earth must have been such as described by Lord Kelvin.* The state presupposed is a globe in a fluid state , on account of its high temperature , losing heat by radiation ; this is the first stage .
I think it is unnecessary to go further back and discuss the most probable way in which this state was arrived at ; it appears a highly probable early state .
The subsequent history of such a globe would be as follows :\#151 ; First of all an outer layer would cool and eventually solidify .
If , as occurs in practically all known substances\#151 ; and surely in the great bulk of the materials which make up the Earth\#151 ; the material of the crust contracts with cooling , it accordingly becomes more dense than the fluid below it , and it breaks up and sinks into that fluid .
Probably it melts again , but by doing so it chills the surrounding fluid to some extent .
This process seems to be continuous until a solid core is formed ; and this core will keep on increasing in size as the successive surface crusts fall in , until we eventually arrive at the second stage\#151 ; a solid globe of nearly uniform temperature .
The uniformity in temperature is due to the convection effect of the successive sinking of the crust and rising of molten matter from below .
When the whole globe is solidified , this convection ceases and the result is a very rapid cooling of the outer crust , which now depends for its heat on conduction from the interior of the globe .
After a comparatively short time the crust approximately reaches its final temperature , which depends on the exchange of radiation between the Earth and other bodies of the universe .
This is the third stage .
Considerations of radioactive substances may slightly modify this result , but not in a way which affects the subsequent argument .
During this process of cooling of the crust , cooling below has also been going on , but at a much smaller rate .
The contraction , which has already been assumed to accompany cooling , must during the third stage have thrown the crust into a state of great tension .
We have to consider the crust cooling rapidly from a temperature of the order of that of melted rock to a temperature such as prevails at present at the Earth 's surface .
Inevitably cracks must occur .
This state of affairs is prior to the existence of oceans , for the temperature until nearly the end of this state would be above the boiling-point of water .
There would not be any rush of water into such cracks , but gravity * ' Mathematical and Physical Papers , ' vol. 3 , Art .
XCIV .
On the Origin of the Ind. would be sufficient to partially close them up by the upper edges of the crack breaking off , until the slopes attained the angle at which equilibrium was possible .
Later on , the water would condense and find its level round the globe .
By so doing it seems probable that the level ( equipotential ) surfaces throughout the globe would be disturbed and further fractures might take place , probably with a tendency to follow parallels of latitude .
By this time the fourth stage has begun , in which the surface of the Earth would be , as regards temperature and existence of oceans , similar to what it is now .
It would not be an exact geometric figure , but I imagine the main features would be continents and oceans and the cracks which occurred in the third stage , and that there would not be any appreciable mountains .
The increase of temperature with depth near the crust would at the beginning of the fourth stage be very much more rapid than it is now , and the material a little way in from the surface would continue to cool at a rate which was now greater than the rate at which the crust would be cooling , the crust having now approximately reached a steady temperature .
The inner earth would then proceed to contract more rapidly than the crust .
It would itself crack , and the most likely places for such cracks to occur would be those already exposed to air or ocean by the cracks of the outer crust .
In such cases the debris which had fallen into the outer cracks would sink lower into the earth .
This cooling of the portion below the outer crust would result in one of two things , or a combination of them , namely ( 1 ) the crumpling of the crust and ( 2 ) the slipping of the crust and attendant partial closing up of its cracks .
These surface cracks , however , could never be wholly closed up by contraction of interior matter until the whole Earth had reached a steady ( low ) temperature .
As time went on , lower and lower levels would reach the state of contracting more | rapidly than those both below and above them , resulting in cracks in the particular i layer and a tendency to crumpling , or closing up of cracks , in the upper layers .
We are apparently now at the stage when this effect has penetrated to the comparatively small depth at which earthquakes have their origin .
It appears that , as this depth increases , the chances of crumpling of the upper layers diminish and that of the partial closing of [ cracks increases .
But , as I have said above , the cracks cannot be entirely closed up by | contraction alone until the whole Earth is cooled .
A further effect is to be expected .
The cracks which are formed in any layer , except a j few of the uppermost , will in due course be partially filled up by fractured material j falling down from an upper layer ; and with contraction in still lower layers ( due to I further cooling ) will be entirely closed .
Still further contraction below will inevitably | cause crumpling , for there is now no alternative in the way of cracks closing .
This | crumpling in the lower layers must cause a vertical lifting of the surface layers , which | will then form mountains .
The cracks in the surface layer will not , in the main , be j closed by this upheaval , for the area of the lower layers has been increased by crumpling , I and the surface layer must either stretch or crack to accommodate itself to the enlarged ; v area on which it rests .
In this way new cracks might actually open , while mountains j were being formed in the outer crust .
It appears impossible to assign any limits to the depths up to which this effect might I occur .
The cracks on the outer surface could never be wholly filled up .
They would only be partially filled by fractures in the third stage and by the products of denudation in the fourth stage .
The following is an extract from Prof. Shaler 's ' Comparison of the Features of the Earth and Moon , ' p. 8:\#151 ; " The surface of the moon exhibits a very great number of fissures or rents , VOL. xci.\#151 ; A. u Sir S. Burrard .
which when widely open are termed valleys , and when narrow , rills .
Both these names were given because these grooves were supposed to have been the result of erosion due to flowing water .
The valleys are frequently broad ; in the case of that known as the Alpine valley , at certain places several miles in width ; they are steep-walled , and sometimes a mile or more in depth ; their bottoms , when distinctly visible , are seen to be beset with crater-like pits , and show in no instance a trace of water-work , which necessarily excavates smooth descending floors such as we find in terrestrial valleys .
The rills are narrow crevices , often so narrow that their bottoms cannot if be seen ; they frequently branch , and in some instances are continued as r branching cracks for 100 miles or more .
The characteristic rills are far more abundant than the valleys , there being many scores already described ; the slighter are evidently the more numerous ; a catalogue of those visible in the best telescopes would probably amount to several thousand .
" It is a noteworthy fact that in the case of the rills , and in great measure \#166 ; \#187 ; also in the valleys , the two sides of the fissure correspond , so that if brought f together the rent would be closed .
This indicates that they are essentially * cracks which have opened by their walls drawing apart .
" The " canals " of the planet Mars have given rise to much interesting*\#174 ; discussion .
I have no right to express an opinion upon this subject , but f as astronomers have differed widely in their views , I may perhaps be f ' permitted to invite the attention of students of Mars to the rifts on the / t Moon 's surface and to the apparent rifts on the Earth 's surface , and to i ask whether the canals of Mars may not be openings in its outer crust .
Mr. Hunter , in his note which I have quoted above , has considered a ||.t cooling globe , and has shown that it is liable to crack .
This liability will be ||l increased by the strains to which the Earth 's figure and upper crust are 111 subjected .
If the Earth 's rotation has decreased in the past , the spheroidicity m\ of its figure must have decreased also .
The superfluity of rock accumulated Mi at the equator under a higher rotation velocity could not have moved to the ; -i poles without great distortions of the rock surface occurring .
It has been estimated that the Earth picks up from 10 to 20 millions of Jti tons of additional matter from space in the shape of meteors every year , mi If at any time in the past the Earth was ever struck by a very large , |ii body from space , ages may have ensued before the Earth 's figure was able to accommodate itself to the new conditions .
In geological history there Jp !
appear to be epochs , especially the Permian and the Cretaceous , when f\lt ; large changes of figure began , and it may have been that some abnormally | : large addition of rock was then picked up by the Earth from space .
Even the accumulation of ice at the poles in the glacial epoch may have On the Origin of the Trough .
23 been sufficient to affect the spheroidicity of the Earth , and to set up strains in its outer shells .
13 .
Departures from Isostasy .
It has been shown by geodetic observations that the Earth 's crust is in a i condition approaching isostatic equilibrium .
If any departure from isostasy occurs , the Earth 's figure becomes subjected to strains , and its surface becomes i liable to crack ( or to stretch ) .
A considerable departure from isostasy cannot t persist indefinitely ; the force of gravitation and the Earth 's rotation are i always tending to produce complete isostasy .
When isostasy is disturbed by j the irregular cooling of the sub-crust , or by the slowing down of the Earth 's rotation , or by the impact of meteors , or by the conversion of equatorial ( water into polar ice , equilibrium can be restored by the compression of the crust in some regions and by stretching of the crust in others .
Crustal t tension and crustal compression are among the means by which isostasy is l| .
maintained .
The readjustments in the isostasy of a continent that become necessary , as the Earth undergoes changes , may bring about disturbances in the isostasy h of smaller regions .
In India , the Indus-Ganges trough appears to have been opening north-\gt ; ; wards , and the Himalaya Mountains seem at the same time to have been 11 undergoing elevation along the northern edge of the trough .
If this view ilf is correct , a certain amount of rock must have been moved northwards out of the trough into the mountains .
The northward movement may have been i caused by the cooling of the Earth or by readjustments of its figure or mass i to new conditions .
The disturbing effects upon local isostasy of this north-i j ward movement have been partially counteracted by denudation , for , although IK rock-mass may have been moved northwards by the opening of the trough , lJ rivers have been bringing silt southwards from the rising mountains and \gt ; pouring it back into the trough .
In this paper I have discussed the hypothesis that the Earth 's crust is f being depressed by the weight of riverain silt deposited upon it , and it may .
I not be out of place to attempt to discover from observation the weight of M actual loads which the Earth 's crust is seen to be supporting .
Colonel Lenox-Conyngham writes : " Under the Himalayan station of M Mussooree , height 6924 feet , there appears to be standing above sea-level an jl extra uncompensated mass equal in bulk to about a quarter of the visible M mountain .
" This is Colonel Conyngham 's deduction of the most probable result ; he emphasises the fact that there are elements of uncertainty in the calculation .
On the Origin of the Indo-Gangetic Trough .
A considerable departure from isostasy is exhibited by the Ranchi Plateau .
This plateau forms part of the Vindhya Mountains , and is a relic of an ancient tableland ; it is situated immediately south of the Indus-Ganges : trough in longitude 84 ' , opposite to the Himalayan peaks of Mount Everest and Dhaulagiri .
Ranchi lies near the crest of the " hidden chain " of excessive density .
The pendulum observations seem to indicate that the Ranchi Plateau is mainly supported by the rigidity of the Earth 's crust ; and the plumb-line observations show that there is a considerable excess of mass south of the Ganges at Ranchi .
The Earth appears to be supporting this load without appreciable deformation .
As , however , certain geodesists have modified to a slight extent Prof. Helmert 's formula for the normal value of gravity , and as the calcu- i lation of any departure from isostasy is dependent upon that formula , I li asked Colonel Lenox-Conyngham to give me his opinion concerning the load 1 supported at Ranchi .
He considers that the Ranchi mass may possibly not be wholly supported by the crust 's rigidity , but that probably half of it is.\ If this cautious estimate is accepted , then the Earth is strong enbugh to b ' sustain a weight of 1000 feet of rock ( density , 2'67 ) over an area of two square degrees ( 8500 square miles ) without yielding .
I have now given my reasons for thinking that the hypothesis of a sub- 1 crust opening under tension is more in accordance with observed facts and is more deserving of consideration than the idea of strata sinking under their own weight .
|
rspa_1915_0015 | 0950-1207 | On thermophones. | 239 | 241 | 1,915 | 91 | Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character | P. De Lange|Lord Rayleigh, O. M., F. R. S. | article | 6.0.4 | http://dx.doi.org/10.1098/rspa.1915.0015 | en | rspa | 1,910 | 1,900 | 1,900 | 4 | 44 | 1,273 | http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1915_0015 | 10.1098/rspa.1915.0015 | null | null | null | Electricity | 32.341319 | Biography | 20.390712 | Electricity | [
17.71907615661621,
-58.514549255371094
] | On Thermophones .
By P. de Lange .
( Communicated by Lord Rayleigh , O.M. , F.R.S. Received December 3 , 1914 .
) The invention which I desire to communicate to the Royal Society ( and of which I have already , with the permission of your President , demonstrated the models at your informal gathering on the evening of October 29 ) has been made by me in co-operation with my friend Otto Fischer , Some of the models have been made in the laboratory of the University of Utrecht by the assistant , Mr. Stellema , under the supervision of my cousin , Prof. Zwaarde-maker , who was so kind as to introduce me to Lord Rayleigh .
I have been demonstrating with these models for over six months , and they do not show the slightest wear .
The origin of the thermophones may be traced back to the invention made 34 years ago by your late Fellow , the former engineer-in-chief to the Post Office , Sir William Preece.* Sir William Preece attached a stretched wire to a diaphragm which , by extending and contracting , owing to the changes in an electric current passing through it , moved the diaphragm , and thereby made it speak .
The great difference between his invention and that of the thermophone lies in the mechanical action of the wire on the diaphragm , the latter being dispensed with in the thermophone , the action of which simply and solely rests upon a change of temperature in a wire unconnected with any mechanical contrivance .
In the thermophone the wire speaks without a diaphragm , and the basis of this invention has been laid by Mr. Gwozdz .
About seven years ago , the Russian engineer , Gwozdz , made various experiments in a small village in the neighbourhood of Lodz , in Poland , with a thermophone without a diaphragm and without an electromagnet .
Gwozdz fixed a Wollaston wire on an insulating medium , and then treated the Wollaston wire with acid .
He obtained thereby a good thermophone , but ( as far as I know ) it was impossible by this process to obtain instruments which conveyed the required volume of sound , and Gwozdz never succeeded in rendering the thermophone of any practical utility .
Curiously enough , at the same time , Prof. Abraham , of Paris , made some experiments with a thin platinum wire which he connected with electrodes in a straight line , and then again with a transmitter .
These experiments also did not meet with a practical result , because the stretched wire had no * ' Roy .
Soc. Proc. , ' vol. 30 , p. 408 .
Mr. P. de Lange .
freedom , and thereby was exposed to too great a danger of breaking by the alternate extensions and retractions .
With my invention I follow the process of Gwozdz regarding the treatment of the Wollaston wire , hut I claim that my invention is of the greatest practical value , and this I will now explain .
By fixing a platinum wire of a diameter of from 2 to 12 microns in a gothic curve , I claim to have succeeded in making the thermophone of practical everyday use , because the silver of the Wollaston wire is eliminated , whilst the whole Wollaston wire is freely suspended in the acid in such a way that at any time such part of the platinum wire can be set free , as is considered desirable , without it being liable to breakage .
Thermophones have value only if they have been made on this basis .
In order to know something more about the working of the thermophone , Prof. Zwaardemaker and myself have measured the volume of the sound with Lord Kayleigh 's well-known mirror .
In order to avoid currents of air which might originate through the heating of the wire , we placed a glass diaphragm in a wooden or aluminium frame between the wire and the mirror .
The size of the diaphragm was about the same as that of a diaphragm of the phonograph .
Moreover , we placed a small tube in the cover of the diaphragm in order to prevent the system from working as an air thermometer .
The result of our measurement was that the sound increased with the increased number of platinum wires , but not in the same ratio .
Also thin wires of 2 microns have a greater acoustic effect than wires of 5 microns , the Joule heat remaining the same .
Everything depends upon the exact relationship between the telephone and the microphone .
The thermophone , listened to in the open air , sounds extremely weak .
As soon , however , -as the platinum wire is placed under a cover which has a small opening or several small openings , the sound at once becomes clear and distinct .
The volume of the sound increases in accordance with the decrease of the size of the cover .
Evidently the cover functions as a resonator .
It is a telephonic advantage to make the cover as small as possible , because in that case the high notes and the sound consonants produce a better effect .
The size of the openings in small covers should not be made too large , because in that case the resonance becomes too high and produces a curious sound in addition to the human voice .
I am trying to find an explanation for this most curious phenomenon , but that is a matter which may be the subject of a future communication to this Society .
The maximum admissible size of the cover appears to vary between comparatively speaking wide limits .
The size which approximately agrees with the size of the human ear funnel seems to be the most suitable .
Metal On Thermophones .
covers are better than those of ebonite , and , by surrounding these with some cooling substance , the acoustic effect\#151 ; if measured with Lord Rayleigh 's mirror\#151 ; becomes twice as great .
In this case the sound is conducted through a rubber tube of small width .
It is quite possible to combine a number of these thermophones , but then it should not be forgotten that the whole space occupied by them should remain as small as possible , because the space which they take up together also acts as a resonator .
The acoustic effect appears to increase at least in about the square of the strength of the current .
Thermophones with four rows next to each other , each of six platinum wires of 7 microns with a combined resistance of 35 ohms give\#151 ; measured with Lord Rayleigh 's mirror\#151 ; the following results , viz.:\#151 ; In the case of 6 volts , 2\ degrees .
99 Q 99 1^ 99 ,9 10 " 25 " It is difficult from these items to construct the theory of the thermophone .
The most I can say is that the decrease and increase of heat in the platinum wire of the telephone takes place isochronically with the vibrations in the microphone .
The air surrounding the platinum wire is thereby immediately heated or cooled in accordance with the increase and decrease of heat in the wire , and , if that air is retained within a closed compass of the cover , the expansions and retractions will be noticed as sound .
|
rspa_1915_0017 | 0950-1207 | A bolometric method of determining the efficiencies of radiating bodies. | 245 | 254 | 1,915 | 91 | Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character | William A. Bone, F. R. S.|H. L. Callendar, F. R. S.|H. James Yates. | article | 6.0.4 | http://dx.doi.org/10.1098/rspa.1915.0017 | en | rspa | 1,910 | 1,900 | 1,900 | 3 | 140 | 4,606 | http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1915_0017 | 10.1098/rspa.1915.0017 | null | null | null | Thermodynamics | 30.76772 | Tables | 26.249137 | Thermodynamics | [
5.837047100067139,
-16.37938690185547
] | 245 A Bolometric Method of Determining the Efficiencies of Radiating Bodies .
By William A. Bone , F.B.S. , H. L. Callendar , F.B.S. , and H. James Yates .
( Beceived February 15 , 1915 .
) Introduction .
With the increasing use , within recent years , of gas fires , electric radiators , incandescent surface combustion diaphragms , and the like , there has arisen a demand for a reliable general method for testing their radiant efficiencies .
The problem is important also in its purely scientific aspects , inasmuch as its solution would enable the relations between the modes of combustion of various combustible gases and their radiant values when burnt at an incandescent surface to be investigated .
The present paper describes a bolometric method which we believe to be applicable to the measurement of the radiant energy emitted from hot terrestrial surfaces generally , but as the source of radiation in our experiments has been a gas fire , it will be convenient if we describe it with reference to that particular mode of heating .
A typical modern gas fire consists of a series of atmospheric burner nozzles , varying usually between seven and fifteen in number , according to the size of the apartment to be heated , arranged equidistantly along a common horizontal supply pipe provided with suitable means for properly adjusting the relative gas and primary air supplies so as to ensure a vertical series of non-luminous and , as nearly as possible , silent Bunsen flames , of uniform height and character .
Above each flame is fixed a hollow fireclay columnal " radiant " perforated in a manner expressly contrived to promote uniform heating of the column throughout , and with each flame rising into the cavity of its particular radiant .
Care is taken to prevent any impingement of the inner cone of the flame upon its radiant .
The back of the fire is formed by a fireclay slab fixed vertically behind the radiants , which are held in position by means of one slight horizontal iron rod .
At a suitable distance above the top of the radiants is fixed a metallic hood or " canopy " by means of which the products of combustion are collected and discharged through the flue vent into the chimney without in any way contaminating the atmosphere of the apartment .
The object of a properly designed fire should be to secure the maxima of radiant and ventilating effects with a minimum of " flue heat/ ' and it is in connection with these aspects of the problem that the need of convenient and 246 Messrs. Bone , Callendar , and Yates .
A Bolometric accurate means of measuring the radiant efficiency of the fire has been mostly felt.* # ' .
A joint committee appointed in 1907 by the University of Leeds and the Institution of Gas Engineers to investigate gas fires adopted a method ( now known as the Leeds method ) for determining their radiant efficiencies .
It consists essentially in firstly establishing , by thermopile readings , a relation between the intensity of the radiation at a central equatorial area on a hemisphere in front of the fire , and the total radiation received over the whole hemisphere ( a relation which will be hereafter referred to as the " distribution factor " of the fire ) , and then determining , by means of a radiometer , of the water-calorimeter type , designed by Prof. B. H. Smith , the actual number of calories radiated by the fire per hour on to the said equatorial area .
The number of such calories multiplied by the " distribution factor " of the fire gives the total energy radiated by the fire per hour , and the relation of this to the total net heat developed by the combustion of the gas in the fire per hour gives the radiant efficiency of the fire.f This method , whilst perfectly sound in principle , is admittedly open to criticism on the following grounds , namely :\#151 ; ( 1 ) The B. H. Smith radiometer is liable to various small indeterminable errors inherent in all such water-calorimeter radiometers , due principally to ( a ) imperfect absorption of the radiation by its blackened surface , ( b ) effects / of " lag , " which , however , if the experimental conditions remain constant , may be disregarded , and ( c ) the difficulty of carrying out a really satisfactory " blank " experiment to determine the allowance to be made in the actual test for heat gained by the instrument from the surrounding warmer atmosphere.^ ( 2 ) It is practically impossible , owing to the large area of the absorbing surface of such a radiometer , to standardise its readings from a known absolute radiation standard .
( 3 ) The time taken to complete both the radiometer ( actual and blank ) tests and the 81 thermopile readings required to establish the " distribution * See also H. James Yates on " Beeent Progress in Gas-Fire Science , " 1 Brit. Assoc. Beports , ' Birmingham , 1913 , pp. 435-9 .
t A full description of the Leeds method is given in the Committee 's First and Second Beports , ' Trans. Inst. Gas Engineers , ' 1909 , pp. 59-81 .
X There is certainly a small systematic error in the " blank " test , due to the impossibility of screening the radiometer perfectly from the fire during the blank , the effect of which is to make the ascertained " blank correction " too high .
By means of the bolometer we have estimated that , in the case of a 10-inch gas fire , and using a single reflecting screen in front of the radiometer during the Leeds blank test , the error may amount to T)*44 kilogramme-calories per hour on a total centre reading ( in the actual test ) of 55-60 kilogramme-calories .
Method of Determining the Efficiencies Radiating Bodies .
247 factor " is considerable , and there is always a risk of some alteration during the test in the experimental conditions which would affect its result .
( 4 ) There is also perhaps a little uncertainty about the absolute accuracy of the " distribution factor " as determined by the Rubens thermopile used in the Leeds method .
In any case , were the method entirely free from any or all such practical objections , it would still be important to compare its results with those obtained by some independent standard method .
The New Bolometric Method .
The problem of measuring the radiant efficiency of a modern gas fire , such as has been described in the introductory part of our paper , is complicated by the fact that the fire front ( .
, the seat of the radiation ) cannot be regarded as a surface of simple geometric form .
The seat of the radiation has , in fact , a measurable depth , and , owing to the line of the fire front being often slightly curved , its exterior surface is not always flat .
Again , the hemispherical distribution of the radiation may be disturbed either by absorption or by reflection from projecting surfaces on the casing of the fire .
It is necessary to determine , not only the whole radiation emitted by a particular fire , but also its distribution factor , because a proper distribution of the radiant energy is almost as important as its total amount .
The Bolometer and its Advantages .
We propose to substitute for the radiometer-cum-thermopile device in the Leeds method a simple bolometer in which the radiation falling from the fire upon a blackened coil of platinum wire can be deduced from the observed increase in its electrical resistance , the area of the receiving coil being sufficiently small to allow of the instrument being standardised directly from a source of radiation of known intensity .
The principal object in employing a bolometer in place of a thermopile is to secure a greater range of accuracy and sensitiveness , and to facilitate the obtaining of automatic records when required .
The sensitiveness of a bolometer is readily varied over a wide range by varying the electric current employed for measuring the resistance .
The sensitiveness may also be determined very easily , under any conditions , by observing the deflection produced by inserting a known resistance in the circuit .
In using the Rubens thermopile ( as in the Leeds method ) , it is found necessary to attach a reflecting cone to the instrument in order to obtain a deflection of 25 scale divisions with a Paul unipivot galvanometer at a distance of 248 Messrs. Bone , Callendar , and Yates .
A Bolometric 3 feet from a 10-inch gas fire .
The use of a reflecting cone narrows the angular aperture , and introduces some uncertainty with regard to the extent of the source from ' which the radiation is actually received .
The 'bolometer , when supplied with the current for which it is designed , and employed in conjunction with the same unipivot galvanometer but without any reflecting cone , is found to have a sensitiveness about thirty times as great as the Eubens thermopile with the cone , and could be used at much greater distances from the fire .
By adjusting the sensitiveness to a suitable figure in scale divisions per ohm , it is always possible to obtain deflections in the neighbourhood of 90 or 100 scale divisions , which greatly facilitates the accurate determination of the radiation .
Construction of the Bolometer .
The familiar type of bolometer invented by Prof. Langley has a sensitive receiving surface in the form of a grid cut from thin metal foil , and is blackened with smoke black or platinum black .
This method of construction was adopted with the object of securing the greatest quickness of action , but it involves extreme fragility and is wanting in constancy .
The coating of black invariably deteriorates , and cannot be renewed without altering the constant of the instrument .
Constancy is much more important for the present purpose than quickness of action , and fragility would be a serious defect .
A different method of construction was accordingly adopted in our experiments ; the delicate grid of the Langley bolometer has been replaced by a coil of platinum wire wound on a thin piece of mica , and coated to an even surface with hard black enamel , which is extremely permanent , and can be cleaned without risk of injury .
Two exactly similar coils , each 4 cm .
square and of 20 ohms resistance , are mounted back to back on either side of a circular gunmetal box , provided with water circulation , and with suitable covers for the coils , so that either coil can be exposed to radiation or screened .
When both coils are screened they are kept at the same temperature as the box , their resistances remain equal , and there is no deflection of the galvanometer , however much the temperature of the box may change .
But if one of fcthe coils is exposed to radiation , its temperature and resistance are increased by an amount depending on the intensity of the radiation , and the galvanometer shows a deflection proportional to the increase of resistance , which serves as a measure of the intensity of the incident radiation .
Method of Determining the Efficiencies of Radiating Bodies .
249 Calibration of the Bolometer .
An instrument of this type can be directly calibrated to give the intensity of the radiation in absolute measure , by observing the magnitude of the electric current required to produce the same rise of temperature , or increase of resistance , as the radiation to be measured .
This method has often been adopted , but is not quite satisfactory , on account of the uncertainty of the absorption factor of the surface for radiation , which is one of the commonest sources of error in all measurements of radiation .
The constant of the bolometer , giving the intensity of the radiation in terms of increase of resistance , was accordingly determined by comparison with a radio-balance , an instrument specially designed to give total absorption of the radiation.* In the radio-balance , the radiation to be measured is admitted through a small circular aperture and received in a blackened copper cup , in which the absorption is practically complete .
The heat received from the radiation is balanced by absorption of heat due to the Peltier effect in a thermojunction through which a measured electric current is passed .
This method is very accurate , but is not well suited for ordinary use outside a physical laboratory , because it requires a 'sensitive galvanometer for indicating the balance , and a delicate ammeter or potentiometer for measuring the electric current .
Nevertheless , a bolometer such as the one herein described can , without risk of fracture of its working parts , be sent to a physical laboratory for comparison with a radio-balance .
The following Table contains all the results for the constant of this particular bolometer obtained by comparison with two different radiobalances , denoted by I ) and E respectively .
Two different sources of Observations of Bolometer Constant K. Date .
Radio -balance .
Temperature of bolometer .
Air .
Source of radiation .
Constant of bolometer .
1914 .
July 25 E o 21 -5 o 22 -0 Gias fire 27 -71 " 26 E 21 *0 21 5 Focus lamp Gras fire 27 '85 Nov. 28 D 15 *7 18 *0 28 -09 " 29 D 17 2 18*7 Focus lamp Gas fire 28 -02 Dec. 1 D 17 *7 18 -0 27 '82 " 3 E 18 -9 18 *2 Focus lamp 27 96 " 3 D 18*7 18 *3 27 '86 " 5 E 20 *7 19 *2 Gas fire 27 '82 " 6 E 18*3 21 *2 .
27 '78 Means 18 *9 19 *4 K = 27 '88 * ' Proc. Phys. Soc. Lond. , ' vol. 23 , pp. 1-34 ( 1910 ) .
250 Messrs. Bone , Callendar , and Yates .
A Bolometric radiation were employed\#151 ; ( 1 ) a 10-inch gas fire at a distance of 1 metre , ( 2 ) a focus lamp of 100 candle power , having a small radiant 1 inch square , at a distance of 30 cm .
It was unfortunately impossible to vary the temperature of the laboratory materially , but the temperature of the bolometer was altered 5 ' or 10 ' on each occasion , by changing the water circulation , in order to determine the correction for the difference of temperature between the bolometer and the air .
The results given for the constant are corrected for the observed difference .
The value of the constant is given as the intensity of the radiation in kilocalories per square foot per hour required to produce an increase of resistance of 1 ohm in the exposed coil of the bolometer .
The chief source of error in the comparisons was the uncertainty of temperature of the surrounding air and the walls of the room , which cannot be well avoided in measurements of this kind with a source of large area like a gas fire , since the receiving instrument is necessarily exposed to the air and to radiation from surrounding objects , which may be at different temperatures .
The correction for difference of temperature between the air and the bolometer was found to be 0*028 ohm per 1 ' C. , and amounted in some cases to as much as 4 per cent. , when the difference of temperature was considerable , but the divergence of the corrected results from the mean in no case reaches 1 per cent. , and is generally less than 0*5 per cent. The Distribution Factor .
The " distribution factor " of a gas fire , or other approximately flat source of radiation , may be defined as the factor by which the normal intensity at a given distance D must be multiplied in order to obtain the total radiation emitted over a hemisphere .
If the source is a plain circular disc of uniform intensity and of radius B , the value of the factor given by the theory of radiation for a self-luminous surface , would be simply 7t(D2 + B2 ) .
Thus , for example , in the case of a plane source 1 foot in diameter , tested at a distance of 9/ nr feet , or 34#38 inches , the value of the distribution factor should be 26*58 , which is about the value generally obtained for a 10-inch gas fire , tested at this distance , by taking a large number of readings equally distributed over the surface of a hemisphere .
In the case of a gas fire the surface is , however , seldom flat , and there are considerable extensions , such as the canopy , which contribute an appreciable fraction of the radiation .
The chief uncertainty arises in estimating the distance D. An error of 1 inch in^D in the above example would make an error of nearly 6 per cent , in the mathematical formula , and it may be doubted whether this error Method of Determining the Efficiencies of Radiating Bodies .
251 can be eliminated in practice by taking observations over a hemisphere of fixed radius .
The obvious method of reducing this uncertainty , especially with a large gas fire , would be to increase the distance .
But this introduces some practical difficulties if a large number of readings are to be taken over a hemisphere of large radius .
It is doubtful whether an accurate result can be obtained by mere multiplication of readings .
Since the deviation of the distribution factor from the theoretical value for a flat surface is evidently small , it would probably suffice to take a few readings at suitably selected angles .
It appears from theory , and also from comparison of observations , that the sum of four readings taken at 60 ' along the equator and meridian , together with the central reading , multiplied by ' ?
rD2/ 3 , ( 8*6 , when D = 9/ 7t feet ) , gives as good an approximation to the total radiation as can be obtained by taking 81 .
readings .
The distribution factor is represented by the sum of the five readings divided by the central reading and multiplied by 7tD2/ 3 .
Effect of Variation of Temperature of Receiver .
The importance of keeping the temperature of the receiver , whether bolometer or thermopile , constant , is best appreciated by taking a case in which this precaution is omitted .
If a Rubens thermopile with a Paul indicator ( such as is used in the Leeds method ) is exposed to a steady source , giving an intensity of 46 kilocalories per square foot per hour , the deflection rises to about 25 mm. in 15-20 seconds , and creeps up to 27*5 , a further 10 per cent. , in three or four minutes .
The deflection then diminishes to about 25 mm. if the exposure is prolonged , on account of rise of temperature of the case , which may amount to 5 ' or 10 ' C. If , now , the hot instrument is screened from the source , or turned towards the wall of the room , which is at a lower temperature , it falls quickly to zero and gradually takes up a negative deflection of 3 or 4 mm. In other words , the rise of temperature of the instrument may produce an effective change of zero equivalent to 10 or 15 per cent , of the deflection .
Variations of this magnitude make it impossible to employ the pile with a constant reduction factor for determining the absolute value of the radiation .
In using the pile merely for the distribution factor , the errors are not so obvious , but , being systematic , they produce a marked effect on the results , as is shown by the following typical comparison of readings taken with thermopile and bolometer , along the equator in front of a gas fire .
vol. xci.\#151 ; A. x Messrs. Bone , Callendar , and Yates .
A Bolometric Position 60 ' West .
0 ' .
60 ' East .
Thermopile 16 *0 23 *3 13 *0 Bolometer 58 *2 91 *2 58 *0 Thermopile 15 *2 22 *9 13 0 The thermopile readings make the distribution appear about 20 per cent , greater on the west than on the east .
There is no reason why this should be the case , and the bolometer readings show practically no difference between east and west .
The explanation is that in the case of the thermopile the west readings were taken first , while the deflection was still increasing , whereas the east readings were taken after the instrument had become hot , with the consequent depression of zero .
The opposite errors on the two sides tend to neutralise each other to some extent , but the general effect is to reduce all the smaller readings unduly as compared with the central reading , so that the distribution factor obtained with the thermopile may be as much as about 3-5 per cent , too small .
This point may be illustrated by reference to the following Table of the " Distribution factor " of the same 10-inch gas fire as determined on several different occasions by means of ( 1 ) the bolometer , and ( 2 ) a Rubens thermopile .
The Distribution Factor of a 10-inch Gas Fire as determined by\#151 ; Bolometer .
Thermopile .
28-23 27-42 2856 27-55 28-65 27-12 28-30 27-55 28-70 27-57 28-16 27-68 27-97 27-52 28-52 27-81 27-13 28-52 Mean = 27*44 28-47 Ratio _ ^'36 _ 1-034 .
Mean = 28-36 27-44 Method of Testing a Gas Fire .
It is usually the most convenient method , in testing a gas fire , to mount the bolometer or thermopile on a revolving sector of fixed radius , the centre of Method of Determining the Efficiencies of Radiating Bodies .
253 which is adjusted to coincide approximately with the centre of the fire .
If the radius of the hemisphere over which the bolometer moves is 9/ 7t feet , or 34*4 inches , as employed in the Leeds method , an error of 1 inch in the adjustment of the sector along the normal will produce an error of 6 per cent , in the central reading .
It is difficult to specify accurately how this adjustment should be made , especially if a radiometer of large receiving surface , such as 1 sq .
ft. , is employed for the central reading .
The Leeds method of testing throws too much weight on the central reading , which is the most uncertain so far as the adjustment is concerned .
The reasons for taking four readings at an angle of 60 ' with the normal are ( 1 ) that these readings take very fair account of the variation of distribution in different directions , ( 2 ) that the sum of the four readings will be very nearly independent of small errors of adjustment of the sector , and will reduce to about one-third the probable error of adjustment on the central reading .
Automatic Records .
It is possible with the bolometer to obtain automatic records in ink on a large scale , which are useful in recording the progress of a test , or showing the effect of variation of conditions .
The scale is readily varied from 10 to 40 cm .
per ohm .
The reading obtained with a 10-inch gas fire at a distance of 3 feet is generally between 1*5 and 2 ohms with the bolometer already described .
This reading would correspond to a vertical height of 15 to 80 cm .
on the record according to the scale employed .
The smaller scale is quite sufficient for an ordinary test , but the larger scale is useful in investigating small corrections , due to variation of temperature of the room or similar causes .
Leadings can be taken more quickly with an indicator such as the unipivot galvanometer already mentioned , but the recorder has the advantage that its scale is more accurate and uniform , and that it is easier to see when r the conditions of observation are satisfactorily steady .
Radiant Efficiency of a Gas Fire .
In conclusion , we may tabulate the results of a series of determinations of the radiant efficiency of a 10-inch gas fire working on London coal gas of average net calorific value 32*88 K.C.Us .
per cubic foot at N.T.P. , with an average consumption of 24*25 cu .
ft. per hour at N.T.P. , supplied to the fire at a constant pressure of 1*9 inches ( water gauge ) above the barometric pressure .
Determination of Efficiencies of Radiating Bodies .
Date .
Barometer .
Dry gas consumption per hour at N.T.P. Net calorific value dry gas K.C.U. 's per cub. ft. at N.T.P. \#171 ; Radiant efficiency .
1914 .
mm. cub. ft. per cent. Dec. 9 750 -3 24 *00 132 *0 44 *8 " 10 752 -5 24 *49 131 0 45 -0 " 11 746 -1 24 *25 130 *6 43 *2 " 14 732-7 23 *78 130 *2 46 -0 " 16 748 -4 24 *19 131 *8 46 *6 " 17 761 -1 24 *77 132 *3 44 -6 764 -7 24 -49 132 *3 44 -6 763 -2 24 *51 131 *7 45 5 763 -2 24 *26 131 *7 45 *5 " 18 751 -4 23 *82 130 *6 44 *0 Mean 45 -0 The testing room was a laboratory 38 ft. x 32J ft. x 15 ft. high , the temperature of which varied only between 14 ' and 17 ' C. during the various tests .
The fire was mounted on a special stand , with its flue outlet under a large hood communicating with a chambered wall and chimney which gave a sufficient draught to prevent any of the products of combustion getting into ; the room .
The five bolometer readings in each test were taken at radial distances of 34*4 inches from the centre of the fire : one central reading and four other readings in positions 60 ' N. , S. , E. , and W. respectively , of the central position .
A mean " distribution factor " of 28*36 , as determined for the said fire , was i used in the calculations .
Finally , the authors desire to thank Messrs. A. Forshaw , M.Sc .
, and S. Farrar , B.Sc. , for their assistance in connection with the experimental part of the investigation .
|
rspa_1915_0018 | 0950-1207 | The laws of series spectra. | 255 | 272 | 1,915 | 91 | Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character | J. W. Nicholson, M. A., D. Sc.|A. Fowler, F. R. S. | article | 6.0.4 | http://dx.doi.org/10.1098/rspa.1915.0018 | en | rspa | 1,910 | 1,900 | 1,900 | 1 | 17 | 402 | http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1915_0018 | 10.1098/rspa.1915.0018 | null | null | null | Tables | 73.166398 | Atomic Physics | 23.244735 | Tables | [
17.258420944213867,
-50.271488189697266
] | ]\gt ; The last figures in are not all exact , and , in certain cases , the errors , which .
are larger than were estimated by and Paschen , amount to 1/ 100 of an ngstrom unit .
In the investigation , however , where the limit is calculated from every pair of successive lines , ) mean must be very accurate if the errors in the lines are not systematic .
The Hicks formula shows that they can be represented by , ( 8 ) where never exceeds .
If be expanded The fourth term of this very convergent series is .
Since is about , this cannot exceed 3 .
even when .
If we take all the lines beyond , it cannot exceed , so that for all these lines ; 'Handbuch der Spectroscopie , ' vol. 6 , p. 891 .
* Trans. Intern .
Union Solar Research , Bonn , 1913 .
The resulting weighted mean is xhaustive treatment drinci aseri , treated ieyond m , gives The general mean is from which we see that if , the only bad values are the first and last .
Now the first pertains to the lines most readily measured , and we ust conclude that the strict applicability of the method has not commenced this stage , so that the first two lines at least should be weighted on this ( account .
A similar error of opposite sign does not appear in the second value , as it should if an error of measurement accounted for the discrepancy the first value , according to the method used for the calculation .
The divergencies in the first and last values practically balance , so that the general mean must be nearly accurate , so far as casual observational errors are concerned .
By attaching weights 1 , 2 , 3 , 4 , 5 , 6 to the first six values , roughly to the degree to which the formula is applicable , and a weight 1 to the last value , we shall obtain a mean nearly free from errors formula .
The result is , and this result must possess considerable accuracy , beyond , in fact , the accuracy of individual lines .
We may now consider the values of The limits are ( Diffuse ) , ( Sharp ) , Principal )
|
rspa_1915_0020 | 0950-1207 | The elastic properties of steel at moderately high temperatures. | 291 | 303 | 1,915 | 91 | Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character | F. E. Rowett, B. A. (Whitworth Scholar)|Prof. B. Hopkinson, F. R. S. | article | 6.0.4 | http://dx.doi.org/10.1098/rspa.1915.0020 | en | rspa | 1,910 | 1,900 | 1,900 | 40 | 218 | 4,441 | http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1915_0020 | 10.1098/rspa.1915.0020 | null | null | null | Measurement | 48.918953 | Thermodynamics | 30.6134 | Measurement | [
46.098812103271484,
-61.86756896972656
] | 291 The Elastic Properties of Steel at Moderately High Temperatures .
By F. E. Rowett , B.A. ( Whitworth Scholar ) , Research Student in the University of Cambridge .
( Communicated by Prof. B. Hopkinson , F.R.S. Received February 6 , 1915 .
) In a recent paper the author gave the results of measurements of the elastic hysteresis of steel tubes , when subjected to torsional stress , within what is ordinarily regarded as the elastic limit .
Those measurements were made at ordinary room temperature , and the chief points established by them were , that the hysteresis of the hard-drawn tubes is much less than that for the same tubes after annealing , and that in the latter case , the loss of energy in the cycle of stress is independent of the speed of performance of the cycle , or , in other words , time is not a factor in the stress-strain relation .
The present research is the outcome of a suggestion by Prof. B. Hopkinson , that at a suitable temperature the hard-drawn tube , which contains a good deal of amorphous material , would begin to behave like a viscous fluid , that is , it would flow more or less freely when under stress , whereas at the same temperature , the annealed tube , being crystalline , though it might take a permanent set , could not flow , or would flow in a much less degree corresponding to the small amount of amorphous material in it .
These predictions have been verified .
At a temperature about 300 ' C. , the hard unannealed tube began to show properties similar to those of pitch at ordinary temperatures , or of glass at a temperature rather below the softening point .
It is still highly elastic under rapidly varying stress , but flows perceptibly when the stress is applied for a long time .
The energy dissipated in a cycle of stress now depends on the speed of the cycle .
If the cycle is performed in 5 seconds the area of the closed stress-strain loop is not much greater than at ordinary temperatures , and is less than that given by an annealed tube .
But if the cycle takes a quarter of an hour , the dissipation is increased four-fold .
On the other hand , in the annealed tube at 300 ' C. the energy lost per cycle of stress is still almost independent of the time .
At a higher temperature , for example at 540 ' C. , the hard-drawn tube flows rapidly and continues to flow for a long period , though at a diminishing rate , under a shear stress of less than 1 ton per square inch .
Moreover , again like pitch or glass , the steel at this temperature shows considerable elastic afterworking .
If the stress be suddenly removed the immediate elastic recovery is followed by a slow backward flow which persists for many minutes .
Some Mr. F. E. Rowett .
The Elastic Properties of flow and elastic afterworking were also observed in the annealed tube at this temperature , but both were much less than in the hard tube.* Apparatus .
' The apparatus was an improved form of the static apparatus described in \lt ; Roy .
Soc. Proc. , ' A , vol. 89 , p. 537 , and the method of obtaining the area and shape of the hysteresis loop has been explained there .
The experimental tube was rigidly fixed at one end to a much longer and stronger hard tube .
The stiff tube was rigidly fixed at one end , and the torque was transmitted to it through the experimental tube , the twist in the stiff tube providing a means of measuring the torque .
Fig. 1 gives a general view and details of the apparatus .
The compound tube G-H was rigidly fixed at G- , and the end H securely fixed to lever L , which worked between adjustable stops E and F. By movement of this lever any desired stress could be applied .
Sensitive micrometer levels were fixed to the tubes in the positions A , B , C , D , and at Mi and M2 small concave mirrors were arranged in conjunction with lamp and scales Si and S2 .
The weights W exactly balance the weight of lever L. The mirrors in conjunction with scales supply the means of measuring extreme ranges of strain and thus of stress .
The tube was heated by passing an alternating electric current through the tube itself , and the temperature of the tube was ascertained by three thermocouples in conjunction with galvanometer J and scale .
The current was led into and from the tube by means of small arms dipping into mercury baths , a mode of connection which did not exert appreciable force on the tubes .
It was found by experiment that by taking a tube sufficiently long , a fairly uniform temperature could be maintained along the central portion of the experimental tube .
Three thermo-couples were brazed to the tube at points G inches apart , and these showed a variation of 3 ' or 4 ' C. at 500 ' C. , the ends being below the centre in temperature .
The mirrors were set 8 inches apart , so that , for the length under observation , the temperature has been taken as that given by the central thermo-couple .
The thermo-couples were calibrated by observing the melting points of pure metals , and temperatures given may be taken as true to within 2 ' C. The heating current was taken from a transformer , the secondary circuit consisting of four coils arranged in parallel , each sending its current through the tube .
The temperature was readily regulated by external resistances in * Hopkinson and Rogers found considerable elastic afterworking in steel at 600 ' C. and upwards after applying and removing a load of 1^ tons per square inch ( ' Roy .
Soc. Proc. , ' A , ^ol .
76 , p. 419 ( 1905 ) ) .
Steel at Moderately High Temperatures .
the primary circuit , a resistance slide giving a delicate means of adjusting the current to give any desired temperature .
An electromotive force ranging from 20 to 200 volts by steps of 20 volts could be applied to the primary circuit , which together with adjustable resistances above mentioned allowed any temperature between that of the room and 600 ' C. being maintained for any period of time .
294 Mr. F. E. Rowett .
Th Elastic Properties of To obtain a uniform temperature along the tube all the heat was allowed to radiate freely to the atmosphere , no lagging being used .
The mirrors were protected from radiation by reflectors , and heat was prevented from conduction to them by supporting them at the ends of glass tubing as shown in fig. 1 .
The steel tubes had the following chemical composition:\#151 ; Carbon 017 percent .
; manganese , 0'24 per cent. ; sulphur , 0'02 per cent. ; phosphorus a trace , the remainder being iron .
The tubes as supplied by the makers were hard as the result of the drawing .
The elastic limit in torsion in this state was 13'8 tons per square inch shear stress in either direction , giving an elastic range of 27'6 tons per square inch .
By annealing at 800 ' C. for 15 minutes and cooling in an electric furnace , the effect of the drawing was removed .
The tubes were then quite soft and ductile and had a well marked yield point in torsion of 5'58 tons per square inch shear stress , giving an elastic range of 11T6 tons per square inch .
Hysteresis Experiments .
A hard-drawn tube was introduced into the apparatus and subjected to a stress range of 8-32 tons per square inch ( + -T16 tons per square inch ) ; 200 cycles between these limits were performed to bring the tube into a cyclic state , and the stress was reduced approximately to zero by bringing the lever L into the central position .
The micrometers were then adjusted to make the levels A and B both read zero .
The load was then applied and removed , thus completing another half-cycle of stress , and the stress again adjusted by movement of lever L until the levels A and B again read zero .
The effect of this procedure is to bring the stress in the thin tube to exactly the same small value that it had before the half-cycle was performed , but this condition has been approached from the opposite direction and the strain is slightly different by reason of the elastic hysteresis .
This change of strain is shown by a small difference in the movements of the levels C and D which have occurred as the consequence of the half-cycle of stress .
The following results were obtained , for the above stress range:\#151 ; Movement of C 0'3 , movement of I ) 24 , and the difference , T8 , is a measure of the elastic hysteresis .
The tube was then heated to 100 ' C. and 100 cycles were performed at this temperature .
The result was:\#151 ; Movement of C 0-3 , movement of 1 ) 2'2 , and the difference , 1-9 , is greater than before by a small but unmistakable amount .
The above cycles were performed at the rate of 5 seconds per cycle .
A slow cycle was next performed lasting in all 2 hours , the temperature of the tube being maintained at 100 ' C. The hysteresis was found to be exactly the samoas in the quick cycle , namely , T9 .
The experiment showed that the Steel at Moderately High Temperatures .
295 hysteresis increased slightly with temperature up to 100 ' C. , but was still independent of the time .
At temperatures in the neighbourhood of 200 ' the hysteresis was greater when the cycle was performed slowly , the material showing some signs of how .
Table I gives the results obtained with stress range throughout of 11-60 tons per square inch ( \#177 ; 5*8 tons ) , this stress being well within the elastic limit as ordinarily measured .
Table I ( Stress Range , 1160 tons per square inch ) .
Hard-drawn Tube .
Thermo-couple temperatures C. Movements of levels .
Difference = hysteresis .
1 .
2 .
3 .
C. D. Value cold 19 19 19 0*8 3*3 2-5 Cycle performed in 5 secs .
194 198 196 0*8 4T5 3*35 " " 16 mins .
195 199 198 0*9 4*70 3 *8 Cycle performed in 5 secs .
227 230 225 1 *0 4*8 3 *8 " , ,16 mins .
227 229 225 1 -1 6*7 5 *6 Cycle performed in 5 secs .
290 294 289 1 T 6*0 4*9 " " 16 mins .
290 294 291 2 0 23 *7* 21 *7 Value cold after above 19 19 19 0*8 3 *3 2*5 * Equivalent in level motion .
Micrometer head used for measurement .
The above Table shows that , at temperatures above 200 ' C. , time is an element in the stress-strain relation .
It also shows that the tube was not changed in structure appreciably by being so treated , since , when allowed to cool , the hysteresis returned to its normal value .
In the paper previously referred to it was pointed out that the hysteresis of a hard-drawn tube was increased about eight-fold by annealing at 800 ' C. and cooling in the furnace .
Flow Experiments .
At temperatures above 300 ' C. the flow became too great for measurement by the spirit levels and the strain was read direct by means of the mirrors .
The levels B and C were used for measuring stress , level B being adjusted to read zero when the tube was subjected to a definite stress , and level C being placed on the large tube near level B and adjusted to read zero when the tubes were free from stress .
In making an experiment the large tube was first released from stress by releasing the fixed end .
Level C was then adjusted to read zero , and the large tube fastened down at the fixed end .
A stress was then applied and its amount calculated from movements of mirrors .
Level B was adjusted to read zero with the stress Mr. F. E. Rowett .
The Elastic Properties of applied .
To keep the tube while flowing at a constant stress it was only necessary to adjust lever L so as to keep level B at zero .
The tube could be freed from stress by adjusting lever until level C read zero .
Throughout the tests described below the tube was subjected to 'a constant shear stress of 079 ton per square inch .
The application of the stress and its adjustment to the desired value took about half a minute , and a similar time was occupied in removing the stress and adjusting it to zero .
Test .
I.\#151 ; Tube Unannealed ( Stress = 0-79 ton per square inch ) .
Time from start .
Stress .
Temperature .
Scale readings .
Difference = strain .
M , .
Mo. mins .
0 1 Stress being 340 320 i J applied 1 299 *5 268 -25 11 *25 y Stress on 20 J .
1 Stress being 337 ' C. 297 *5 265 -25 12 *25 20k j removed 339 318 1 *0 x Stress off 25 J .
339 318 *25 0*75 At this temperature the strain which develops in 20 minutes after the application of the stress is about one-tenth of the initial elastic strain , and about one-quarter of this flow is recovered after removing the stress , leaving three-quarters as permanent set .
Time from Stress .
Temperature .
Scale readings .
Difference start .
Mj .
m2 .
= strain .
Test II .
mins .
0 k 2 4 6 8 10 15 20 20k 21 22 24 * j- Stress being applied y Stress on - Stress being removed | Stress off 394 ' C. 342 297 -5 296 6 295 -7 295 294 -5 294 293 292 336 -5 337 1 337 -5 337 -8 321 264 *5 263 261 *8 260 7 260 259*3 257 *7 256 312 *5 313-6 314 *3 314 9 12 *0 12*6 12 *9 13*3 13*5 13*7 14 *3 15 *0 3*0 2*5 2 *2 1 *9 Steel at Moderately High Temperatures .
Time from start .
Stress .
Temperature .
Scale readings .
Difference = strain .
mins .
0 20J Test III .
1 - Stress being applied 337 315 *5 \gt ; 291 *3 256 *5 290 *5 253 8 289 *3 250 *5 288 *2 248 *3 287 *2 246 *5 286 *3 244 *9 285 *5 243 *6 1 \gt ; Stress on 284 *8 242 *5 284 *2 241 *5 442 ' C. 283 239 *6 282 238 281 236 *6 280 T 235 *4 279 *2 234 *2 \lt ; * Stress being removed 278 *5 233 \lt ; 324 *2 292 325 293 *2 -Stress off 326 *5 295 *5 327 *5 297 328 297 *7 328 *2 298 *0 Test IV .
j* Stress being applied -Stress on Stress being removed Stress off 492 ' C. 329 *5 275 *5 271 *0 259 *5 238 *5 286 290 *5 293 *5 295 '5 298 298 *5 298*5 227 *5 220 209 *5 202 *25 197 192*5 189 186 183 178 173 *5 170 166 162 *5 159 230 237 241 *5 244 *5 248 *5 249 *75 13 *3 15 *2 17 *3 18 *4 19 *2 19 *9 20 *4 20 *8 21 *2 21 *9 22 *5 22 *9 23 *2 23 *5 10*7 10 *3 9*5 9*0 8 *8 8 *7 20 *5 23 *5 26 *25 28 29 *5 31 *0 32 *0 33 0 35 *0 36 *5 37 *5 40 *5 42 22 *5 18 *5 17 *75 Mr. F. E. Bowett , The Elastic Properties of Time from start .
mins .
0 20| Stress .
Temperature .
Scale readings .
Test Y. j- Stress being applied [ \gt ; Stress on j- Stress being removed \ [ \gt ; Stress off 542 ' C. M* Difference = strain .
348 *5 330 282 239 24*5 279 227 *5 33 *0 274 -5 216 40 *0 271 208 44 *5 268 201 48 *5 265 196 50 *5 263 191 53 -5 259 183 57 *5 255 *5 176 61 -0 253 '5 170 *5 64 *5 251 *5 166 67 *0 249 162 68 *5 245 155 71 *5 302 233 50*5 306 238 *5 49 309 243 47 310 *5 246 *5 45*5 311*25 248 44*75 312 *0 249 *5 44 *0 Test VI.\#151 ; The tube after Test Y was lowered in temperature to 491 ' C. , that is to approximately the temperature of Test IV , and records were taken of the flow under the same stress .
The following Table shows the results , and ( in the last column ) the amount Test YI .
Scale readings .
Time from Stress .
Tempera- Difference From start .
ture .
= strain .
Test IV .
Mj .
m2 .
mins .
0 i 1* Being applied 36 *5 -38*5 i J 84 *0 25 *5 16 *5 3 6 *9 1 1 88 3L *2 18 -2 20 *3 2 90 35 *2 20 *2 23 *3 4 93 41 23 27 *7 5 8 \gt ; Stress on 491 ' C. 94 96 *2 43 47 *6 24 26 *4 28 *2 32 *6 11 98 *5 51 *7 28 *2 34*3 13 100 54*5 29 *5 36 *6 15 101 *8 57 *5 30 *7 37 *8 20 * 105 *5 63 *5 33 *0 41 *5 - - - *\#151 ; 1 1 Steel at Moderately High Temperatures .
of flow observed at corresponding times in Test IV when the temperature was the same , correction being made for the 1 ' C. difference in temperature .
The difference is probably due to the annealing effect of Test V ( during which the tube was kept at 542 ' C. for half-an-hour ) , which would make the metal more crystalline and less liable to flow .
h to / CURVE I. UNANNEALED TUBES Stress 79 tens persq.in .
/ \lt ; o* 4/ / to / / / 'o* \amp ; \ .'\V .\#171 ; * ' ^:oo0- .1- \#166 ; I / / / w " 3^Te^P-4A2 / hi / " ' ' ' ' 7 -/ ' 20 1 / / / / ^ I/ / ?
' 16^ / f / 12j^ - ---------------2.Temp .
394 ' l \ I r 8r L i v o\lt ; - 1 .
Temp. 337 C. I [ \ I I l I .-I II II 'IP '|k *1 !
i L 10 12 14 16 Time in Minutes .
V. VOL. XCI.\#151 ; A. Mr. F. E. Rowett .
The Elastic Properties Test VII.\#151 ; An experiment was performed at 600 ' C. upon the same tube as Test YI and the following values were obtained :\#151 ; Test VII .
Time from start .
mins .
20^ Stress .
Stress on 0*79 ton per square inch Stress off Strain .
Temperature .
600 ' C. Experiments with Annealed Tube .
The tube was annealed by heating it to 800 ' C. in an electric furnace fox 15 minutes and allowing it to cool in the furnace .
The stress for annealed tubes was the same as that for unannealed tubes , namely 0-79 ton per square inch .
Time from start .
Stress .
Temperature .
Scale readings .
M2 .
Difference = strain .
mins .
0 20 \#163 ; Test I. j- Being applied 17*5 54 *5 -21 *5 27 y Stress on 55 28 J j- Being removed 401 ' C. 55 *5 18 *5 28 *8 -19 *7 | Stress off 18 *4 -19-9 Test II .
j- Being applied j- Stress on | Being removed Stress off 451= C. 18*0 56 *5 59 *0 61 T 22 *6 22 *5 -20 *5 37 *3 -13 *6 -13-9 11 *5 12*0 12 *3 0*8 0*7 12 *4 13*5 14 *7 2*1 i 0 h Steel at Moderately High Temperatures .
Time from start .
Stress .
Temperature .
Scale readings .
Difference = strain .
Mj .
Mo. F Test III .
mins .
o 18*5 -21 \#163 ; j- Being applied 59 -5 33 5 13 *5 10 ?
Stress on 62 *8 39 *3 16*0 20 J 499 ' C. 65 *5 43 *9 17 *9 20\#163 ; - Being removed 24 *5 \#151 ; 10 1 4*9 1 t Stress off ' 25 J 23 *9 -11 2 4*4 Test \gt ; HH 0 34 *5 -5'7 ?
Being applied i 75 *6 50 *6 15*2 2 77 *5 54 *5 17 2 5 80 *0 59 *3 19 *5 8 - Stress on 81 *7 62 *6 21 1 10 r are \o n 82 *6 64 *2 21 *8 15 ooU O. 84 *6 67 *7 23 *3 20 i 86 *3 70 *6 24 *5 ?
Stress being re20\#163 ; ; moved 45 *2 15 *5 10 *5 22 42 *5 11 *0 8*7 23 * Stress off 40 *8 8*5 7*9 25 38 *8 6*0 7*4 CURVE n. ANNEALED TUBES Stress *79 tons per sq .
in .
1.Temp .
40TC .
Time in Minutes .
\#166 ; ciin .
302 Elastic Properties of Steel at Moderately High Temperatures .
In the following Table the flow and recovery of the annealed ( S ) and nnannealed tubes ( H ) at the same temperature are compared .
The figures are corrected by interpolation from the results given in the above Tables to reduce them to the same temperatures .
\#151 ; Unannealed tube ( H ) .
Annealed tube ( S ) .
Temperature 500 ' C. 500 ' C. Probable elastic strain* 13 *3 13*3 Strain after J minute 19 *7 13 *8 Plow in 20 minutes 33*4 4-7 Recovery in 4| minutes 6*5 0*55 Stress 0 *79 ton per square inch 0 *79 ton per square inch * The elastic strain is that corresponding to an instantaneous application and removal of the load , and is calculated on the assumption that the elastic modulus falls 5 per cent , per 100 ' C. \lt ; o curve m. Relation between Flow in UNANNEALED \amp ; ANNEALED TUBES .
XX s ^ / p Stress *79 tons per sq .
in .
Temp. 500'C . .
\#151 ; ---------.TlSc *7ED TUBE -\#169 ; \#151 ; \#166 ; \#187 ; 2 4 6 8 10 12 14 16 18 Time in Minutes .
20 22 24 26 28 A Chemically Active Modification of Nitrogen .
The above work was carried out in the Engineering Laboratories of Jambridge University , and I wish to express my sincere thanks to Prof. B. Hopkinson for his many suggestions and inspiring interest .
A Chemically Active Modification of Nitrogen , produced by the Electric Discharge.\#151 ; VI.# By the Hon. B. J. Strutt , Sc. D. , F.R.S. , Professor of Physics , Imperial College , South Kensington .
( Received March 9 , 1915 .
) S 1 .
Effect of Catalysts in Promoting the Formation of Active Nitrogen .
There has been considerable controversy on the question of whether or not pure nitrogen would give the afterglow , which , as I have shown in the previous papers of this series , is associated with the presence of chemically active nitrogen .
E. P. Lewisf was disposed to think that the presence of oxygen or nitric oxide was essential , but in a much later paper J though still inclined to the same opinion , he states that the afterglow continually increased in intensity as the proportion of oxygen was reduced .
Warburg , in some experiments on the " luminous electric wind " in nitrogen at atmospheric pressure , S found that the intensity of the effect was much diminished by prolonged heating with sodium at 300 ' C. , though he expressly states that he was unable to get rid of it altogether .
It is not clear that the " luminous electric wind " ( which was not bright enough for adequate spectroscopic examination ) is the same phenomenon as the active nitrogen glow obtained at low pressures .
Experiments made later in Warburg 's laboratory by von Mosengeil|| on the active nitrogen glow at low pressure led to the conclusion that it was not diminished by heating the gas with sodium in a closed discharge vessel .
* I , 'Roy .
Soc. Proc. , ' A , vol. 85 , p. 219 ; II , ' Roy .
Soc. Proc. , ' A , vol. 86 , p. 56 ; III , 'Roy .
Soc. Proc. , ' A , vol. 86 , p. 262 ; IY , 'Roy .
Soc. Proc. , ' A , vol. 87 , p. 179 ; Y , ' Roy .
Soc. Proc. , ' A , vol. 88 , p. 539 .
+ ' Astrophys .
Journ. , ' vol. 12 , p. 8 ( 1900 ) ; ' Ann. der Phys. , ' vol. 2 , p. 249 ( 1900 ) ; and also 'Astrophys .
Journ. , ' vol. 20 , p. 49 ( 1904 ) .
t 'Phil .
Mag. , ' June , 1913 , p. 326 .
S ' Ann. der Phys. ' [ 4 ] , vol. 10 , p. 180 ( 1903 ) .
II ' Ann. der Phys. ' [ 4 ] , vol. 20 , p. 833 ( 1906 ) .
|
rspa_1915_0021 | 0950-1207 | A chemically active modification of nitrogen, produced by the electric discharge.\#x2014;VI. | 303 | 318 | 1,915 | 91 | Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character | Hon. R. J. Strutt, Sc. D., F. R. S. | article | 6.0.4 | http://dx.doi.org/10.1098/rspa.1915.0021 | en | rspa | 1,910 | 1,900 | 1,900 | 11 | 367 | 7,938 | http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1915_0021 | 10.1098/rspa.1915.0021 | null | null | null | Thermodynamics | 40.938278 | Atomic Physics | 18.785817 | Thermodynamics | [
-0.5064578056335449,
-46.90959930419922
] | A Chemically Active Modification of Nitrogen .
The above work was carried out in the Engineering Laboratories of Jambridge University , and I wish to express my sincere thanks to Prof. B. Hopkinson for his many suggestions and inspiring interest .
A Chemically Active Modification of Nitrogen , produced by the Electric Discharge.\#151 ; VI.# By the Hon. B. J. Strutt , Sc. D. , F.R.S. , Professor of Physics , Imperial College , South Kensington .
( Received March 9 , 1915 .
) S 1 .
Effect of Catalysts in Promoting the Formation of Active Nitrogen .
There has been considerable controversy on the question of whether or not pure nitrogen would give the afterglow , which , as I have shown in the previous papers of this series , is associated with the presence of chemically active nitrogen .
E. P. Lewisf was disposed to think that the presence of oxygen or nitric oxide was essential , but in a much later paper J though still inclined to the same opinion , he states that the afterglow continually increased in intensity as the proportion of oxygen was reduced .
Warburg , in some experiments on the " luminous electric wind " in nitrogen at atmospheric pressure , S found that the intensity of the effect was much diminished by prolonged heating with sodium at 300 ' C. , though he expressly states that he was unable to get rid of it altogether .
It is not clear that the " luminous electric wind " ( which was not bright enough for adequate spectroscopic examination ) is the same phenomenon as the active nitrogen glow obtained at low pressures .
Experiments made later in Warburg 's laboratory by von Mosengeil|| on the active nitrogen glow at low pressure led to the conclusion that it was not diminished by heating the gas with sodium in a closed discharge vessel .
* I , 'Roy .
Soc. Proc.,5 A , vol. 85 , p. 219 ; II , ' Roy .
Soc. Proc. , ' A , vol. 86 , p. 56 ; III , 'Roy .
Soc. Proc.,5 A , vol. 86 , p. 262 ; IY , 'Roy .
Soc. Proc.,5 A , vol. 87 , p. 179 ; Y , ' Roy .
Soc. Proc. , ' A , vol. 88 , p. 539 .
+ ' Astrophys .
Journ.,5 vol. 12 , p. 8 ( 1900 ) ; ' Ann. der Phys.,5 vol. 2 , p. 249 ( 1900 ) ; and also 'Astrophys .
Journ.,5 vol. 20 , p. 49 ( 1904 ) .
t 'Phil .
Mag.,5 June , 1913 , p. 326 .
S ' Ann. der Phys. ' [ 4 ] , vol. 10 , p. 180 ( 1903 ) .
II ' Ann. der Phys.5 [ 4 ] , vol. 20 , p. 833 ( 1906 ) .
Hon. R J. Strutt .
In my own earlier experiments in which the presence of chemically active nitrogen was first demonstrated , * I employed various methods of preparing nitrogen , but obtained no indication that anything else than nitrogen was essential .
F. Comtef found that after very prolonged passage of nitrogen over hot coppc'r a gas could be obtained which did not give the glow , and he was able to restore the glow by admission of minute quantities of oxygen .
Attempts were made by Koenig and ElodJ and by myselfS to repeat Comte 's result , but without success .
I had , indeed , frequently used hot copper purification before that time , and obtained the glow as usual .
In the note cited I described a technique of purifying nitrogen for this work by prolonged contact with cold phosphorus .
It was made practically certain that such nitrogen could not contain one part of oxygen in 100,000 , for admission of oxygen to that extent distinctly restored the luminosity and cloud formation which attend oxidation of moist phosphorus .
Shortly after Comte 's publication E. Tied || published some experiments which he regarded as confirming Comte 's conclusion .
Passing over these , which were not very strongly emphasised , we come to a publication of Tied and DomckelT describing the preparation of nitrogen from barium or potassium azide .
They found that nitrogen thus prepared gave no glow , but : that the glow could be restored by admission of a trace of oxygen .
This experiment was repeated by Koenig and Elod** and by myself , in collaboration with Prof. H. B. Baker.ff In each case the opposite conclusion to that of Tied and Domcke was recorded .
Prof. Baker and I also introduced the liquid alloy of sodium and potassium into a sealed vacuum discharge vessel containing rarefied nitrogen .
The glow remained very bright even on prolonged standing .
Tied and Domcke in a third paperJJ returned to the use of hot copper .
Bomb nitrogen was passed over copper heated to about 400 ' C. , and the glow was almost completely got rid of , At high temperatures it returned , a result attributed to dissociation of any copper oxide that might be formed .
No drying agents or other absorbents were used .
* * * S ** * I , of this series .
t ' Phys. Zeits .
, ' vol. 14 , p. 74 ( 1913 ) .
t 'Phys .
Zeits .
, ' vol. 14 , p. 165 ( 1913 ) .
S ' Phys. Zeits .
, ' vol. 14 , p. 215 ( 1913 ) .
|| ' Berichte , ' vol. 46 , p. 340 ( 1913 ) .
IT ' Berichte , ' vol. 46 , p. 4065 ( 1913 ) .
** 'Berichte , ' vol. 47 , p. 523 ( 1914 ) .
++ ' Berichte , ' vol. 47 , p. 801 ( 1914 ) .
* 'Berichte , ' vol. 47 , p. 420 ( 1914 ) .
A Chemically Active Modification of Nitrogen .
Prof. Baker and I were unable to repeat this result.* The glow occurred admirably with the copper at any temperature up to a red heat .
Finally , J. de Kolowski , working with the electrodeless discharge , obtained the glow as usual with nitrogen which had been purified from oxygen by means of potassium.* !
* Tied and Domcke argued from their experiments that there was no such thing as active nitrogen .
The palpable weakness of this reasoning , J combined with the failure of Prof. Baker and myself to confirm either of the experiments which were described as so easy and certain of repetition , obscured from us the real value of their work .
This was not realised until Tied and Domcke came to London with their apparatus and materials and repeated their azide experiment at the Imperial College .
The glow was much reduced , though ( at all events in all the experiments made on this occasion ) it was still conspicuously visible ; when a trace of oxygen was admitted by heating a little silver oxide enclosed in the apparatus , the glow was restored .
These results were obtained with a discharge tube like that illustrated in my first paper .
S Using a discharge tube like that shown in fig. 1 , which has a large bulb in which the glowing gas accumulates , we did GAS STREAM Fig. 1 .
not succeed in diminishing the glow much , if at all .
These experiments were described jointly by Baker , Tied , myself and Domcke.|| During this visit a further attempt was made by Prof. Baker and myself , * 'Berichte , ' vol. 47 , p. 1049 ( 1914 ) .
t ' Comptes Rendus , ' vol. 158 , p. 625 , March 2 , 1914 .
X The glow associated with the presence of active nitrogen is not obtained from ordinary nitrogen unless a trace of oxygen is present : therefore there is no such thing as active nitrogen\#151 ; such was their argument .
To obtain a clear view of the value of this kind of reasoning , apply it to the following more familiar case .
Formation of sodium chloride by the interaction of sodium and chlorine is not observed unless a trace of moisture is present : therefore there is no such thing as sodium chloride .
S I , p. 228 . .
|| ' Nature , ' vol. 93 , p. 478 ( 1914 ) .
Hon. R. J. Strutt .
with the benefit of such suggestions as Tied and Domcke could make , to repeat their experiment with copper moderately heated , but with the same ill success as before .
Dr. Tied , if I understood him rightly , regarded the failure as due to some difference of our copper or crude nitrogen .from that used by him in Berlin ; but exactly what difference he was unable to say .
During a brief visit it was impossible to go into the matter further .
After these joint experiments I felt that the position of the question was very unsatisfactory .
For , though now convinced that it was possible to prepare nitrogen which would give a much increased glow when oxygen was added to it , my previous conviction was unshaken that the phosphorus-purified nitrogen above mentioned , which gives the nitrogen glow excellently , did not contain oxygen to the extent of 1 part in 100,000 .
It might , indeed , be possible to get out of the difficulty by assuming , with Tied and Domcke , that almost incredibly minute quantities of oxygen were sufficient ; but I soon found experimentally that this was not the case .
In taking up the matter again after Dr. Tiede 's visit , I sought to avoid the use of azide , the preparation of which in any quantity is troublesome and unpleasant , and not altogether free from risk .
It was found that a sample of nitrogen which did not give much glow could be prepared by prolonged treatment of the commercial bomb nitrogen with sodium or potassium at 300 ' C. A flask A , fig. 2 , of about 4 litres capacity , contained 10 or 20 c.c. of EXHAUST EXHAUST TO RESERVOIR OF CAS Fig. 2 .
the liquid alloy of sodium and potassium.* The flask w^as in an asbestos oven ( shown by dotted lines ) , with an electric resistance heater on the bottom .
The flask was supported about an inch above the heater , and the temperature just under it was somewhat over 300 ' C. The lid of the oven was thin , so that the top of the flask was by no means so hot as the bottom , where lay " he pool of alloy B. Thus a good circulation of the gas over the surface of This was introduced by means of a pipette , after the flask had been filled by displacement with bomb nitrogen .
A Chemically Active Modification of Nitrogen .
307 the alloy by convection currents was assured .
Some of the metal distilled on to the top of the flask , and also into the neck , which was necessarily kept cold , because of its greased stopcocks .
A tin screen , D , in two semi-circular halves , carried on the neck , protected the latter from radiation .
Bomb nitrogen was admitted to this flask at a reduced pressure , so that on heating the pressure did not rise above the atmospheric .
The heater was turned on after the gas had been admitted , and left on all night .
In the morning the gas was allowed to cool , and was ready to be passed through the vacuum discharge tube E on its way to a Gaede pump .
The regulating stopcock F and the pressure gauge G enabled the pressure in E to be kept at a standard value of 6 mm. , in spite of the gradual reduction of pressure in A during the experiment .
Under these circumstances , the gas passing out through the pump measured 2600 litres per hour .
A constant jar discharge was maintained between the platinum electrodes .
The K.M.S. current measured on a Duddell thermo-ammeter was 7 milliamperes .
Under these conditions the nitrogen afterglow was not bright , and it seemed to get dimmer still after a charge of the alloy had been heated several times with successive fillings of nitrogen .
The glow still remained visible both in the neck and in the body of the bulb J. But it was reduced as low , or lower , than in the most successful experiment which Tied and Domcke had shown us .
Although the glow was feeble , there was no indication that what there was of it died out sooner than usual , as the stream of gas passed along the tubes leading to the pump .
The proportion of oxygen necessary to get the optimum glow was investigated by means of the capillary inlet tube H , * by means of which air could be admitted .
The capillary drew its supply from the outer tube K in which it was placed .
K was connected with a large reservoir .
The rate of intake could be adjusted by altering the air-pressure in this reservoir .
Its exact value under given conditions was determined after the experiment by observing , with the manometer , the rate at which the pressure rose in the vacuum tube E , the volume of which was known.f The stopcock used to shut off the capillary inlet at pleasure is necessarily made of much wider bore tubing than the capillary itself .
Thus there is a considerable dead space between the capillary and the stopcock .
Without * The various capillaries used were drawn out in the blowpipe .
After a little practice , capillaries can be drawn giving approximately the rate of intake desired .
A special apparatus was used for testing them rapidly .
Preliminary inspection with a magnifier is useful .
t With a capillary of non-uniform bore the intake of air into a vacuum bears no simple relation to the feeding pressure .
Hence the necessit}^ for determining it directly at each pressure .
Hon. R. J. Strutt .
special arrangements this would fill up with air when the stopcock was shut , and the accumulation would suddenly pass in when it was opened again , thus disturbing comparative observations .
The difficulty was avoided by using a two-way stopcock as shown at L. When the How through the capillary was not directed into the apparatus , the dead space was kept exhausted by a supplementary air pump , connected to the other branch of the two-way stopcock .
When it was desired to observe the effect of admitting air , the stopcock was quickly turned through 180 ' , and the normal rate of inflow was at once established.* A capillary was used which allowed 18 c.c. of air ( measured at N.T.P. ) to enter into a vacuum per hour from a reservoir at atmospheric pressure .
This is equivalent to about 3'5 c.c. of oxygen per hour .
By substituting pure oxygen for air , the rate of admission could be increased .
By rarefying the air it could be diminished .
In this way the following results were obtained:\#151 ; Oxygen admission .
Intensity of glow .
c.c. per hour .
O'O 0*4 1 *0 3 *5 18*0 Faint .
No perceptible increase .
Distinct increase .
Strong glow .
No further increase .
It appears , then , that an admission of 3*5 c.c. of oxygen per hour produced about the maximum effect .
Since the nitrogen flow was 2600 c.c. per hour , this represents an oxygen concentration of about 1/ 750 of the whole .
If the oxygen admission is increased much beyond the quantities given in the Table , it begins to have a prejudicial effect .
About 2 per cent , of it is enough to destroy the glow altogether.^ It appears , then , that in mixtures of nitrogen with oxygen the optimum effect is got when the oxygen present is something rather over one part in a thousand .
Yet it had been clearly shown that nitrogen purified from oxygen by prolonged standing over phosphorus could not contain oxygen to the extent of one part in a hundred thousand , and yet nitrogen thus purified * An alternative method , useful when direct intake from the atmosphere is desired , is to close the capillary with an indiarubber pad , brought up from below by a rack movement .
In this case there is no dead space .
When working with these very narrow capillaries it is necessary to be constantly alive to the possibility that they have become plugged by specks of dust , t See V , j3 .
541 .
A Chemically Active Modification of Nitrogen .
309 gives the glow as well , or even better than nitrogen purified with hot sodium , to which the optimum percentage of oxygen has been added .
Minute admixtures other than oxygen are capable of performing the same function , and can act as catalysts for promoting the formation of active nitrogen by the discharge .
This was established by means of the apparatus already described , other gases being introduced into the tube from which the capillary drew its supplies .
In these experiments I did not attempt to determine the optimum percentage of each admixture .
A capillary was used admitting 3*3 c.c. of air per hour .
The rate of admission of other gases by this tube would be somewhat different , depending upon the viscosities , which , however , do not vary widely .
Roughly speaking , this capillary admits about 1/ 1000 part of foreign gas to the nitrogen stream under the standard conditions adopted .
It is to be observed that the purity , or dryness , of the added gas is not of the first consequence , since the total admission is so small .
Impurity in it , in fact , only enters into the second order of small quantities .
Still , reasonable care was taken .
Methane from aluminium carbide : strong restoration of glow .
The quantity admitted was enough to slightly tinge the nitrogen afterglow with violet of the cyanogen spectrum , owing to reaction of methane with active nitrogen after the latter is formed .
If the admission was stopped , the glow passed through a brilliant yellow stage of simple afterglow spectrum as the percentage of methane diminished , and then became very dim as the methane was eliminated .
By experiments in which the feed of methane was at reduced pressure , it was found that 0*09 c.c. of methane per hour , 1/ 30,000 of the nitrogen flow , was enough to produce a perceptible effect .
Ethylene from sulphuric acid and alcohol , and Acetylene from calcium carbide , gave the same results as methane .
Carbon Monoxide from potassium ferrocyanide , washed with potash , strongly restored the glow , which was yellow , showing only a faint trace of cyanogen spectrum .
Carbon Dioxide induced a strong and pure nitrogen afterglow .
Sulphur Dioxide did the same .
Hydrogen Sulphide induced a specially bright and pure yellow nitrogen afterglow .
When the entrance of hydrogen sulphide was stopped , it was not found that the glow passed off at all quickly or easily .
Indeed , to reduce it to the point reached before admission of hydrogen sulphide , the tube had to be dismounted and washed out with aqua regia .
It seems that exceptionally small traces of sulphur are sufficient to induce formation of active Hon. H. J. Strutt .
nitrogen .
These traces cling about the apparatus , probably in the solid state , with great obstinacy .
Chlorine , purified by fractional distillation of liquid chlorine , gave anabsolutely definite though not very strong restoration of the glow .
This case is peculiar , in that the glow restored by chlorine is notably greener than that obtained in other cases .
The spectrum is the same as usual , but the yellow band is less intense relative to the green one .
It is intended to study the question further , but it would seem as if chlorine atoms must remain in some kind of association with the atoms of active nitrogen , damping the vibrations which give rise to the yellow band .
It takes time to get rid of this green tint .
The chlorine seems to hang about the apparatus persistently .
Hydrogen was prepared from pure zinc and sulphuric acid , and freed from condensable impurities such as arsine , by passing through a tube packed with copper gauze and maintained at \#151 ; 180 ' C. in liquid air .
It was thought that a definite effect was produced in increasing the glow , but it was slight and difficult to observe , being much less in amount than in any of the previous cases .
Argon and Helium , each carefully purified , gave no observable effect .
The method of regulated admission by a capillary tube , so far used , is not easily applicable , except to permanent gases .
In addition , I have tried water vapour and mercury vapour , but the exact rate of admission was not measured in these cases .
A drop of Mercury was placed in a side tube , so that by warming it could be made to give off vapour which mingled with the nitrogen stream .
Marked restoration of the glow was observed , though it was less brilliant than that observed with the best catalysts .
The glow was tinged with green from the green mercury line , but , apart from this , there was marked brightening of the true nitrogen afterglow bands .
The glass all round the mercury was carefully heated , so as to get rid of all adherent carbon dioxide or water vapour , and the effect of warming the mercury was repeatedly observed .
There is no doubt of the fact that the restoration is really due to mercury .
A drop of Water in a side tube was frozen in liquid air .
As its temperature was allowed to rise very strong restoration of the glow was observed .
The quantity of vapour soon became excessive and the glow diminished again , until it was destroyed altogether .
Tiie relative efficiency of the various admixtures in inducing the nitrogen glow cannot be very satisfactorily compared , since no attempt was made to adjust each to its exact optimum amount , nor were any photometric measurements made .
Howrever , the following roughly approximate list A Chemically Active Modification of Nitrogen .
represents my general impressions , first:\#151 ; Hydrogen sulphide .
Water .
Carbon dioxide .
Carbon monoxide .
r Acetylene .
-\lt ; Ethylene .
L Methane .
The most effective substances are placed Oxygen .
Mercury .
Chlorine .
Hydrogen .
r Argon .
J Helium .
LNitrogen .
It is then established that to obtain active nitrogen at all abundantly , it is necessary that a quantity of some foreign gas should be present to the extent of something like 1/ 1000 part .
This gas may be oxygen , or some compound of oxygen , but it may as well , or better , be sulphuretted hydrogen .
Thus it is perfectly clear that , whatever the function of the admixture may be , oxidation of nitrogen has nothing to do with it .
In the controversy which has been reviewed it was maintained , on the one side , that pure nitrogen would give the full effect , and , on the other , that the presence of oxygen was essential .
It is now seen that , as in so many previous scientific controversies , neither side was entirely right .
Almost any contamination , with the exception of argon and helium , increases the yield of active nitrogen , as judged by the intensity of the nitrogen afterglow .
To exactly explain why each of the numerous experimenters quoted got the result he did would be too ambitious an attempt .
At the best there would be a large element of conjecture in it which could not be checked experimentally .
But a few suggestions may be offered .
Methods of purification , designed chiefly to remove oxygen , may result in the unintentional introduction of other substances which have the same effect in producing the glow that the oxygen itself had .
Carbonaceous impurities are , perhaps , the most likely to be concerned ; indeed I have frequently observed , particularly at high pressure , a trace of violet cyanogen in the nitrogen afterglow , when there was no other special reason to suspect the presence of carbon .
Unless my memory deceives me , this was observed in those experiments with azide nitrogen in a large globular discharge-vessel , made on the occasion of Tied and Domcke 's visit .
Visible cyanogen spectrum implies the presence of more than enough hydrocarbon to act as a catalyst and induce the glow .
The grease of stopcocks may , sometimes act as a source of carbon , particularly when stray electric discharges come in contact with it .
In experiments where oxygen is removed with hot copper , I suspect that carbon dioxide is very apt to remain in the gas .
Thus , in one attempt to Hon. E. J. Strutt .
repeat Tied and Domcke 's experiment with copper at 400 ' C. , the copper gauze employed had originally contained a great deal of paraffin oil used as a lubricant in the wire-drawing process .
This was removed , as far as possible , by heating and oxidising the copper , which was afterwards.reduced by plunging it in methyl alcohol and drying it in warm air .
It would require special tests directed to that end to make absolutely sure that no carbonaceous matter remained after this treatment .
If there was a trace , it would be oxidised by traces of oxygen in the nitrogen used , thus introducing carbon dioxide .
The gas which had stood over moist phosphorus also contained carbon dioxide , as was proved by bubbling it through baryta water .
The amount of precipitate was decidedly more than the same volume of air gave under similar conditions , and thus indicates something like 1/ 1000 part of carbon dioxide , just such a quantity as would give the glow well .
I have not particularly examined where this carbon dioxide came from\#151 ; it is enough for the present purpose that it was there .
In all probability phosphorus vapour would also induce formation of active nitrogen , though I have no definite evidence of the fact .
As regards earlier attempts to get rid of the glow by treatment with sodium or potassium : if the metals have been stored in oil ( as potassium almost always is ) enough hydrocarbons will probably cling to them to explain such experiments as that made by Prof. Baker and myself , allowing nitrogen to stand over the cold liquid alloy .
But in any experiments on vacuum tubes charged with gas , and sealed up , the quantity of nitrogen present is so small that the absolute quantities of impurity needed are infinitesimal , and may be derived from the electrode or the glass .
When a large quantity of nitrogen is purified and allowed to sweep through the apparatus , this source of contamination is practically eliminated .
These questions cannot be discussed in more detail , for lack of space .
But , in short , it is easy to understand that methods designed to get rid of oxygen do not in general get rid of carbon compounds .
The prolonged use of very hot sodium , however , is capable of removing both .
S S 2 .
Probable Mode of Action of the Catalysts .
If it is considered how diverse chemically the different catalysts are , it will not seem likely that their action can be interpreted by purely chemical considerations .
We must remember that the impurity added performs its function , whatever that may be , inside the region where the electric current is passing . .
It is useless to add a trace of , e.g. , oxygen after the stream of A Chemically Active Modification of Nitrogen .
313 nitrogen has left the discharge , for in that case the addition produces no effect in increasing the yield of active nitrogen.* The question is essentially one of processes occurring in the electric discharge , and must be considered in the light of our knowledge of the properties of electrons and gaseous ions .
In this connection the results of Franckf are very suggestive .
He investigated the velocity with which negative ions travelled through nitrogen at atmospheric pressure , under potential gradients far too small to produce luminous discharge .
It was found that with perfectly pure nitrogen the velocity was very large , indicating that the ions travelled over the greater part of their path as free electrons .
A small admixture ( something like 1 per cent. ) of oxygen or chlorine diminished the mobility of the negative ions two hundred-fold , and made it about equal to that of the positive ions .
In short , in pure nitrogen the negative ions were free electrons : the addition of a trace of oxygen or chlorine loaded them so that they became of atomic dimensions .
Argon and helium , even when present in much more than traces , were unable to produce this effect .
Another property of pure nitrogen , namely , its capacity to yield active nitrogen under the discharge , is also extraordinarily influenced by a trace of oxygen or chlorine , but not by argon or helium .
Can it reasonably be doubted that there is an intimate connection between the two sets of phenomena ?
That the properties of a substance should be modified in tins way by a large multiple when slightly contaminated is always surprising and exceptional .
When we find two such cases running parallel , as these do , the suspicion of some connection becomes very strong .
* It is possible that someone casually glancing at this paper without being acquainted with its predecessors may be confused on this point .
In the former papers I have studied the effect of adding various gases and vapours to active nitrogen after it is formed .
In this case , of course , the addition is made by a tributary stream flowing into the stream of nitrogen after it has flowed past the place where electric discharge is maintained .
In the apparatus , fig. 2 , it would flow in at a side tube placed in some such position as M. But the present investigation studies the effect of added substances in assisting the production of active nitrogen .
In this case the amount added is much smaller , and the addition is made before the nitrogen is submitted to electric discharge .
Some substances have an important and distinct effect in both ways .
Thus acetylene is .
capable of assisting formation of active nitrogen ( pure yellow afterglow nitrogen bands ) if a trace of it is added before the nitrogen is acted on by the discharge ; while , if introduced in larger quantities after the gas has been submitted to discharge , it unites chemically with the active nitrogen , forming hydrocyanic acid ; and , from the place where the acetylene flows in onwards , the yellow nitrogen glow is entirely replaced by a violet one showing cyanogen spectrum .
t ' Deutsch .
Phys. Gesell .
Verh./ vol. 12 , p. 613 ( 1910 ) ; see also vol. 12 , p. 291 ( 1910 ) .
Hon. R. J. Strutt .
Sir J. J. Thomson 's experiments on positive rays* were made on the luminous discharge at low pressures , with the ions moving under large potential gradients , and thus under conditions approaching somewhat to those used for generating active nitrogen .
Thus the information they yield with regard to the loading of electrons by atoms and molecules of various gases is more directly applicable than that obtained by the method used by Frank .
J. J. Thomson foundf that negatively charged atoms of hydrogen , carbon , oxygen , sulphur , and chlorine were present among the rays which had passed through a hole in the cathode .
Since such an atom had acquired its momentum in moving up to the cathode , it was necessary to assume that it had been positively charged while doing so , that it had picked up an electron subsequently which neutralised it , and then another which electrified it negatively .
Some atoms appeared never to acquire a negative charge under these conditions .
These were nitrogen , mercury , helium , argon , and the other rare gases .
It will be observed that , with the exception of mercury , the atoms which promote the formation of active nitrogen are precisely those which can become attached to an electron , while those which do not have this effect are precisely the ones which never become attached to an electron in the canal rays .
I think therefore it will be admitted that we have strong grounds for believing that the effect of certain admixtures in promoting formation of active nitrogen is produced by a loading up of the moving electrons in the discharge .
In pure nitrogen the electrons are free .
When a slight admixture of some gas containing , e.g. , oxygen , sulphur or carbon , is present , atoms of the element introduced , set free in the discharge , attach themselves to the free electrons .
To develop the explanation further , some element of hypothesis is unavoidable .
It will be supposed , as in previous papers , that active nitrogen consists of monatomic nitrogen .
A nitrogen molecule is separated into atoms by the impact of a negative ion in the discharge .
If , however , this ion consists of a free electron it is not so effective in administering the right kind of blow as when it is loaded so as to be of atomic dimensions .
Hence the great increase in the production of active nitrogen when atoms of a kind suitable to effect this loading are introduced .
It may be asked , If an ion of atomic dimensions is needed , why do not the * The title is unfortunate as applied to the particular experiments here quoted , which deal with negatively charged rays .
t 'Boy .
Soc. Proc. , ' A , vol. 89 , p. 10 ( 1910 ) ; see also his ' Bays of Positive Electricity , p. 39 , Longmans , 1913 .
A Chemically Active Modification of Nitrogen .
315 positive ions of nitrogen , which are present even when the nitrogen is absolutely pure , serve the purpose ?
The fact that they move in the other direction cannot make the difference .
I think that this objection can be answered without additional hypothesis .
The mean free path of an electron is greater than that of a positive ion , on account of its small size .
If the positive ion is comparable in radius to the molecules of the gas , the ratio of free paths may be taken as 4 to 1 .
If , therefore , the electron only acquires its load towards the end of a free path it will have passed over a potential difference four times as great , and therefore have acquired four times the kinetic energy that a positive ion , which of course retains its atomic dimensions throughout , would possess .
This possibility of possessing fourfold kinetic energy seems a sufficient explanation of why the negative ions should be so much more capable of producing active nitrogen than the positive ones .
It remains to discuss the exceptional case of mercury , which is moderately efficient in promoting formation of active nitrogen , but which does not take a negative charge in the canal rays .
The mercury atom also shows an exceptional behaviour in the canal rays\#151 ; it occurs with much larger positive electric charges than do other atoms , * the charge being in some cases as much as seven times the electronic charge .
Such highly charged positive atoms in the electric field will acquire between collisions the large amount of kinetic energy which we have supposed necessary to administer the necessary shock to a nitrogen molecule .
So that this exception may perhaps not unfairly be considered rather confirmatory than otherwise of the theory suggested .
As already mentioned , I have never been able to really reduce the glow to nothing , by any method of purification tried .
It is difficult to decide whether this is possible , and even if it did seem to be accomplished in any experiment the doubt would remain whether somewhat different methods of stimulationf would not restore it .
In the experiments described the glow was reduced to a point where the addition of 1/ 30,000 part of a hydrocarbon , such as methane , would distinctly improve it , so that to decide the question experimentally would be very difficult .
It seems not inconsistent with the theory suggested that occasionally under favourable circumstances the impact of an unloaded electron might lead to formation of active nitrogen .
If so , no purification could reduce the glow to nothing .
The above discussion has purposely been placed in a separate section of the * J. J. Thomson , loc. cit. t Particularly the electrodeless discharge at low pressures .
It is certainly a matter of great difficulty even to appreciably reduce the glow in this case .
VOL. XCI.\#151 ; A. 2 B Hon. R J. Strutt .
paper .
If exception is taken to it as too speculative , it is hoped that the experiments of the preceding section will be judged independently .
S 3 .
Action of Active Nitrogen on Liquid Metcds . .
It has been shown* that active nitrogen reacts with metallic vapours , yielding the nitrides .
At the same time there is a development of the line spectrum of the metal .
No apparent effect is produced when the active gas is passed over clean cold metals or over a film of mercury held on copper , f I now find that if a small quantity of mercury is placed in the bottom of a fairly wide U-tube , and shaken while the active gas passes over it , all luminosity is extinguished , and the mercury becomes foul , clinging to the walls of the vessel , as it does when treated with ozone .
If the shaking is discontinued the glow again passes .
After having treated the mercury in this way for a short time it is easily proved , chemically , to contain nitride .
If water is added ammonia is formed , and can be distilled off and recognised by the Nessler reaction .
It is of interest to notice that when active nitrogen unites in this way with liquid mercury there is no development of the mercury spectrum .
This is in contrast to what is found with mercury vapour , which gives the mercury spectrum strongly with active nitrogen .
Other melted metals also react with active nitrogen .
This was readily demonstrated with fusible metal ( bismuth-tin-lead alloy ) melting at about 100 ' C. Metals melting much above this temperature are less easily experimented with , because active nitrogen passes almost instantly into ordinary nitrogen by the catalytic action of hot surfaces.j Thus the active nitrogen is destroyed by contact with the heated walls of the glass tube containing the melted metal before getting to the latter .
In spite of this difficulty it has been found possible to demonstrate the chemical action upon melted tin and melted lead .
As in the case of liquid mercury , the spectrum of the metal is not developed .
S4 .
Experiments with Other Liquids .
These experiments with melted metals naturally suggested trying other liquids .
Since a stream of active nitrogen at low pressure can alone be used , we are limited to liquids of small vapour pressure .
The glowing gas was bubbledS * I , p. 224 ; V , p. 542 .
t I , p. 225 .
X See III , p. 363 .
S Bubbling is feasible with a " head " of 1 or 2 cm .
of a light liquid .
Active nitrogen cannot well be bubbled through molten heavy metals , because the pressure in the discharge tube which this would require would be unfavourable to formation of active nitrogen .
Shaking the liquid in the stream of active gas must then be resorted to .
' A Chemically Active Modification of Nitrogen .
317 through glycerine in a U-tube without any apparent action .
The glow got through quite well .
It was also bubbled through a concentrated solution of stannic chloride .
Nothing was seen of the beautiful blue light developed when the vapour of this salt mixes with active nitrogen .
A dilute solution of indigo in concentrated sulphuric acid was slowly decolorised by bubbling active nitrogen through it .
The exact nature of the action was not studied further , but the experiment clearly proves that active nitrogen is capable of acting on dissolved substances as well as on vapours and liquid metals .
S 5 .
Chemical Action on the Paraffins .
Active nitrogen , it is agreed by all experimenters , acts freely on the majority of carbon compounds , with formation of hydrocyanic acid .
Doubts , however , have been expressed as to its having this action on the paraffins.* I have re-examined this question as carefully as I could , with the advantage of having specially purified materials at command .
In all cases abundant hydrocyanic acid was obtained .
Heptane.\#151 ; The specimen was one which was specially purified by Sir Edward Thorpe.f Its origin was from This was treated with active nitrogen for a few minutes , and an abundant precipitate of Prussian blue , enough to colour several litres of water strongly , was obtained .
The excess of oil , condensed out along with the hydrocyanic acid , had acquired a strong smell suggestive of nitriles .
Pentane.\#151 ; The specimen was obtained thi'ough the kindness of Dr. A. G. Vernon Harcourt , F.E.S. , and had been prepared for use in his standard lamp .
It had passed the tests imposed by the Metropolitan gas referees for absence of olefines .
This again behaved in just the same way as the heptane had done .
The hydrocyanic acid was estimated quantitatively , and the yield was about the same as that formerly obtained^ with commercial light petroleum ( motor spirit ) .
Methane.\#151 ; The first sample was prepared from sodium acetate and soda lime and condensed with liquid air .
It was then allowed to evaporate fractionally , the less volatile half of the gas being rejected .
About 2 litres was retained for the experiment .
After treatment with active nitrogen it yielded hydrocyanic acid equivalent to about 6 c.c. of nitrogen gas .
Two litres of methane prepared from aluminium carbide , and similarly * Koenig and Elod , ' Ber .
d. Deutsch .
Chem. Ges .
, ' vol. 47 , Heft 4 , p. 516 ( 1914 ) .
t ' Chem. Soc. Proc. , ' p. 299 ( 1879 ) .
I V , p. 546 .
318 A Chemically Active Modification of Nitrogen .
purified by fractional distillation , gave about the same result as the foregoing .
# With methane the cyanogen spectrum is not nearly so conspicuous as with some hydrocarbons ; but if the conditions are suitably adjusted , with not too large a feed of methane , it is quite well seen .
S 6 .
Summary .
1 .
The past controversy as to whether active nitrogen can be freely obtained from pure nitrogen , or whether a trace of oxygen must be present , is reviewed .
It is shown that neither alternative is correct .
Perfectly pure nitrogen will not give more than a little active nitrogen .
On the other hand , to get a good yield it is not necessary that free oxygen or any oxygen compound should be present , for almost any small admixture of a foreign gas will enormously increase the yield of active nitrogen .
The amount of admixture required to produce the best effect is usually of the order of 1/ 1000 part , but , to quote one case particularly examined , a very distinct effect is produced by adding a 1/ 30,000 part of methane .
2 .
The view is suggested that the impurity acts by loading the electrons in the discharge , and thus altering the character of their impact with the nitrogen molecules .
This view is supported by the fact that gases carrying oxygen , sulphur , chlorine , carbon , and hydrogen are capable of promoting formation of active nitrogen .
These are atoms which , according to the investigations of J. J. Thomson and Frank , are capable of attaching themselves to electrons in the discharge .
On the other hand , argon , helium , and ( of course ) nitrogen itself , which are not able to load electrons , do not promote formation of active nitrogen .
The case of mercury is at first sight anomalous , but reasons are given which seem to explain the anomaly .
3 .
Active nitrogen shaken with cold liquid mercury unites with it , forming nitride , but no development of mercury spectrum attends the action , as when mercury vapour unites with active nitrogen .
Similar results have been obtained with other melted metals .
4 .
Active nitrogen bubbled through a weak solution of indigo in sulphuric acid slowly discharges the blue colour .
5 .
Active nitrogen acts freely on the purest heptane and pentane obtainable , with formation of hydrocyanic acid .
On pure methane the action , though perhaps rather less , was still considerable .
These experiments do not bear out the view that it is only olefine impurities in the paraffins that can yield hydrocyanic acid .
|
rspa_1915_0022 | 0950-1207 | Some temperature refraction coefficients of optical glass. | 319 | 321 | 1,915 | 91 | Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character | Lieut.-Col. J. W. Gifford|Prof. S. P. Thompson, F. R. S. | article | 6.0.4 | http://dx.doi.org/10.1098/rspa.1915.0022 | en | rspa | 1,910 | 1,900 | 1,900 | 2 | 58 | 1,336 | http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1915_0022 | 10.1098/rspa.1915.0022 | null | null | null | Optics | 41.540022 | Tables | 29.066813 | Optics | [
1.2380191087722778,
-34.41059494018555
] | Some Temperature Refraction Coefficients of Optical Glass .
By Lieut.-Col. J. W. Gifford .
( Communicated by Prof. S. P. Thompson , F.R.S. Received February 6 , Revised March 18 , 1915 .
) In a previous paper , * the refractive indices of a number of typical samples of glass were given , but the temperature coefficients\#151 ; although measured\#151 ; were omitted at the time .
The late Sir David Gill having shortly before his death expressed a wish that they should be published , the following paper complies with this desire .
In addition a table is given of the refractive indices of glass meltings since measured , together with an account of an attempt to determine , if only approximately , the influence of atmospheric pressure ( barometer changes ) on measurements of refractive index generally . .
The special methods employed to obtain the indices and to estimate the probable error , as well as the instruments used , are the same , f except in the case of Schott 's Fluor Crown .
In this case , the melting being a small one , only one prism was cut , and the limit of uniformity in its production has , therefore , not been ascertained ; it may , however , be noted in this connection that its temperature refraction coefficient is a minus quantity as with quartz and fluorite .
In no other glass melting has this been found by the author , all others having the plus sign , that is , the refractive index in air rises with the temperature .
In order to determine the change in the apparent refractive index due to the varying barometric pressure , a number of experiments were made in which on different days the refractive indices were compared , the temperature so far as possible being the same .
It was pointed out to me by Prof. Schuster that these experiments indicated that far the greatest part of the change was due to alteration of the refraction in air .
Tables of the temperature refraction coefficients of all the glasses and of the refractive indices of those meltings not previously given follow .
It should be noted that the numbers indicating the " probable error " include the actual differences in the refractive indices of different specimens of glass from the same melting and the accidental errors of the determination of the index of each .
The former , as pointed out in my previous paper , is much the larger of the two .
The refractive indices are referred to air .
The * 'Roy .
Soc. Proc.,5 vol. 87 , p. 189 ( 1912 ) .
t 'Roy .
Soc. Proc. , ' vol. 70 , p. 329 ( 1902 ) ; and 'Monthly Notices R.A.S. , ' vol. 69 , p. 118 ( 1908 ) .
VOL. XCI.\#151 ; A. 2 C Lieut.-Col. J. W. Gifford .
Temperature Telescope Flint .
S. 8204 0 -010242 \#177 ; 0 *000048 51 *594 ( 1 -521858 ) 1 -523635 ( 1 -524834 ) ( l -525410 ) 1 -528425 1-530041 ( 1 -530959 ) 1 -532278 ( 1 -535652 ) 1 -537488 1 -540550 ( 1 -541495 ) 1 -546024 Dense Flint .
S. 5403 0 016582 \#177 ; 0-000084 36 -966 1 -602868 1 -605543 1 -607396 1 -608240 1 -612974 1 -615558 1 -617055 1 -619212 1 -624822 1 -627918 1 -633193 1 -634899 1 -642868 Barium Silicate Crown .
S. 7714 .
0 -009086 \#177 ; 0-000083 59 -516 1 -534892 1 -536492 1 -537580 1 -538061 1 -540738 1 542186 1 -543001 1 -544154 1 -547146 1 548749 1 -551389 1 -552261 1 -556187 Silicate Crown .
S. 7181 .
0 *008749 \#177 ; 0 -000079 60 -246 1 -521432 * 1 -522924 1 -523988 1 -524465 1-527078 1 -528428 1 -529212 1 -530359 1 -533214 1 -534801 1 -537401 1 -538204 1 -541964 Cro*wn of lowest Md. S. 3113 .
0 -008586 \#177 ; 0 -000020 59 *467 1 -505025 1 -506545 1 -507559 1 -508028 1 -510560 1 -511928 1 -512703 1 -513825 1 -516613 1 -518137 1 -520699 1 -521491 1 -525211 Borosilicate Crown .
S. 6107 .
0 *008517 \#177 ; 0 *000014 62 -120 1 *523550 1 *525075 1 *526076 1 *526533 1 *529077 1 *530400 1 *531182 1*532271 1*535050 1 *536570 1 *539041 1 *539820 1 *543462 Fluor Crown .
S. 8897 .
0 -006896(5 ) Undetermined 70 -775 1 -483498 1 -484749 1 -485624 1 -486012 1 -488102 1 -489187 1-489823 1 -490702 1-492909 1 -494114 1 -496091 1 -496731 1-499605 Designation ... F-C = 8fi Probable error ... " = ( M-l \#166 ; \#166 ; \#166 ; Wave-lengths .
A ' .
7682 .
E. B ' .
7066 .
He 6708 .
Li C. 6763 .
Ha D. 5893 .
Na A. 5607 .
Pb 5461 .
Hyl ... E. 5270 .
Fe F. 4861 .
H^ 4\gt ; .
4678 .
Cd6 ... 4415 .
Cd7 ... G ' .
4341 .
H , 4046 .
Hy2 ... .\#151 ; Indices in brackets have been interpolated .
Refraction Coefficients o f Optical Glass .
321 temperature coefficients indicate the changes of the index due to a rise of 1 ' C. , the normal temperature being 15 ' C. In order to reduce these indices to vacuo , corrections have to be applied which are easily calculated .
Approximately the correction is minus 10 in the last decimal place , so that " Silicate Crown ( S. 7181 ) " would have a zero coefficient for the refractive index referred to vacuo .
Table of Temperature Befraction Coefficients = 5270 ) for 1 ' C. Type .
0,6781 Fluor Crown ( S. 8897 ) -0-0000035* 0,2188 Borosilicate Crown ( S. 6115 ) 0 -0000021 411 a \gt ; ) ( C. 557 ) 0 -0000019 0,144 \#187 ; \#187 ; ( S. 5077 ) 0 '0000030 0,3832 a \#187 ; ( S. 5028 ) 0 -0000102 0,141 ) ) \#187 ; ( S. 6141 ) 0 -0000011 3790 j\gt ; \#187 ; ( M. 6132 ) 0 -0000040 0,3390 3 ) 33 ( S. 3581 ) 0 -0000020 0,3512 33 33 ( S. 6107 ) 0 0000010 0,3453 33 \#187 ; ( S. 4812 ) 0 -0000015 0,2118 Crown of lowest juld ( S. 3113 ) 0-0000036 0,138 Silicate Crown ( S. 7181 ) 0 -oooooio 0,3655 Telescope Crown ( S. 3418 ) 0 -0000007 0,3551 Zinco-silicate Crown ( S. 4705 ) 0 -0000033 0,227 Barium Silicate Crown , ( S. 7714 ) 0 -0000049 0,211 Densest Barium Silicate Crown ( S. 4962 ) 0 -0000012 4087 Baryta Light Flint ( M. 4087 ) 0 *0000035 0,3439 Telescope Light Flint ( S. 8204 ) 0 -0000047 0,826 Baryta Light Flint ( S. 4677 ) 0 -0000012 0,3439 Telescope Light Flint ( S. 4805 ) 0 -0000053 0,2071 Dense Barium Crown ( S. 4674 ) 0 -0000004 4078 Heavy Barium Crown ( M. 5201 ) 0 0000035 0,3439 Telescope Flint ( S. 5992 ) 0 -0000040 0,3961 Densest Barvta Crown ( S. 4704 ) 0 -0000055 0,3338 Borosilicate Flint ( S. 3338 ) 0 -0000045 0,527 Baryta Light Flint .
( S. 3187 ) 0 -0000018 0,364 Borosilicate Flint ( S. 3193 ) 0 -0000105 0,578 Baryta Light Flint ( S. 5042 ) 0 -0000035 0,364 Borosilicate Flint ( S. 0364 ) 0 -0000041 0,154 Ordinary Light Flint ( S. 3831 ) 0 0000033 3885 Light Flint ( M. 6812 ) 0 -0000039 0,748 Baryta Light Flint ( M. 4870 ) 0 -0000046 384 Dense Flint ( C. 629 ) 0 -0000070 0,118 33 33 ( S. 5403 ) 0 -0000025 * The temperature refraction coefficients for\#151 ; Quartz ( ordinary ray ) ... . .
= \#151 ; 0*0000052 Fluorite ... ... ... ... ... . .
= \#151 ; 0*0000102 2 c 2
|
rspa_1915_0023 | 0950-1207 | The effects of different gases on the electron emission from glowing solids. | 322 | 337 | 1,915 | 91 | Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character | Frank Horton, Sc. D.|Sir J. J. Thomson, O. M., F. R. S. | article | 6.0.4 | http://dx.doi.org/10.1098/rspa.1915.0023 | en | rspa | 1,910 | 1,900 | 1,900 | 9 | 208 | 5,870 | http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1915_0023 | 10.1098/rspa.1915.0023 | null | null | null | Thermodynamics | 38.742002 | Electricity | 37.089604 | Thermodynamics | [
5.185369968414307,
-61.65779113769531
] | 322 The Effects of Different Gases on the Electron Emission from Glowing Solids .
By Frank Horton , Se .
D. , Professor of Physics in the University of London .
( Communicated by Sir J. J. Thomson , O.M. , F.R.S. Received March 4 , 1915 .
) The original theory of the origin of the electron emission from glowing solids , which is based on the electron theory of metallic conduction , has recently been subjected to criticism on account of the manner in which the emission can be reduced by continually removing impurities from the discharge tube .
The critics maintain that the emission occurs as a result of chemical action between the hot cathode and the surrounding gas , or between the constituents of the cathode itself .
In a recent paper* the author has summarised the evidence in favour of this latter view , and has described experiments which show that the results which it leads us to expect do not always occur .
In particular it has been shown that the chemical action theory of the origin of the activity of a Wehnelt cathode , as propounded by Fredenhagenf and by Gehrts , j cannot be accepted .
The experiments described in the present paper were designed to test further the theory that the electron emission is due to chemical action .
The experiments consisted in studying the ionisation produced by Nernst filaments heated in various gases , of different chemical affinities for the material of the cathode .
The apparatusS and method of experiment were similar to those described in the paper already referred to .
The filament was heated by an alternating current from a transformer , and its temperature was determined by means of a specially standardised Fery optical pyrometer which was kindly lent to me by Prof. T. Mather , of the City and Guilds Engineering College , London .
The anode consisted of two parallel platinum plates , fixed in the discharge tube at equal distances on opposite sides of the filament , and connected together outside the apparatus .
The potential difference applied to the ends of the filament was measured by a Siemens alternating voltmeter , which was used in series with a resistance of equal magnitude , the total resistance in parallel with the filament being 4572 ohms .
The junction of the voltmeter and series resistance was connected to earth , and thus the mid-point of * * * S * F. Horton , 'Phil .
Trans. , ' A , vol. 214 , p. 277 ( 1914 ) .
t K. Fredenhagen , 'Ber .
K. Sachs .
Ges .
Wiss .
, ' Leipzig , vol. 65 , p. 42 ( 1913 ) . .
X A. Gehrts , ' Ber .
d. Deutsch .
Phys. Ges .
, ' p. 1047 ( 1913 ) .
S The author is indebted to the Government Grant Committee of the Royal Society for the means of purchasing some of the apparatus used in these experiments .
Effect of Gases on Electron Emission from Solids .
the glowiug filament was kept at zero potential .
The platinum plates forming the anode were connected through a delicate galvanometer to the positive pole of a high potential battery , the negative pole of which was earthed .
A diagrammatic view of the arrangements is given in fig. 1 , in which for simplicity the discharge tube is not shown .
The filaments experimented Fig. I.\#151 ; A , A , platinum anodes ( connected together ) ; B , battery ; C , C , heating current leads ; F , Nernst filament ; G , galvanometer ; Y , voltmeter ; S , series resistance .
with were all of the same type and were intended for use on a 100-volt alternating circuit .
The thermionic currents in air under similar conditions varied slightly for different filaments , but in every case the currents measured after heating for some time were remarkably constant .
In this respect the electron emission from a Nernst filament is very different from that obtained with a metal cathode , which usually decreases continuously with time .
Measurements of the thermionic currents in air , nitrogen , oxygen , and hydrogen were made .
In each case the variation of the current with the pressure of the gas under a constant applied potential difference was observed , and also the variation of the current with the potential difference with a constant gas pressure in the discharge tube .
The observations were usually made with the filament at a temperature of 1525 ' C. , but measurements were also made at other temperatures .
A difficulty in making comparisons of the thermionic currents in different gases , and at different pressures in the same gas , arises from the fact that , in Prof. F. Horton .
Effects of Different order to maintain the filament at a constant temperature , the heating current has to be altered at each change in the nature or density of the surrounding gas .
As the thermionic current is usually unsaturated , an alteration of the potential difference .between the ends of the filament causes an alteration in the current measured by the galvanometer .
For this reason the comparisons were generally made with a potential difference of 210 volts applied between the centre of the filament and the platinum anodes , this large potential difference being used so as to minimise the effect of the variations in the heating circuit .
Another difficulty occurred in the measurement of the temperature , for it was found that at very low pressures ( less than about 0-15 mm. ) the luminosity of the filament fell off , although the heating current was maintained steady .
It is thus possible that the thermionic currents measured at these low pressures are larger than they should be , on account of the temperature of the filament being greater than the value obtained from the reading of the optical pyrometer ; but I do not think this introduces a serious error , for the pyrometer measures the temperature by the intensity of the red rays only , and it was found that , if the heating current were kept constant , the intensity of the red rays hardly altered as the gas pressure was reduced from about 01 mm. , although the general luminosity of the filament decreased perceptibly .
A Xernst filament seems to require the presence of oxygen in order to emit a brilliant white light at high temperatures , for it was noticed that the luminosity was less , and that the filament appeared redder , when heated in nitrogen or hydrogen than when heated in the presence of oxygen to the same temperature as measured by the pyrometer .
In comparing the thermionic currents in air with those under similar circumstances in another gas , a series of observations in air was usually taken first .
The filament was fitted into the apparatus and left glowing for some time in air at the highest pressure to be used .
During this period the air in the apparatus was dried by the large phosphorus pentoxide drying tube connected to the discharge bulb , and the measured thermionic current gradually attained a steady value .
Even with a new filament , the thermionic current became constant after a few hours ' heating .
The pressure of the air in the apparatus was then gradually reduced , the temperature and applied potential difference being kept constant , and observations of the thermionic current at different pressures were taken .
The vacuum was finally made as complete as possible by means of charcoal cooled in liquid air , and then the other gas was gradually let into the apparatus , through two stopcocks , from a large glass flask , where it had been stored for many hours over phosphorus pentoxide .
Several filaments were used in the course of these experiments , and , as these gave slightly different thermionic currents under similar Gases on the Electron Emission from Glowing Solids .
325 conditions , it was necessary to make a series of experiments in air in connection with each series of observations in another gas .
The results will therefore all be given in the form of a comparison of the ionisation produced in air with that produced in the second gas .
I. The Ionisation Nitrogen .
The current-pressure curves for air and for nitrogen are shown in fig. 2 .
The filament was at a constant temperature of 1525 ' C. throughout the observations , and a potential difference of 212 volts was applied across the tube .
It will be seen that in both cases the maximum thermionic current fi 8o O 20 millimetres Pressure ; Fig. 2 .
was obtained at about 1*3 mm. pressure , and that at pressures below this the current was practically the same in the two gases , while at higher pressures the current in nitrogen was rather greater than that in air at the same pressure .
This is also shown by the current-E.M.F .
curves at different pressures in the two gases .
At very low pressures the curves were nearly identical , but at pressures of several millimetres the currents in nitrogen were always greater than those under similar conditions in air .
Fig. 3 shows these curves for the two gases at 48 mm. pressure .
Both with air and with nitrogen the current-E.M.F .
curves showed the usual characteristics , approximate saturation at very low pressures , and at pressures approaching atmospheric , with evidence of considerable ionisation Prof. F. Horton .
Effects of Different by collisions at intermediate pressures , as , for instance , is shown by the curves in fig. 3 .
It should be mentioned that all the currents measured with the particular filament used in this series of experiments were rather larger.than those o IOO zoo 300 400 Volbs Fig. 3 .
usually obtained , probably owing to some slight difference of composition of the filament .
II .
The Ionisation in Oxygen .
Ihe current-pressure curves obtained in oxygen were practically identical with those obtained with the same filament in air .
The pressure of maximum thermionic current was found to be about 1 mm.\#151 ; a little lower than that Gases on the Electron Emission from Glowing Solids .
327 measured with the filament used in the experiments with nitrogen .
The current-E.M.F .
curves were also very similar .
The equality of the currents measured at low pressures in the two gases may be judged from the following Table , which gives the galvanometer deflections for different applied potential differences , in air atOT61 mm. pressure and in oxygen at 0T48 mm. pressure , the temperature of the filament in both cases being 1525 ' C.:\#151 ; Potential difference ( volts ) .
Thermionic currents : ] L = 1 *40 x 10 8 ampere .
Air .
Oxygen .
43 48 51 86 79 84 129 102 118 172 129 146 258 189 199 344 245 255 430 310 316 In taking the observations for a current-E.M.F .
curve in any gas it was usually found that the currents measured with increasing electromotive forces were in each case slightly less than the currents measured under the same potential differences with decreasing electromotive forces .
This was the case during the observations recorded in the above Table , and the numbers given for the currents are the means of the " increasing E.M.F. " and the " decreasing E.M.F. " values .
III .
The Ionisation in Hydrogen .
The effect of hydrogen on the discharge of negative electricity from a glowing solid was first investigated by H. A. Wilson , * who experimented with a hot platinum wire and found that hydrogen produced a very large increase in the thermionic current , which , at low pressures , was nearly proportional to the pressure of the hydrogen .
From these results Wilson was led to the conclusion that the negative emission ordinarily observed from a platinum wire at a high temperature in air , or in a vacuum , was probably due to traces of hydrogen in the wire , and he showed that the thermionic current may be reduced to 1/ 250,000 of its ordinary value by taking precautions to remove such traces .
Further experiments , f however , convinced Prof. Wilson that the electron emission from glowing platinum is not entirely due to traces of hydrogen , but that the presence of this gas in the surface layers of the platinum assists the escape of electrons from the metal by diminishing the * H. A. Wilson , 4 Phil. Trans. , ' A , vol. 202 , p. 243 ( 1903 ) .
t H. A. Wilson , ' Phil. Trans. , ' A , vol. 208 , p. 247 ( 1908 ) .
Prof. F. Horton .
Effects of Different work which an electron has to do in passing through the surface .
Other experimenters have , nevertheless , used the fact that the thermionic current can be increased by the presence of hydrogen , as an argument in favour of the view that the electron emission from glowing solids is purely the result of chemical action between the cathode and impurities present in it , or gases surrounding it\#151 ; that the electrons are liberated by chemical action and are not simply escaping from the cathode at the high temperature .
The main object of the experiments recorded in the present paper was to investigate the electron emission from a Nernst filament in hydrogen , and to compare it with the emission in other gases .
Many more experiments were , therefore , made in hydrogen than in oxygen or nitrogen , and the thermionic currents from several filaments in this gas , under different conditions , were very thoroughly investigated .
It is clear that the possibilities of chemical action with a Nernst filament ( consisting of a mixture of oxides ) at a high temperature are much greater when the gas in the apparatus is hydrogen than when oxygen , nitrogen , or air are used .
If the emission of electrons is due to chemical action , it would seem reasonable to expect a much larger emission from the filament in hydrogen than under similar conditions in other gases .
But the results of the experiments given below show that the emission in hydrogen is not greater than the emission in air , although at certain pressures the thermionic current is enormously increased by the ionisation of the hydrogen molecules by collisions .
The increase in the current due to this cause in hydrogen is very much greater than the corresponding increase in air , oxygen , or nitrogen .
The curves given in fig. 4 show the alteration with gas pressure of the thermionic current from a filament at 1525 ' C. in air and in hydrogen , the currents measured in the latter gas being plotted to one-hundredth the scale of those in air .
It will be seen that the pressure of maximum conductivity in hydrogen is about 8-5 times the pressure of maximum conductivity in air .
On the theory of ionisation by collisions the pressure at which the current attains a maximum value is proportional to the electric force .
A series of observations with the filament at 1525 ' C. in air showed that the pressure of maximum thermionic current was roughly proportional to the potential difference applied from the cells for voltages of 200 and 250 .
The voltage applied from the cells is , however , only a measure of the potential difference between the centre of the filament and the anodes .
The potential at other points of the filament is different from that at the centre owing to the fall of potential along the heating circuit .
In hydrogen the heating current required to maintain a temperature of 1525 ' C. is much greater than in air , and it increases considerably as the pressure of the hydrogen is increased .
The Gases on the Electron Emission from Glowing Solids .
329 lectric field , due to the heating current is therefore by no means constant luring a series of experiments at different gas pressures , and it is very lifferent in hydrogen at 12 mm. pressure and in air at 1*4 mm. pressure .
It s thus probable that the pressure of maximum thermionic current in hydrogen is shown in the curve is considerably higher than it would be if the electric field were the same as in the case of air .
It follows from the theory of ionisation by collisions that with a given uniform field the pressure of maximum current in hydrogen is about three times the corresponding pressure in air , oxygen , or nitrogen .
In the present experiments the io Pressure , \#151 ; millimetres Fig. 4 .
electric field is not uniform , and it alters when the heating current is adjusted at each change of pressure , so that we should not expect this ratio to be obtained , although the general form of the curves indicates that the variations in the thermionic current with gas pressure are due to ionisation by collisions .
Several series of experiments made with different filaments in hydrogen and in air gave pressures of maximum conductivity in the former gas ranging from 8 0 to 9*5 times the pressure of maximum conductivity in air .
To give some idea of the manner in which the field due to the heating current varied it may be mentioned that , with the filament at 1525 ' C. , and with air in the apparatus , the potential difference 330 Prof. F. Horton .
Effects of Different between the ends of the filament ranged from 74 to 66 volts as the pressure was reduced from about 40 mm. to zero ; while in hydrogen the corresponding alteration was from 128 to 66 volts .
In order to compare the electron emissions in air and in hydrogen it is necessary to prevent , as far as possible , the original emission from being altogether swamped by the new ions formed by collisions .
It was not possible to prevent ionisation by collisions altogether , for it was necessary to have some gas present in the discharge tube , and it was found that the field due to the heating current alone was sufficient to cause this ionisation ; but the effects of ionisation by collisions are not large if the experiments are made at low pressures\#151 ; at pressures well below those of the maxima shown in the curves of fig. 4 .
A series of observations of the thermionic currents in air and in hydrogen with various applied potential differences , and at pressures up to 0*2 mm. , was therefore made .
Fig. 5 shows currentO IOO 200 300 400 500 Volbs Fig. 5 .
E.M.F. curves for air and for hydrogen at 0*17 mm. pressure , the temperature of the filament being 1525 ' C. in both cases .
From these curves it will be seen that the thermionic current is nearly the same in the two gases .
With 400 volts the current in hydrogen appears to be saturated , whereas that in air is approximately obeying Ofim 's law .
A similar result is shown in fig. 6 for hydrogen at 0*099 mm. and for air at 0 110 mm. The experiments for the curves in fig. 6 were made with a different apparatus from that used in obtaining the results of fig. 5 , the distance apart of the electrodes being rather greater .
Fig. 6 also contains Gases on the Electron Emission from Glowing Solids .
331 curves for hydrogen and for air at 0*040 mm. pressure , under which conditions the currents in the two gases are still more nearly equal .
At this lower pressure the effects of gas ionisation are no doubt smaller , for not only are fewer collisions possible , but also the electric field is more nearly the same in the two gases , as the heating currents required to maintain the same temperature in the filament are not very different .
These curves , and others which I have obtained , show that at low pressures saturation is more easily attained in hydrogen than in air , oxygen , or nitrogen ; a result which is accounted for by the fact that the mean free path of the ion in hydrogen is greater than it is in air , oxygen , or nitrogen , and so becomes comparable with the distance between the electrodes at a higher pressure than in the case of these other gases .
The curves clearly indicate that if ionisation by collisions could be completely eliminated , the electron emission from the filament would be found to be the same in hydrogen as it is in air .
1Y .
A Comparison of the Electron Emission from Lime Heated on a Nernst Filament in Air and in Hydrogen .
In the course of an earlier research* the author found that the thermionic current from a lime-covered platinum strip heated in pure helium at about 3 mm. pressure was enormously increased if a small quantity of hydrogen was allowed to enter the discharge tube .
Since the amount of hydrogen admitted was very small , it is probable that the increased current obtained is due to an * F. Horton , ' Phil. Trans./ A , vol. 207 , p. 149 ( 1907 ) .
Prof. F. Horton .
Effects of Different actual increase in the emission from the cathode , and is not merely the resul of ionisation of the hydrogen atoms by collisions .
It was also found that tb thermionic current in pure hydrogen at O'Ol mm. pressure was enormouslj greater than the current measured in air at the same pressure .
Recentlj Fredenhagen* has attempted to explain this effect from the point of view o : the chemical action theory of the emission of electrons from solids at high temperatures , by supposing that the hydrogen combines with the oxygen of the lime , and possibly also with the calcium , and that electrons are emitted : as a result of these chemical actions .
An obvious objection to this explanation is that it involves the rapid disappearance of the oxide layer , and consequently the cessation of the activity of the cathode\#151 ; results which do\#187 ; not occur in practice .
There is also the objection that , so far as the author is aware , there is no evidence that the chemical actions mentioned give rise to f an electron emission .
The experiments described in the present paper suggested that the increased emission from a lime-covered platinum cathode in hydrogen might i be due to the effect of the hydrogen on the emission from the platinum supporting the lime , so that if the lime were heated without the platinum support , its electron emission in hydrogen might perhaps be not very different from that in air .
In order to test this , a Nernst filament which had been found to give equal thermionic currents in air and in hydrogen at low pressures was covered with lime and was again tested in these gases .
The results of these tests will be seen from the curves given below .
Fig. 7 shows the current-pressure curves at 1525 ' 0 .
in air and in hydrogen .
It will be seen that at 100 mm. pressure the thermionic current in hydrogen was about 55 times the current in air , but the shape of the curve indicates that ionisation by collisions is already occurring at this pressure in hydrogen , whereas it is producing no noticeable effect in air ; moreover the potential difference between the ends of the filament at 100 mm. pressure was 136 volts in hydrogen and only 79 volts in air .
The alteration of the thermionic currents with pressure , at pressures below about 1 mm. , is shown in fig. 8 .
Ionisation by collisions takes place throughout this region of pressure , especially when a high potential difference is applied across the tube .
Both with air and with hydrogen there was a luminous discharge throughout the series of observations represented in fig. 8 .
At high pressures the discharge with a potential difference of 206 volts ( as in the curves of fig. 7 ) was not luminous , but the luminosity appeared on reducing the pressure to about 33 mm. with hydrogen , and to about 4 mm. with air .
In comparing these results in the two gases it must be borne in mind that * K. Fredenhagen , ' Physik .
Zeitschr .
, ' vol. 15 , p. 19 ( 1914 ) .
Gases on the Electron Emission from Glowing Solids .
333 apart from the effects of ionisation by collisions , there are two things which tend to make the currents measured in hydrogen greater than those measured IOO millimetres Fig. 7 .
in air .
One of these is the greater potential difference between the ends of the filament , due to the greater heating current required in hydrogen ; the other is the fact that the luminosity of the filament in hydrogen is less than Prof. F. Horton .
Effects of Different it is in air With the optical pyrometer , only the red light is used to measure the temperature , and I do not think that much error is made in adjusting the temperature with a low pressure of air or of hydrogen in the apparatus ; but at high pressures , where the difference of luminosity in the two gases is more marked , it is not unlikely that a higher temperature of the filament is required in hydrogen to give the same intensity of red light as is obtained with the filament at 1525 ' C. in air .
It is probably for these reasons that the ratio of the thermionic currents in the two gases was found to increase at high pressures .
At atmospheric pressure the current in o*5 i-c Pressure. .
millimetres Fig. 8 .
hydrogen was about 400 times as large as the current measured in air under the same applied potential difference and at the same temperature as measured by the pyrometer .
Unfortunately , no other method of temperature measurement could be employed , for it was desired to have no metal in contact with the lime .
These experiments at atmospheric pressure can be compared with those of Martyn , * who found that the thermionic current from a lime-covered platinum wire at 1600 ' C. in hydrogen at atmospheric pressure was 20,000 times the current in air under similar conditions .
In Martyn 's experiment there was no uncertainty in the temperature adjustment , which * G. H. Martyn , 4 Phil. Mag. , ' VI , vol. 14 , p. 306 ( 1907 ) .
Gases on the Electron Emission from Glowing Solids .
335 was performed by measuring the resistance of the platinum wire .
It is therefore obvious that hydrogen increases the thermionic current from a lime-covered platinum cathode to a much greater extent than it does the current from a lime-covered Nernst filament .
That the electron emission from lime is practically the same in air and in hydrogen is perhaps best shown ( as in the case of the Nernst filament alone ) by current-E.M.F .
curves obtained at low pressures .
Two such curves are given in fig. 9 , the lower one being for air at 0'0103 mm. pressure , the upper one for hydrogen at 0 0121 mm. pressure .
During both sets of observations the gas in the discharge tube was very faintly luminous .
The luminosity O IOO 200 300 400 Volbs Fig. 9 .
was not sufficient to enable the spectra of the gases to be examined , but this was done before reducing the pressure in each case ; the air showed no sign of the hydrogen lines , and the spectrum of the hydrogen showed that the gas was pure .
To illustrate the striking difference between these results and the effect of hydrogen on the thermionic current from a lime-covered platinum strip , an experiment described in an earlier paper* may be quoted .
The thermionic current from a lime-covered platinum cathode was measured in oxygen gas at 0-002 mm. pressure .
This gas was pumped out and hydrogen was let into the apparatus , which was then pumped down to the same pressure as before .
On warming up the cathode the thermionic current was at first only slightly greater than its previous value , but it rapidly increased until in a few minutes it was over 10,000 times as great as it had been in oxygen at the same temperature ( 740 ' C. ) .
In view of the results of the experiments described * F. Horton , 'Phil .
Trans. , ' A , vol. 207 , p. 149 ( 1907 ) .
VOL. XCI.\#151 ; A. 336 Effect of Gases on Electron Emission from Solids .
in the present paper , this increase in the thermionic current is probably entirely due to the effect of the hydrogen upon the platinum .
In the first observation , in oxygen , the platinum was quite free from hydrogen .
It had been boiled for a long time in strong nitric acid before being covered with lime , and the cathode had been heated in oxygen at a considerable pressure for hours before the final readings at 0*002 mm. were taken .
When hydrogen is let into the apparatus it is only very slowly absorbed by the platinum when that is cold , but as the temperature is raised the absorption rapidly increases .
This probably accounts for the increasing thermionic current which was observed in the experiment .
Summary and Conclusion .
The experiments described have shown that the emission of electrons from a glowing Nernst filament is independent of the nature of the gas in the discharge tube , at least for the gases air , oxygen , nitrogen , and hydrogen , and that the same may be said of the electron emission from lime .
At low pressures the thermionic current from a given cathode under definite conditions is practically identical in all four gases .
At higher pressures the thermionic currents under similar conditions vary , but an increased thermionic current does not necessarily mean an increased electron emission from the cathode ; the large currents which are obtained at certain gas pressures , particularly with hydrogen , are the- result of ionisation of the gas molecules by collisions .
Oxygen and hydrogen differ very widely in their chemical affinities for the material of an oxide cathode , so that the equality of the electron emission in these two gases is evidence that the electrons are not produced by chemical action between the cathode and the surrounding gas .
In the case of a platinum cathode , hydrogen seems to produce a genuine increased emission , which appears to be brought about by the absorption of the gas by the platinum .
This result was first obtained by H. A. Wilson , * who , by means of a careful investigation of the connection between the thermionic current and the gas pressure , was able to establish the fact that the hydrogen dissolves in the platinum and does not , under ordinary circumstances , combine with it to form a compound .
It is improbable , therefore , that the increased emission from platinum produced by hydrogen is due to chemical action .
The exact manner in which the hydrogen acts is at present unknown , but Wilson has shown that the experimental results can be explained on the supposition that the hydrogen atoms in the surface layers * H. A. Wilson , 'Phil .
Trans. , ' A , vol. 208 , p. 247 ( 1908 ) .
Corpuscular Radiation Liberated in Vapours .
337 of the platinum are positively charged and have the effect of lessening the work which an electron must do in order to escape from the metal .
With a substance like lime or the oxides of a Nernst filament , by which the hydrogen is not absorbed , the electron emission is unaltered by the presence of this gas .
On the Corpuscular Radiation Liberated in Vapours Homogeneous X-radiation .
By H. Moore , B.Sc. , A.R.C.S. , Assistant Lecturer in Physics at King 's College , London .
( Communicated by Prof. O. W. Richardson , F.R.S. Received March 22 , 1915 .
) It is recognised as a result of numerous independent experiments* that ionisation by X-rays is the result of corpuscular radiation liberated by the X-rays .
In a recent paperf it was shown by the author that , in the case of carbon and oxygen compounds , the corpuscular radiation liberated by a beam of X-radiation was an " atomic " phenomenon , i.e. that the number of corpuscles given out by an atom of carbon or oxygen in a beam of X-rays is the same whether the atom is in combination or not .
The resulting ionisation is not , however , " atomic , " the ionisation produced in different gases or vapours by a given amount of corpuscular radiation being dependent on the nature of the gas or vapour .
In the present paper an attempt has been made to test whether this " atomic " law holds good for other elements of higher atomic weight .
These , giving much larger ionisations than the lighter elements , also allow of greater accuracy in the observations , although as the absorption is correspondingly increased , large absorption corrections are rendered necessary in some cases .
As in the former experiments , the gases or vapours were subjected to a beam of homogeneous ( copper ) radiation , the ionisation chamber being a cylinder with aluminium ends , and containing an axial electrode connected with an electroscope .
The rate of leak due to the ionisation current was compared with that of a standard electroscope containing air , and after each * Barkla and Simons , 'Phil .
Mag. , ' February , 1912 ; C. T. R. Wilson , 'Roy .
Soc. Proc. , ' June , 1912 ; Barkla and Philpot , ' Phil. Mag. , ' June , 1913 .
t 'Phil .
Mag. , ' January , 1914 .
|
rspa_1915_0024 | 0950-1207 | On the corpuscular radiation liberated in vapours by homogeneous X-radiation. | 337 | 345 | 1,915 | 91 | Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character | H. Moore, B. Sc., A. R. C. S.|O. W. Richardson, F. R. S. | article | 6.0.4 | http://dx.doi.org/10.1098/rspa.1915.0024 | en | rspa | 1,910 | 1,900 | 1,900 | 1 | 7 | 266 | http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1915_0024 | 10.1098/rspa.1915.0024 | null | null | null | Thermodynamics | 55.238983 | Atomic Physics | 24.233724 | Thermodynamics | [
-22.493602752685547,
-48.57866668701172
] | ]\gt ; With the vapours whose saturation vapour-pressure was less than atmospheric , a mixture of hydrogen and the vapour was used , the mixture being passed through a long spiral surrounded by ice , so that the vapour was saturated at C. Hydroohloric aoid and ammonia were each used at atmospheric pressure , as were also nitrous oxide and carbon dioxide .
In the case of ammonia , and to a lesser degree with hydrochloric acid , insulation diffioulties were met with , vulcanite proving quite useless even if the chamber was dried with air over .
The difficulty was , however , completely overcome by covering the vulcanite with paraffin wax , the insulation leak being praotically zero when this was used .
In order to obtain the ratio of the amounts of oorpuscular radiation liberated iu equal lengths of the gas in question and of air , by beams of equal intensity , the following method was used : icating the intensity of the beam by I , the ionisation per centimetre in any gas is , where A represents the corpuscular radiation liberated in the gas per centimetre by a beam of " " unit\ldquo ; intensity and is the oorpuscular factor for the gas .
The coefficient of absorption in the gas being per , I at any distance cm .
from the incident end of the chamber will be being the intensity of the inoident beam .
The ionisation in the chamber , after deducting the small ionisation due to corpusoular radiation from the ends , is thus ' .
|
rspa_1915_0025 | 0950-1207 | Deep water waves, progressive or stationary, to the third order of approximation. | 345 | 353 | 1,915 | 91 | Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character | Lord Rayleigh, O. M., F. R. S. | article | 6.0.4 | http://dx.doi.org/10.1098/rspa.1915.0025 | en | rspa | 1,910 | 1,900 | 1,900 | 2 | 18 | 320 | http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1915_0025 | 10.1098/rspa.1915.0025 | null | null | null | Fluid Dynamics | 84.756586 | Tables | 13.828063 | Fluid Dynamics | [
43.829933166503906,
-38.436954498291016
] | ]\gt ; .
( 5 ) The surface conditions are ( i ) that be there zero , and ( u ) that ) ) .
( 6 ) : The first is already virtually expressed in 5 ) .
For the second .
This equation is to hold good to the second order for all values of , and therefore for each Fourier component separately .
The terms in and give The term in gives , ( 10 ) and , similarly , that in gives In like manner , ( 12 ) and so on .
These are the results of the surface condition From the other surface condition ) we find in the same way .
( 13 ) .
( 14 ) .
15 The corresponding terms in represent merely such waves , propagated in either direction , and of wave-lengths equal to an aliquot part of the principal wave-length , as might exist alone of infinitesimal height , when there is no primary wave at all .
When these are included , the aggregate , even though it be all propagated in the same direction , loses its character of possessing a permanent wave shape , and further it has no tendeney to acquire such a character as time advances .
If the principal wave is stationary we may take .
( 21 ) If , vanish , and .
( 22 ) According to ( 22 ) the surface comes to its zero position every heze when , and the displacement is a maximum when Then , ( 23 ) so that at this moment the wave-form is the .
am as for the progressive wave ( 18 ) .
Since is measured downwards , the maximum elevation above the mean level exceeds numerically the maximum depression below it .
In the more general case still with evanescent ) we may with .
,
|
rspa_1915_0026 | 0950-1207 | Discontinuous fluid motion past a bent plane, with special reference to aeroplane problems. | 354 | 370 | 1,915 | 91 | Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character | G. H. Bryan, Sc. D., F. R. S.|Robert Jones, M. A. | article | 6.0.4 | http://dx.doi.org/10.1098/rspa.1915.0026 | en | rspa | 1,910 | 1,900 | 1,900 | 1 | 7 | 174 | http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1915_0026 | 10.1098/rspa.1915.0026 | null | null | null | Fluid Dynamics | 72.070411 | Tables | 24.658271 | Fluid Dynamics | [
40.138946533203125,
-16.346296310424805
] | ]\gt ; \mdash ; Values FIG. 12 .
not desirable in the case of an aeroplane .
the ratio of lift to drift is greatest when the angle between the planes is least , but the lift is small .
These two conclusions agree with the experimental results that aerofoils with a large camber give a better ratio of lift to surface , whereas nearly flat aerofoils give a better ratio of lift to drift .
The figures given in Iable I show , however , that the ratio of lift to drift , for a large value of even , is greater than the corresponding ratio for the chord , and the lift on a bent plane is much greater than on its chord .
Hence it appears that a bent plane is decidedly more efficient than its chord .
Further , from the last Table it is seen that as the length of the front plane increases , the total lift decreases , whereas the ratio of lift to drift increases .
|
rspa_1915_0027 | 0950-1207 | The difference between the magnetic diurnal variations on ordinary and quiet days at Kew Observatory. | 370 | 381 | 1,915 | 91 | Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character | C. Chree, Sc. D., LL. D., F. R. S. | article | 6.0.4 | http://dx.doi.org/10.1098/rspa.1915.0027 | en | rspa | 1,910 | 1,900 | 1,900 | 2 | 9 | 297 | http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1915_0027 | 10.1098/rspa.1915.0027 | null | null | null | Meteorology | 42.486356 | Tables | 25.766671 | Meteorology | [
45.24183654785156,
3.9082109928131104
] | ]\gt ; , where represents the equivalent angle ( at per hour ) to the time elapsed since Greenwich midnight , the component of the horizontal difference vector inclined at any angle to the magnetic meridian ( or direction of ) is 2 nt Here is supposed to be expressed in terms of as unit , which means , for the place and epoch considered , writing as the equivalent of 1 ' .
The mean declination at Kew for the eleven years 1890-1900 was W. , so that , to get the component called above , we must write for , and similarly for X. The results finally obtained for X , , and the vertical component of the vector , in terms of as unit , were as follows:\mdash ; , ( 1 ) , ( 2 ) .
( 3 ) The fact that is insignificant was , of course , implied by fig. 2 , but it is interesting to find that the 24-hour term in it is especially insignificant , while the 24-hour term in X dominates all the others .
The 24-hour term in is also largely dominant , so that the difference vector is essentially a phenomenon of a regular kind with a 24-hour period .
between the angles and those deduced rom the complete period .
The only oonspicuous difference between the sunspot maximum and minimum results il in the amplitude of the difference vector .
The excess for the sunspot mmnm group is in much the same proportion as in the case of the quiet day vector itself . .
The N. quiet day inequalities were given in my previous paper Uy for March .
, and December , in addition to the year as a whole .
|
rspa_1915_0028 | 0950-1207 | On the origin of the \quot;4686\quot; series. | 382 | 387 | 1,915 | 91 | Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character | Thomas R. Merton, B. Sc. (Oxon.)|A. Fowler, F. R. S. | article | 6.0.4 | http://dx.doi.org/10.1098/rspa.1915.0028 | en | rspa | 1,910 | 1,900 | 1,900 | 1 | 11 | 239 | http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1915_0028 | 10.1098/rspa.1915.0028 | null | null | null | Atomic Physics | 41.832853 | Tables | 23.689215 | Atomic Physics | [
-2.131185531616211,
-35.71028137207031
] | ]\gt ; The pressure in the tube was very low , so that the glass walls fluoresced , the 4686 line appearing only outside the capillary , in accordance with the hrown beans o interferometer , and the ring system was focussed by means of an achromatic lens on to the slit of the spectograph , which consisted of a large Hilger constant deviation spectloscope provided with a camera attachment .
With this instrument a series of photographs could be taken on the same plate .
experiments were conducted as follows:\mdash ; The interferometer plates were set at a small difference of path and a erraph was taken .
The difference of path was then successively increased and a series of exposures was made .
From the series of photographs thus obtained the limiting order could be estimated .
In estimating the limiting order , it will be seen that since on each exposure the order number increases with decreasing wave-length , it is usually possible ( if the differences of path have been suitably chosen ) to pick out some line in which the are just visible .
The determination cannot be made with a high degree of accuracy , but all the photographs taken have yielded concordant results .
In Plate 3 , I shows a raph taken an e'talon giving a : V0L .
Monthly NoticesAstro .
Journ. .
Proc. , , Vol. 91 Pl .
|
rspa_1915_0029 | 0950-1207 | Observations on the fluorescence and resonance radiation of sodium vapour.-I. | 388 | 395 | 1,915 | 91 | Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character | Hon. R. J. Strutt, Sc. D., F. R. S. | article | 6.0.4 | http://dx.doi.org/10.1098/rspa.1915.0029 | en | rspa | 1,910 | 1,900 | 1,900 | 3 | 168 | 3,611 | http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1915_0029 | 10.1098/rspa.1915.0029 | null | null | null | Atomic Physics | 52.403893 | Thermodynamics | 20.000662 | Atomic Physics | [
7.366830825805664,
-48.951576232910156
] | 388 Observations on the Fluorescence and Resonance Radiation of Sodium Vapour.\#151 ; I. By the Hon. R. J. Strutt , Sc. D. , F.R.S. , Professor of Physics , Imperial College , South Kensington .
( Received April 7 , 1915 .
) S 1 .
Experiments on Duration of the Resonance Radiation .
In a paper entitled " Luminous Vapours Distilled from the Arc , " * I have shown that sodium vapour , stimulated to give the line spectrum by electric discharge , and caused to distil away from the region of discharge , will carry its luminosity with it for a distance of many centimetres .
In other words , the luminosity is persistent , and goes on after the electrical stimulation has ceased .
In this case the spectrum emitted is the arc spectrum .
It includes not only the D lines , but also the lines of the subordinate series .
We have another method of exciting sodium vapour to emit the line spectrum\#151 ; I mean fluorescent excitation .
If the vapour is illuminated by a soda flame , it will emit the D lines by resonance .
It is true that in this case the subordinate series of lines are not excited , but still we should certainly expect at first sight that the D-line radiation would behave as it does with electrical excitation , and that the luminosity would move with the vapour if the latter was rapidly distilled away from the place of excitation .
An important experiment has been described by Dunoyerf which seems to show that this is not so .
He projected the distilled sodium vapour in a jet across a wide globe ; part of the jet was illuminated by a beam of sodium light ; and it was found , that when the vapour passed into the shadow it abruptly ceased to be luminous .
It may possibly be objected to Dunoyer 's experiment that , since the bulb traversed by sodium vapour was not kept hot , a cloud of condensed sodium may have been formed and that the observed luminosity may have been due to the diffusion of sodium light by this cloud , rather than to genuine resonance radiation .
For this and other reasons it has been thought desirable to repeat Dunoyer 's experiment in a modified form , under conditions more closely comparable with those of my own experiments on the electrically excited vapour .
* ' Roy .
Soc. Proc. , ' A , vol. 90 , p. 364 ( 1914 ) .
\#187 ; t ' Comptes Rendus , ' vol. 157 , p. 1068 ( 1913 ) .
Fluorescence and Resonance Radiation of Sodium Vapour .
389 Fig. 1 shows the arrangement .
The glass bulb , 4 cm .
in diameter , contains a few grammes of dry sodium .
It is inserted in b , the chimney of a small gas furnace , which supplies heat for distilling e sodium through the tube c ( 18 mm. inside diameter ) into the cold condensing bulb d , of 9 cm .
diameter .
It was necessary to prevent condensation in and this was achieved by warming it from time to time with a large Bunsen burner held in the hand .
The vessel was connected at eto a Gaede molecular pump .
A metal diaphragm , backed by a soda flame not too heavily salted , * was focussed on the side of c by means of a short-focus lens , indicated at / .
A lantern condenser of 4 inches diameter was generally used , but a cinematograph lens , giving less light but a better defined cone of rays , was sometimes substituted .
The most rapid distillation of the vapour was at the rate of about 15 grm. per hour .
In this case the vapour in c was so dense that the resonance radiation at g was limited to a superficial patch .
In other experiments , with less rapid distillation , a cone of luminosity converging to a point could be seen in the vapour.f In neither case was there the slightest indication of the luminosity being carried along with the vapour current .
The appearance down stream of the place of excitation was in no way different from the appearance on the up-stream side .
The experiment confirms Dunoyer 's conclusion , and emphasises the difference between electrical and fluorescent excitation .
In the former case the D luminosity is persistent .
In the latter case it is not so .
This will appear still more remarkable and anomalous if we compare the behaviour of sodium emitting the D line with mercury emitting the ultra-violet line at \2536 .
Mercury through which the electric discharge is passing emits this line along with the rest of the arc spectrum , and continues to do so for a time when distilled away from the place of excita-tion .
J As Wood has shown , mercury vapour can also emit the line \ 2536 * See Dunoyer , ' Journ. de Physique , ' January , 1914 .
+ After an experiment sodium can be removed from the vessel by washing it out with alcohol .
If the glass has become brown with reduced silicon , it can readily be cleaned by washing with dilute hydrofluoric acid .
+ For references , see ' Roy .
Soc. Proc. , ' A , vol. 91 , p. 92 ( 1914 ) .
390 * Hon. K. J. Strutt .
Observations on the without the other mercury lines when light of precisely this wave-length falls upon it .
So far the behaviour of mercury and sodium run parallel .
Now comes the difference .
The luminous centres emitting mercury resonance radiation of wave-length 2536 can be .
distilled away from the place of excitation as well and easily as if they had been excited electrically.* The centres emitting the resonance radiation of sodium cannot , as we have seen , be distilled away from the place of excitation at all .
I cannot at present make any suggestion as to how these facts should be regarded .
It seems very strange that the analogy between the behaviour of sodium and mercury should go so far , and then suddenly break down .
S 2 .
Invisibility of the Resonance Radiation through Dilute Sodium Vajpour .
Dunoyer 's improved methods of observing the resonance radiation of sodium have already been referred to .
He noticed that when a soda flame a , fig. 2 , is focussed by a lens b , on to the wall of a bulb d containing sodium vapour at a density corresponding to a temperature of , say , 300 ' C. , I Fig. 2 .
the resonance radiation did not penetrate into the depth of the vapour but was confined to a very thin layer at c. The light from this layer of superficial resonance could be seen from any direction in front of the plane ee , but from any direction behind this plane ( looking through the bulb ) was invisible .
Dunoyer suggests that this may be explained simply by the opacity of the vapour for the particular radiation , though he apparently had some alternative * See F. S. Phillips , ' Roy .
Soc. Proc. , ' A , vol. 89 , p. 39 ( 1914 ) .
The rate of distillation of mercury used by Phillips was only about twice as great as the rate of my most rapid sodium distillation , measuring the rate in each case by the number of molecules passing per second.^ Fluorescence and Resonance Radiation of Sodium Vajpour .
391 explanation in mind .
The absorption is , however , a sufficient explanation , as is proved by the simple experiment illustrated in fig. 2 .
The spot of resonance radiation was viewed through a second exhausted bulb / containing sodium .
This bulb was heated , and as the temperature rose the resonance radiation appeared dimmer , finally becoming invisible .
The temperature at which it disappeared was 160 ' C. as nearly as could be determined .
The thickness of the layer of vapour in f was 4*5 cm .
, but this bulb was not very well exhausted , and it may be that with the sharper absorption band obtained in the pure vapour a less thickness or density of vapour would have sufficed .
The bulb f is , of course , at this low vapour density quite transparent to daylight or lamplight , and the inability to see the spot of resonance radiation through it produces so strange an impression that the observer almost feels as if he is being tricked .
air .
PUMP | 3 .
Resonance Radiation with the Vapour a Magnetic Field .
The conical poles of a Dubois half-ring electromagnet were adjusted to a distance of 8 mm. apart , and a glass tube of 4*5 mm. inside diameter was arranged between them as shown in fig. 3 .
The tube was kept in connection with a Gaede molecular pump , and , by warming it with a Bunsen burner held in the hand , sodium vapour could be distilled up into the region between the poles .
A salted flame was focussed on this part of the tube , as in previous experiments .
The effects depend upon how much salt is introduced into the flame .
Two kinds of flame have been used .
The first , referred to as the weak flame , was an ordinary Bunsen flame , with a dilute salt solution sprayed into the gas mixture .
This spray was obtained by electrolysis of the dilute salt solution.* The second , referred to as the strong flame , was from a Meker burner , with abundance of salt melted on to the nickel grid .
Illuminating the sodium vapour with the weak flame , the intensity of the resonance radiation was diminished by exciting the magnet .
The stronger the field , the weaker the resonance .
With a field of 19,000 units , which was the limit attainable , the resonance was reduced to a very small intensity .
It is difficult to say definitely whether it disappeared altogether , since there * The arrangement is described in ' A Treatise on Practical Light , ' by R. S. Clay , p. 507 .
Macmillan , 1911 .
UpSODIUM Fig. 3 .
Hon. R. J. Strutt .
Observations on the is inevitably some diffusion of soda light by the striae in the glass , and by specks of dust ; this diffused light cannot be easily distinguished from the resonance radiation , and remains when the latter is quenched by the magnetic field .
The explanation of this experiment presents no difficulty .
The D lines produced by the weak flame are narrow .
They were examined visually in the second order of a 10 feet concave grating , and the breadth of Dx was estimated at 0*2 Angstrom , that of D2 at 0*3 Angstrom .
Dx is split by the Zeeman effect into four components , and with the field employed the two inner ones would be separated by 0 41 Angstrom.* The component lines of the resonance radiation are so narrow that their breadth may be neglected .
Al ] the components of Dx in the resonating vapour would , therefore , be thrown off the exciting line , and the resonance of Dx would be destroyed .
D2 is split into six components .
In a field of 19,000 units the distances of the respective pairs would be about 02 , 0*6 , and 1 Angstrom .
The two outer pairs , but not the inner pair , would be thrown off the exciting line 0*3 Angstrom broad .
We see , therefore , that the field should extinguish the whole of the Dx resonance , and half of the D2 resonance.^ This is in good agreement with the observations .
Using the strong flame instead of the weak one , the effects are more complex .
When the full magnetising current is switched on , the resonance radiation is observed to become brighter , to pass through a maximum , and then to diminish again .
On switching off , the maximum is passed through again , and then the brightness sinks back to its initial value .
These changes each take perhaps two seconds .
The magnetic field takes time to reach its full value , and the maximum brightness corresponds to a particular value of the field .
This value was determined , though not , of course , very accurately , by diminishing the ( steady ) magnetising current until , on switching on , the light could not be observed to pass a maximum any longer .
This condition was first satisfied when the steady field was about 12,000 units .
To interpret the observations , it is necessary to consider the structure of the D lines in the strong flame .
As observed visually in the second order spectrum of the grating , they were seen to be very much broader than the lines emitted by the weak flame .
The breadth of Dx was estimated at 0*8 Angstrom , and of D2 as IT Angstrom .
Further , the lines showed extremely distinct reversals .
The breadth of the relatively dark centre of the line was perhaps in each * See Rung and Paschen , Kayser 's ' Handbuch , ' vol. 2 , p. 670 .
+ The polarisation phenomena indicate that the two outer pairs of D2 contain only half the total light .
Fluorescence and Resonance Radiation of Sodium Vapour .
393 case about a quarter of the total breadth of the line .
This would give 0 '2 and 0'3 Angstroms for Di and Da respectively .
In the absence of magnetic force the resonating lines fall on the comparatively dark centres of the exciting lines .
As the magnetic force increases a resonating line is split into components which fall on to the brighter parts of the exciting line , and the intensity of the resonance increases .
A further increase in the field pushes the components of a resonating line beyond the maxima of the exciting line , and the resonance begins to fall off again .
To predict the exact field strength at which the maximum should be attained it would be necessary to know the precise distribution of intensity in each exciting line , as well as the comparative intensity of each Zeeman component of each resonating line .
Such data are not available .
At the observed optimum field , 12,000 units , the components of Di would all be off the dark centre of the exciting line , though well within the limits of the bright part of this line .
In the case of Da the innermost pair would not be clear of the dark central strip of the exciting line , but the two outer pairs would be on the bright part of this line .
Thus the explanation of the maximum which has been given is in good general agreement with the observed breadth and structure of the exciting lines .
To see the resonance clearly pass the maximum it is necessary to use a tube only a few millimetres wide , as described , for the strong field required cannot be produced in a larger vessel .
But if it is desired merely to show the increase it is better to use a tube 2 or 3 cm .
wide between large flat pole pieces .
The light should be limited to a strip 1 cm .
wide , along that part of the tube which is in the field .
A suitable diaphragm should be placed in front of the flame and focussed upon the tube .
S 4 .
Exciting Flame in the Magnetic Field .
The flames used were as before , and either of them could be placed between large flat pole , 'pieces , allowing of a maximum field of 9000 units .
The flame in each case was focussed on the wall of a bulb of 300 c.c. capacity containing sodium .
The bulb was kept hot over a gas burner , and was continuously exhausted by the Gaede molecular pump .
With the weak flame the resonance was diminished by the field .
The experiment serves as a striking demonstration of the Zeeman effect , and of the various experiments described it is perhaps the best for this purpose .
Since the vessel containing sodium vapour has not to get into the space between the magnet poles , it can be made large , and a large patch of resonance radiation produced upon it .
The effect of the field on this could quite well be shown to 10 or 20 persons at once .
Hon. R. J. Strutt .
Observations on the The explanation is , of course , analogous to that already given for the case when the same flame is used , applying the field to the resonating vapour , In the present instance the exciting line is split up and displaced so that the resonating line no longer falls upon it .
The case of the strong flame in the field is less simple .
The observed result is that the resonance radiation is increased , though this is not quite so striking as the diminution with the weak flame in the field .
In interpreting this result we have first to consider what effect the field will produce on the broad bright line .
Assuming that the Zeeman components are each as broad as the original bright line , the field is insufficient to separate them to any important extent .
We have , therefore , still a continuous bright background .
On the other hand , the comparatively narrow lines of the reversing layer are definitely separated .
Thus they may have uncovered the centre of the bright line , which is the part of it effective in producing resonance.* As a matter of fact when the source was examined with the concave grating , it was observed that the dark reversed centre of Di became brighter , on exciting the magnet , so that it was now difficult to see that the line was reversed .
In the case of Da the reversal became broader , though I could not be sure that it was less dark .
But the increase in the central intensity of Di accounts for the observed increase of resonance radiation .
Both the experiments of this section can readily be made with the volume resonance as well as with the superficial resonance .
It is merely necessary to work at a lower temperature . !
The effect on the volume resonance is the same as that on the superficial resonance\#151 ; decrease by magnetising weak flame , increase by magnetising strong flame .
S 5 .
Summary .
1 .
The centres emitting resonance radiation of sodium vapour excited by the D lines are not persistent enough to be carried along when the vapour is distilled away from the place of excitation .
This result is extraordinary , because it contrasts absolutely with the behaviour of sodium vapour excited electrically .
It also contrasts absolutely with the behaviour of mercury vapour , whether excited optically ( 2536 resonance radiation ) or electrically .
2 .
The resonance radiation of sodium cannot be seen through even a very dilute layer of sodium vapour placed in front of it\#151 ; a layer quite transparent to white light .
This explains why the spot of superficial resonance produced * Of course this discussion of the subject makes no pretensions to completeness , t See Dunoyer , loc. cit. \#166 ; Fluorescence and Resonance Radiation of Sodium Vapour .
395 on the wall of a glass bulb can only be seen from in front , when the light passes to the eye without traversing sodium vapour .
From the back it cannot be seen , as Dunoyer has observed .
3 .
The resonance radiation of sodium vapour is changed in intensity when the vapour is placed in a magnetic field .
If the exciting flame is weakly salted , the radiation diminishes with increasing field strength .
If the exciting flame is strongly salted , the radiation increases to a maximum and then diminishes again .
4 .
A change in intensity of resonance radiation can also be observed when the exciting flame is placed in the magnetic field .
In this case a weak flame gives diminished radiation in the field , while a strong flame gives increased radiation in the field .
5 .
All the facts summarised under 3 and 4 can be explained qualitatively and quantitatively , so far as the available data will go , by taking into account the known Zheman resolution of the D lines , and the observed width and structure of these lines as emitted by the flames used .
The latter data were obtained by observation with a concave grating of high resolution .
I have much pleasure in thanking Prof. A. Fowler , F.R.S. , and Mr. F. S. Phillips for help in making these observations with the grating .
|
rspa_1915_0030 | 0950-1207 | The absorption in lead of the \#x3B3;-rays emitted by radium and radium C. | 396 | 404 | 1,915 | 91 | Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character | H. Richardson, M. Sc.|Sir Ernest Rutherford, F. R. S. | article | 6.0.4 | http://dx.doi.org/10.1098/rspa.1915.0030 | en | rspa | 1,910 | 1,900 | 1,900 | 7 | 133 | 3,392 | http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1915_0030 | 10.1098/rspa.1915.0030 | null | null | null | Atomic Physics | 63.216176 | Tables | 22.3398 | Atomic Physics | [
9.794438362121582,
-78.09126281738281
] | 396 The Absorption in Lead of the y-Rays emitted by Radium B and , Radium C. By H. Richardson , M.Sc .
, Demonstrator in Physics , School of 'Technology , Manchester .
( Communicated by Sir Ernest Rutherford , F.R.S. Received April 3 , 1915 .
) In a previous paper by Rutherford* and the author attention has been drawn to the fact that the two types of 7-radiation emitted by radium B and radium C which are exponentially absorbed by aluminium both show irregular absorption curves when lead is used as the absorbing material .
The curve obtained for pure radium C was observed to fall far more rapidly than was to be expected from an exponential law of absorption , and was found to become exponential only after traversing a thickness of 1*5 cm .
of lead .
The absorption curve in lead of the 7-rays from radium B was obtained by taking the difference between the radium ( B + C ) and the radium C curves .
The results so obtained were not determined with very great accuracy , but they served to show that in this case , too , the absorption is not exponential , and that the absorption coefficient rapidly diminished from about / x = 11 ( cm."1 ) to / x = 2 ( cm.-1 ) .
The accuracy of the curves did not , however , permit of their complete analysis as in the case of those previously obtained for aluminium .
During the course of his work on characteristic radiations Barklaf has pointed out and investigated the anomalous effect on the absorption of a characteristic radiation by an element whose atomic weight is near to that of the element which emits the radiation .
His experiments were , however , confined to elements of comparatively low atomic weight .
As the atomic weights of radium B and radium C can only differ by a small amount , and as they have atomic numbersj differing only by unity , viz. , radium B = 82 and radium C = 83 , it seemed of importance to determine accurately the absorption curves in lead , and to examine whether any additional information can be obtained which may indicate whether the radiations emitted by radium B and radium C are characteristic of these elements and fall into the series given by Barkla .
Method of Experiment.\#151 ; It has been pointed out that the absorption curve for the radium B radiation was previously obtained as a difference curve by * Rutherford and Richardson , ' Phil. Mag. , ' vol. 25 , p. 722 ( 1913 ) .
t Barkla , ' Phil. Mag. , ' vol. 22 , p. 396 ( 1911 ) .
Rutherford and Andrade , 'Phil .
Mag. , ' vol. 27 , p. 854 ( 1914 ) .
Absorption of y-Rays .
finding first of all the curve using an a-ray tube as the active source , and by allowing for the effect due to the radium C. In order to obtain direct results it was thought better if possible to determine the curve using radium B itself as the source .
This is rather difficult owing to the rapid transformation of radium B into radium C. The ideal arrangement was therefore to obtain a source of pure radium B , and then to find several points on the absorption curve whilst the percentage of radium C present was small .
In order to do this it was necessary to have a source of pure radium B. This was obtained in the following manner : 200 millicuries of radium emanation were enclosed in a glass tube over mercury as shown in fig. 1 .
The whole was then allowed to remain for a period greater than four hours so that radioactive equilibrium was established .
The emanation was then pumped off , and the glass tube was washed with absolute alcohol in order to remove all traces of grease and emanation .
By this method one obtains on the glass a deposit of radium A , radium B , and radium C in equilibrium .
In order to remove the radium C some nickel filings were placed in the tube , which was then filled with boiling dilute hydrochloric acid .
The acid was then kept boiling for about 15 minutes .
Experiment* had previously shown that in such a case the radium C is deposited on the nickel , and that the separation is very efficient .
It was hoped that by this means the whole of the radium C would be completely removed .
Moreover , since the nickel was kept in the solution for 15 minutes the whole of the radium A had in that time become transformed into radium Br and consequently only pure radium B should remain in solution in the acid .
The solution was then quickly poured off on to a quartz plate and evaporated to dryness .
The time at which the acid was poured off was noted and in the calculations it was assumed that at that moment only pure radium B existed in the solution .
In order to determine how far the assumption was accurate it was only necessary to measure the growth of the radium C by measuring the rise of activity in the ordinary way through a thickness of 1*5 cm .
of lead .
This can then be compared with the theoretical rise curve as deduced from the theory of successive changes , by assuming the matter to be initially pure radium B. The results of several experiments showed a perfect agreement between the theoretical and actual rise curves and thus justified the assumption that the removal of the radium C by the nickel was quite complete .
In order to determine the absorption curves the apparatus and method already adopted and described in a previous paperf was used .
* Rutherford and Richardson , ' Phil. Mag. , ' vol. 25 , p. 722 ( 1913 ) .
t Rutherford and Richardson- ' Phil. Mag. , ' vol. 26 , p. 324 ( 1913 ) .
Mr. H. Richardson .
Absorption in Lead of the The absorption curve in lead for the radium C radiation was , first of all , carefully determined .
For this experiment a source of pure radium C on a nickel wire was used , the soft radiation excited in the nickel being cut out by a very thin sheet of lead .
The curve was obtained up to a thickness of 1-8 cm .
of lead , after which point the absorption was found to be exponential with an absorption coefficient / x = 05 ( cm.-1 ) , the value already obtained in previous experiments.* The curve , fig. 2 , shows the results obtained .
Thickness in mm. of lead .
The radium B absorption curve was next obtained by using the deposit of radium B prepared in the manner already indicated .
This curve was , of course , difficult to determine owing to the variation of the amount of radium C present from moment to moment , and also owing to the rapid decay of the radium B itself .
The actual curve was obtained in the following manner .
The total ionisation was measured for the various thicknesses of lead foil required , in the usual manner .
During the course of the experiments several readings were taken of the ionisation through a thickness of 2 cm .
of lead , that is , a thickness sufficiently great to cut out entirely the effect due to the radium B. By this means it was possible to calculate the effect due to the radium C present at any time during the experiment , and hence , from fig. 2 , * Rutherford and Richardson , 'Phil .
Mag./ vol. 25 , p. 722 ( 1913 ) .
y-Rays emitted , by Radium B and Radium C. 399 the effect corresponding to the particular thickness of the absorber being used .
The difference between this and the observed ionisation gives the true effect due to the radium B alone .
All that is then necessary is to correct the readings for the decay of the radium B itself .
In this manner the absorption curve shown in fig. 3 was obtained .
This experiment was 0 15 30 4-5 60 75 90 Thickness in mm. of lead .
repeated several times , the agreement between the separate experiments being very good .
* In order to examine whether the absorption curve for the radium B radiation could be accurately obtained by using an a-ray tube as source and allowing for the effect of the radium C , the curve was also again carefully determined .
The following Table , which gives the results actually obtained by the two methods , shows that the agreement is well within the limits of experimental error .
Analysis of the Radium B Absorption Curve.\#151 ; The curves obtained were analysed in the manner already described in previous papers ( loc. cit. ) .
The results showed that the radium B radiation consists of three types which are exponentially absorbed .
The hardest type has an absorption coefficient p = 1*5 ( cm.-1 ) .
The ionisation ( measured with an electroscope filled with methyl iodide vapour ) due to this type comprises about 12 per cent , of the Mr. H. Richardson .
Absorption in Lead of the Table I._Absorption in Lead of the 7-Bays of Radium B. Thickness of lead .
Radium B as source .
o-ray tube as source .
mm. 0*1 100 100 0*2 85 *7 82 -0 0*4 63 1 62 *7 0-7 47 *9 47 *1 1 *09 34 *4 35 *4 2T3 26 *2 22 *8 3*06 16*5 16 *3 4 15 9 *0 .
10 -8 6-12 6*2 6*2 9*18 3*5 3*6 total ionisation under the experimental conditions .
The two remaining types have coefficients / x== 6*0 ( cm.-1 ) and ya = 46 ( cm."1 ) .
About 26 per cent , of the total ionisation is due to the former type of radiation and 62 per cent , to the latter .
Examination of the Radium C Absorption Curve.\#151 ; Attention has already been drawn to the fact that the absorption curve for the radium C 7-radiation is not exponential from the beginning , but no analysis had so far been attempted .
The analysis , performed as in the previous cases , of the curves obtained showed that , under the experimental conditions , about 85 per cent , of the total ionisation produced by radium C is due to the very penetrating type for which jx = 0*5 ( cm.-1 ) .
The absorption curve of the remaining 15 per cent , of the radiation seemed to be very similar in character to that obtained for radium B. The respective curves are shown in fig. 4 .
The agreement is well within the errors of experiment and gives conclusive evidence that these radiations are indistinguishable by absorption methods .
Discussion of the Results.\#151 ; The examination of the absorption curves in lead thus shows that radium B and radium C both emit three types of radiation which are exponentially absorbed , in addition to the very penetrating type of radiation emitted by the latter body .
These results are quite in agreement with those recently obtained by Rutherford and Andrade* in their determination of the spectrum of the penetrating 7-rays from radium B and radium C. They concluded that some of the lines in the spectrum were probably close doubles , the lines being considerably wider than would be the case for a radiation of single frequency .
The results thus appeared to indicate that part of the spectrum of radium B is not very different from that of radium C. Of course such a small difference of frequency in the radiations as * Rutherford and Andrade , c Phil. Mag.,5 vol. 28 , p. 264 ( 1914 ) .
y-Rays emitted by Radium B and , Radium C. indicated by the above experiments would be difficult to detect by the ordinary absorption methods .
It will be observed that the radiations emitted by radium B evidently correspond to that which was previously thought to consist of one single type 0 *6 12 1*8 2*4 Thickness in mm. of lead .
O Radium B\#151 ; absorption curve in lead ; \lt ; \#163 ; Radium C\#151 ; absorption curve in lead ( soft type only ) .
and for which / x = 0'51 ( cm.-1 ) in aluminium .
Moreover , from the results given previously ( loc. cit.)7 it was assumed that the radiation from radium C consisted of the very penetrating type only , which has the absorption coefficient P = 0T15 ( cm."1 ) in aluminium .
It was , however , pointed out that the presence of a few per cent , of the fx = 0*51 type of radiation mixed with the more penetrating type would be very difficult to detect .
Owing , however , to the much more rapid absorption of this particular radiation by lead it is easy to demonstrate that it actually does exist .
It should be observed that nope of the radiations whose absorption in lead VOL. XCI.\#151 ; A. 2 I Mr. H. Richardson .
Absorption in Lead of the has been investigated correspond with that emitted by radium B* and radium Cf and for which ya = 40 ( cm.-1 ) in aluminium .
The latter radiation would probably have an absorption coefficient of the order 1000 , in lead , and hence would be entirely cut out by the thinnest absorbing layers used in these experiments .
The examination of the absorption in lead of this radiation has not yet been completed on account of the impossibility of obtaining absorbing layers of lead sufficiently uniform and thin .
Characteristic Radiations of Radium B and Radium C.\#151 ; Evidence has already been given by KutherfordJ which indicated that the penetrating radiation emitted by radium C might be the K series characteristic radiation of this element .
The more recent results of Butlierford and Andrade have , however , led them to conclude that the 7-radiation from radium B is the K series characteristic of this element , whilst the very penetrating radium C radiation belongs to some higher series not before observed .
It seemed of importance therefore to examine the absorption of these radiations by elements of atomic weight very nearly the same as that of radium C in order to find whether any anomaly in the absorption occurs such as was previously found by Barkla for the elements of low atomic weight .
It will be remembered that the absorption coefficient of the radiation characteristic of an element is abnormally high for an absorber of atomic number slightly less than that of the element emitting the radiation .
It would appear therefore that if the very penetrating radiation emitted by radium C is the K series characteristic of this element then it should be more readily absorbed in mercury or gold than in lead .
It was not found practicable to determine complete absorption curves in the elements of high atomic weight , owing to the difficulty of obtaining large thicknesses of these materials , but comparative values of the absorption coefficients have been determined under the same conditions of experiment .
Care was of course taken in every case to cut out all the radium B radiation by inserting a suitable thickness of lead .
The results obtained are given in the following Table .
Table II .
Absorber .
Atomic number .
n/ d. Uranium 92 0 *0475 Lead 82 0 *0435 Mercury 80 0 0416 Gold 79 0 *0426 Barium 56 0 *0371 * Rutherford and Richardson , ' Phil. Mag. , ' vol. 25 , p. 722 ( 1913 ) .
t Richardson , ' Roy .
Soc. Proc. , ' A , vol. 90 ( 1914 ) .
* J Rutherford , ' Phil. Mag. , ' vol. 24 , p. 453 ( 1912 ) .
y-Rays emitted by Radium B and Radium C. 403 It will be seen that no decided change in the absorption coefficient can be detected for the absorbers of different atomic number .
The examination of the absorption curves for the radiation emitted by radium B was then undertaken , the elements uranium , lead , and mercury being taken as absorbers .
The absorbing sheets had to be in the form of very thin layers of the oxides , and hence the curves could not be obtained with very great accuracy .
Moreover , the actual curves could not be analysed owing to the impossibility , under the experimental conditions , of finding the complete curve for each absorber .
The results actually obtained are compared in the following Table :\#151 ; .
Table III .
Weight per unit area of lead oxide .
Ionisa- tion .
Weight per unit area of uranium oxide .
Ionisa- tion .
Weight per unit area of lead .
Ionisa- tion .
Weight per unit area of mercuric oxide .
Ionisa- tion .
grm. 0*238 0*461 0*790 1 *237 1*689 2*411 4*100 5*337 6*127 6*588 100 89 *7 78 *9 72 *5 68 *6 63 *8 54 *4 49 *5 46 *7 44 *6 grm. 0*233 0*453 0*785 1 *239 1 *705 2 *404 4*109 5*348 6*133 6*586 100 87 *2 75 *0 69 *4 65 *9 62 *6 51 *9 47*0 43 *9 42 *6 grm. 0 *227 0*454 0*794 1 *236 1 *690 2*415 100 87 *5 76 *0 70 *9 62 *4 58 *6 grm. 0*226 0*448 0 *806 1 *262 1 *700 2 *962 100 87 *8 73 *7 69 *4 62 -0 51 *4 It will be seen from these results that the curves obtained are almost identical , and hence it seems certain that in the case of the radium B radiation , too , no rapid change in the value of the absorption coefficient takes place .
If the radiations emitted by radium B and radium C are characteristic of these elements then it would appear that the characteristic radiations of the elements of high atomic weight do not behave as regards absorption in quite the same way as those emitted by elements of lower atomic weight .
The direct excitation of the characteristic radiations of the elements of high atomic weight has not , so far , been obtained .
If this could be undertaken and the absorption of the radiations then examined the results should give much information on this subject .
Summary .
1 .
The absorption curves in lead of the radiations emitted by radium B and radium C have been determined and analysed .
2 .
In addition to the penetrating type of radiation for which yu = 0*5 ( cm."1 ) Absorption of y-Rays .
in lead , radium C has been found to emit soft types for which ^ = 46 , / x = 6*0 , and jul = 1*5 , and which are practically absorbed by 1*5 cm .
of lead .
3 .
The analysis of the radium B absorption curve shows that in addition to the radiation / / , = 40 in aluminium , the rays emitted consist of three types for which = 46 , ya = 6*0 , and / / , = 1*5 for lead .
The close similarity of this latter radiation with that of the soft portion emitted by radium 0 , already observed by Rutherford and Andrade , has been established .
4 .
The absorption of the radiations in different elements has been examined and the bearing of the results discussed .
No evidence of anomalous absorption has been found in the case of the penetrating radiations .
I I have much pleasure in thanking Sir E. Rutherford for the constant help and valuable advice which he has given me throughout the course of these experiments .
|
rspa_1915_0031 | 0950-1207 | Local difference of pressure near an obstacle in oscillating water. | 405 | 410 | 1,915 | 91 | Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character | Mrs. Hertha Ayrton.|Lord Rayleigh, O. M., F. R. S. | article | 6.0.4 | http://dx.doi.org/10.1098/rspa.1915.0031 | en | rspa | 1,910 | 1,900 | 1,900 | 5 | 131 | 2,847 | http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1915_0031 | 10.1098/rspa.1915.0031 | null | null | null | Agriculture | 43.812474 | Fluid Dynamics | 20.034381 | Agriculture | [
-0.6913609504699707,
-27.14669418334961
] | 405 s/ ' ^Vecr- ' cr/ r. Odstcre^e r/ r. Oser^\#171 ; tr-r^ I^crke^ .
l^Irs .
ULirruX ^virro^ . !
( Oonimunieatsd b^ Lord Ita^leigb , O.^I .
, L.L.8 .
Iteeeived Lebruar^ 22 , 1916 .
) kkl^lLS 4 ^.Kv 5.^ In a kormer paper* I sbowed that when a barrier dts tigbtl^ against tbs sides and across tbs bottoin ok a vessel ok oscillating water ( 1 ) a vortex korms against saob side ok tbs barrier in turn as it becomes tbs Iss sids ; ( 2 ) this vortex nsvsr korms while tbs water is attaining to tbs insan level , but on^ while it is tailing below and rising above that level .
I suggested that snob vortioes were due to tbs conjunction ok tbs inain strearn bowing over the barrier with opposing looal streams oreated b/ looal diberences ok pressure set up in the nsigbbourbood ok tbs barrier b^ tbs oscillating water .
Exception was taken to this explanation , and also , later , to experiments mads with a box partially voversd with tbin gutta peroba diapbragms , kor the purpose ok proving the kormation ok the local dikkerenoes ok pressure alluded to .
lbs oldest ok the present paper is to give an aeoount ok kurtber experiments carried out kor this same purpose , with pressure indicators which are kree krom the objection urged against tbs diapbragms , vir .
: that the^ tbemselves migbt cause variations in the distribution ok pressure .
Lig .
1 sbows the korm ok pressure indicator I now employ , magniked .
is a glass tubs ok inner diameter about ^ inch and lengtb about A inch , in which a cork 0 is kitted , .
bolding a ver^ small glass tubs D , tbrougb which a stem ^ ok grapbite passes , carrying two small cork beads L and I ' .
Ibe stem and bea , ds ok the plunder LI ' are so proportioned that the whols either just boats or just kails to boat in water , which ensures its moving to and kro tbrougb tbs carrier tubs I ) with the least possible kriction , when the whols pressure indicator is in position in the submerged obstacle .
Lines D is so small that no current can pass tbrougb it , an^ movement ok the submerged * " lbs Origin and Orovtk ok Lipplo-mark , " Loo .
I'roe .
, ' vol. 64 , pp. 290 , 291 ( 1910 ) .
V0Q .
XOI.\#151 ; X. .
2 L I'lO .
1.\#151 ; Tessin'S Indieator , Mrs. 8 .
priori .
DrM-'e-rees 0/ plunger in the direction I'D must indicate a. greater pressure OQ I ' than on L , and in the contrary direction a greater pressure on D than OQ D. 0/ t/ sr-r.^ ^essr-^s ^^ocr^o/ 'S .
IVith these pressure indicators the various dikkerences ok pressure set up in oscillating v^ater can he explored , hut I shall tiers conkne m^selk to those which arise close to a suhmerged obstacle .
Iu my koriuer paper* each halk oscillation , or swing ok tire water iu oue direction , was called a swing .
Ike time during which the water approaches the ineau level position was called the kirst part ok the swing , and that during which it departs krona the level was called the second part ok the swing .
Using the sains tsrins , the suggestions inade on pp. 292-294 as to the dikkerences ok pressure set up h^ the presence ok an ohstacle in oscillating water ina^ he thus expressed : ( 1 ) During the 6rst part ok an^ swing the pressure at an^ point in the lee ok a suhnaerged ohstacle is less than the pressure at an^ point\#151 ; however near it\#151 ; on its suinlnit .
( 2 ) During the second part ok an^ swing the ahove applies still to the upper portion ok the lee side , hut over the lower portion the case is reversed , and the pressure at an^ point there is than the pressure at any point on the summit ok the ohstacle .
In proving these conclusions h^ means ok pressure indicators , the ohstacle used is a hlock ok wood with vertical sides , padded at the ends and underneath to enahle it to he pressed tightly against the sides and hottom ok the tank , and hollowed out in the part where the pressure indicators are placed .
Dig. 2 shows a vertical section in perspective ok the hollow portion ok the hlock and ok the pressure indicators , DD , which are held in position h^ tightly kitting hored corks , D , X. The circular hole 8 , alrout ^ inch in diameter , is the sole means ok communication hetween the water in the cavity and that outside .
Through this hole the pressure ok the water passing over the ohstacle can he communicated to Ih , D ?
, the inner heads ok the plungers ok the pressure indicators , hut no oscillation can he set up in the cavity through so small a hole , and on^ the ver^ small yuantit^ ok water that is displaced h^ the graphite rods in their movements to and kro passes in and out .
( Ireat care has to he taken to rid this ohstacle and pressure indicators ok all air hekore this^ are placed in position , as the smallest air * ^,06 .
or'r .
, pp. 287 , 292 .
duddle IQ one ok the glass tubes ML/ impels the motion ok the plunger , lirsd tbs pressure indicators were completely enclosed in the obstacle , all except the outer edges ok their tubes , which were Lusb with its right-band side , instead ok protruding as in Lg .
2 .
8bort lengtbs ok borsebair driven into the beads Li , Ls ( 6g .
2 ) , parallel to the axes ok tbs tubes , then enabled tbs movements ok the plungers to be observed , ^s , bow ever , it was sound that exactly the same results were obtained when the tubes protruded a quarter ok an inch or so beyond the obstacle , the more convenient metbod sbown in bg .
2 was adopted .
Lbe meaning ok an/ movements ok the plungers , when the water is oscillated , is quite clear .
Lbe on/ variable pressures acting on the plungers are the pressure at HI , transmitted tbrougb the water in the cavit/ to Li , L ?
, and the pressures at Li , L ? .
Ik botb plungers are pressed outwards it sbows that the pressure is greater at HI than that either at Li or at Ls ; ik botb are pressed in , the reverse is the case .
Ik one is in and the other out , the pressure at HI is less than the external pressure on the List and greater than that on the second .
Lig .
3 ( Llate 4 ) is a pbotograpb ok the obstacle with the pressure indicators in position and the water at rest .
Lbe obstacle was well to the lekt ok the middle ok the trougb , the ends ok which , as well as the surkace ok the water , are out ok the picture .
In order that the direction ok 6ow ok the water at various points migbt be recorded , the three stream indicators made ok ravelled silk tipped with cork were used .
Lbe one over the obstacle was mounted on a ver/ long beadiess pin so as to beep it well awa/ krom the local disturbances near the obstacle .
Lbe one on the door ok the trongb close to the obstacle was to the right ok the tubular indicator , and the kurtber one was in a line with it .
Lbe bole ok communication with the cavit/ marked HI in bg .
2 can be seen sligbtlv to the right ok the upper tubular indicator , ^s the indicators are placed , the/ are evidentl/ in the lee ok the obstacle during a swing ok the water krom lekt to right , and on its weatber side during one krom right to lekt .
ok Obstacle kitted vitb pressure Indicators .
2x2 Nrs .
8 .
^.vrton .
DrFe-'enoes 0/ Lo \#171 ; ^ ^'M/ 'e-ress 0/ ^essrr-'e as ^6ssr^-6 / -reiroa^o- 's .
I'igs .
4 , 5 , and 6 are instantaneous pbotograpbs taken while tbs water ^as being oscillated\#151 ; 6g .
4 during the Lrst part ok a swing krom lekt to ^ riZkt , 6g .
5 during the second part ok one in tbs sains direction ; and 6g .
8 ^vbile the water swung krona right to lekt .
Hie stream indioators in Lg .
4 sbow that during this klrst part ok a swing the whole ok the water was moving krom lekt to right\#151 ; that eloss to the lee side ok the obstacle as well as that over it and that at some distanoe awa^ .
Ibe plungers ok the pressure indioators are botb puslied out as kar as the^ will go , sbowing that the pressure at saoli ok the points I'l , ^2 ( bg .
2 ) , on the lee side ok this obstacle was less tlian that at the point lVl on top .
Ibis is entirely in aooordanos withr the kirst suggestion made in m^ kormer paper and restated on p. 406 .
Idg .
5 was taken during this seeond part ok a swing krom lekt to right .
lbs distribution ok pressure kormerl^ suggested , and given again on p. 406 , is here also ' instilled .
I'or while the upper plunger still remains kull^ out , the lower is pressed liome , sbowing that during this ssoond part ok a swing , altbougb the pressure on the upper part ok the lee side ok the obstacle remains less tlian that on top , the pressure on its lower part is greater tlian that on top .
Hot on^ tliis , liowever , but the stream indioators point to tbs kaot that while the main stream oontinned to llow krom lekt to right , tbere was a current in tbs opposite direction close to the obstacle ; kor the stream indicator close to the block bas a distinct trend krom right to lekt , altbougb tbs otbsr two are bent right down in the opposite direction .
Here , then , is evidence , not on^ ok the suggested ditkerenoes ok pressure , but also ok the kaot that the obange in the direction ok pressure on the lower part ok the lee side is tbs result ok no general turning movement on the part ok the lower water , but is purely local , and is due to the presence ok the obstacle .
Idg .
6 was taken in dbe course ok a swing ok the water krom right to lekt , and sbows , as was to be expected , that the pressure at an^ point on the weatber side ok an obstacle is greater than that at a point on top .
1 ?
o return to the conditions in tbs lee ok the obstacle .
In m^ paper on " lbs Origin and Orowtb ok Hippie-mark " I remarked , " tbs second condition kor tbs kormation ok a ripple vortex is that tbs resultant gravity pressure along the ridge on its lee side sball tend upwards."* ^Vitb the obstacle having perkeotl^ vertical sides with whiob tbs above experiments were made , tbere was , ok course , no vertical component in the pressure ok the water on tbs sides , but tbs direction ok the vertical component ok the pressure ok * ^oo .
or'F .
, p. 294 .
r'-r Oser'/ ^tr-r^ Il^cr^er ' .
409 lire evader close to the side was easily tested b^ another experiment .
I embedded a pressure indicator in a 8o1id obstacle 9.8 sbown in section in LZ .
7 , and , in order to Lavs a psrkectl^ kair test , I U8sd sometimes a plunger having a sligbtl^ greater specibc gravity than water aQd sometimes 0Q6 with 1s88 .
His rs8ult was the same in eacb ease , and was such a8 was to be expected krom tbs experiments with bori^ontal indicators\#151 ; during tbs Lrst part ok a swing krom Iskt to right the plunger was pressed downwards , during the sseovd part it was raised .
It is vlear that these local dibsrences ok pressure , in water that would otherwise be at rest iu tbs lee ok a barrier , roust eause loeal eurreuts tbere\#151 ; downwards during tbs brst part ok a swing and upwards during the ssooud .
During the brst part ok a swing , tberekore , there is a loeal pressure dikkerence which ereatss the eouditiou necessary to give rise to sueli ^ets as I Lavs observed b^ placing a grain ok permanganate ok potasli ou tbs suiuruit ok an obstacle.* During tbs seeoud part ok tbs swing tbs pressure iudioators sbow that tbere uiust be a looal eurrsut iu the lee ok tbs obstavle , soiuewbere below the surkaos , whieb uioves iu opposition to the roain streani tbv obstaole and Iwo ourrents opposing one another in this wa^ are all that is needed to vauss sueb a vortex as was made maniksst in the lee ok tbs obstacle b^ the grain ok permanganate ok potasb* during the second part ok the swing .
I 'm .
7.\#151 ; Obstaels ^vitb Vsrtios.1 krsssurs In-dieator kor lestbig Vertical pressure .
6i0-re^sro-r .
I subniit , tberskore , that these pressure indicators akkord conclusive prook ok tbs trutb ok tbs kollowing suggestions , that I brst made in 1904 , in explanation ok the ^et and vortex that I bad observed in tbs lee ok a submerged obstacle under oscillating water:\#151 ; 1 .
^Vben the water is approacbing tbs inean level tbers is a diininution ok pressure , or partial vacuum , created in tbs lee ok the obstacle , ( krook in Lg .
4 .
) 2 .
V^ben the water is departing kroni tbs inean level tbs diminution ok pressure continues bigb up on tbs lee side , but over tbs lower part tbsrs is a pressure in tbs opposite direction to that ok tbs main stream , ( krook in tig .
5 .
) * -^oo .
or'6 .
, p. 294 .
Mr. O. ^Valksr .
3 .
Ibe let in tbs Lrst park ok a swing is due to the local current created dv the local ditterencs ok pressure ; the vortex in the second part ok rbe 8^vinS i3 due to tire conjunction ok tde main stream with tbs opposing local eurrent 86t up b^ tbs local xre88ure diberence .
Mv warm tbanks are due to Mr. Madinne^ kor the 2eal and ability be displaced in taking tbs instantaneous pbotograxbs from which bgs .
3-6 are reproduced .
VL86ir , iriI0^ Op pb^1L8 .
I'iZ .
3.\#151 ; Obstacle vitb pressure and 8trcain Indicators in position in land , ^vitb tbs ^Vatcr at rest .
I'iZ .
4.\#151 ; 8wiug krom I^skt to ItiZIit\#151 ; I'irst park .
I'is .
5.\#151 ; 8wing krorn lbokt to piZIik\#151 ; 8ccond part .
piZ .
6.\#151 ; 8wing krorn pigdl , to bekk .
OL0K6L 'W .
HV^LLK , ^.It .
O.Lc .
, M.^ .
, Ht.8 .
, kormerl^ I'ellow ok lrinit^ Oollege , Oambridge .
( Iteceived Marcb 27 , 1915 .
) Hie possible korms ok distribution ok a mass ok gaseous material under the inkluence ok it8 own gravitation are ok considerable intere8t in the nebular tbeor^ .
lire law ok density which it appears ino8t reasonable to a88uine i8 Louie 's kaw , in which tbs pre88ure i8 proportional to the density , unle88 the pre88ure becomes 80 great that the material begins to re8eml)l6 an incompressible substance .
^Itbougb it i8 unlikely that the temperature i8 unikorm tdrougb-out , 8till tbs 8olution under tlii8 re8triction would lie ok value as a 8tep in tbs direction ok greater knowledge a8 regard poeeiliilitiee in agronomical pbenomsna .
Ibe equations can be kormed and lead to a differential equation kor the 8urkacc8 ok sexual density .
lbis equation is not linear , and in the three-dimensional ca86 little progre88 to a general solution bas been made .
In tbs two-dimen8ional case , liowever , considerable progreee can de made .
^ number ok ^ears ago I obtained the exact solution ok the statical case ok s^mmetr^ about the origin .
Ltiortlv akter I kound that pockels bad obtained the complete solution ok the statical two-dimensional equation , and
|
rspa_1915_0032 | 0950-1207 | Some problems illustrating the forms of nebul\#x153;. | 410 | 420 | 1,915 | 91 | Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character | George W. Walker, A. R. C. Sc., M. A., F. R. S. | article | 6.0.4 | http://dx.doi.org/10.1098/rspa.1915.0032 | en | rspa | 1,910 | 1,900 | 1,900 | 3 | 91 | 2,172 | http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1915_0032 | 10.1098/rspa.1915.0032 | null | null | null | Fluid Dynamics | 53.062359 | Tables | 27.275337 | Fluid Dynamics | [
48.924339294433594,
-24.976224899291992
] | ]\gt ; DESCRIPTION OF PLATES .
Water at rest .
Fig. 3.\mdash ; Obstacle with Pressure and Stream Indicators in Position in Tank , with the Fig. 4.\mdash ; Swing from Left to Right\mdash ; First Part .
Fig. 5.\mdash ; Swing from Left to Right\mdash ; Second Part .
Fig. 6.\mdash ; Swing from Right to Left .
Some Problems the Forms of Nebnloe .
By GEOBGE W. WALKER , A.R.C.Sc .
, , F.B.S. , formerly Fellow of Trinity College , Cambridge .
( Received March 27 , 1915 .
) The possible forms of distribution of a mass of gaseous material under the influence of its own gravitation are of considerable interest in the nebular theory .
The law of density which it appears most reasonable to assume is Boyle 's Law , in which the pressure is proportional to the density , unless the pressure becomes so great that the material begins to resemble an incompressible substance .
Althougb it is unlikely that the temperature is uniform throughout , still the solution under this restriction would be of value as a step in the direction of greater knowledge as ards possibilities in astronomical phenomena .
The equations be formed and lead to a differential equation for the surfaces of equal density .
This equation is not linear , and in the threedimensional case little progress to a general solution has been made .
In the two-dimensional case , however , considerable progress be made .
A number of years ago I obtained the exact solution of the statical case of symmetry about the origin .
Shortly after I found that Pockels had obtained the complete solution of the statical two-dimensional equation , and particular cases and have arrived at results indicating such a close analogy with actual astronomical forms that I venture to hope they may be of interest as gesting types that may be expected in three dimensions .
We begin by consideration of the fundamental equations .
Let be the gravitational potential , the gravitational constant , the pressure at any point of the gas , the density at any point of the gas , , the Cartesian co-ordinates of any point .
The hydrostatic equations of equilibrium are and the potential must further the equation If , where is a constant , we get as an constant , or Hence This is the equation of which Pockels has obtained the solution in terms of two arbitrary functions as follows .
As is the solution of , then the solution for and is We require to put this in a which gives real positive values to , and I find that this can be secured by taking Otherwise , if and are conjugate functions , so that , we get and hence of interest to pure mathematicians to investigate this point , just as it would be of value to applied mathematicians to know the most eneral form .
I\mdash ; If we take we This is the most general case of circular sy1nmetry .
We note that when the density becomes infinite at the elsewhere finite , and vanishes at co .
When the density is finite at the origin , and elsewhere is finite , at co .
When the density is zero at the origin , rises to a finite maximum .
and then diminishes and vanishes at infinity .
Writing the equation in the form the curves in fig. 1 show as a function of , for the four special values , and 2 ; is still at our disposal while is determined when and are fixed .
ring nebula .
Case II\mdash ; Take we get The surfaces of equal density are given by The curve , fig. 2 , shows the particular surface drawn to a scale of 10 .
This case is somewhat peculiar .
Starting with when , the curve for positive values of proceeds as shown , continually approaching the origin by a succession of diminishing spirals .
The locus is , however , symmetrical about .
If now we proceed to draw another surface of different density it would be found to cross the original curve at a succession of points for which .
This would mean that at such points two densities are possible , and we cannot admit this .
We must , therefore , stop the curve at the nodal point , and then the complete series of curves of equal density form a series of non-intersecting curves of this rem.arkable researches of Darwin , Poincare , and Jeans .
Case llI.\mdash ; Let us take the elliptic co-ordinate transformation , and let Then we get sin2 .
Thus the surfaces of equal density may be written in the form For , we get Fig. 3 shows the curves obtained for , 1 , 2 .
The density falls off to zero towards infinity , while for values the locus breaks up into two oval curves about and , which are the foci of the original ellipses in the transformation .
and are singularities at which would be infinite .
The general character of the loci is not altered by giving some finite value .
For comparison fig. 4 shows on the same scale the result of putting .
The equation is and the curve drawn is for is seen to be rather flatter than the corresponding curve for This case then , as a whole , has some analogy in the case of a nebula with two fundamental equal nuclei .
: these three cases are sufficient to indicate the generality of the method , and [ the remarkable interest of the forms that can be obtained .
I pass to the consideration of an important related problem .
The material of an actual nebula may be moving and not at rest , and in particular it may be rotating .
As the rotation , if it exists at all , is very slow , the divergence from the statical equilibrium in such a case would be extremely small , so that the statical solutions are themselves of value .
It is , however , of interest to know what the effect of motion may be .
The simplest case we can consider is the final state in which the material rotates about an axis like a rigid body , with steady angular velocity There the problem reduces to a statical one , when we take axes rotating with the material and add to the gravitational forces the centrifugal effect .
In case of a gas such a rotation , however small , can hardly be expected to extend indefinitely , and we should rather expect the motion to fall off and finally cease at a great distance .
While keeping this in view , it is not without interest to examine what effect such an imposed uniform rotation would have .
Mr. Jeans*has referred to this problem , but without giving details .
Some of my results are in agreement with his conclusions and others apparently diverge .
If the components of velocity are and , and we neglect viscosity , the equations for a steady motion referred to fixed axes 'Phil .
Trans vol. 213 , p. 462 ( 1914 ) .
Mr. G. .
Walker .
In the case of , where is a function of where is a function of only .
' The equations then reduce to If , we get the case of body rotation , and If , we get an " " irrotational\ldquo ; motion , and In the latter case the velocity falls off as increases but is infinite at the origin .
We might make any function of ; and among these we may select one , e.g. , which makes the velocity zero at the origin and also zero at great distances .
But such cases are not steady and the influence of viscosity would arise .
We cannot , in general , integrate in finite terms the equation ' but if suppose so small that differs from its value in the statical case by a small quantity we have approximately while Let , and , then the equation may be transformed to Now the equation has a solution A Hence the equation may be written* and the particular integral which we require is *Cf .
Boole , ' Differential Equations , ' p. 205 .
roblems Illustrating tVeor m. buloe .
417 In the case this gives for \ldquo ; where These curves are shown to scale in figs. 5 and 6 , and we note that in both cases z when , is everywhere positive , and finally becomes infinite and proportional to when is reat .
The general effect of the rotation is then to increase the density from what would obtain in the statical case , and by increasing proportion as increases from the origin , but even if it were permissible to pass to large values of the density would still diminish to zero .
We cannot , however , extend our #$ value and to move the point of maximum density further out with increasing ; but there is no indication of a tendency to throw off the outer layers .
This latter result disagrees with the general conclusion stated by Jeans .
cit. cmte ) .
For " " irrotational\ldquo ; motion and the particular integral we require is where In this case is egative and infinite when , rises to a maximum positiye value , and again declines to a negative and infi1lite value as becomes indefinitely great .
As before , we cannot extend our solution to reat values of , but we may say that the tendency of the motion is to make the distribution hollow near origin , to increase the concentration towards the maxirnum density at a finite value of and finally to tend to throw off the outer layers when .
becomes great .
This latter conclusion is in agreement with Jeans .
When we pass to other cases such as Cases II and III , where the original distribution of density is not symmetrical about the origin , it is rather difficult to think of any steady motion other than uniform rotation which would leave the distribution in anything like a permanent form .
We must , therefore , confine our attention at present to this case , artificial though it may be .
.or , if In Case II of the distribution of pear-shaped character I find that the .solution will have to be obtained by a somewhat complicated series , and as I have not yet gone very far with it I pass to Case III , which can be integrated in finite terms .
We had as the statical solution Hence the equation we have to solve is - or , on changing to elliptic co-ordinates , we get .
The solution is , where and are functions of only , and satisfy and respectively .
A solution for , when , is .
Hence the particular integral is A solution for , when , is .
Hence the particular is - taJlh 2 This function is - at , increases and becomes positive as we increase , and becomes infinite and oive with as becomes infinite .
Again , along the axis of , so that sech \mdash ; log cosh At the origin this function is - , it increases as increases and becomes positive , finally being infinite and positive with as becomes infinite .
The effect of the rotation is then .
to diminish the density near the origin and to increase it at greater distances , but there is no clear tendency to throw off the outer layers , since the function becomes positive and infinite and not negative and infinite .
This is , again , in apparent conflict with Jeans ' conclusion .
It would thus appear from the cases considered here that a finite boundary of a gaseous mass is not to be looked for as a consequence of rigid body rotation , but rather as a consequence of some other type of motion in which viscosity may play a part .
My sincere thanks due to Sir Joseph Larmor for kindly criticism and advice .
[ Note added April , 1915.\mdash ; It has been pointed out to me that in Case II discontinuous the line .
Hence this is a line of singularities .
In accordance with the principle already stated we must , therefore , suppose this lirle to be occupied by so.lid matter of the proper density at any point , determined by the change of in crossiIJg this line .
Theoretically this distribution would extend indefinitely , but practically the density of solid matter required at any point on becomes very small as the distance from the origin increases .
]
|
rspa_1915_0033 | 0950-1207 | On the application of interference methods to the study to the study of the origin of certain spectrum lines. | 421 | 431 | 1,915 | 91 | Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character | Thomas R. Merton, B. Sc. (Oxon).|A. Fowler, F. R. S. | article | 6.0.4 | http://dx.doi.org/10.1098/rspa.1915.0033 | en | rspa | 1,910 | 1,900 | 1,900 | 2 | 163 | 4,533 | http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1915_0033 | 10.1098/rspa.1915.0033 | null | null | null | Atomic Physics | 63.756232 | Tables | 15.532253 | Atomic Physics | [
15.348159790039062,
-51.38591384887695
] | ]\gt ; the Application of In Methods to the Study of the Origin of Certain Spectrum Lines .
By THOMAS R. MERTON , B.Sc. ( Oxon .
) , Lecturer in Spectroscopy at University of London , King 's College .
( Communicated by A. Fowler , F.R.S. Received May 4 , 1915 .
) Introductory .
In recent years , yreat progress has been made in the study of the nature of spectra and of spectral series , but it may be said that very little is yet known as to the nature of the luminous particles from which different spectrum lines originate .
It is generally supposed that band spectra are in some way due to molecules , whilst series spectra are usually associated with the atom .
Enhanced lines were for many years supposed to be due to proto-elements , or simplified forms of the chemical atom , a view which has recently to some extent fallen into discredit .
The evidence for all these hypotheses is of a circumstantial nature , and very little definite evidence as to the nature of the luminous particles is available .
In their recent important researches , Buisson and have opened up a new method of attacking the problem .
The method adopted by these investigators consists in measuring the limiting order of interference at which fringes can be observed for different radiations .
The limiting order of interference depends on the widths of the spectrum lines , from which certain deductions may be made with regard to the temperature of the sourGe of the radiations , and the masses of the particles which are concerned in their production .
The theory of the method has recently been discussed by Lord and by Schonrock .
The chief circumstance which need be considered as the widths of spectrum lines produced in ases at low pressures is the Doppler effect due to the motion of luminous particles in the line of sight .
Ths researches of MichelsonS have shown that at higher pressures a broadening of the lines occurs , this broadening being attributed to disturbances caused by collisions between the luminous particles , but that at pressures below one thousandth of an atmosphere this cause of broadening may be considered negligible .
'Journ .
de Physique , ' vol. 2 , p. 442 1912 ) .
'Phil .
Mag vol. 170 , p. 274 ( 1915 ) .
'Ann .
der Physik , ' vol. , p. 995 ( 1906 ) .
S 'Phil .
Mag vol. 34 , p. 280 ( 1892 ) ; 'Astrophys .
Journ vol. 3 , p. 251 ( 1896 ) .
VOL. XCI.\mdash ; A. 2 onstant Kgiven bayleigh ( the inert gases , the validity of the formula has been experimentally proved by Buisson and Fabry ( loc. cit and in the case of sodium by Schonrock cit. ) on the assumption that the radiation inates in the sodium atom .
We may now consider more exactly the conclusions which may be drawn from a measurement of the limiting order of interference .
If we suppose that at low pressures ffie only circumstance which can possibly influence the width of the lines is the Doppler effect considered in the theory , it is evident that if the temperature of the source is known , the masses of the luminous particles can be calculated , and conversely , if the masses of the particles be known , the temperature of the source can be determined .
In the simple case of two radiations from the same source , if the mass of the luminous particle from which one radiation originates is known , the mass .
the luminous particle concerned in the production of the second radiation can be calculated independently of the temperature of the source or the exact value of the constant K. Any deductions made on the assumption that the only cause of broadening is due to the Doppler effect must be accepted with caution , since there is some reason to suspect that under certain conditions some other cause of broadening may be operative , although such cause of broadening is not at present theoretically indicated .
Let us therefore assume that some hypothetical cause of broadening exists .
We may write for the breadth of a line , as due to Doppler Let the breadth of the line as determined by some hitherto unsuspected circumstances be , then the ctive breadth of the line which determines the limiting order of interference will be ; whatever circumstances are operative in determining the breadth of a line , the breadth can never be less than , that is to say the value of found can never be greater than the value indicated by the equation .
It may further be pointed out that any imperfection in the experimental ements , any ill adjustment of the ometer plates , or any deficiency in the technique of observing the indistinct fringes can only give too low a value for N. Any observed value of may therefore be confidently accepted as an infsrior limit .
If therefore the mass of the luminous particle is assumed , erior In the experiments recorded in the present investigation the values of have been determined in the following manner .
A convergent beam of from the source was thrown by means of a lens on to the plates of a Fabry and Perot sliding interferometer , and the systems were focussed by means of an achromatic lens on to the slit of a large Hilger constant deviation spectroscope , each spectrum line thus appearing as a narrow strip of a ring system .
In making visual observations , the interferometer tes were slowly separated until a point was reached at which the fringes were only just visible .
From the separation of the plates at this point , the value of could be calculated .
In making observations , the telescope of the spectroscope was replaced by a c , amera attachment and a series of spectra were photographed on the same plate in juxtaposition , with the interferometer plates set at successively increasing differences of path .
The photographic method may be regarded as satisfactory in the determination of the relative values of for radiations photographed on the same plate , but the author has found that , for radiations which can be sufficiently well seen , visual determinations are greatly to be preferred , especially in the determination of the absolute values of the limiting order of interference .
With regard to the constant , it is evident that the value must vary somewhat with the observer , the density of the silvering on the ferometer plates , and other circumstances .
An observer must , therefore , determine his own value for the constant .
I have determined this from a series of observations of the spectra of helium and neon , produced in vacuum tubes with an uncondensed from an induction coil , and the average value of obtained in this way agrees so closely with the value given by Buisson and Fabry ( loc. cit. ) that I have adopted their value , in the discussion of the results .
The arc spectra which have been investigated were produced between carbon poles containing small quantities of the substances under investigation .
The arc was maintained in a glass globe of about a litre capacity , which was exhausted by means of a Fleuss pump , and a mercury gauge to the apparatus showed that a of less than 1 mm. of mercury could be maintained .
The current consumed varied between 1 and 2 amperes .
424 Mr. T. R. Merton .
Study of the Origin of Comparison of the , and Lines of Calcium .
The lelative behaviour of these lines has for many years been a subject of oation , more especially in respect of their appearance in the sun an stars .
The line is a typical flame line , appearing brightly when a calcium salt is volatilised in the Bunsen , and also in arc and spark spectra .
The and lines , on the other hand , are enhanced lines .
Whilst scarcely visible in the Bunsen flame , they are well developed in the arc , and in powerfnl sparks are strongly enhanced relatively to the line .
The and lines recently been shown by Fowler*to be the first pair of a series in which the Rydberg constant " " \ldquo ; is replaced by the value " " this type of series being apparently characteristic of enhanced lines .
The and lines are amongst the most conspicuous of the Fraunhofer lines and line is also .
The former , however , occur at very altitudes in the chromosphere , where the line is not visible , and this is also found to be the case in the spectra of nlany stars .
Lorenser has shown that the line is the first nlember of a single line Principal series with which Diffuse and Sharp series are also associated .
The observations of these lines were necessarily carried out photographically , and although a considerable number of photographs were taken , the absolute values of obtained were not satisfactory , though it is believed that the relative values are worthy of some confidence .
This is due to a number of circumstances .
The unsteady and the sudden evolution of denser calcium vapours in the arc very troublesome in raphic observations , of much less inconvenience in visual work .
The photographic techn ique is difficult , and a series of spectra on the plate are seldom of the same intensity .
The following results were obtained from a nber of plates .
the line , were observed up to a difference path of 80 mm Putting , we get and whence 1662o Abs .
, a value which would appear to be too low for the temperature of the vacuum arc .
The and lines are identical in their behaviour .
The greatest erence of path at which interference has been observed for the line was mm. Putting as before , we get , and Abs .
It be supposed that the line and the and lines are produced in * ' Phil. Trans , vol. 214 , p. 225 ( 1914 ) .
Dissertation , Tubingen , 1913 .
Certain Lines by ference Methods .
different portions of the arc , but the great difference in temperatures involved would appear to discredit this explanation .
Assuming that all three radiations are produced simultaneously , the elative masses of the luminous particles may be calculated .
Thus a number suspiciously near and , within the limits of experimental error , equivalent to 1/ 2 .
This would indicate that the and lines are due to particles having one-half the mass of the particles concerned in the production of the line .
The simplest explanation would appear to be that the line , which is essentially a low energy line , is due to calcium molecules of mass 80 , the and lines being due to calcium atoms of mass 40 , which would give a temperature of about 3000o C. as a superior limit for the temperature of the vacuum arc .
This view receives confirmation from the observations of the flame lines of strontium and barium .
The " " absolute values\ldquo ; of for the calcium lines are undoubtedly much too low , so that the value 3000o C. for the temperature is correspondingly too high .
The Flame Lines of Strontium In the spectra of strontium and bal'ium , the lines and respectively are strictly analogous in their behaviour to the calcium line In the case of the strontium line , Lorenser ( toc .
cit. ) has shown that this line is the first member of a series analogous to the series in calcium of which is the first member .
For ( Sr ) fringes were observed visually up to a rence of path of 183 mm. If a strontium atom were responsible for this radiation , the superior limit for the temperature of the arc would be , clearly an inadmissible value .
It is eyident that molecules must be concerned in the production of this radiation .
For the barium flame line , the limit could not be reached , as the interferometer used was not made to give diflerences of path reater than 240 mm. , and at this difference of path the fringes were still very distinct .
Even this incomplete result is suflicient to show that molecules are concerned in the production of the radiation .
The appearance of band spectra is usually associated with molecules , and the interpretation given to the results would require the recognition of the fact that molecules may give rise to line series as well as loand spectra .
Another point arises .
If two calcium or two strontium atoms can combine at the temperature of the electric arc , and yield spectrum lines peculiar to In the spectrum of the mixture no lines were found which did not occur in the spectra of either calcium or strontium .
The matter , requires an explanation .
Are calcium and strontium , which are chemically very similar , able to combine to form and , but yet unable to form the compound CaSr ?
Or does the calcium atom in CaSr yield the same spectrum as the calcium atom in ?
It was hoped to investigate all the lines in the visible region of the calcium and strontium , but experimental difficulties have at present led to unsatisfactory results .
With respect to the flame lines and the and lines , the arc will sometimes burn steadily for a considerable time , but the other lines in the spectrum flash in and out in a manner which makes measurement very difficult .
In this respect the strontium spectrum was less troublesome than that of calcium .
No exact results can be given for these lines , but it may be stated the limiting differences of path at which were seen were generally less , and never greater , than would be expected on the assumption that the luminous particle was the atom , and no evidence has been found that particles of greater mass than the atom are concerned .
The Two pectra of Argon .
The two spectra of argon appeared to be especially well suited to the study of the relative widths of arc and enhanced lines .
At low pressures the red spectrum produced by means of an uncondensed discharge usually shows lines of the blue spectrum also , but under these conditions they are too faint for investigation with the interferometer , and a small condenser with a -gap in the circuit was necessary to develop the blue spectrum sufficiently brightly .
I indebted to Prof. Herbert Jackson for the loan of two argon tubes of the ordinary Plucker form , but it was found necessary to make use of the greatly increased illumination obtainable with end-on tubes .
The tubes were filled by adnutting air , the diatomic constituents of which were removed , according to the well-known method of Prof. Soddy , by means of metallic calcium .
Small pieces of in a ] boat were heated in a quartz tube connected with the vacuum tubes , and air was admitted in small qusntities until the tubes showed a pure argon spectrum .
just vifference owhich gives Ntting M le value .
It has been pointed out in a previous communication that the lines of the ordinary helium spectrum become wider when a condenser and sparkgap are introduced , keeping the current the primary of the induction coil constant , and it was suggested that this broadeniI ) might be due to the sudden rise of temperature at each impulse .
It is evident , however , that the differences in the widths of the lines in the red and blue spectra of argon are of a different order to any widening that can be accounted for in this manner .
The only other explanation at present provided for by theory is that bhe luminous particles concerned in the production of the blue spectrum are smaller than the particles from which the red spectrum inates .
But this would lead to so low a value for the mass of the particle responsible for the blue spectrum that such an explanation could hardly be gested in the absence of further evidence in this direction .
It may be necessary to admit the existence of some hypothetical cause of broadening in this case , as Buisson and Fabry ( loc. cit. ) have done in the case of the Balmer series of hydrogen .
The Band Associated with Ildium .
The band spectrum associated with helium has been described by Goldstein* and by Curtis , who has investigated the conditions most favourable to its production .
More recently , has made a more exhaustive investigation of this spectrum , and has made accurate measurements of the bands , resulting in the remarkable discovery of relations hitherto only associated with line spectra .
Curtis .
cit. found that the bands were best developed at moderately high pressures , and that with an uncondensed discharge they were faintly visible both in the capillary and in the bulbs , but that they could be obtained much more brightly by introducing a small capacity , with a short spark-gap in the circuit .
Curtis points out that , although the spectrum in question is probably due to helium , this 'Deut .
Phys. Ges vol. 15 , p. ( 1913 ) .
'Roy .
Soc. Proc , vol. 89 ( 1913 ) .
'Roy .
Soc. Proc , vol. 91 , p. 208 ( 1915 ) .
Although little is known as to the origin of band spectra , it has usually been assumed that 2 atoms more , at least indirectly , are erned in their production , and the very existence of a band spectrum associated with helium must modify our outlook either on the of band spectra in general or on the usually accepted properties of helium .
For a number of vacuum tubes containing helium in a high state of purity I am indebted to Prof. Herbert Jackson , who has also given me his valuable in some experiments on the efl'ect of low temperatures on the band spectrum .
The tubes were of the ordinary Plucker form , and showed no cvidence of any inlpurit , y excepting a trace of hydrogen , which was just visible at the ends of the capillary , in one tube a trace of mercury , which disappeared after the tube had been run for a few minutes .
In the experiments at low temperatures , the tubes were excited by a moderately weak discharge from the induction coil , the intensity of the arge corresponding to about one-third of an inch spark in air .
No condenser or spark-gap was used , and the spectrum of the pink the electrodes was observed .
The spectra were photographed with the single-prism raph , and visual observations were also made .
In making the raphic observations , the glow from one of the electrodes was focussed on the slit of the spectroscope by means of a lens , and a definite exposure was .
The vacuum tube was then immersed in liquid air contained in an unsilvered vacuum vessel , and a second exposure was made for the same time , the second spectrum being photographed on the same plate in juxtaposition to the first .
When the vacuum tube was wholly immersed in liquid air , the band spectrum appeared as bef.ore in both bulbs , but was much brighter than at room temperature .
Photographs of the spectra of the tube at room temperature and at the temperature of liquid air show clearly the difference in the intensity of the bands .
In the capillary , no change was observed .
The effect of immersing only the lower bulb of the tube in liquid air was very striking .
The intensity of the band spectrum in the cooled bulb was greatly enhanced , the eHect being especially noticeable in the case of the head at .
At the same time , the band spectrum entirely disappeared from the upper bulb , the upper electrode surrounded by a green glow , showing the helium spectrum with the parhelium lines greatly enhanced .
When one bulb only is immersed , a lowering of the pressure would result , together with an increase of density in the cooled bulb .
This would fall into Cf .
Curtis , .
cit. , p. 148 .
mperatures tnhancement ireater density apectrum iperatures , xistence oeing uwhich abservation ( that tpectrum iressure without.change oensity.oped aressures.vident tpectrum Lethods .
band spectrum associated with an inert , might justify the suspicion that in helium , though inert in the ordinary sense of the word , more than one atom may be involved in the processes resulting in the production of a band spectrum .
This suspicion is not confirmed by an investigation with interferometer .
For this purpose , it was found necessary to introduce a small capacity with a very small ) into the circuit , since with the uncondensed discharge the spectrum is too feebly developed , and even with the condensed discharge the spectrum was too weak for visual observations .
Photographs were taken in which the for the lines of the band spectrum produced in this way were compared on the same plate with the lines of the ordinary helium spectrum produced with an uncondensed discharge .
It was necessary in tlJese experiments to employ a narrow slit in order to separate the components of the bands sufficiently for the fringes to be seen without confusion , and the lines of the bands in the neighbourhood of could be successfully examined in this way .
Only a very narrow strip of the ring system could , thel.efore , be examined , with the result that the limiting difference of path at which interference could be seen was considerably reduced , since the are more difficult to uish in these very narrow strips .
The visibility of the fringes in this band spectrum and the ordinary lines appeared to be identical , and there was no evidence that the fringes for the band spectrum persisted at greater differences of path than for the ordinary lines .
It can be seen that if the band spectrum were due to helium molecule the ratio of the limiting differences of path would be about .
It might be imagined that the lines of the band spectrum were broadened by the condensed discharge , in which case it would not be possible to conclude that any evidence a molecular origin had been obtained .
This is most unlikely .
The condensed discharge employed was not powerful enough to broaden appreciably the ordinary helium lines .
If the band spectrum of helium were analogous to the secondary spectrum of hydrogen , discharge , since Buisson and Fabry ( loc. cit. ) have shown that the lines ot the secondary spectrum of hydrogen are not broadened under conditions , whilst the reverse is the case with the Balmer series .
It may , therefore , be considered extremely probable that the band spectrum is due to atomic helium .
The effect of low temperatures on the series and the secondary spectrum has been investigated by Lemo has found that at the temperature of liquid air the secondary spectrum is relatively enhsJlced .
This result may possibly be explained as being due to the condensation of minute traces of water vapour present on the walls of the tube at low temperatures , since it is well known that the presence of water vapour in hydrogen results in an enhancement of the lines of the Balmer series .
A similar explanation may perhaps account for the enhancement of the band spectrum of helium at low temperatures , since this spectrum is adversely affected by the presence of impurities .
The removal by condensation of impurities , which spectroscopically may not be detectable , might result in au enhancement of the band spectru1n .
It is probable that the trace of hydrogen which can be detected in almost every vacuum tube is present as water vapour ; the hydrogen lines could not be detected at the temperature of liquid air in a neon tube in which they were brightly visible at ordinary temperatures .
The Characteristics of Series Lines .
From the characteristics of series of hnes in spectra produced at atmospheric pressure , Bydberg , in his classical researches , was led to adopt the terms Diffuse and Sharp series .
At the present time these terms do not denote the character of the lines in the series , but rather their numerical relations to one another and to the Principal series , and Kayser and Rung refer to these series as the First and Second subordinate series respectively , owing to the fact that the lines of the Diffuse series are not always diffuse in character .
According to he circumstances which are at present recognised as determining the widths of spectrum lines , it might be supposed that the diffuse character .
of many Diffuse series lines at atmospheric pressure is due to the effect of collisions , which must be supposed to affect lines of the Diffuse series to a much greater extent than lines of the Sharp series .
'Astrophys .
Journ vol. 35 , p. 109 ( 1912 ) .
iffuse aharp sthese characteristics oinesdisappear aressures , ppear wcondensed distics oines.very striking instance othepectrum oited Apressure estimated about oCertai Snterjerence Methods .
of interference of the lines in the visible spectrum .
This confirms the observations of Buisson and Fabry .
cit who have concluded that particles of the same mass are concerned in the production of all the series .
When , however , the tube was excited by a powerful condensed discharge , the diffuse character of the Diffuse series at once appeared , more especially in the parhelium series , and could easily be recognised under the small dispersion of a single prism without the use of the interferometer .
The experiment would appear to show that the difference in character between Diffuse and Sharp series is a general one under suitable conditions of electrical excitation , and would indicate that calculations of the actual mass of the luminous particles must be accepted with some reserve , especially in cases in which the law has not been experimentally verified under identical conditions of excitation .
An inferior limit for the mass may be determined with c , onfidence .
|
rspa_1915_0034 | 0950-1207 | The band spectrum associated with helium. | 432 | 439 | 1,915 | 91 | Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character | J. W. Nicholson, M. A., D. Sc.|A. Fowler, F. R. S. | article | 6.0.4 | http://dx.doi.org/10.1098/rspa.1915.0034 | en | rspa | 1,910 | 1,900 | 1,900 | 3 | 98 | 2,453 | http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1915_0034 | 10.1098/rspa.1915.0034 | null | null | null | Tables | 64.457471 | Atomic Physics | 34.357677 | Tables | [
15.058870315551758,
-49.45643997192383
] | ]\gt ; The Band Spectrum Associated with Helium .
By J. W. NICHOLSON , M.A. , D.Sc .
, of Mathematics in the University of London .
Communicated by A. Fowler , F.R.S. Received May 4 , 1915 .
A very significant addition to our knowledge of the nature of band spectra .
has been made by Prof , Fowler , has lately described the results of his examination of the band spectrum found in connection with helium and hydrogen , and believed to be a spectrum of helium .
For Halm has maintained that the formulae which must be used to represent line and band spectra are intinlately associated , and , in fact , spectroscopists have been generally inclined to suspect that the laws of line spectra have some counterpart in band spectra also .
Fowler has taken the first step in the elucidation of this connection by showing that the universal constant of Rydberg belongs ; to this individual band spectrum , which contains two series of double " " heads\ldquo ; * arranged essentially in the same manner as the lines in a series spectrum .
One feature , however , of these double " " heads\ldquo ; or doublets appears at first sight to differentiate them from the doublets found in line spectra , and one purpose of this paper is to show that the difference in character is only apparent , and that the formal analogy with line spectra extends very far .
In ordinary Diff.use or Sharp series of doublets , the intervals between the components , when expressed in wave numbers , are constant , whereas in a Principal series the intervals rapidly become smaller , and vanish at the limit of the series .
The intervals decrease , moreover , in a very regular manner .
In the band-doublets discussed by Fowler , although the intervals decrease as the series proceed towards their limits , the decrease is not very regular , as shown by the differences , and the intervals do not obviously vanish at the limits .
Without a very precise ement in series , it is not possible to of their limiting behaviour .
Fowler has shown that the less refrangible components can be arranged in series of a very ordinary simple form , that of Rydberg being almost sufficient .
But the more refrangible components cannot be arranged in a satisfactory manner , even in a Hicks series .
They are , in fact , an example of a phenomenon not unknown in line spectra , where lines which obviously belong to a series cannot be fitted in a satisfactory way into the usual formulae , because those formulae do not , in these individual cases , converge with sufficient rapidity .
* Boy .
Soc. Proc , vol. 91 , p. 208 ( 1915 ) .
'Roy .
Soc. Edin .
Trans vol. 41 ( 1906 ) .
become apparent iaper tpproximate superposition o The Band Spectrum Associated with Helium .
and this series may be most conveniently discussed first .
Its wave numbers , expressed in International units in vacuo , are and the separations are respectively .
Fowler has represented the less refrangible components by the formula , ( 1 ) which only gives errors , and there is no doubt that these components follow the usual laws of series .
The simple formula calculated for the other components is , ( 2 ) with errors , and is not satisfactory .
Fowler has , therefore , added one more constant , and , from the first , second , and fourth lines , obtains , ( 3 ) with errors .
This is more satisfactory , but not completely so .
The doubleC separations become , in the two cases , , and we are led to the question of a possible further reduction of these separations by formulae of accuracy .
In order to test this point , we may notice that in a formula where proceeds in inverse powers by a series which is not very convergent , a more accurate limit will be obtained by calculations which do not include the first line , in which the enceo is most serious , provided , of course , that all the lines are measured with an equal degree of accuracy .
This is the case for the four lines of the present series .
Calculating , therefore , from the second , third , and fourth lines and using the betber form of the series will serve almost equally well .
Adopting this form , the calculated limit becomeo This already further reduces the limiting separations by , and it no becomes , representing the best value which can be obtained by a formula , only three lines .
The next step in the demonstration makes use of all the four lines for the calculation of a formula with an extra constant , and of the more appropriate form .
The final result of this calculation is where .
( 7 ) The limit falls 10 more units , the divergence of the doublets at the limit being now only about 27 units .
This is not the most accurate formula which can be obtained from the four lines , and it is not yet very convergent for the earlier lines .
It is evident that the next term in will be important in the lines , 3 , and , therefore , that the limit is still incorrect .
Since every improvement in the formula has led to a marked depression in the limit , which now only differs by about 27 from the value for the companion series , there is every reason to believe that the limits are actually identical , and that the correspondence with line series extends further than the occurrence of the series relation .
The most accurate formula which can be obtained from Ghe four lines is calculated as shown below , and involves a further decrease in the limit .
Details of the calculation are given , as it takes the form which appears to be most convenient for general application .
the limit of the series as where is small , and ( 8 ) being a more exact limit for the other components with a simpler law , and being the ydberg constant , we find for the four lines , on calculation , 5 'Roy .
Soc. Proc , vol. 91 , p. 255 ( 1915 ) .
, ( 12 ) whence .
The correction to this value , dependent on , is , if is the corresponding correction for any number , determined by and ultimately .
( 13 ) With the extreme value of which is possible , we can show to be so small that for , the term in does not contribute a significant amount to and the contribution to is small in comparison with that to .
A similar calculation to the above , performed with , 4 , 5 , 6 , would therefore give a result very close to that for , 4 , 5 , only , and the value for combined with that for ( 2 , 3 , 4 , o ) expressed in ( 13 ) will lead to a limit more accurate than even that in ( 7 ) , although still not exact enough .
The calculation with , 4 , 5 , proceeds by writing whence and the ultimate solution by the preceding method is .
( 14 ) the values ( 13 ) and ( 14 ) for the approximation available , .
( 15 ) The limit has again decreased by units , and this decrease therefol.e continues to be systematic as formulae of increasing accuracy , and of the type necessary in line spectra , are employed .
The doublet separation is now only at the limit as against the value which accords with the best Hicks formula given by Fowler .
It is evident , moreover , from a glance at the series below , and a comparison with 7 ) , that it is not yet in any way absolute , and that limit would again fall .
This final series is where ( 16 ) That is certaiIlly much less even than can be proved at once .
For a calculation from the first three lines gives , by this method , .
( 17 ) This cannot be so accurate as ( 14 ) , which again is not so accurate as ( 13 ) .
Let us suppose that ( 13 ) , which has the least error , and uses all four lines simultaneously , is correct .
Then the errors in ( 17 ) and ( 14 ) are mainly derived from neglect of the term in , and are roughly in the ratio .
If , therefore , is the error in ( 14 ) , we may write with a close approximation ( 18 ) and , solving these three equations , This is most probable value of which can be derived from the four doublets , and it is very conclusive .
We can now hardly doubt that the limit is identical with that of the simpler series .
On this supposition , the doublet series is analogous to a Principal series in line spectra .
Without measureents of further members of the more refrangible components , however , no formula can be iven for these members of a much more satisfactory character than ( 7 ) , and the question of the relation of the constants , , to those of known helium series cannot be fated .
The rapid of these constants with the addition of an extra term to the formula precludes arly precise specification of their values at present .
First Series of DouUets .
The other series of doublets isolated by Fowler has for its leading members the way nulnbers given in the Table , where denotes the doublet separations , and , their first and second differences .
The differences appear to be quite irregular , there is a remarkable oscillation in the second differences .
A stndy of the values of indicates a definite .
towards zero , but in an ular manner .
This irregularity is exactly of the type which would be expected if the refrangible components followed a series law of the form where the coefficients , not rapidly to zero , and being alternately positive and ative , whereas in the .
series for the less refrangible components , the convergence of , to zero is rapid .
The preliminary series given by Fowler accord with this result .
For the less refrangible components , he finds a simple .
formula , to.be nearl.y satisfactory , and a corresponding Hicks formula does not show much improvement .
It must be borne in mind , of course , that only the first three doublets are measured with great accuracy , although the next three or four must be fairly accurate .
The later values are admittedly approximate .
A formula of the proper generalised Rydberg type has been calculated from the first four lines of this simple .
series , and the result is The limit is almost exactly that obtained by Fowler from the simpler series , VOL. XCI.\mdash ; A. 2 series remains .
The application of the simple and the Hicks formulae by Fowleg 3$ for this the limits , the more accurate formulQ a limit nearer to that of less refra1lgible series of components .
has also used a Hicks formula with an extra constant , giving a limit , which is cvain noticeably nearer .
But even this formula is by no means satisfactoryas a representation of the lines , and the steady decrease which already baken place in the limit with improvement in the representatiol ) , with the results of our examination of the other set of doublets , eaves little doubt that this series of doublets is also of a Principal type , if : calculation is pushed further .
For even the apparent separation doublets is by no means so large as it was in the first series with which this paper deals .
The complete lvestigation follows so closely along the lines already described for the other doublet series that there is no need to give it in detail here .
One or two of its main features may be mentioned .
If the limit of the series is taken as , the values of in flre The last crures are not very reliable beyond , and even the last three figures may be incorrect in later entries .
Fowler 's Hicks formula was derived from the first , second and seventh lines .
The seventh may not be very accurate , and the first should not be used in the problem of merely determinin the limit accurately , which is our presenLpurpose .
) The Band Spectrum Associated with .
439 3 Applying the Hicks formula to the second , third and fourth lines , as the suitable and accurate trio , in the form , .we find But on the theory of the preceding paper , a better value must be iven by nearly , for is evidently close to unity .
This leads to or very nearly zero .
On the supposition , therefore , that the second , third and fourth hnes are measured accurately , the limit of the series is almost certainly that of the less refrangible components .
Further examination on these lines need not be given , but we may perhaps notice that with we can deduce a formula with three constants from the first three lines , which satisfactory as that calculated by Fowler according to the Hicks model and with a later line .
With the same number of constants , more satisfactory formulae have been obtained throughout when the generalised Rydberg form has been used .
Summary .
1 .
The paper gives further support to Fowler 's conclusion that the heads of the bands in the band spectrum of Goldstein and Curtis follow ordinary line-series laws , by showing that the doublet separations tend to zero at the limits of the series .
2 .
Both the doublet series isolated by Fowler are strictly analogous to Principal series in line spectra .
3 .
The generalised Rydberg formula gives the most suitable representation of these series as well as of line series .
|
rspa_1915_0035 | 0950-1207 | On the shapes of the equipotential surfaces in the air near long walls or buildings and on their effect on the measurement of atmospheric potential gradients. | 440 | 451 | 1,915 | 91 | Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character | Charles H. Lees, D. Sc., F. R. S. | article | 6.0.4 | http://dx.doi.org/10.1098/rspa.1915.0035 | en | rspa | 1,910 | 1,900 | 1,900 | 10 | 99 | 2,950 | http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1915_0035 | 10.1098/rspa.1915.0035 | null | null | null | Fluid Dynamics | 36.182912 | Tables | 30.545631 | Fluid Dynamics | [
37.37286376953125,
0.3394324481487274
] | ]\gt ; On the Shapes of the Equipotential ces in the Air Walls or Buildings on their Effect on the Atmospheric Potential Gradients .
By CHAItLES H. LEES , D.Sc .
, F.R.S. ( Received May 10 , 1915 .
) S1 .
In considering the most suitable arrangements for recording variations of the atmospheric potential gradient at the East London where no large horizontal surface is available , I frave had occasion to the distribution of potential in the neighbourhood of walls and buildings simple shapes .
As the results can be applied in practice it seems to put them on record for the use of other observers .
Observation shows that during fine weather the potential at a the atmosphere over a level portion of the earth 's surface in these increases as the point is raised , at the rate of about 150 volts per metre .
This rate of increase diminishes slowly as the point ascends , owing to ths slight excess of positive over negative ions in the air near the earth 's surface , and at an altitude of a kilometre is reduced to about per cent. of its value at the surface .
* The potential differences between points on the earth 's surface 1000 metoes apart or between a point on the surface of a building and one on the ground near it are found to be small compared to those present in the atmosphere .
For the present purpose we shall neglect the small effect of the ions near the earth 's surface on the potential gradient for the first few metres above the surface and shaJl treat the earth 's surface as plane and the earth and buildings as being conductors .
In order further to simplify the problem as much as possible , the walls of the buildings are taken to be long in comparison to their heights , so that the effects of the corners on the distribution of * The article " " Atmospheric Electricity by Chree , in the 'Encyclopaedia Britannica , 11th edition , or that by Gerdien in the 'Handbuch der Physik , ' vol. 4 , p. 687 , or Mache and von Schweidler 's 'Atmospherische Elektrizitat , ' chap .
I , may be consulted for accounts of the methods used and the results obtained .
For recent results obtained at Kew , Chree Phil. Trans , and , p. 133 ( 1916 ) ) and Dobson ' Proc. Phys. Soc. Lon vol. 26 , p. 334 1914 ) ) may be consulted .
Benndorf ( ' Wiener Ber vol. 109 , p. 923 ( 1900 ) , vol. 115 , p. 425 ( 1906 ) determined with the same simplifications the changes in the vertical potential near a long plateau with rounded edges , a circular plateau , and an ellipsoidal Sir J. Larmor and J. S. B. Larmor ' Roy .
Soc. Proc , vol. 90 , p. 312 ( 1914 ) ) diagrams of potential surfaces , etc. , for an ellipsoidal column and an sphere .
Equipotential Surfaces in Air near Long Walls .
near the middle of their length may be neglected .
The walls are taken to be vertical , and in the case of more than one to be parallel other .
Roofs are taken to be horizontal .
Case I.\mdash ; A long thin vertical wall projects from a horizontal surface which , at a considerable distance from the wall , the potential gradient constant .
T.o find the distribution of potential near the wall .
Take the plane , where , vertical and perpendicular to the wall , axis along the horizontal plane , and the axis up the wall .
If is height of the wall , the Schwarzian transformation , converts the and axes into the axis of in the plane the first quadrant in the former into the first two quadrants in the latter plane .
Integrating , we have or .
( 1 ) If is a point in the air whose bi-polar co-ordinates are , from the top of the wall and from the image of the top in the plane respectively , the last equation gives us at . .
( 2 ) Thus the potential at any point whose bi-polar co-ordinates are given is easily calculated .
To calculate the potential at a point whose co-ordinates are , or to draw the surfaces of equal potential , it is more convenient to use equation ( 1 ) , which gives on equating separately the real and unreal parts and on eliminating Thus the potential at the point , is given by and the factor by which the observed potential at the point , should be multiplied to give the potential at the height above an infinite plane is The equipotential lines are readily drawn from the equation .
( 4 ) They are shown in fig. for the case * I have to thank Lieut. B. Barnes , 10th East Surreys , one of my senior students , for drawing these curves .
Dr. C. H. Lees .
S3 .
If is constant we have , since ) If , further , , then and when is infinitely large .
The last two equations show that the ratio of the vertical potential gradient at a point on the ground to the normal vertical gradient is equal to the cosine of the angle subtended at the point by the height of the walL The following Table*shows the vertical gradient at points on the ground whose distances from the foot of the wall are given in terms of the height of the wall .
* This Table and the corresponding ones on pp. 445 and 449 are added at the suggestion of Dr. Chree so as to be available for discussion of the effects of vertical potential gradients on plants and animals .
S4 .
If is constant we have in the same way At this gives , if is less than The horizontal potential gradient at on the wall is therefore identical with the normal vertical gradient if tha.t is if As we proceed outwards from the wall the horizontal potential radiant decreases , but at the height we may move outwards a distance ] without the potential being 1 per cent. less than that which would have been found at the point if the horizontalgradient had remained constant and equal to the normal vertical gradient .
At a distance from the wall the potential is 5 per cent. less than the normal gradient would give .
At larger distances from the wall the change of potential should be calculated directly from either of the expressions ( 2 ) and ( 3 ) for it in terms of the co-ordinates of the point .
S5 .
Case II .
\mdash ; A long vertical retaining wall separates from each other two horizontal plane surfaces over which the potential gradient at a considerable distance from the wall is the same and independent of height above the planes .
To determine the distribution of potential near the wall .
Taking the plane , where , vertical and perpendicular to the retaining wall , the axis along the lower plane , and the axis up the surface of the wall , we have the Schwarzian transformation Dr. C. H. Lees .
which converts the lower boundary of the the plane into axis of in the plane , where Writing , the equation becomes integral of which is .
Expanding and separating real and unreal parts , we have and sjnh If we must have either or or In the first case , in the second .
, in the last .
height of the wall is therefore equal to , that is , and equations connecting and may be written To find the potential at a given point , it is necessary to solve , the second set of transcendental equations ( 8 ) or ( 9 ) , and substitute values of and in the equation for To draw the equipotential surfaces we use the equations:\mdash ; and assign to all values from to and to values exceeding The curves obtained are shown in fig. 2 for the case in which the height the equipotential surface of potential unity is equal to that of the wall , is and Equipotential Surfaces in Air near Long On differentiating equations ( 9 ) we have ( 11 ) S 6 .
If is constant we have Hence the vertical potential gradient at the point corresponding to , is given by ( 12 ) if if In each case if is The vertical potential gradient is therefore over both planes at considerable distances from the retaining wall .
At smaller distances it is less than the normal over the lower and greater than it over the upper plane .
Table of , near the Middle of a Long Retaining Wall or Flat-roofed Building .
Dr. C. H. Lees .
The preceding Table gives in terms of the normal gradient the adient at points whose distanoes from the foot and top of the on each of the horizontal surfaces are expressed in terms of the wall .
S 7 .
If is constant we have Thus and Hence the horizontal potential ooradient at the point corresponding to by ; if , that is when It will be noticed that the ratio of the vertical to the horizontal at the point corresponding to , is The horizontal potential radiant close to the wall will be identical the vertical gradient over the planes at great distances from the wall if that is if The point / ?
on the wall corresponding to , is given by Hence the point on the wall at which the horizontal gradient equal to the normal vertical gradient is at a height equal to the total height of the wall , that is to of the total height .
As we proceed outwards from the wall at this height the horizontal gradient decreases , but at a distance from the wall not exceeding of height of the wall the potential is less than 2 per cent. smaller than would be if the horizontal gradient been equal to the normal gradient for the whole distance .
S 8 .
Case III.\mdash ; Two thin vertical walls parallel to each other rise to same height above a horizontal plane .
To find the distribution of the space between the walls .
Equnpotential Surfaces in Air Long Walls .
To simplify the calculation we shall take the walls as being two consecutive of a regular series on both sides to infinity .
Taking the where , vertical and perpendicular to the series of planes , axis along the horizontal plane , and the axis vertical through the point on the axis half way between the planes , the transformation where and are constants , being less than unity , converts the lower boundary of the atmosphere into the axis of in the plane , where Expanding the circular functions we have and If , and Thus either or , where is an integer .
If , and and increase from zero together till and arcsin If , and increases from zero to argcosh , while increases from to The distance of the walls apart is therefore , and their is a .
Hence , and the equation connecting and may be written .
The equation to the equipotential lines is therefore , a quadratic in and from which at any point , may be calculated and the reducing factor to convert readings taken at , ?
/ , into readings in the open may be found .
In drawing the equipotential curves it best to use the equation in the form .
* The somewhat more general transformation fiin sitl be in the same way throughout .
S 9 .
If is constant we have , from equation At this reduces to , and For large values of this gives the normal vertical potential gradient At it gives that is ] .
At the point on the ground half-way between the planes Thus the ratio of the vertical gradient on the ground half-way between planes to the normal vertical gradient is .
The following Table gives the values of this ratio for different values of ratio of height of planes to distance apart .
Equipotential Surfaces in Air near Long Walls .
on the Ground Midway between Two Vertical Planes for Different Ratios of Height of Planes to Distance apart .
The vertical gradient at other points on the ground between the planes is by the equation ( 17 ) above , and is tabulated below for several values of of height of the planes to distance apart .
of on the Ground between Two Vertical Planes .
These figures are sufficient to show how great is the effect of the walls on the vertical gradient on the ground between them .
They may be taken as representing with a fair degree of accuracy the vertical gradient on the ground in a street with buildings on each side of it .
S10 .
If is constant we have At this becomes Equipotential Surfaces in Air Long Walls .
is less than , this gives , and If the horizontal potential gradient at on the wall is to be equal normal vertical gradient , we must have , that is .
When the height becomes small compared to the distance apart planes , this gives the distance up the plane as times the height , found by direct calcuJation .
The following Table gives the relation between the ratio of the the planes to their distance apart and the fraction of the height at horizontal potential gradient outwards is equal to the normal potential gradient over a plane surface .
As the planes approach each the potential surfaces near sullmits become more nearly horizontal , so that the potential gradient is nearly vertical than horizontal .
S11 .
It follows from the previous work that where plane horizontal of considerable extent are not available for the determination of the vertical potential gradient in the atmosphere , observations in the hood of buildings can be utilised , value of the reducin factor calculated from the forms of the buildings in the simple cases dealt In many cases observations of the horizontal potential gradient from the walls of buildings which are not too close together may be and , if the position of the point of observation is properly chosen , horizontal gradient observed will be identical with the normal radiant over a horizontal surface .
For a long wall of a building with a roof or with a parapet , the horizontal gradient outwards should be Enhanced Series of Lines in Spectra of Alkaline Earths .
451 point near the middle of the length of the wall and at a distance up it is generally about three-quarters of the height .
The horizontal for a distance outwards not exceeding 1/ 10 the height of the wall not differ by more than 2 per cent. from the normal vertical , radiant a large horizontal area .
On the Enhcmced Series of Lines in of the Alkaline By W. M. HICKS , Sc. D. , F.R.S. ( Received May 15 , 1915 .
) The problem of the limits and numerical relations between the lines of the enhanced series of doublets in the earths has for long been a difficulty to spectroscopists .
Ritz*in 1908 gave arrangements for the Sharp series from Mg to Ra inclusive , and proposed series formulae for Ca , Sr , Ba , in which alone he had three lines from which to calculate the constants .
The absence of extra lines endered it impossible to test his formulae , but the values of the constants obtained for his formulae were quite out of hne with those of the analogous constants in other series , and produced an instinctive doubt as to whether it gave the correct relation .
It is now possible to test his limits by considering whether the denominator differences which give the observed separations have any relation to the oun or not .
The result of this consideration is definitely adverse .
In none of the three is it possible to make the differences multiples of the oun without supposing observation errors in the doublet separations which are quite inadmissible ; and even then in the cases of Ca and Ba by taking odd multiples of , which is never the case for doublets in any other known series .
There can be little doubt but that has at last settled this question by taking the Rydberg numerator constant to be in place of , thus combining in one set lines which on the old supposition would be arranged in two series , depending on Sharp and Principal sequences .
The object of the present note is the determination of the connection of these series with certain laws which have been arrived at in previous to this Society * Phys. Zeitschr vol. 16 , p. 521 .
' Phil. Trans , p. 225 ( 1914 ) .
' Phil. Trans , vol. 210 , p. 57 ( 1909 ) ; , vol. 212 , p. 33 ( 1912 ) ; , vol. 213 , p. 323 ( 1913)\mdash ; referred to in the following as ( I ) , ( II ) , and III ) respectively .
|
rspa_1915_0036 | 0950-1207 | On the enhanced series of lines in spectra of the alkaline earths. | 451 | 463 | 1,915 | 91 | Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character | W. M. Hicks, Sc. D., F. R. S. | article | 6.0.4 | http://dx.doi.org/10.1098/rspa.1915.0036 | en | rspa | 1,910 | 1,900 | 1,900 | 8 | 193 | 4,450 | http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1915_0036 | 10.1098/rspa.1915.0036 | null | null | null | Tables | 68.331155 | Atomic Physics | 30.18855 | Tables | [
15.895549774169922,
-48.904598236083984
] | ]\gt ; Series of Lines in Spectra of Alkaline Ear.ths .
451 a point near the middle of the ]ength of the wall and at a distance up it which is enerally about three-quarters of the height .
The horizontal adient for a distance outwards not exceeding 1/ 10 the of the wall ill not differ by more than 2 per cent. from the normal vertical yradient over a large horizontal area .
On the need Series of Lines in Spectra of the Earths .
By W. M. HICKS , Sc. D. , ( Received IsIay 15 , 191.5 .
) The problem of the limits and numerical relations between the of the enhanced series of doublets in the alkaline earths has for been a difficulty to spectroscopists .
Ritz*in 1908 gave arrangements for the Sharp series from Mg to Ra inclusive , and proposed series formulae for Ca , Sr , Ba , in which alone he had three lines from which to calculate the co1lstants .
The absence of extra lines rendered it impossible to test his formulfe , but the values of the constants obtained for his formulae were quite out of line with those of the constants in other series , and produced an instinctive doubt as whether it gave the correct relation .
It is now possible to test his limits by considering whether the denominator differences which the observed separations have any relation to the oun or not .
The result of this consideration is definitely adverse .
In none of the three is it possible to make the multiples of the oun without supposing observation errors in the doublet separations which are quite inadmissible ; and even then in the cases of Ca and Ba by taking odd multiples of , which is never the case for doublets in any other known series .
There can be little doubt but that Fowler has at last settled this question by taking the Rydberg numerator constant to be in place of , thus combining in one set lines which on the old supposition would be in two series , depending on Sharp and Principal sequences .
The object of the present note is the determination of the connection of these series with certain laws which have been arrived at in previous to this Society 'Phys .
Zeitschr vol. 16 , p. 521 .
' Phil. Trans , vol. 214 , p. 225 1914 ) .
Phil. Trans , vol. 210 , p. 57 1909 ) ; , vol. 212 , p. 33 ( 1912 ) ; , vol. 213 , p. 323 ( 1913)\mdash ; referred to in the following as ( I ) , ( II ) , and ( III ) respectively .
, , and series and for the series of .
These values will be in what follows .
In order to get a conspectus for the whole group I dded a discussion for the corresponding lines in Ba and A few preliminary remarks on the series formulae may not be out of In ( II , p. 35 ) I have reasons that in the triplet series of this group the series depend on the sequence which in the alkalies give the , and rice ( .
If weassume the same result for the doublet series it will be found that the new formulae reproduce the other lines with much greater closeness han those used by Fowler\mdash ; who has very naturally taken a Sharp sequence for a Sharp series .
The modification consists in taking the constant as. .
fraction or , which comes to the sallle thing , writing the denominator .
The formulae on this basis , using the first three lines for data , are Ca and the values of , compared with Fowler 's , are Ca Sr In the case of Ba ( as allocated below ) the formulae calculated from the second , third , and fourth reproduce the first line with values of when fraction , and 159 when fraction .
It is probable that a formula with would reproduce the lines of each element with very fair accuracy .
But the residual errors show that these limits as well as those of Fowler are too large .
The cause is probably due to the fact that the first line is not the calculated but the observed .
They never exactly agree .
In the case of and series I feel some doubt as to whether the actual lines follow a given formula sequence , although it may be possibl : they are in some way related to such typical sequences .
There can be little doubt , I think , but that the values of the wave numbers are determined by an expression of the general type but the Series of Lines in Spect of the Alkaline ioertainly cannot itself be a mathematical function of the for both the and lines , or for both the and lines .
They are best discussed Wy calculating the actual values of from the observed wave nbers , then attempting to investigate the relationships between them .
This is the method adopted in ( III ) and it will be followed in the present note .
The values of for the elements in question are ( III , pp. 344-346 ) Mg .
Ca. Sr. Ba .
Ra .
The theory that the separations of the series depend on multiples of the oun , and that the satellite separations of the , and consequently the separations , also depend on multiples of the sauue quantity , can , I think , be considered as established , and ma .
be taken as a tesb for new cases .
This part of the discussion will then be taken first .
The exactness of the determination of the denominator differences which produce the observed separations depends almost wholly on the exactness of the separations as measured , and only htly on the true of the lilllit .
In fact the value of the difference is ected by the same percentage error as the value of the separation adopted .
Any error in the limit produces only a small effect , because it enters as the difference of two numbers each affected by nearly the same errors .
To illustrate this point the ca]culation is given for Ca , and the results only for the other elements .
Fowler quotes for Ca a doublet separation and limits for and for .
Take the true limits as being greater and that the value of is affected with an error .
Using the numerator the denominators for these limits are respectively and .
The difference of these digits , for the in is , therefore , In this will be less , and unless the value of the limit is very much in error the true difference cannot differ from 3952 by more than 2 units in the last place .
Now for Ca is , and .
The possible error in is probably much less than one per .
These numbers agree easily within any possible observation errors , and may say that the separation is due to a denominator difference .
In ( III ) , , have been used to denote the corresponding values in the triplet series , and for .
In order to have a consistent notation we might denote the multiplicity of the series by a corresponding dash and write respectively for triplets or two separations ) and for doublets .
The same notation might be extended to the series themselves , thus would VOL. XCL\mdash ; A. 2 and the other elements as showing no line corresponding to negative values in the Diffuse .
A similar difference is shown also in the triplet series ( III , p. 356 ) , and seems to show that Mg is more analogous to the low melting 1 point elements of this group than to the earths .
This difference is exemplified also when the atomic volume term is considered as is done below ( p. 462 ) .
$$13 Passing on to the sec.ond law , the separations of the satellites in the Diffuse series are caused by denominator differences in and .
That for the first set is always greater than for succeeding sets , for which latter they are in many cases , though not always , the same .
Moreover they are generally multipIes of .
The calculated results are here affected by observed errors in the single lines , but again almost independent of the limit error .
The results are of course independent of any formulae beyond the fact that the wave number is of the form The values of the denominators are given in I. The figures in brackets denote sible errors , and as the effect of the change of limit is practically the same for and it is only entered for the first .
Mg shows no satellites , as is the case also in its triplet series .
The corresponding numbers for Ba and Sr are also placed in this Table from the discussion given below .
In order to obtain the corresponding quantities in Ba and Ra it will be necessary to make a digression to discuss the enhauced series in general in these elements .
gave for the series the Iines ; to which Saunders*has since added 2287 , 2202 .
The Zeeman for the first two pairs have been observed and the ' Phys. Bev vol. 28 , p. 152 .
Series of Lines in Spectra the Alkaline Earths .
Table I. Ca. 858 880 lculated from The satellite differences are therefore 59 , although , as third line probably has large observatiou errors , the 55 , in spite of its exact agreement with the observed separations , , 56 , or even the same as for second line .
The denonlin{tor difference for and 6 is so excessive as to throw some doubt on the allocation of the last to Sr. 4587 2429940 ( 16 ) 4284 3 4 .
4197 The satellite therefore 66 .
The values for the second and third not so cIose as in Ca , but are both within error )nits .
( so ) 8087 85662\mdash ; 26376 \mdash ; Zeeman patterns are those for a doublet series .
The doublet separation is .
There can be no doubt but that the allocation is correct and also that they form an enbanced series .
The formula calctllated from the 2nd , 3rd .
and 4th is This reproduces the first with an error\mdash ; 143 .
The limit may be taken as probably correct within .
The two limits are then and additional or .
These give a denominator difference .
Dr. W. .
Hicks .
On the Enhanced Now , for with an uncertainty of about unity in fourth Hence For Ilifluse series take the set\mdash ; 887 .
1690.59 ( 4 ) 416624 205.41 1690.97 ( 4 ) 37845 97 94.90 ( s ) 3794087 169066 ( 5 ) 2528 In the first set , the line ( 614S ) is taken from an observation by Moore* in the course of bis investigation of the Zeeman effect in the Ba spectrum , and it was strong enongh to enable him to determine its Zeeman pattern .
There can be little doubt as to the allocation of the first two sets , as they both show the Zeeman patterns for diffuse doublets .
It is curious , ever , the of the first old be so luch weaker than the , which is abnormally strong .
It would seem that only a small proportion of the urations which give tlJenorn ) line split up and laterally displaced to the set .
As a ltlle they appear to be l\amp ; ecaron ; ss stable than those giving .
It will be seen later that a similar effect is shown by Ha .
In the third set ] ( is a line observed ) Exner and Haschek .
The other lines in the first three sets are measures of Kayser and Bunge , whose estimates of ) ossible errols , lated to vave n are inserted in brackets after the measures .
The remaining lines are by Saunders .
cit Using the limit and the second and third lines , the formula for is This gives for , which is Saunders ' 2234 , and for , which establishes the set .
denominators are given in Table I. It is seen that the denominator difference for the first satellite is close on , but the diHerence between and the observed is too large to give so satisfactory a decision as in other cases .
This , however , may well be due to the nown observation error in .
This line was not observed 'Ann . .
Phys vol. 25 , p. 314 .
kaline Emake teparation 8outhan 5rror bthrown oation ohenonuenon Trror iconfirm Ra.\mdash ; The case of 1s more difficult as the spectrum has not been measured above 6640 nor below .
Moreover , with increasing atomic weight the .
appear to get more unstable and to break up into numerous others , with the consequent disappearance of regularities .
By far the best measurements are those of the spark spectrum by Rung and Precht .
* Their plates were not sensitive above 6500 .
Exner and Haschek observed a few above this .
Ritz ( loc. cit. ) for the series the two sets \mdash ; ( 100 ) , -(50 ) , and ( 15 ) , ( 10 ) These givo doublet separations respectively of and .
To these may be added for , ( 20 ) , ( 50 ) , ( 50 ) These selections are probably correct\mdash ; although we have not their Zeeman patterns as in Ba .
They are not sufficient , however , to determine the limits unless a Rydberg formula were exact , in which case the two SliItes would be sufficient .
But in the other elements limits as thus found are ab 1800 too high , and thus quite inadmissible .
We are , therefore , driven to apply the ethod which is used in ( III , p. 405 ) in the spectrum of Au .
The Rydberg limit lrom the two lines is about .
Fronl with the other elements real limit shotlld be about 1800 less , in the neighbourhood of 56000 .
It should be that the value of for the observed separation is a mnltiple of the oun\mdash ; of from analogy with the others\mdash ; and that the difference for the separation of should also be a multiple .
If the first condition is applied , a series of values for the limits are obtained .
Using these , they are tested for the second condition .
It is found that one alone satisfies it , and this is then taken as the real limit .
In order to apply this method it is necessary to know beforehand the degree of accuracy of } the data are susceptible .
These data are respectively the values of , and the separation .
For Ra , where is probably less than , or say 1 in 3700 .
the other data it is necessary to know the possible errors of observation , which unfortunately and Precht do not give .
But for the special lines in question to the third decimal place ( excepted ) .
'Ann . .
Phys vol. 14 , p. 419 .
Sharp separations cannot be exactly the same if our error limits are correctly uned .
Those of and may be equal , and as is possibly really its is in apparent reement with indications in other series .
In any case they do not differ by an amount sufficient to affect the determination of the satellite difference .
] will , therefore , be detel.mined by The satellite separation , with the same supposed observation errors , is , or say Between and 55000 nine limits were found which satisfied the first colldition .
The values of the denominator difference ran from to .
These were tested on .
They all distinctly failed to satisfy the condition except that due to .
This belonged to limits and the actual limits to be ]arger , the denominator difference is .
With the assumed maximum values of above for @ , can vary only by .
This limit value is now used for , only will be slightly different if the for is .
The denominators for and are now and .
The difference is , where are the errors in observed and .
Now .
If hese are to be equal .
This equality can be met by values of well their maximum possible errors assunled above .
We are justified , therefore , in taking and the limit The set of lilles should be } reverse ordel in the red .
As no separation 4857 occurs there observed lines , at least is outside the observed , but it may still happel ) that the lines and are within .
If so , their denominator rence should be a multiple of and mantissae considerably less than the corresponding ones for .
Also the lines should be strong , and fro1n analogy wirh the other elements the satellite separation should be rather greater than four times that for .
There are * There are several other lines with } separation , but it will be safer to deal only with lineh .
and differ very closely by multiples of result by all rong .
denominator with a mantissa smaller than for , and latter one with a value much higher than with other } ) ectra would lcad us to expect .
Exner and Haschek give a spark line at with Tllis gives a denominator , with mantissa above that for which again is 146708 above that for ? .
It is .
therefore , in fair order of nitude .
The difference 58814 should be a multiple of , but it is affected with an observation errol of .
With , this is 7 Now , and as , even the large possible error of could not alter the multiple .
It is quite possible , therefore , that is ; the satellite is too faint to have been observed and is outside the region of observation .
If , as in Ba , the satellite differences for and 4 are the same , these unobserved lines would be at ) and and the satellite separation would be The first three sets of as thus arranged are therefore [ -l280351 ] [ -l280351 ] [ -l280351 ] [ -l280351 ] [ -l280351 ] [ -l280351 ] [ -l280351 ] [ -l280351 ] [ -l280351 ] [ -l280351 ] [ -l280351 ] [ -l280351 ] [ -l280351 ] [ -l280351 ] [ -l280351 ] 496.55 4857.34 [ 27627 ] 2428 [ 4117478 ] Series.\mdash ; In the series as given by Fowler the separations are both than in the satellites , for instance as against in Ca , and 4 ; as against in Sr. The differences are too large and too systematic to be ascribed to observation errors .
They seem to be constant for the lines oairs exist withth aration.iscussion oseries hhown thatdifferent owhich would point tisplacements iimits i uggested values forrect , eparation oshould bseparation s andthatinRa , expected .
These are found , and logous sets can be found in all four 5 .
spectra wseparations ahich tZeeman pattern one of excepted)iven boor ( Of these one is probably negative corresponds to , the other to The laws relating to the dependence of the separations of doublets , triplets , and satellites on the oun may be considered so well established that they can be used as tests for ) theories .
The foregoing thus affor strong testimony in your of 's explanation .
We may use these new series as tests for certain other relations , which , although perhaps they cannot be considered as proved , yet have a considerable body of evidence in their favour .
( 1 ) We will take as the first of these , the relation that the inator of the first term of the -sequence\mdash ; that which in the alkalies ives the series\mdash ; is proportional to a multiple of the atomic volume .
It lvould appear that there is in connection with each atom a fundamental quantity , of the nature of a volume .
It is roughly proportional ( probably to about 2 per cent. ) to the atomic volume as measured the ratio of the atonnic weight to the density of the substan ce in .
the solid state , a measure which is dependent to some extent on temperature and other effects .
The law would state that the mantissa of the denominator of the first line should be ) , where is the atomic volume , a whole number , and a number in the hbourhoodo of , this number being probably correct to about ) per cent. The difficulty in determining its value more accurately depends 011 the facts that the true value of is not known within that percentage and to the uncertainty as to whether the fractional part of the denominator itself follows the law , or whether there , is some group constant to the term is added .
But , if so , this constant is so near unity , hat it is quite sible to determine whether the multiple exists\mdash ; and in that case its \mdash ; without uity , allowing factor .
lies the sequence colves the series and 462 Dr. W. .
Hicks .
On the Diffuse sites ivhich tuter sromsequence more ftype tasiest , therefore , which the more intense lines are formed by lateral displacement .
Here S is formed from b.y adding .
In certain ofher cases it would appear that the Sharp series depends on the sequence and the Principal on $ sequence .
In this case we look for the presence of the law in , which is .
is apparently the case in the triplets of Group 2 .
The values of the multiples for the elements already tested are given in ( III , p. 47 ) .
In the present case .
then , both and the must be tested .
The result is that Mg follows ) in and not in .
On the contrary , in Ca , , Ba the law is followed in and not for .
The densities used are the same as in ( II ) , , , , Ba .
The results are given in the following table:\mdash ; of ( 2 ) Ca. .
, , , , Ba .
, , , , .
, , With density of greatest deviation is shown by Sr , in which the density determinations different observers vary greatly .
It is clear that these enhanced series support the truth of the law at as a first approximation .
If is to ehave like Ca , Sr , Ba , its density must ) , where is an integer .
From it would be 6 or 7 , oo.iving a density of or A theory applied triplet serie .
, in which the numbers are less defillite , gave with or 6 .
( 2 ) Apparently the Diffuse sequence depends on multiples of the oun in a similar manner to that in which the sequence depends on the atomic volume .
In a very large number of cases the denominator of the outermost satellites of the first set is a multiple of the , and in all other cases the difference between the denominator and nearest multiple of is itself a nultiple of the oun .
Ill the latter case the nature of the evidence for low atomic weights is not decisiye as in them the oun is so small that it is easily smothered by observation errors .
In the present discussion , then , the question to be tested is whether the first satellite denominator is a multiple of , or differs froru such multiple by a multiple of the oun .
In the case of Mg the is too.small to settle the question no way or the other .
Series of Lines in Spectra of the Alkaline .
463 Ca , using Paschen 's value of For , mantissa with Sr , using Randall 's value of For , mantissa , is not a multiple of For , , , If , however , the limit be determined from the second , third , and fourth lines\mdash ; which is generally to be preferred\mdash ; it co1nes out 49lower .
To make the mantissa an exact multiple , the limit should be lower by , and probably also more correct than .
It is curious that Sr shows precisely the same kind of displacement in the triplet system , the exact multiple being there found in instead of in Ba.\mdash ; Here neither nor give multiples of , but they differ from such by multiples of the oun .
For , mantissa Now it was seen above in considering the satellite ) arations that with a large possible error makes the denominator too by 58 .
This corrected value would give for above Iantissa Ra\mdash ; For , lnantissa With the relations hold , within small observation errors , for both .
As to the changes in the limits equired by the above values of , it is to be noted that for Ba and Ra they should not be , because if the theory used to determine the Ra limit is correct the value obtained must be close to the real value\mdash ; and is quite allowable .
For Ba the limit is obtained from the second , third , and fourth lines and is a better value erefore than that obtained from the first or fifth .
Fowler 's limits for Ca and Sr are on the face too large , as the for the later lines .
Hence , here again the evidence of the enhanced series gives support to relation obtained in ( III ) from a study of other series .
|
rspa_1915_0037 | 0950-1207 | Gaseous combustion at high pressures. | 464 | 465 | 1,915 | 91 | Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character | William Arthur Bone, D. Sc., F. R. S.|Hamilton Davies, B. Sc.|H. H. Gray, B. Sc.|Herbert H. Henstock, M. Sc., Ph. D.|J. B. Dawson, B. Sc. | abstract | 6.0.4 | http://dx.doi.org/10.1098/rspa.1915.0037 | en | rspa | 1,910 | 1,900 | 1,900 | 2 | 40 | 834 | http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1915_0037 | 10.1098/rspa.1915.0037 | null | null | null | Agriculture | 48.909781 | Thermodynamics | 21.842833 | Agriculture | [
-4.482679843902588,
-37.675865173339844
] | 464 Lv 'Wii.i.i^Lr ^LrniiL Lor^L , v.8o .
, L.R.8 .
, in oollaboration with Messrs. v^viLS , L.8o .
, H. H. Ok^ , L.8o .
, RLkLM'r L. ULns'rooL , L4.8o .
, Lb.v .
, and d. L. v^wso^ , L.8o .
( Reeeived Deeember 22 , 1914 .
) ( ^.bstraot .
) His paper gives an aooount ok investigations on gaseous oombustion under bigb pressures earried out in tire Luel Department ok tire University ok Deeds during the ^ears 1906-12 , with a speoial installation ok apparatus , tbs oost ok whiob was dekra^ed out ok grants made kroin time to time b^ the ( Government Orant Oommittse .
Experiments in whiob inixtures ok metbane with less than its own volume ok oxygen were exploded in steel bombs at initial pressures ok between 8 and 32 atinosplieres liavs given results in barmon^ withi the " b^drox^la-tion " tbeor^ ok b^drooarbon oombustion put korward some ^ears ago b^ Lrok .
Lone .
lbs induenos ok various seoondar^ reaetions upon the produots ok the primary oxidation whilst the gases are eooling down akter the attainment ok maximum pressure is diseussed in the light ok the experimental results .
Results ok experiments upon an e^uimoleoular mixture ok etliane and oxygen , wliose bebaviour is eruoial in respeot ok the dikkerent views ok b^drooarbon oombustion advaneed in reeent vears , have again oondrmed rbe li^droxvlation tlieor^ .
^notber seetion ok the paper deals with an experimental determination ok tbs relative akkinities ok metlians , b^drogen , and oarbon monoxide kor oxygen in dames .
It is sliown ( 1 ) that the akdnit^ ok metbane is at least twenty times as great as that ok b^drogen , and ( 2 ) that wlren mixtures corresponding to 6H44 O24-LVH2 are kirsd under liigli initial pressures , in wliioli the partial pressures ok metbane and oxygen are bept oonstant and M on^ varied , the distribution ok oxygen between the metbane and b^drogen varies with a ?
, a eireumstanee whieb means that b^drogen is burnt to steam in dames as the result ok tbs trimoleeular ebange 2H2-I- O2 \#151 ; 282O , and not ( as some have supposed ) tbrougb b^drogen peroxide .
Ibe akdnit^ ok oarbon monoxide is sbown to bo oomparable with that ok b^drogen kor oxygen in dames .
Experiments are also desoribed in whiob mixtures ^k etb^lene , oxygen , and b^drogen , oorresponding to 62H4 d-O2 d-MD2 , Deesnr-x-srtron .
o/ ' ( 7s--2^)ort-rc^s .
were exploded at bigb initial pressures ; r'-r^s- ' \#171 ; /r\#171 ; it was kound possible to increase \#171 ; up to 8 without causing an^ deposition ok carbon on explosion .
Ike tbeoretical bearing ok the results is kull^ discussed .
Mis dual section ok the paper describes expsriinents in which the whole pressure curves , up to and kar beyond the attainment ok maximum pressure , were recorded when mixtures corresponding to ( 1 ) 2Hz-l-0s 4-41^2 .
( 2 ) 200-p O2-l-41^2 , and ( 3 ) 684-K O2 4-4X2 , are exploded under initial pressure ok about 50 atmospberes .
It is sbown that tbs rates ok attainment ok maximum pressure in eacb case have no direct relation to tbs order ok albnities ok the various gases kor oxygen .
Oo-nV\lt ; )rtn\lt ; Fs .
II.\#151 ; /o-rr'satro , r 0/ t/ i , e ( ^crses Id. 6 .
Do'rrLir , 8c.D .
, lVI.^. .
, Drokessor ok Botany in the University ok Durbam .
( Oonununieated b^ Dr. D. waller , D.It.8 .
Deeeived Debruar^ 26 , 1915 .
) It is well known that the gases liberated during certain chemical actions carr^ cbarges ok electricity , Ibus Davoisier and Daplace kound that the b^drogen liberated krom the action ok b^drocbloric acid upon iron is cbarged positively .
Idore recently Dnrigbt(l ) bas noted the same ekkect , and lownsend ( 2 ) bas sbown that the gases liberated during electrolysis are also cbarged .
In a previous paper ( 3 ) evidence bas been brougbt korward to sbow that tbs decomposition ok organic matter gives rise to electrical eKeels which are ok tbs same nature as tboss produced b^ the action ok acids upon metals .
It seemed tberekore an interesting point to investigate whetber tbs OO2 escaping krom the kermentation ok a saccbarine solution migbt carr^ an electric ebargs and be ionised .
1o determine this point a sSries ok experiments were carried out b^ tbs employment ok a gold leak electroscope and a Dolesalek electrometer .
Ibe metbod adopted was to suspend a metal plats with rolled edge a kew centimetres above the surkace ok glucose undergoing kermentation tbrougb the action ok ^east , the metal plate being connected with the electroscope or electrometer , and tbs whole suitably screened in a box lined with tinkoil .
Headings were tbsn taken in the ordinary manner , von .
xoi.\#151 ; x.
|
rspa_1915_0038 | 0950-1207 | Electrical effects accompanying the decomposition of organic compounds. II.- Ionisation of the gases produced during fermentation. | 465 | 480 | 1,915 | 91 | Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character | M. C. Potter, Sc. D., M. A.|Dr. A. D. Waller, F. R. S. | article | 6.0.4 | http://dx.doi.org/10.1098/rspa.1915.0038 | en | rspa | 1,910 | 1,900 | 1,900 | 6 | 250 | 6,604 | http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1915_0038 | 10.1098/rspa.1915.0038 | null | null | null | Biochemistry | 28.738058 | Electricity | 25.345739 | Biochemistry | [
-15.322754859924316,
-50.43023681640625
] | Decomposition of Organic Compounds .
465 were exploded at high initial pressures ; alia it was found possible to increase a ; up to 8 without causing any deposition of carbon on explosion .
The theoretical bearing of the results is fully discussed .
The final section of the paper describes experiments in which the whole pressure curves , up to and far beyond the attainment of maximum pressure , were recorded when mixtures corresponding to ( 1 ) 2H2 + 02+4U2 , ( 2 ) 200 + 02 + 41^2 , and ( 3 ) CH4 + O2+4N2 , are exploded under initial pressure of about 50 atmospheres .
It is shown that the rates of attainment of maximum pressure in each case have no direct relation to the order of affinities of the various gases for oxygen .
Electrical Effects accompanying the Decomposition of Organic Compounds .
II.\#151 ; Ionisation of the Gases produced during Fermentation .
By M. C. Potter , Sc. D. , M.A. , Professor of Botany in the University of Durham .
( Communicated by Dr. A. D. Waller , F.R.S. Received February 26 , 1915 .
) It is well known that the gases liberated during certain chemical actions carry charges of electricity .
Thus Lavoisier and Laplace found that the hydrogen liberated from the action of hydrochloric acid upon iron is charged positively .
More recently Enright ( 1 ) has noted the same effect , and Townsend ( 2 ) has shown that the gases liberated during electrolysis are also charged .
In a previous paper ( 3 ) evidence has been brought forward to show that the decomposition of organic matter gives rise to electrical effects which are of the same nature as those produced by the action of acids upon metals .
It seemed therefore an interesting point to investigate whether the C02 escaping from the fermentation of a saccharine solution might carry an electric charge and be ionised .
To determine this point a series of experiments were carried out by the employment of a gold leaf electroscope and a Dolezalek electrometer .
The method adopted was to suspend a metal plate with rolled edge a few centimetres above the surface of glucose undergoing fermentation through the action of yeast , the metal plate being connected with the electroscope or electrometer , and the whole suitably screened in a box lined with tinfoil .
Readings were then taken in the ordinary manner .
VOL. xoi.\#151 ; a , 2 p 466 Prof. Potter .
Electrical Effects accompanying the Description of the Apparatus ( fig. 1).\#151 ; To avoid , as far as possible , the large accumulation of froth which always accompanies alcoholic fermentation , the fermenting glucose was enclosed in a shallow tin dish { a ) , 25 cm .
in diameter and 7 cm .
in depth , the large free surface permitting the C0a to escape more freely .
For the purpose of insulation the dish was supported upon three amberoid plugs ( / ) fixed in a wooden base ) , the key providing the means of earthing the dish , if required , through the earthed wire ( m ) .
The metal plate ( b ) , 2 25cm .
in diameter , was suspended by a copper wire ( c ) soldered to its upper surface , this copper wire passing through a sulphur plug ( d ) held firmly in a support ( e ) .
This portion of the apparatus was enclosed in a light wooden box ( A ) lined with tinfoil and Fig. 1 .
having a detachable front also lined with tinfoil .
By this means the fermenting glucose and accessory apparatus were effectually screened from external influence .
Attention has already been drawn to the well known fact that the COa evolved during fermentation does not escape freely from the fermenting liquid , and thus it is necessary to provide some means of stirring the yeast-glucose solution .
This was accomplished by means of a glass rod ( h ) bent at right angles ( with a short rod of ebonite ( j ) inserted for insulation ) and fixed to the inside of the box ( A ) by passing through the support ( ) , the lower portion being held horizontally just above the bottom of the dish and immersed in the fermenting liquid .
The upper end of this rod projected through small hole in the top of the box , and by turning the projecting Decomposition of Organic Compounds .
467 piece backwards and forwards the liquid in the dish could be stirred without disturbing its insulation .
The electroscope ( r ) employed was of the ordinary type , with a gold leaf measuring 4*5 cm .
in length by 1 mm. in breadth .
This was enclosed in a brass box with windows , protected by glass slips , cut in opposite sides for the observation of the gold leaf , sulphur being used for insulation .
The electroscope was screened by a wooden box ( B ) lined with tinfoil , similarly to the box A. It was charged from a battery of 220 volts by a bent wire ( l ) which passed through the sulphur plug ( s)fitted into a hole in the top of B. A convenient and inexpensive battery was contrived by connecting in series a number of " refills " used for electric torches .
Such a battery of 150 cells gave an E.M.F. of 220 volts , which remained constant for a considerable time .
The boxes A and B were carefully earthed and connected by a metal tube through which passed a copper wire ( ?
i ) insulated by the amberoid plugs ( o ) , the copper wire serving to connect the electroscope with the metal plate .
The movement of the gold leaf was observed by means of a horizontal microscope with a micrometer eyepiece .
It was found that five scale divisions of the eyepiece corresponded to a difference of charge of 4'4 volts upon the electroscope and plate .
The times at which the gold leaf passed over the divisions were taken by means of a stop-watch .
During each series of observations the times were noted for the fall of the gold leaf over the same divisions , which could readily be effected , as both the electroscope and plate were charged from the battery of 220 volts .
Before commencing any series of observations the insulation was carefully tested , especially that of the ebonite ( J ) inserted in the stirrer , which was rubbed with glass paper to ensure a clean surface .
For the glucose solution 100 grm. of ordinary commercial glucose were dissolved in one litre of water , and the solution was placed in the box A for some hours that it might acquire the same temperature as the box and its contents .
About 800 c.c. of this solution was then poured into the tin dish , the metal plate was placed in position , and a series of readings taken to determine the rate of leak of the gold leaf .
To the remaining 200 c.c. was added approximately 100 grm. of commercial pressed yeast to start the fermentation .
When the rate of leak had been determined the 200 c.c. containing the yeast was added to the solution already in the tin dish and readings were taken for the fall of the gold leaf under these conditions .
As the result of many observations it was found that when the dish contained glucose solution without yeast , the rate of electroscope leak was uniform over the same five scale divisions of the eyepiece , whether the electroscope was charged positively or negatively , and this rate of leak was 2 p 2 468 Prof. Potter .
Electrical Effects accompanying the uninfluenced by the action of the stirrer in the glucose .
That is the curve representing the rate of leak is a straight line .
The way was therefore clear for further advance .
The general plan of the experiments was to introduce the glucose and yeast in the manner just described , adjust the metal plate so that it would be suspended approximately 4 cm .
above the surface of the fermenting glucose and concentric with the dish , then connect the metal plate with the electroscope and charge them to the standard voltage ( 220 ) , recharging after each reading .
Owing to the necessity of stirring the glucose , the readings to determine the rate of leak of the electroscope were taken in sets of three , one immediately after the other : that is one reading before stirring ( ( I ) in the diagram ) , one during which the stirring was in operation ( II ) , and a third in which no stirring took place ( III ) .
Experiments with the .
Two sets of observations were required , viz. the electroscope and plate charged positively , and the electroscope and plate charged negatively .
In each case the disc containing the fermenting glucose was connected to earth .
Electroscope and Plate Charged Negatively.\#151 ; An example typical of many observations is shown in the diagram , fig. 2a and B. The curves in A refer to readings taken almost immediately after the introduction of the yeast , and before the full rate of velocity of the fermentation had been reached .
The times are plotted horizontally in minutes and the divisions of the eyepiece vertically .
The curves I and III are practically straight lines , and show that the rate of leak in the absence of stirring is uniform .
It will be noted that in III , after the stirring , the rate of leak is slower than in I. In II the curve is slightly bent , but as there is little evolution of CO2 at such an early stage the curves do not exhibit any very perceptible difference .
The three curves in B represent readings taken later than those in A , at a time when the fermentation would be actively proceeding .
Some 17 minutes elapsed between the curve II in b , and the corresponding one in A , and during this interval a large quantity of CO2 would be formed and not liberated from the fermenting solution until stirring took place .
Curves I and III are again straight lines , but the times occupied by the gold leaf passing over the five divisions are somewhat faster than was the case in A. The curve III also again shows a decreased rate of leak as compared with I , owing no doubt to the liberation of the entangled CO2 during the process of stirring .
Curve II shows in a marked degree the sudden evolution of the CO2 due to the action of the stirrer .
At the commencement of the Decomposition of Organic Compounds .
stirring the entangled CO2 rapidly escaped , and simultaneously the gold leaf fell through one and a half divisions in 36 seconds , a great contrast MINUTES Fig. 2b .
to the rate of leak in I and II , when the time occupied for the leaf to fall over the first division was and 2 minutes respectively .
After the sudden ebullition of the COa , due to the action of the stirrer , the stirring was stopped , and the fall of the gold leaf then became very slow , taking 4 minutes 24 seconds to reach the next division .
During 470 Prof. Potter .
Electrical Effects accompanying the this time C02 would accumulate , and on proceeding again to stir the gold leaf fell through the next division in 48 seconds .
The stirrer was now stopped again , and 3 minutes 42 seconds were occupied by the .
leaf in falling to the fourth division .
Then on the re-commencement of stirring 1| .
minutes only were occupied in falling to the last division .
As mentioned above , five scale divisions are equivalent to a difference of 4'4 volts .
Thus curve II shows that at the commencement of the stirring the electroscope and plate lost a charge of 1*32 volts in 40 seconds , in striking contrast to curve 1 , which represents a discharge of 0*88 volt in 1 minute 30 seconds .
During the next period ( 4 minutes 24 seconds ) , when the stirrer was not in action , the fall of the leaf was very slow , and the discharge only 0 44 volt .
As soon as the leaf reached the second division , and stirring took place , the same rapid discharge of the electroscope was repeated , a discharge of 0'88 volt occurring in 48 seconds .
Similarly there was again a quick discharge when stirring took place at the fourth division .
Electroscope and Plate Charged Positively.\#151 ; The results obtained under these conditions ( fig. 3a and b ) are of the same character as those indicated when the electroscope and plate were charged negatively , and need not , therefore , be dealt with in detail .
As in the latter case , the readings taken just after the introduction of the yeast ( fig. 3a ) show little difference between the curves I , II , and III , as there would be only a slight evolution of C02 .
But after the lapse of half an hour the effect of the escaping C02 is again plainly shown ( fig. 3b ) .
Curves I and III are as before straight lines , showing that approximately the same rate of discharge had been maintained .
Curve II shows the rapid discharge of the needle consequent upon the action of the stirrer , then a slow rate of discharge when the stirring was discontinued , followed by a rapid discharge upon the re-commencement of stirring , and so on .
With a 10-per-cent , solution of glucose there is always a considerable amount of froth , and it might be objected that the accumulation of this froth , diminishing the distance between the surface of the fermenting glucose and the metal plate , would alter the capacity of the electroscope and plate , and thus cause an error in the electroscope readings .
Many experiments were tried with the object of diminishing the froth , and it was found that with a 2'5-per-cent , solution of glucose it was reduced to a few bubbles and no accumulation occurred .
Also with this strength of solution the fermentation proceeded rapidly , and the quantity of C02 evolved was sufficient to give reliable readings during the time required for each experiment* It seemed , therefore , desirable to adopt this formula for further Decomposition of Organic Compounds .
471 j tests , and the following set of experiments were carried out in the same manner as the two just described , but with the employment of a 2-5-per-cent .
glucose instead of the 10-per-cent .
I 2 -64 ) J 1176 .88 2 4 6 8 10 MINUTES Fig. 3a .
MINUTES Fig. 3b .
Electroscope and Plate Charged Negatively.\#151 ; In fig. 4a and B are given the curves obtained from a 2*5 solution of glucose , with approximately 100 grm. of yeast .
A comparison of these figures with figs. 2 and 3 shows that with the weaker solution much steeper curves were obtained , but they retained Prof. Potter .
Electrical Effects accompanying the the same characteristics .
Curves I and III are again straight lines .
In fig. 4a , taken from observations made as soon as possible after the introMINUTES Fig. 4b .
MINUTES Fig. 4a .
duction of the yeast , curves I and III were identical in the particular experiment here described ; while curve II coincided with these in the initial stages , but after the gold leaf had passed the second division its rate of discharge was somewhat slower .
Pig .
4b gives the result of observations made some 20 minutes after the introduction of the yeast , and when its full activity had been reached .
The effect of stirring is shown in curve II , the time occupied for the gold leaf to fall through the first two divisions being equal to that taken for the leaf to fall through one division in the case of curves I and III .
On account of the gradient of the curves the slow rate of discharge after stirring is not a noticeable feature , but it may be remarked that the rate of fall in curve II , after stirring , is the same as in curve III .
Electroscope and Plate Charged Positively.\#151 ; The curves for this experiment Decomposition of Organic Compounds .
with a positive charge are given in fig. 5a and B , and repeat in character the results obtained with the negative charge .
Fig. 5a , representing MINUTES MINUTES Fig. 5a .
_ Fig. 5b .
readings taken immediately after the introduction of the yeast , presents the same features as the other curves already given from similar observations ; and fig. 5b , derived from readings after the lapse of half an hour , when the fermentation was fully established , again strikingly illustrates the sudden fall of the gold leaf as the result of stirring .
In curve II the leaf fell through two divisions in 30 seconds , whereas in curves I and III it fell through one division in 45 seconds and 60 seconds respectively .
A comparison of the results obtained from the1 10-per-cent , and 2'5-percent .
solutions of glucose show that they are confirmatory one of the other .
An explanation of the fact that the 2'5-per-cent , solutions give much steeper curves is afforded by the observations of Adrian Brown ( 4 ) , O'Sullivan ( 5 ) , and others , who found that within certain limits the amount of sugar did not influence the rate of fermentation .
Slator(6 ) , working with a definite number of yeast cells , has also shown that the rate of fermentation is practically the same from 0'5-per-cent , to 10-per-cent , solutions of glucose .
The experiments with the 10-per-cent , and 2*5-per-cent , glucose were conducted at approximately the same temperature , and with roughly the same number of yeast cells per litre of glucose solution , and hence approximately the same quantity of CO2 would be formed in equal intervals 474 Prof. Potter .
Electrical Effects accompanying the of time .
But , on account of the greater viscosity of the stronger solution , the COg is in great measure prevented from escaping , as evidenced by the accumulation of froth ; but in the weaker solution the CO2 escapes more readily , and , as a consequence , the rate of fall of the gold leaf is more rapid and the curves are steeper .
9 Experiments with the Electrometer .
With the object of testing the results obtained with the gold leaf electroscope , a series of observations were made by substituting a Dolezalek electrometer for the electroscope in the box B. One pair of quadrants was connected to the metal plate and the other pair earthed , the arrangements otherwise remaining the same .
The dish containing the fermenting glucose was raised to a potential of 110 volts , this potential being found sufficient to produce a saturation current .
The electrometer needle was suspended by a fine wire of phosphor bronze and was also maintained at a potential of 110 volts .
It was found , by connecting one pole of a Clark cell to the plate and the other to the earth , that a deflection of 50 scale divisions corresponded to 1*4 volts when the needle was charged to 110 volts .
For the reasons given in the account of experiments with the electroscope , a 2'5-per-cent , solution of glucose , with approximately 100 grms. of yeast , was again employed as the formula from which the most reliable results could be obtained .
A 10-per-cent , glucose solution was also used for comparison of results , as well as a 1-per-cent .
Many trials were made with the electrometer to test the effect produced by the action of the stirrer in a solution of glucose without the addition of yeast .
The stirring was found to have no influence upon the electrometer readings .
The same system of reading was followed as has been previously described for the electroscope , that is : one reading without stirring , * one immediately after while the stirring was in progress , and a third directly after the stirring ceased , the dish and quadrants being earthed after each reading .
The Dish and Fermenting Glucose Charged to 110 Volts Negatively.\#151 ; The readings taken as soon as possible after the introduction of the yeast showed little or no difference in the rate of movement of the spot of light across the scale , whether the stirrer was in operation or not .
After allowing an interval of about half an hour for the fermentation to be thoroughly set up , it was found from many experiments that a great difference was at once noticeable between the readings taken when the stirrer was wording and those immediately preceding or following .
When the Decomposition of Organic Compounds .
475 fermenting glucose was left undisturbed the spot of light moved at a uniform rate , but when stirring took place it at first instantly moved rapidly over the scale and was then succeeded by a slower movement .
In one particular experiment selected for illustration , 4 minutes 20 seconds were occupied by the spot of light in moving over 10 scale divisions in the absence of stirring , whereas immediately upon the commencement of stirring the spot moved quickly , eight divisions being passed over in 1 minute and the next two divisions in 1 minute 15 seconds .
In the next observation , during which the medium was again left quiescent , the spot of light moved uniformly at the same rate as in the first case .
The Dish and Fermenting Glucose Charged to 110 Volts Positive.\#151 ; In this case also , immediately after the introduction of the yeast , the action of the stirrer produced no alteration in the rate of movement of the spot of light .
But after allowing sufficient time for a vigorous fermentation to be set up , the spot of light moved rapidly as soon as stirring commenced , reverting to a slower rate of movement after the escape of the CO* To cite one experiment , before the glucose was stirred it took 3| minutes for the spot of light to traverse 10 scale divisions , while seven divisions were passed over within one minute of the commencement of the stirring .
Then following this escape of COa , minutes were required for the next three divisions to be passed over .
It is thus seen that whether the fermenting glucose is charged negatively or positively the same results are obtained .
That is , readings taken immediately after the addition of the yeast to the glucose solution , when fermentation had hardly commenced , show the charging of the metal plate to be influenced in a very slight degree by stirring .
But at a later stage , when agitation produced a sudden liberation of CO2 , the metal plate is rapidly charged .
The results obtained from the Dolezalek electrometer are in all respects in close agreement with those obtained from the electroscope .
From these experiments it may be deduced that the CO2 , when emerging from a saccharine solution , carries an electric charge or , in other words , is ionised .
Also , since the electroscope is discharged , whether it be negatively or positively electrified , and as the electrometer needle is deflected , whether the fermenting glucose is charged positively or negatively , it may be concluded that both positive and negative ions are carried by the escaping CO2 .
With regard to the different times quoted in these experiments , it should be remarked that to equate the results the fermentation must be carried out with solutions of glucose of precisely equal strength , maintained at the same temperature and fermented by means of an accurately determined number of actively living yeast cells , taken from a pure culture of the same biologic 476 Prof. Potter .
Electrical Effects accompanying the form .
Up to the present it has not been found possible to satisfy these necessary conditions .
Nor has it yet been possible to compare the ionisation produced by yeast with a standard solution of a radium salt .
The investigation goes no further than to indicate that the escaping CO2 carries both positive and negative ions .
Lord Kelvin ( 7 ) has shown that air when bubbled through water is ionised , and this fact , as Sir J. J. Thomson ( 8 ) has pointed out , renders the interpretation of results difficult when they concern the evolution of gases through a liquid .
But air bubbled through water carries with it a negative charge , and when , as in this case , the emerging gas is both negatively and positively electrified it may be assumed that the electrification is due to the fermentation and not merely to the bubbling .
* The author ( 3 ) has already demonstrated that electrical effects accompany the decomposition of organic compounds , and as the CO2 escaping from a fermenting saccharine solution also shows the presence of both positive and negative ions , it may be inferred that the gases liberated during the process of putrefaction are also ionised .
This possibility introduces another element for consideration in connection with the researches on the radioactivity of water and soils .
Many investigations have been made upon the presence of radium emanation in various waters and in the soil air , the detection of the radium emanation being determined by the electroscope and electrometer , and a comparison of the results of these researches with those which are now described offers an interesting parallel .
Sir J. J. Thomson ( 9 ) has shown that air when bubbled through Cambridge tap water " shows all the peculiarities of a gas in which continuous ionisation is taking place .
" He also considers that if the effects produced are due to the deposition of a radioactive substance , such substance must have come from the water .
Yet upon evaporating the water to dryness upon a metal plate this did not show any ionising power .
Adams ( 10 ) has followed up the results of Sir J. J. Thomson by an investigation into the nature and properties of this radioactive gas .
When comparing it with air blown through distilled water in which a radium compound was dissolved , he found that while these two gases possessed many similarities there were important differences .
For instance , the solution containing the radium salt , when thoroughly boiled and all the emanation expelled , does not recover its radioactive properties even after a long time , whereas the radioactivity \#174 ; f tap water cannot be entirely destroyed by boiling , and on allowing it to stand it becomes again radioactive , though not to the same extent as before .
He also showed that the residue obtained from evaporating large quantities of tap water is not Decomposition of Organic Compounds .
477 radioactive .
Adams considers that these results can only be explained by assuming a continuous production of a radioactive emanation in the water .
These , observations of Thomson and Adams appear to lend considerable support to the suggestion that much of the radium emanation found in various waters may be really due to ionised gases formed during the natural decomposition of organic matter through the action of micro-organisms .
In such a case " continuous ionisation " would be a natural result , but the residue , after evaporation to dryness , would not be likely to yield any ionising power , as it would not provide suitable conditions for bacterial life .
It may be pointed out that in the account of these experiments there is no mention of their being carried out in such a manner as to exclude bacterial contamination .
Boiling would kill all the micro-organisms actively living in the water , but not necessarily those in the spore stage , some of which would probably survive and germinate when the conditions once more became favourable .
In certain special cases boiling is even of positive advantage .
Miquel(ll ) has shown that during the process of boiling certain toxins inimical to bacterial life are destroyed , and this is further supported by the experiments carried out by the Massachusetts State Board of Health ( 12 ) , which show that the power of multiplication of certain bacteria is increased enormously in water which has been boiled .
While it is also thoroughly established by the experiments of Mead Bolton and others ( 13 ) that certain water bacteria possess the remarkable power of extensive multiplication in sterilised distilled water , these special forms might not be present ; and further , in the absence of organic constituents , one may presume that no ionisation would take place .
Thus it is possible to account for the fact that Adams found radioactivity regenerated in tap water but not in boiled distilled water .
Unless special precautions were taken it is almost certain that tap water would contain many active bacteria after standing for some time , especially as this contains a small amount of organic matter .
In this connection it is of interest to note that Satterly ( 14 ) has found that Cam water taken at Sheep 's Green , which would presumably contain more organic matter than Cambridge tap water , also contains twice as much radium .
Joly ( 15 ) found a greater amount of radium at Valencia Harbour and at certain localities round the Irish coast than in the open ocean some miles from land .
He also found that a part of the radium may be filtered from sea water which contains much organic matter and has been left standing for some weeks , and suggests that it is possibly precipitated by bacterial action in the decomposing organic particles .
478 Prof. Potter .
Electrical Effects accompanying the Satterly ( 16 ) has found that marsh gas ( CH4 ) collected in the Cam and ditches around Cambridge is radioactive .
It is significant that marsh gas is one of the products arising from the decomposition of vegetable matter through the action of bacteria .
The question of atmospheric ionisation has also been the subject of many investigations , since Elster and Geitel demonstrated the presence of radioactivity and ionisation in the atmosphere , and the source of this ionisation has been much studied .
These authors , and later Satterly ( 17 ) , have shown that air sucked up from the earth is ionised , and it is generally admitted that the ionisation of the air is due to ionised gases escaping from the soil or from water .
The influence of meteorological conditions upon the amount of atmospheric ionisation does not at present seem to be very conclusively established .
Satterly ( 18 ) failed to demonstrate any definite connection between the variations of the barometer and the variations of the ionisation , though some of his observations point to the fact that the ionisation increases with a falling barometer unless accompanied by wet weather .
On the other hand , Eve ( 19 ) has shown that the emanations increase in amount during cyclones accompanied by heavy rain or rapid thaw and decrease during anticyclones with dry weather and , in winter , low temperatures .
He explains that diminishing pressure causes radium emanation , together with other gases , to escape from the ground , and that the moistening of the soil through rain and melting snow promotes the liberation of these gases .
On this point it may be noted that , when estimating the bacteria in the Rivers Thames and Lea , Erankland ( 20 ) found that during rainy weather the number of bacteria increased enormously as a consequence of the washing of organic matter from cultivated land into the rivers , and hence these micro-organisms were much more numerous during the rainy winter months than in those of the dry summer .
Parallel results have been obtained from similar investigations of other rivers .
It is also to be observed that the conditions of sudden warmer temperatures with heavy rainfall noted by Eve for the promotion of radium emanation in the atmosphere are also those which favourably influence the activity of bacterial life .
Here again it seems a reasonable hypothesis that part at least of the atmospheric ionisation may be due to ionised gases escaping from the putrefying organic matter present in the soil and water .
It has been recognised that the radium emanation by no means accounts for the whole production of ions in the air , and Satterly 's ( 18 ) experiments bring him to the conclusion that " only a small proportion of the natural ionisation of the air is due^o the presence of radium emanation and its products .
" Decomposition of Organic Compounds .
479 Keference may here be made to a former paper ( 3 ) , in which it was shown that in the case of fermenting glucose separated by a membrane from nonfermenting glucose , the former was negative ( zincative ) with respect to the latter and also that this proposition was true with regard to putrefying organic matter .
From this it may reasonably be inferred that decaying organic matter may have an influence upon the electric potential of the earth 's surface , at least in its immediate vicinity .
Though it has not been possible so far to determine quantitatively the ionisation derivable from the activity of the yeast cells nor to give any indication of the relative importance of the processes of ionisation passed in review , yet sufficient evidence has been adduced to establish the fact that fermentation gives rise to ionised gases .
Many observations also seem to support the conclusion that some of the ionisation effects noted in the air and in the gases derived from water and the soil may be traced to the natural decomposition of organic matter .
I venture , therefore , to set forth a plea that biologic forces should be taken into consideration in seeking the sources of natural ionisation .
Nothing is yet known of the possible electrification of the air through the metabolic and physiological activities in plants , and the putrefactive processes alone throughout the whole realm of nature may represent a potent factor in the production of ions and play a part in the cloud and mist formations and other manifestations included in the phenomena of electrification .
The occupation of Armstrong College by the military and its conversion into the Northern Base Hospital in August , 1914 , put an end to any further research in my laboratory , and I regret that there has been no opportunity to complete some other work which I had intended to carry out , and many problems connected with this investigation must await further elucidation .
Summary .
The CO2 liberated during fermentation of glucose through the action of yeast carries both positive and negative ions , and the suggestion is offered that the gases set free during the putrefaction of organic matter are also ionised .
Part of the ionisation of the atmosphere may be attributed to the presence of such ionised gases escaping from the soil and water , and it may be assumed that putrefactive processes in nature exercise an important influence upon various electrical phenomena .
Decomposition of Organic Compounds .
LITERATURE .
Adams ( 10 ) .
" Water Radioactivity , " ' Phil. Mag. , ' 1903 .
Brown , Adrian ( 4 ) .
" Influence of Oxygen and Concentration on Alcoholic Fermentation , " ' Journ. Cbem .
Soc. , ' 1892 .
Enright(1 ) .
" On Electrifications due to the Contact of Gases with Liquids , " 'Phil .
Mag. , ' 1890 .
Eve ( 19 ) .
" On the Amount of Radium Emanation in the Atmosphere near the Earth 's Surface , " ' Phil. Mag. , ' 1908 .
Frankland ( 20 ) .
' Micro-organisms in Water , ' 1894 .
Joly ( 15 ) .
" Radioactivity of Sea Water , " ' Phil. Mag. , ' vol. 15 ( 1908 ) .
Kelvin ( 7 ) .
" Electrification of Air and other Gases by Bubbling through Water and other Liquids , " ' Roy .
Soc. Proc. , ' vol. 57 ( 1895 ) .
Massachusetts(12 ) .
See Frankland , 'Micro-organisms in Water , ' p. 229 .
Mead Bolton ( 13 ) .
See Frankland , ' Micro-organisms in Water , ' p. 231 .
Miquel(ll ) .
See Frankland , 'Micro-organisms in Water , ' p. 228 .
O'Sullivan ( 5 ) .
" On the Rate of Alcoholic Fermentation , " 'Journ .
Soc. Chem. Ind. , 1898 .
Potter ( 3 ) .
" Electric Effects accompanying the Decomposition of Organic Compounds , " 'Roy .
Soc. Proc. , ' B , vol. 84 ( 1911 ) .
Satterley ( 14 ) .
" Note on the Radium-content of the Waters of the Cam , Cambridge Tap Water , and some Varieties of Charcoal , " ' Camb .
Phil. Soc. Proc. , ' vol. 15 ( 1910 ) .
----(16 ) .
" The Radioactivity of Marsh Gas , " 'Camb .
Phil. Soc. Proc. , ' vol. 16 ( 1911 ) .
----(17 ) .
" A Study of the Radium Emanation contained in the Air of Various Soils , " ' Camb .
Phil. Soc. Proc. , ' vol. 16 ( 1911 ) .
----(18 ) .
" The Amount of Radium Emanation in the Atmosphere , " ' Phil. Mag. , ' 1908 .
Slator ( 6 ) .
" Studies in Fermentation .
I.\#151 ; The Chemical Dynamics of Alcoholic Fermentation by Yeast , " 'Journ .
Chem. Soc. , ' 1906 .
Thomson ( 8 ) .
' Conductivity of Electricity through Gases , ' 1906 .
----(9 ) .
" Experiments on Induced Radioactivity in Air , and on the Electrical Conductivity produced in Gases when they Pass through Water , " ' Phil. Mag. , ' 1902 .
Townsend ( 2 ) .
" Electrical Properties of Newly Prepared Gases , " ' Camb .
Phil. Soc. Proc. , ' vol. 9 ( 1898 ) .
|
rspa_1915_0039 | 0950-1207 | The effect of temperature on the hissing of water when flowing through a constricted tube. | 481 | 485 | 1,915 | 91 | Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character | Sidney Skinner, M. A.|F. Entwistle, B. Sc.|Dr. W. N. Shaw, F. R. S. | article | 6.0.4 | http://dx.doi.org/10.1098/rspa.1915.0039 | en | rspa | 1,910 | 1,900 | 1,900 | 4 | 64 | 1,969 | http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1915_0039 | 10.1098/rspa.1915.0039 | null | null | null | Thermodynamics | 50.774021 | Fluid Dynamics | 14.310466 | Thermodynamics | [
40.124542236328125,
-28.347627639770508
] | ]\gt ; Effect of on the Hissing of when Flowing through Constricted Tube .
By SIDNEY SKINNER , M.A. , and F. ENTWISTLE , B.Sc. ( Communicated by Dr. W. N. Shaw , F.R.S. Received May 20 , 1915 .
) The tensile strength of liquids has been the subject of study under two conditions , the first of which may be called the statical condition , was used by Berthelot* and Worthington , and more recently by H. Dixon .
In this method some liquid , at rest in regard to the walls of containing vessel , is submitted to a stretching force .
The second condition , in which the liquid is moving in relation to the walls of the vessel , and is at the same time submitted to a stretohing force , has not been studied in detail .
Osborne Reynolds has given a general description of the phenomenon , which is of common occurrence .
When a liquid is flowing through a pipe of varying section , at the constriction the velocity may be so high that the corresponding diminished pressure in the liquid is sufficient to break it .
This was the subject of his paper read before the British Association at Oxford , 1894 .
He regarded the effect as a boiling of the liquid under diminished pressure , just as boiling may be produced in warm water by removing the surface pressure .
The experiments about to be described suggest that the phenomenon in the constricted tube is a true tensile rupture produced in the moving liquid .
Osborne Reynolds describes his experiment thus : " " Take a glass tube , say , inch internal diameter and 6 inches long , and draw it down in the middle so as to form a restriction with easy gradual curves so that the inside diameter in the middle is something less than 1/ 10 inch , leaving the parallel ends of the tube something like inches each .
And then connect one of these parallel ends by flexible hose to a water main which is controlled by a tap .
Then , on first opening the tap , the water entering from the main will fill the tube as far as the restriction , and pass through the restriction , but it will not , in the first instance , of necessity fill the tube on the far side of the restriction .
If the water is turned on very slowly and the open end of the tube is inclined upwards , then the water will accumulate and fill the tube , displacing the air .
But if the water is turned on sharply so that when it reaches the neck it has a velocity of 40 or 50 feet a second , the * Berthelot , M. , ' Ann. de Phys. et de Chim .
' 1850 ) .
Worthington , A. M. , ' Trans. Roy .
Soc London ( 1892 ) .
Dixon , H. H. , ' Transpiration and the Ascent of Sap in PIants ' ( 1914 ) .
VOL. XCI.\mdash ; A. 2 Messrs. S. Skinner and F. Entwistle .
water after the minimum section will preserve its velocity shoot out as a jet a squirt , not touching the sides of the glass , if the open end of the tube be held downwards the water , whatever velocity , will , after passing the restriction , run out of the tube filling it .
In neither of these cases is there any hiss or sound except such as caused by the free jet passing through the air .
" " But on holding the open end of the tube upwards and quietly filling both limbs of the tube by opening the tap very quietly , and then on more water , the water will not shoot out in a jet but will come out like any other stream\mdash ; as it might do if there were no restriction .
' At first , while the velocity through the neck is below 50 feet per second , there is no sound , but as soon as a velocity of 54 feet per second is attained , or a little more , a distinct sharp hiss is heard\mdash ; exactly resembling that of the kettle or the hiss of the water through a tap If this phenomenon was the simple boiling of the water it is evident that , if the water were raised to 10 C. and then passed through such a tube the hissing would occur with practically no velocity .
This critical point of hissing has been studied with water and with certain other liquids .
The first experiments were with tap In order to have a large supply of hot water to force through a constricted tube a 2-gallon can was taken and a tubulure was fixed in the base which could be connected with the high-pressure water supply , and a second tubulure was attached near the top of the can , to which could be attached a constricted glass tube , the ordinary mouth of the can being closed with a wired-on cork , carrying a brass stopcock .
The high-pressure water supply was fed by a cistern about 70 feet above the level of the apparatus , so that the pressure could be of any value up to 70 feet of water .
The constricted glass tube was bound on to the upper tubulure of the can by means of a rubber and wire .
The can was placed on a tripod and could be heated from below .
The investigation of the velocity required to give the hiss was made by raising the water in the can to the required temperature , closing the tap at the top of the can , and then forcing that bulk of warm water through the constriction by turning on the tap connected to the high-pressure supply .
When the pressure had been adjusted so as just to get the hiss at the constriction the velocity of the stream was measured by collecting the water which flowed out in a given time .
The temperature of the water was obtained either by plunging a thermometer into the collected water , or by arranging the thermometer in the escape tube so that the erature of the escaping stream observed .
The results , which are given in the following Table , Tlre Effect of Temperature on the Hissing of were plotted in diagrams which showed the mass of water passing in a time ainst the temperature ; when these points were examined it was that they could be represented in general by straight lines .
These straight lines when cut the axis of temperature.at a point which , if the mean of the above observations to be taken , is 32 C. , or , in other ords , they appear to cut the temperature axis at a temperature which is approaching the critical point of vater , .
In this they resemble the temperature coefficient of surface tension .
This result at once indicates that , in the case of water , the phenomenon of the hiss would apparently cease near the critical temperature of the water\mdash ; a result which be expected if the view is taken that the critical temperature is the temperature at which the tensile strength is zero .
It certainly is the view , which was put forward by Osborne Reynolds , that the phenomenon is ordinary boiling .
When a calculation is made to find the critical velocities of flow , using the formula where is the viscosity , the density , and the radius of the constriction at the smallest section , cm .
in the case of the tube used in many of these experiments , it appears that the observed velocity in these experiments is always greater by far than the critical velocity .
This result would show that the flow is not the orderly flow of stream-line motion , although on the inflowing side of the constriction owing to the trumpet shape of the constriction it may be flow of this character ; and the turbulent portion may be confined to the outflowing portion of the stream .
These considerations have led us to be ltious in applying Bernouilli 's formula , by which the fall of pressure at the constriction might have been calculated .
If this had been justifiable an estimate might have been obtained of the actual pressure to which the water was exposed .
When the experiment is working properly the bubbles formed at the constriction are extremely small , and give the stream a cloudy appearance .
When the temperature of the water is high , nearing that of the ordinary boiling point , on some occasions large bubbles were formed , breaking up the hot stream .
These bubbles were like those of ordinary and it is probable were formed when the stream coming from the hot tank where the water was under pressure bursts into , somewhat after the manner of a geyser .
The water may have been superheated to a slight degree when this was observed .
If it had been possible to maintain in the apparatus some back pressure this have been prevented ; but it was not possible with the apparatus at command .
The conclusions to which the experiments lead are : 1 .
That the phenomenon of hissing of water passing a constriction is due to a true rupture of the stream at the point where the pressure is lowest .
Ionisation of Mercury , , and Zinc .
485 2 .
That the temperatures at which the hissing just occurs , between and follow a law which may be expressed , V is the velocity of the stream at a temperature the critical temof water , and a constant .
Experiments are continued with other liquids , but the form of has to be modified with them , and we are not yet satisfied thaG the form reproduces the required conditions .
Ionisation of , Cadmium , Zinc , and the Single- -lined Spectra of these By J. C. , and J. P. HENDERSON , University of Toronto .
( Received May 28 , 1915 .
) [ PLATE 6 .
] .
In a paper by Frank and Hertz in the ' Physikalische Zeitschrift , ' *these investigators have shown that the minimum required to ionise an atom of mercury is that acquired by an electron in a fall of of volts .
These writers have also shown in a later communicathat when heated mercury vapour is traversed by electrons possessing energy htly above this amount the vapour is to the emission of the single spectral line .
This result constitutes a new and most interesting application of the quantum theory , for it will be seen that in the relation , where erg volts is the potential fall which corresponds to the frequency of the line A.U. If the relation just pointed out be applicable generally to all the elements it follows that if the vapour of an element can be shown to be capable of exhibiting a single-line spectrum , the frequency o this single spectral line may be used to deduce the minimum amount of required to ionise the atoms of.that element .
With the object of establishing such a generalisation , if possible , some experiments were recently made by the writers , and it has been found that .
D. Phys. Ges vol. 10 , pp. 457-467 .
' Verh . .
D. Phys. Ges vol. 11 , p. 512 .
|
rspa_1915_0040 | 0950-1207 | Ionisation potentials of mercury, cadmium, and zinc, and the single- and many-lined spectra of these elements. | 485 | 491 | 1,915 | 91 | Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character | J. C. McLennan, F. R. S.|J. P. Henderson | article | 6.0.4 | http://dx.doi.org/10.1098/rspa.1915.0040 | en | rspa | 1,910 | 1,900 | 1,900 | 4 | 107 | 3,246 | http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1915_0040 | 10.1098/rspa.1915.0040 | null | null | null | Atomic Physics | 64.790006 | Electricity | 23.667763 | Atomic Physics | [
5.859703540802002,
-50.10137176513672
] | Ionisation Potentials of Mercury , Cadmium , and Zinc .
485 2 .
That the temperatures at which the hissing just occurs , between 0 ' and 100 ' C. , follow a law which may be expressed y = c where Y is the velocity of the stream at a temperature t , 6 the critical temperature of water , and C a constant .
Experiments are being continued with other liquids , but the form of apparatus has to be modified with them , and we are not yet satisfied that the new form reproduces the required conditions .
Ionisation Potentials of Mercury , Cadmium , and Zinc , and the Single- and Many dined Spectra of these Elements .
By J. C. McLennan , F.R.S. , and J. P. Henderson , University of Toronto .
( Received May 28 , 1915 .
) [ Plate 6 .
] I. Introduction .
In a paper by Frank and Hertz in the \#163 ; Physikalische Zeitschrift/ * these investigators have shown that the minimum energy required to ionise an atom of mercury is that acquired by an electron in passing through a fall of potential of 4'9 volts .
These writers have also shown in a later communica-iionf that when heated mercury vapour is traversed by electrons possessing energy slightly above this amount the vapour is stimulated to the emission of the single spectral line X = 2536 72 A.U. This result constitutes a new and most interesting application of the quantum theory , for it will be seen that in the relation Ye = hv , where h = 6*6 x LO-27 erg sec. , 4*9 volt3 is the potential fall which corresponds to the frequency v of the line X = 2536,72 A.U. If the relation just pointed out be applicable generally to all the elements it follows that if the vapour of an element can be shown to be capable of exhibiting a single-line spectrum , the frequency of this single spectral line may be used to deduce the minimum amount of energy required to ionise the atoms of'that element .
With the object of establishing such a generalisation , if possible , some experiments were recently made by the writers , and it has been found that * 'Verh .
d. D. Phys. Ges .
, ' vol. 10 , pp. 457-467 .
t ' Verh .
d. D. Phys. Ges .
, ' vol. 11 , p. 512 .
Messrs. J. C. McLennan and J. P. Henderson .
the vapours of cadmium and zinc as well as that of mercury can be stimulated to the emission of single-line spectra when traversed by electrons possessing the requisite amount of energy .
With cadmium vapour the wave-length of the line constituting this single-line spectrum is X = 3260 17 A.U. , while that of the single-line spectrum of zinc vapour is X = 3075-99 A.U. By the quantum theory it follows then that the minimum ionising potentials for cadmium and zinc vapours are respectively 3-74 volts and 3 96 volts .
II .
Apparatus .
In carrying out the experiments the form of arc used is that shown in fig. 1 .
H\ / K / Tf\ [ C ... .
J 1 p -JA Fig. 1 .
The apparatus consisted of a tube of fused quartz possessing three arms E , S , and MN , and a receptacle L. Some of the metal to be used in the arc was placed in the receptacle L , and two rods of the same metal FE and DC were attached to two wires and these latter were in turn fastened to two brass plugs , A and B , which were sealed into the tubes E and S with mastic wax .
A small piece of sheet platinum was attached to two wires which constituted the heating circuit and these were sealed with platinum wire into a glass tube PQ at H and K. The open end of the glass tube PQ was ground so as to fit exactly into the end of the quartz tube MN as shown in the diagram .
The arms MN , E , and S were each about 40 cm .
long , and it was found with this length that when the receptacle L was strongly heated with a Bunsen burner the wax joints at A and B and the ground one at the end of the tube MN remained quite cool .
Ionisation Potentials of Mercury , Cadmium , and Zinc .
487 In the experiments the plate G was coated with a thin layer of either calcium oxide or barium oxide .
When the tube was in operation the terminals of an auxiliary heating circuit were attached at H and K , B and K were joined by a wire and the arcing voltage was applied between B and A , the latter being the positive terminal .
With this arrangement G and D constituted a double cathode .
The tube was highly exhausted with a Gaede mercury pump through a glass tube which was sealed into an opening in the brass end-piece at A. In taking photographs the plate G was brought to incandescence by means of the auxiliary heating current , the metal in L was strongly heated with the flame of a Bunsen burner so as to keep the plate G surrounded with the vapour of the metal , and the collimator of a small spectrograph with a quartz train was directed at the incandescent plate G. A short tube of asbestos was attached to the quartz tube directly in front of this plate , so that the radiation from the arc passed through it to the slit of the spectroscope .
This arrangement was found necessary in order to cut off the radiation from the Bunsen flame itself .
It should be noted that in studying the radiation from mercury vapour the electrodes CD and FE were simply stout iron wires .
III .
Characteristics of Arcs of the Different Metals .
With the arrangement just described it was found that when the direct current 110-volt circuit , with suitable resistances in series , was applied to the terminals A and B , and the plate G brought to incandescence , strong arcs could be maintained for hours with all three metals .
With the 220-volt circuit applied the arcs of all three metals could be made most intense , and could also be maintained for long periods .
With the 220-volt circuit it was found that , when the arc was once struck , it could be easily maintained for a considerable time without the continued use of the oxy-cathode G. With low voltages , however , it was always necessary to maintain the plate G at incandescence in order to keep the arc established .
In commencing the investigation efforts were first directed to ascertaining the minimum voltages which should be applied between G and E in order to produce what may be called the many-lined spectrum of the different metals .
These spectra are shown in the upper parts of figs. 2 , 3 , and 4 .
With mercury a difference of potential 12*5 volts was found to be necessary , with zinc 11*85 volts , and with cadmium 15*3 volts .
With differences of potential below these respective values , but above 3 volts , it was found that the only spectrum which could be obtained for each of the metals was one which contained but a single line .
Illustrations of these single-line spectra are shown in the lower portions of figs. 2 , 3 , and 4 .
488 Messrs. J. C. McLennan and J. P. Henderson .
That for mercury , and shown in fig. 2 , X = 2536*72 , was obtained with an arcing potential difference of 9 volts , with an exposure of two hours and a-half .
This single-line spectrum was also obtained with a potential fall of 5 volts , but it was only just visible on the plate with a five-hour exposure .
With 3 volts and a five-hour exposure the line was not obtained .
The continuous white band shown on the left of the spectrogram was due to the incandescent platinum .
The line X = 3075*99 A.U. , shown in the lower spectrogram of fig. 3 , was obtained with zinc vapour , with an arcing potential of 10*5 volts , with an exposure of three hours .
According to the quantum theory relation , Ye = hv , this line should have been obtained with any potential difference above 3*96 volts , but no attempt was made with this element to ascertain with any exactness the least potential difference with which the line could be brought out .
The line X = 3260*17 A.IT .
, shown in the lower spectrogram of fig. 4 , was obtained with cadmium vapour , with an arcing potential difference of 13*6 volts .
With an arcing potential of 3*4 volts and a three-hour exposure no trace of the line was obtained with this element .
With this nietai , as with zinc , no special effort was made to determine with any exactness the least potential difference which would bring out the line .
IY .
Discussion of Results .
The investigation thus far has shown that it is possible to obtain spectra , each consisting of a single spectral line , with mercury , zinc , and cadmium vapours .
To obtain these single-line spectra arcing potentials must be used which are lower than 12*5 volts , 11*85 volts , and 15*3 volts , which values have been found to be the minimum potential differences required to bring out the many-lined spectra for mercury , zinc , and cadmium respectively .
From the work done with mercury , it would appear that the range of voltages which will bring out a single-line spectrum for an element is a very definite one , and extends from the potential difference corresponding to the frequency of the line given by the quantum theory to the potential difference which brings out the many-lined spectrum .
A point which should be mentioned in connection with this work is that , to bring out these single-line spectra , it was found that the best results could be obtained only when suitable vapour densities were used .
The light corresponding to the lines in the single-line spectra of the three elements is known to be strongly absorbed by the respective vapours , and , if vapours of too great density be used , then the lines do not come out on the plates on account of absorption .
On the other hand , if the vapours be too McLennan and Henderson .
Roy .
Soc. Proc. , A , vol. 91 , PI .
6 .
Fig. 2 .
cm cm Fig. 3 .
Oi JO S cc Oi Fig. 4 .
Ionisation Potentials of Mercury , Cadmium , and Zinc .
489 rare , the intensity of the light is so weak that photographic traces of the lines cannot be obtained without extremely long exposures .
In attempting to offer an interpretation of the following facts : ( 1 ) that single-line spectra can be obtained with mercury , zinc , and cadmium vapours with a definite range of arcing voltages , ( 2 ) that the many-lined spectra for these elements are also obtainable with definite minimum arcing potential differences , and ( 3 ) that the conditions for obtaining these two classes of spectra are sharply differentiated , one cannot as yet speak with certainty .
It will be recalled , however , that Sir J. J. Thomson , * in his work with positive rays , found that it was possible to ionise an atom of mercury in two , and only two , definite ways , that is , by removing either one electron from the atom or by removing eight of them .
An obvious interpretation of his discovery would be that if an atom consists of a positive nucleus with one or more rings of electrons revolving about it , then the mercury atom may be supposed to have eight electrons in its outer ring , and that ionisation consists either in the removal of one electron from the atomic system or else in the removal of the whole eight electrons which constitute the outer ring .
This may be taken to indicate that one can remove one electron , but only one , from the outer ring without completely destroying its stability .
This explanation would fit in with the results described in the present paper , and it would seem , therefore , that the energy required to remove an electron from mercury , zinc , and cadmium atoms is that possessed by an electron which has passed through a fall of potential of 4*9 volts , 3*96 volts , and 3*74 volts respectively .
To remove the outer ring of electrons from the atoms of these three elements the energy necessary would be that acquired by an electron under potential differences of 12*5 volts , 11*85 volts , and 15*3 volts respectively .
The single-line spectra could then be explained by supposing that they had their origin in the recombination of the singly ejected electrons with the parent atoms , and on this view the explanation of the production of the many-lined spectra referred to above would be that they have their origin in the radiations emitted in the re-establishment of the complete outer ring of electrons in the atoms from which they had been removed .
In considering the probable range of wave-lengths covered by the many-lined spectra of the three elements , it may be pointed out that if the quantum theory be applicable the relation Ye = hv , combined with the minimum voltages which produce the spectra , enables one to calculate their upper limiting frequencies .
* Sir J. J. Thomson , 'Rays of Positive Electricity and their Application to Chemical Analysis , ' p. 49 .
490 Messrs. J. C. McLennan and J. P. Henderson .
With the values 12*5 volts , 11*85 volts , and 15*3 volts , it follows that the shortest wave-length in the many-lined spectrum of mercury should be given by \ = 975*3 I.U. , while that in the spectrum of zinc should be given by X = 1281*8 A.U. , and that in the cadmium spectrum by X = 797 A.U. It was pointed out by Paschen* in 1909 that the emission spectra of mercury , zinc , and cadmium should include a series of single lines represented by v = 1*5 , S \#151 ; m , P. The limiting wave-lengths for these series are for mercury X = 1188 A.U. , for zinc X = 1320 A.U. , and for cadmium X = 1378*7 A.U. , which values it will be seen approximate to those calculated by the application of the quantum theory .
The actual existence of the series lines represented by v = 1*5 , S\#151 ; m , P , was demonstrated by Wolfff some two years ago , and members of the series were picked out by him as far down as X = 1402*72 A.U. for mercury , X = 1376*87 A.U. for zinc , and X = 1423*23 A.U. for cadmium .
At present there appears to be no evidence of the existence of lines in the arc spectra of these three elements of wave-length shorter than those given by the relation v = 1*5 , S \#151 ; m , P , so that it may very well be that the limiting lines of these series represent the limiting ones of the spectra arising from disturbances set up in the outer ring of electrons in the atoms of mercury , zinc , and cadmium .
The arcing voltages used by Wolff were higher than the lowest ones found by the writers in the present investigation to be capable of producing the many-lined spectra , but in all probability such higher voltages , while adding to the intensities of the lines obtained , would not add anything to the possible number of lines obtainable , unless these voltages were sufficiently great to produce disturbances in rings of electrons closer in to the nuclei of the atoms than the outermost ones .
That disturbances in the inner rings of electrons are possible seems to be proven by the existence of Kontgen ray and 7-ray spectra .
It would have been interesting to see if the series of lines v = 1*5 , S\#151 ; m , P , predicted by Paschen and discovered by Wolff , were obtainable with voltages so low as those used in the present investigation , but , owing to the lack of a vacuum grating spectroscope , experiments to investigate this point could not be carried out by the writers .
It should be pointed out that the lines X = 2536*72 A.U. , X = 3075*99 A.U. and X = 3260*17 A.U. are respectively the first members of Paschen'sf combination series v = 2 , S for the elements mercury , zinc , and cadmium .
* Paschen , ' Ann. der Phys. , ' vol. 30 , p. 746 ( 1909 ) , and vol. 35 , p. 860 ( 1911 ) .
t Wolff , 4 Ann. der Phys. , J vol. 42 , p. 825 ( 1913 ) .
J Pstechen , loc. cit. Ionisation Potentials of Mercury , Cadmium , and Zinc .
491 Y. Summary of Results .
1 .
It has been shown that a spectrum consisting of a single line is obtainable for mercury , for zinc , and for cadmium .
2 .
The wave-lengths of these lines are for mercury X = 2536*72 A.U. , for zinc X = 3075*99 A.U. , and for cadmium X = 3260*17 A.U. 3 .
The minimum ionisation potentials for mercury , zinc , and cadmium have been shown to be 4*9 volts , 3*74 volts , and 3*96 volts respectively .
4 .
Some considerations have been presented which support Sir J. J. Thomson 's theory of the two type ionisation of atoms of mercury , and others which suggest that the theory is applicable as well to the ionisation of atoms of zinc and cadmium .
5 .
The minimum arcing potential differences which will bring out the many-lined spectra of mercury , zinc , and cadmium vapours were found to be 12*5 volts , 11*8 volts , and 15*3 volts respectively .
These voltages are also probably the minimum ionisation potentials of the second type for the atoms of these three \#166 ; elements .
6 .
Considerations have been presented which suggest the possibility of analysing the spectrum of an element in such a way as to enable one to \#166 ; correlate different portions of the spectrum with disturbances in definite portions of the atomic structure of that element .
The writers , in conclusion , wish to acknowledge their indebtedness to Mr. P. Blackman for assistance in taking the photographs and to Mr. F. Mezen for his help in blowing the quartz tubes .
|
rspa_1915_0042 | 0950-1207 | On a spectrum associated with carbon, in relation to the Wolf-Rayet stars. | 498 | 503 | 1,915 | 91 | Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character | Thomas R. Merton, B. Sc. (Oxon.)|A. Fowler, F. R. S. | article | 6.0.4 | http://dx.doi.org/10.1098/rspa.1915.0042 | en | rspa | 1,910 | 1,900 | 1,900 | 4 | 122 | 2,714 | http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1915_0042 | 10.1098/rspa.1915.0042 | null | null | null | Atomic Physics | 72.782394 | Thermodynamics | 9.828451 | Atomic Physics | [
20.100852966308594,
-32.830291748046875
] | 498 Mr. T. R. Merton .
Indeed , the two theorems , that just given and the previous one , 1 \#151 ; 34 1 \#151 ; R21 .
234.-m 1 \#151 ; R2l-3-4 ... m ' are , verbally expressed , identities , the latter having relation to standard deviations measured from 'planes in higher dimensioned space , i.e. to multiple " linear " regression\#151 ; and the former to standard deviations measured from curved surfaces in higher dimensioned space , i.e. to multiple " skew " regression .
The one theorem passes into the other as the skew regression surfaces become planes .
Unfortunately while the rule for finding Hi .
23 ... m is quite simple , the arithmetic is very laborious .
The next step in advance must be such a study of skew regression surfaces that we shall learn how to express the multiple correlation ratio in terms of total correlation ratios as we know how to express the multiple correlation coefficient in terms of total correlation coefficients .
The first step in this direction has recently been taken by Isserlis in the memoir cited above .
On a Spectrum Associated with Carbon , in Relation to the Wolf-Rayet Stars .
By Thomas It .
Merton , B.Sc. ( Oxon .
) , Lecturer in Spectroscopy at University of London , King 's College .
( Communicated by A. Fowler , F.R.S. Received June 3 , 1915 .
) [ Plate 7 .
] The comprehensive investigations of Campbell* have shown that the spectra of the Wolf-Rayet stars contain in addition to lines due to hydrogen and helium , a number of lines which have not been identified with any spectrum which has hitherto been produced in the laboratory .
Owing to the very diffuse character of the lines in the spectra of the Wolf-Rayet stars , accurate measurements of wave-length are impossible , and any identification of the lines with a terrestrial spectrum must , therefore , depend on the appai'ent coincidence of a relatively large number of lines with the spectrum produced in the laboratory .
* * 'Astronomy and Astrophysics , ' vol. 13 , p. 448 ( 1894 ) .
On a Spectrum Associated with Carbon .
M. Wolf* has materially added to our knowledge in the more refrangible regions of the spectra of these stars , but in the less refrangible regions , few lines have been added to the list given by Campbell .
In a recent investigation , Wrightf has discussed the possible relations between the Wolf-Rayet stars and the planetary nebulae .
In the spectra of these stars , the lines of the f Puppis series are very prominent , and from the high order of energy which is necessary to produce this series in the laboratory it might be expected that other lines in the Wolf-Rayet spectrum would be found in the enhanced lines of some terrestrial element .
Nicholson , J in his remarkable theoretical investigations of the spectra of * the nebulae and the Wolf-Rayet stars , has concluded that the Wolf-Rayet spectrum is due to evolution products of the more simple atomic systems which are responsible for the nebular lines , and his suggested arrangement of the lines in series , somewhat resembling those ordinarily found , would appear to strengthen the possibility of producing the Wolf-Rayet spectrum in the laboratory .
The writer has recently observed a spectrum , apparently associated with carbon , of which the principal lines would appear to coincide with some of the most conspicuous lines in the Wolf-Rayet spectrum .
The spectrum was produced by passing heavy condensed discharges through vacuum tubes containing hydrogen at a moderately low pressure , and which were provided with graphite or carbon electrodes .
The electrodes consisted either of pencil leads , which had been heated to a white heat and subsequently treated with boiling nitric and hydrochloric acids , or thin rods cut from a specially pure block of carbon and treated in the same way .
The electrodes were attached to platinum wires , which were sealed into the vacuum tubes in the usual way .
The tubes were exhausted by means of a Gaede mercury pump and a heavy discharge was passed during the process of exhaustion .
Pure hydrogen was admitted by heating , in a Bunsen flame , a small palladium tube connected with the vacuum tube .
The gas thus admitted was pumped out , and this operation was repeated several times in order to wash out completely any trace of other gases from the tube .
The vacuum tubes , when freshly prepared , showed only the spectrum of hydrogen with a trace of the Angstrom carbon oxide bands , but after running the tube for some time the hydrogen spectrum disappeared and nothing remained but a very brilliant spectrum showing the Angstrom bands .
At the * 'Sitz .
Heidelberger Akad .
Wiss .
, ' Abb .
14 and 22 ( 1913 ) .
t ' Astrophys .
Journ. , ' vol. 2 , p. 466 ( 1914 ) .
I See ' Monthly Notices , R.A.S. , ' vol. 75 , 4 , p. 340 .
Mr. T. R. Merton .
same time , carbon was deposited on the walls of the capillary ; it was thus necessary to use end-on tubes for the spectroscopic observations .
When excited by a condensed discharge , with a spark-gap in the circuit , the tubes showed the line spectrum of carbon and in the more refrangible region the multitude of lines , due to oxygen and the glass walls of the capillary , which appear in every low pressure vacuum tube excited in this way .
The most characteristic lines , however , were a group in the yellow-green .
In Table I are given the principal lines in this spectrum .
Table I. A. Intensity . .
Remarks .
6583 6578 8 9 j- Characteristic carbon pair .
5826 *7 3 5812 *0 5 5801 *4 7 5696 *0 10 5694 *1 Angstrom and Thalen .
5592 *1 8 4651 *6 8 4650 -4 8 4647 *6 10 4267 10 Very strong carbon line .
With the exception of the very characteristic carbon lines at XX6583 , 6578 , and 4267 , the lines included in this list are only those lines which are enhanced by very powerful discharges .
Other lines recorded* as carbon lines were present , and also a pair at X5893 and a line at X6098 , which , Prof. Fowler informs me , have long been regarded as unrecorded carbon lines in the South Kensington laboratories .
Lockyer , Baxandall , and Butler , f with similar conditions of powerful electric discharge , have observed the pair XX46508 and 4647'6 in vacuum tubes containing compounds of carbon , and have attributed these lines to carbon ; they have also drawn attention to the coincidence of this pair with lines in the spectrum of e Orionis , and have suggested that they may possibly also account for the line X4652 of the Wolf-Kayet stars .
These lines are undoubtedly identical with two lines given in the list .
A line has been recorded at X5694-l in the spectrum of carbon by Angstrom and Thalen , but this line was not observed by Eder and Valenta or Gramont .
J Thaldn has recorded lines in the spectrum of aluminium at * Kayser 's ' Handbuch der Spektroseopie .
' ^ t ' Roy .
Soc. Proc. , ' A , vol. 82 , p. 532 ( 1909 ) .
I Kayser , loc. cit. , vol. 5 , p. 225 .
On a Spectrum , Associated with Carbon .
501 XX5695'5 and 5592-5 , but it is extremely unlikely that these are identical with the lines observed in the vacuum tubes .
Aluminium lines are a common impurity in the spectra of vacuum tubes excited by powerful discharges , the pair at XX 3961-7 and 3944'2 being generally present .
This may be due to the aluminium electrodes which are usually employed , or to the alumina ( usually about 4 per cent. ) contained in the glass .
The lines at XX 5696 and 5592 could not be obtained from vacuum tubes provided with aluminium electrodes and filled in the manner described .
Moreover , in the spectrum from the tubes with carbon electrodes , these lines were not accompanied by the line X5722 of intensity 10 , which is given in Thalen 's list of aluminium lines .
The new lines are diffuse in character , and are therefore difficult to measure .
It is dangerous to assume the origin of any lines obtained from vacuum tubes under these conditions of electric discharge , but it would appear justifiable provisionally to assign the lines observed to carbon , since it has not been found possible to obtain them in the absence of carbon .
The new lines are best developed when the walls of the capillary are well coated with the carbon deposit , and are strongly enhanced by powerful discharges , relative to the ordinary carbon lines .
This is especially true of the group at XX5827 , 5812 , 5801 , which are scarcely visible with a weak condensed discharge .
One may perhaps imagine a condition of still more powerful excitation , in which the spectrum of carbon would consist of the new lines , with faint lines at XX 6583 , 6578 , and 4267 as the sole surviving representatives of the ordinary carbon spark spectrum , since these are its most characteristic lines .
We may now compare these lines with the spectrum of the Wolf-Rayet stars .
In Table II is given a list of Wolf-Rayet lines .
It consists essentially of Campbell 's ( loc.cit .
) list , with the following modifications:\#151 ; ( i ) All lines due to hydrogen or helium have been omitted .
( ii ) Two lines observed by Merrill* have been included .
( iii ) Wright ( loc. cit. ) has pointed out that the band X5813 appears to vary in position in different stars , and in the star B.D. + 30'3639 can be seen to be composite , having components at XX 5801 , 5812 , 5828 .
These wavelengths have been substituted for the line X5813 in Campbell 's list .
In Column I are given the Wolf-Rayet lines , and in Column II , under vacuum tube , " lines in the spectrum provisionally assigned to carbon .
For the line given-by Campbell at X4273 , Wolf ( loc. cit. ) finds in the stars 30'3639 , 36'3956 , and 35'4013 respectively the values XX 4268-1 , 4270 , and 4269 , a result which would indicate the possibility of this line being identical * ' Lick Observatory Bulletin , ' yol .
7 , p. 129 ( 1913 ) .
On a Spectrum Associated Carbon .
Table II .
I. Wolf-Rayet .
II .
Vacuum tube .
A. 6583 / 65831 16578/ 6548 6848 5828 5812 1 5813 Campbell .
5826 *7 5812 -0 5801 [ Very strong 5801 '4 5693 Very strong 5696 -0 5593 Strong 5592 -1 5472 Strong 5284 5250 5131 4940 4787 4652 Very strong f 4651 *6 ] .{ 4650 -4 )\#166 ; 4636 Strong [ 4647 '6 J 4626 Strong I. Wolf-Rayet .
II .
Vacuum tube .
A. 4615 4596 4555 4517 Strong 4509 Very strong 4504 Strong 4493 4480 4466 Strong 4457 4442 Strong 4416 4369 4334 4318 4273 4267 4260 4228 4063 Strong with the carbon line X 4267 .
Campbell 's { loc. cit. ) results would appear to suggest a common origin for the lines XX 5813 , 5693 , 5593 , 4650 , which in almost every case occur together .
On the other hand , the visual intensity curves of the spectra of different stars* show that the relative intensities of these lines vary considerably in different stars .
Similar variations of intensity can easily be produced in the lines observed in the vacuum tubes , the triplet at X 4650 being produced with comparatively weak condensed discharges .
The line X 5696 is brought out with more powerful discharges , whilst the group XX 5827 , 5812 , 5801 , is strongly developed only by the most intense discharges .
It will thus be seen that a considerable proportion of the stronger Wolf-Rayet lines are apparently coincident with lines in the vacuum tube spectrum .
It cannot be claimed that the identity of the spectra has been fully established , but the results would appear to warrant the suggestion that the Wolf-Rayet lines in question may possibly be due to the same origin as the spectrum which has been described , and which is probably associated with carbon .
I should like to express my best thanks to Prof. Fowler for the valuable advice which he has given me .
In the plate , Nos. 1 , 2 , 3 , 4 , and 5 represent a series of the spectra obtained from a vacuum tube with successively increasing intensity of electric * Campbell , loc. cit. , p. 7 .
Merton .
Roy .
Soc. Proc. A , Vol. 91 , PI .
7 .
jo CO 4^ CJ1 --- 4267 --- 4650 --- 5592 --- 5696 --- 5813 --- 5893 --- 6098 ( 6578 ---t6583 Hydrodynamical Problems Suggested by Pitot 's Tubes .
503 discharge .
Thus No. 1 was obtained with an uncondensed discharge and No. 5 with a heavy condensed discharge .
No. 2 , with a moderate condensed discharge , shows lines of the ordinary carbon spark spectrum with XX 4650 and 5696 .
In No. 3 , the X 5813 group and X 5593 are just visible , whilst No. 5 shows these lines with considerable intensity ; they are situated in a part of the spectrum to which the plates used are comparatively insensitive , and their photographic intensities are , in consequence , very small in comparison with their appearance in visual observations .
In the more refrangible region , which in the plate was necessarily over exposed , strong lines due to oxygen , etc. , from the walls of the tube are visible .
The use of a filter to counteract the sensibility curve of the plate was only partly successful .
HydrodynamicalProblems Suggested by Pitot 's Tubes .
By Lord Rayleigh , O.M. , F.R.S. ( Received June 5 , 1915 .
) The general use of Pitot 's tubes for measuring the velocity of streams suggests hydrodynamical problems .
It can hardly be said that these are of practical importance , since the action to be observed depends simply upon Bernoulli 's law .
In the interior of a long tube of any section , closed at the further end and facing the stream , the pressure must be that due to the velocity ( - ?
; ) of the stream , i.e. Ipv2 , p being the density .
At least , this must be the case if viscosity can be neglected .
I am not aware that the influence of viscosity here has been detected , and it does not seem likely that it can be sensible under ordinary conditions .
It would enter in the combination v/ vl , where v is the kinematic viscosity and l represents the linear dimension of the tube .
Experiments directed to show it would therefore be made with small tubes and low velocities .
w In practice a tube of circular section is employed .
But , even when viscosity is ignored , the problem of determining the motion in the neighbourhood of a circular tube is beyond our powers .
In what follows , not only is the fluid supposed Motionless , but the circular tube is replaced by its two-dimensional analogue , i.e. the channel between parallel plane walls .
Under this head two problems naturally present themselves .
The first problem proposed for consideration may be defined to be the flow
|
rspa_1915_0043 | 0950-1207 | Hydrodynamical problems suggested by Pitot's Tubes. | 503 | 511 | 1,915 | 91 | Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character | Lord Rayleigh, O.M., F. R. S. | article | 6.0.4 | http://dx.doi.org/10.1098/rspa.1915.0043 | en | rspa | 1,910 | 1,900 | 1,900 | 4 | 127 | 3,557 | http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1915_0043 | 10.1098/rspa.1915.0043 | null | null | null | Fluid Dynamics | 36.239253 | Atomic Physics | 24.158012 | Fluid Dynamics | [
3.1537277698516846,
-57.74640655517578
] | Hydrodyncimical Problems Suggested by Pitot 's .
503 discharge .
Thus No. 1 was obtained with an uncondensed discharge and No. 5 with a heavy condensed discharge .
No. 2 , with a moderate condensed discharge , shows lines of the ordinary carbon spark spectrum with XX , 4650 and 5696 .
In No. 3 , the X 5813 group and X 5593 are just visible , whilst No. 5 shows these lines with considerable intensity ; they are situated in a part of the spectrum to which the plates used are comparatively insensitive , and their photographic intensities are , in consequence , very small in comparison with their appearance in visual observations .
In the more refrangible region , which in the plate was necessarily over exposed , strong lines due to oxygen , etc. , from the walls of the tube are visible .
The use of a filter to counteract the sensibility curve of the plate was only partly successful .
Hydrodynamiced Problems Suggested by Pitot 's Tubes .
By Lord Rayleigh , O.M. , F.R.S. ( Received June 5 , 1915 .
) The general use of Pitot 's tubes for measuring the velocity of streams suggests hydrodynamical problems .
It can hardly be said that these are of practical importance , since the action to be observed depends simply upon Bernoulli 's law .
In the interior of a long tube of any section , closed at the further end and facing the stream , the pressure must be that due to the velocity ( v ) of the stream , i.e. \pv2 , p being the density .
At least , this must be the case if viscosity can be neglected .
I am not aware that the influence of viscosity here has been detected , and it does not seem likely that it can be sensible under ordinary conditions .
It would enter in the combination where v is the kinematic viscosity and l represents the linear dimension of the tube .
Experiments directed to show it would therefore be made with small tubes and low velocities .
In practice a tube of circular section is employed .
But , even when viscosity is ignored , the problem of determining the motion in the neighbourhood of a circular tube is beyond our powers .
In what follows , not only is the fluid supposed frictionless , but the circular tube is replaced by its two-dimensional analogue , i.e. the channel between parallel plane walls .
Under this head two problems naturally present themselves .
The first problem proposed for consideration may be defined to be the flow Lord Rayleigh .
of electricity in two dimensions , when the uniformity is disturbed by the presence of a channel whose infinitely thin non-conducting walls are parallel to the flow .
By themselves these walls , whether finite or infinite , would cause no disturbance , but the channel , though open at the fihite end , ' is supposed to be closed at an infinite distance away , so that , on the whole , there is no stream through it .
If we suppose the flow to be of liquid instead of electricity , the arrangement may be regarded as an idealised Pitot 's tube , although we know that , in consequence of the sharp edges , the electrical law would be widely departed from .
In the recesses of the tube there is no motion , and the pressure developed is simply that due to the velocity of the stream .
The problem itself may be treated as a modification of that of Helmholtz , * where flow is imagined to take place within the channel and to come to evanescence outside at a distance from the mouth .
If in the usual notation^ z == x-f iy , and w = \lt ; f\gt ; + iyfr be the complex potential , the solution of Helmholtz 's problem is expressed by Z ( 1 ) or x \#151 ; \lt ; f\gt ; \#151 ; 6^cos yj/ " , ( 2 ) The walls correspond to yfr = +7r , where y takes the same values , and they extend from x \#151 ; \#151 ; 00 to a ; = \#151 ; 1 .
Also the stream-line ^ = 0 makes = 0 , which is a line of symmetry .
In the recesses of the channel \lt ; f\gt ; is negative and large , and the motion becomes a uniform stream .
To annul the internal stream we must superpose upon this motion , expressed say by \lt ; j\gt ; 1 + iyjn , another of the form \lt ; j\gt ; 2 + ^2 where ( f\gt ; 2 -f \#151 ; \#151 ; x\#151 ; iy .
In the resultant motion , \lt ; f\gt ; = \lt ; f\gt ; \ + \lt ; f\gt ; 2 = \lt ; f\gt ; 1\#151 ; yfr = yjri~\-yjr2 = ^1\#151 ; yr \#166 ; so that \lt ; f\gt ; \ \#151 ; \lt ; f)-\-x , \#151 ; yfr-by , and we get 0 = \lt ; \#163 ; -j-e*+x cos 0 = sin ( 3 ) whence # = \#151 ; \lt ; \#163 ; + log \/ ( ^\gt ; 2 + Vr2 ) , \#166 ; ^ + tan"1(i|r/ \lt ; ^ ) ( 4 ) or , as it may also be written , z \#151 ; \#151 ; w log w. ( 5 ) It is easy to verify that these expressions , no matter how arrived at , satisfy * ' Berlin Monatsber .
, ' 1868 ; ' Phil. Mag./ vol. 36 , p. 337 ( 1868 ) .
In this paper a new path was opened .
t See Lalhb 's 'Hydrodynamics/ S66 .
Hydrodynamical Problems Suggested by Pitot*s Tubes .
505 the necessary conditions .
Since x is an even function of yfr , and y an odd function , the line y \#151 ; 0 is an axis of symmetry .
When = 0 , we see from ( 3 ) that sin = 0 , so that y\#151 ; 0 or +ir , and that cos^ and \lt ; f\gt ; have opposite signs .
Thus when \lt ; f\gt ; is negative , y\#151 ; 0 ; and when ( f\gt ; is positive , + 7r .
Again , when ( f\gt ; is negative , x ranges from + oo to oo ; and when \lt ; f\gt ; is positive x ranges from \#151 ; oo to \#151 ; 1 , the extreme valde at the limit of the wall , as appears from the equation dx/ d(f ) = \#151 ; 1 + 1 = 0 , making 0 = 1 , x = \#151 ; 1 .
The central stream-line may thus be considered to pass along y \#151 ; 0 from x \#151 ; co to X \#151 ; \#151 ; oo .
At x\#151 ; \#151 ; co it divides into two branches along y \#151 ; + tt .
From x = \#151 ; oo to \#151 ; 1 , the flow is along the inner side of the walls , and from x= \#151 ; 1 to x= \#151 ; oo back again along the outer side .
At the turn the velocity is of course infinite .
We see from ( 4 ) that when yfr is given the difference in the final values of y , corresponding to infinite positive and negative values of \lt ; jE\gt ; , amounts to it , and that the smaller is yjr the more rapid is the change in y. The corresponding values of x and y for various values of \lt ; f\gt ; , and for the stream-lines yjr= \#151 ; 1 , \#151 ; are given in Table I , and the more important parts are exhibited in the accompanying plots ( fig. 1 ) .
Table I. \lt ; p. 4 = * = -4- ^ = -1 .
X. * X. y. X. y- -10 12-303 0 -2750 12-30 0-550 12 -31 1 -100 - 5 6 -610 0-3000 6 -614 0-600 6-63 i 1 -198 - 3 4 -102 1 0 -3333 4-112 0-665 415 1 -322 - 2 2-701 0 -3745 2 -723 0-745 2*80 1 -464 - 1 1 *030 0-495 1 111 0-964 1 -35 1-785 - 0 50 ' 0 -081 0*714 0 153 1-285 \#151 ; - 0-25 -0-790 1 -035 \#151 ; \#151 ; \#151 ; .0-00 -1 386 1 *821 -0-693 2 071 o-oo 2-571 0-25 -1 -290 2 -606 \#151 ; \#151 ; \#151 ; \#151 ; 0 '50 -1-081 2 -928 -0-847 2 -881 - 0-388 3 035 1 *0 -0-970 3 -147 -0-888 3-178 !
\#151 ; 0653 3 -356 2 0 -1 -299 3 -267 -1 -277 3-397 j \#151 ; 1 -195 3 678 3 0 -1 -898 3-308 -1 -888 3-477 \#151 ; \#151 ; 4*0 \#151 ; \#151 ; \#151 ; \#151 ; - 2-584 3-897 5 0 -3 -389 j 3 -342 1 -3-386 !
3-542 \#151 ; \#151 ; 10*0 -7-697 3-367 ; _ - 7 -692 4 -042 20 0 ; \#151 ; \#151 ; ; \#151 ; -17-00 4 -092 In the second form of the problem we suppose , after Helmholtz and Kirchhoff , that the infinite velocity at the edge , encountered when the fluid adheres to the wall , is obviated by the formation of a surface of discontinuity , Lord Rayleigh .
Fig. 1 .
Hydrodynamical Problems Suggested by Pitot 's Tubes .
507 where the condition to be satisfied is that of constant pressure and velocity It is , in fact , a particular case of one treated many years ago by Prof. Love , entitled " Liquid flowing against a disc with an elevated rim , " when the height of the rim is made infinite.* I am indebted to Prof. Love for the form into which the solution then degrades .
The origin O ' ( fig. 2 ) of or z is taken at one edge .
The central stream-line ( yjr == 0 ) follows the line of symmetry AB from y = H-oo to y \#151 ; \#151 ; co .
At y = \#151 ; oo it divides , one half following the inner side of the wall CO ' from \#151 ; oo to = 0 , then becomes a free surface O'D from y \#151 ; 0 to y = \#151 ; oo .
The connection between z and w ( = \lt ; f\gt ; 4- tie ) is expressed with the aid of an auxiliary variable 0 .
Thus z \#151 ; tan 0\#151 ; 0\#151 ; tan2 0\#151 ; log cos 0 , ( 6 ) w = \#163 ; sec2 0 .
( 7 ) If we put tan 0 \#151 ; t ' + iy , we get w = i(l + r\gt ; -V+2 ifr so that \lt ; \#163 ; = |(1 + p-772 ) , == \#163 ; ( 8 ) We find further ( Love ) , S = \#163 ; + iy + \#163 ; \#163 ; y\#151 ; 2(\#163 ; 2\#151 ; y2)\#151 ; btan-1-\#151 ; \#151 ; \#151 ; \#163 ; tan"1 \#151 ; 2 4 1 1 + f2\#151 ; V + ilog{(l-^ + f } ( 9 ) sothat ^ = f+'f+ |tan~1 2f +|taa~ ' 4--^ , ( 10 ) y = ''7 \#151 ; HI2\#151 ; { ( 1\#151 ; \#166 ; \#187 ; 7)2+P } ( II ) The stream-lines , corresponding to a constant yfr , may be plotted from ( 10 ) , ( 11 ) , if we substitute 2yfr/ \#163 ; for y and regard \#163 ; as the variable parameter .
Since by ( 8 ) \lt ; *\gt ; = \#177 ; ( i + F)-^7\#163 ; 2 , = \#163 ; \#163 ; +2*2/ f , there is no occasion to consider negative values of and \lt ; f\gt ; and \#163 ; vary always in the same direction .
As regards the fractions under the sign of tan-1 , we see that both vanish when | = 0 , and also when \#163 ; = oo .
The former , viz. , 2\#163 ; -j- ( 4\gt ; /r2/ |2 + \#163 ; 2\#151 ; 1 ) , at first + when \#163 ; is very small , rises to oo when ^2 = ^{l\#177 ; v/ ( l \#151 ; 16 t/ r2 ) } , .which happens when but not otherwise .
In the latter case the fraction is always positive .
When the fraction passes through oo , there changing sign .
The numerically least negative value is reached when f2 = h{ v ' ( 1 + 48-^r2 ) \#151 ; 1 } .
The fraction then retraces its entire course , until * 'Camb .
Phil. Proc. , ' vol. 7 , p. 185 ( 1891 ) .
Lord Rayleigh .
it becomes zero again when g = oo .
On the other hand the second fraction , at first positive , rises to infinity in all cases when \#163 ; 2 \#151 ; \ 16-\lt ; /r2)\#151 ; 1 } , after which it becomes negative and decreases numerically to zero , no part of its course being retraced .
As regards the ambiguities in the resulting angles , it will suffice to suppose both angles to start from zero with f. This choice amounts to taking the origin of a ?
; at O , instead of O ' .
When yfr is very small the march of the functions is peculiar .
The first fraction becomes infinite when \#163 ; 2 = 4 yjr2that is when \#163 ; is still small .
The turn occurs when \#163 ; 2 = 12 ^2 , and the corresponding least negative value is also small .
The first tan-1 thus passes from 0 to while \#163 ; is still small .
The second fraction also becomes infinite when \#163 ; 2 = 4^2 , there changing sign , and again approaches zero while \#163 ; is of the same order of magnitude .
The second tan-1 thus passes from 0 to 7r , thereby completing its course , while \#163 ; is still small .
When yjr = 0 absolutely , either \#163 ; or rj , or both , must vanish , but we must still have regard to the relative values of yfr and \#163 ; .
Thus when \#163 ; is small enough , x \#151 ; 0 , and this part of the stream-line coincides with the axis of symmetry .
But while \#163 ; is still small , x changes from 0 to 7r , the new value representing the inner face of the wall .
The transition occurs when \#163 ; = 2 yfr , 7 ] = 1 , making in ( 11 ) y = \#151 ; oo .
The point O ' at the edge of the wall ( x = 7r , y = 0 ) corresponds to \#163 ; = 0 , rj = 0 .
For the free part of the stream-line we may put 0 , so that x\#151 ; ftan"x = \#163 ; \#151 ; tan-1 \#163 ; + tt , where tan-1 \#163 ; is to be taken between 0 and Also y = -H2+iiog(i+r\gt ; .
When \#163 ; is very great , x = f+ivr , y = \#151 ; if3 , and the curve approximates to a parabola .
When f is small , X\#151 ; IT \#151 ; ||3 , y \#151 ; so that the ratio ( x\#151 ; 7 r)Jystarts from zero , as was to be expected .
The upward movement of y is of but short duration .
It may be observed that , while dx/ di\ is always positive , a6\gt ; tff 2(i + f2 ) ' , r . .
.v which is positive only so long as f\lt ; l. And when f \#151 ; 1 , \#151 ; 7r = 1 \#151 ; ^7r = 0'2146 , y = \#151 ; ^ + log 2 = 0*097 .
( 12 ) ( 13 ) ( 14 ) ( 15 ) Hydrodynamical Problems Suggested by Pitot 's Tubes .
509 Some values of x and y calculated from ( 12 ) , ( 13 ) are given in Table II , and the corresponding curve is shown in fig. 3 .
Table II.\#151 ; yfr = 0 .
X. y- X. \#166 ; * 0*0 3 142 0 | 2*5 4*451 - 0 *571 0*5 3*178 + 0*050 3*0 4 *892 - 1*098 1 *0 3*356 + 0*097 4*0 5*816 - 2*583 1*5 3*659 + 0*027 5 *0 6 *768 \#151 ; 4*62 2*0 | .
4*034 -0 *195 20*0 21 *621 -97 00 Fig. 2 .
It is easy to verify that the velocity is constant along the curve defined by ( 12 ) , ( 13 ) .
We have dx _ eat die _ .
d\lt ; j\gt ; " l + \#163 ; *\lt ; tie * d\lt ; f\gt ; 21 and when = 0 , = 1 + F ) , d\lt ; f\gt ; / dg = | f. Thus dx 2 f die 1 \#151 ; f2 d(f\gt ; 1 + f2 ' d\lt ; f\gt ; ~ 1-ff2 ' and ( dxjd\lt ; t\gt ; Y + ( \lt ; die / d\lt ; f \#151 ; 1 .
The square root of the expression on the left of ( 17 ) represents the reciprocal of the resultant velocity .
510 Hydrodynamical Problems Suggested by Pitot 's Tubes .
Table III.\#151 ; = \#163 ; .
J .
| y- S. X. y , r o !
o 00 0-40 | 2 -9667 + 0 076 0 05 o 1667 9-098 0-50 3 0467 0-130 0 10 0 *2995 3-008 0-60 3 1089 0-162 0-13 !
0-4668 1 -535 0-80 3 -2239 0 -198 0-15 !
0 -6725 0-766 1 -oo 3-3454 0 -207 0-17 i 1 0368 + 0 -109 1 -50 3 '6947 + 0 -125 0-18 j 1 -2977 -0 143 2-00 4-0936 -0*112 0-19 !
1-5907 -0-304 2-50 4 -5234 -0*501 0-20 !
1 -8708 -0-370 300 4 -9725 -1 *032 0 *22 i 2 -2828 -0 -331 4-00 5-9039 -2-536 0-25 1 2 -5954 -0*195 6-00 7-8305 -7 -161 0-30 1 2 -8036 -0-047 1 Fig. 3 .
Fluorescence and Resonance of Sodium .
511 When ylr differs from zero , the calculations are naturally more complicated .
The most interesting and instructive cases occur when yjr is small .
I have chosen \fr = 1/ 10 .
The corresponding values of f , and y are given in Table III , calculated from equations ( 10 ) , ( 11 ) , and a plot is shown in fig. 3 .
As in the former problem , where the liquid is supposed to adhere to the walls notwithstanding the sharp edges , the pressure in the recesses of the tube is simply that due to the velocity at a distance .
At other places the pressure can be deduced from the stream-function in the usual way .
Observations on the Fluorescence and Resonance of Sodium Vapour.\#151 ; II .
By the Hon. R. J. Strutt , Sc. D. , F.R.S. , Professor of Physics , Imperial College , South Kensington .
( Received June 12 , 1915 .
) [ Plate 8 .
] S 1 .
Introduction , Prof. R. W. Wood has made many interesting observations on the fluorescence of sodium vapour .
They are conveniently summarised in his ' Physical Optics ' ( MacMillan , 1911 ) .
The fluorescent spectra he has obtained are apparently connected with the banded absorption spectrum of dense sodium vapour .
If white light is employed , this banded absorption spectrum is re-emitted completely as a fluorescent emission spectrum .
If monochromatic light is used , a portion only of the complete band spectrum is emitted , thik portion consisting of a moderate number of lines approximately equally spaced along a normal spectrum , and including a line coincident with the exciting line .
These observations on the band spectrum are of great interest and importance , but observations on the line spectrum of sodium , in absorption and in fluorescence , are more within the range of theoretical discussion at the present time .
The line spectrum is observed in absorption and in fluorescence at a density of sodium vapour small compared with that needed for the band spectrum .
If a beam of white light traverses such vapour , the D line and the other lines of the same series in the ultra-violet are seen in absorption .
At the
|
rspa_1915_0044 | 0950-1207 | Observations on the fluorescence and resonance of sodium vapour.\#x2014;II | 511 | 523 | 1,915 | 91 | Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character | Hon. R. J. Strutt, Sc. D., F. R. S. | article | 6.0.4 | http://dx.doi.org/10.1098/rspa.1915.0044 | en | rspa | 1,910 | 1,900 | 1,900 | 11 | 273 | 5,874 | http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1915_0044 | 10.1098/rspa.1915.0044 | null | null | null | Atomic Physics | 45.883936 | Optics | 28.357032 | Atomic Physics | [
7.497483253479004,
-48.76323318481445
] | Fluorescence and Resonance of Sodium .511 When ylr differs from zero , the calculations are naturally more complicated .
The most interesting and instructive cases occur when yfr is small .
I have chosen ^ = 1/ 10 .
The corresponding values of f , x , and y are given in Table III , calculated from equations ( 10 ) , ( 11 ) , and a plot is shown in fig. 3 .
As in the former problem , where the liquid is supposed to adhere to the walls notwithstanding the sharp edges , the pressure in the recesses of the tube is simply that due to the velocity at a distance .
At other places the pressure can be deduced from the stream-function in the usual way .
Observations on the Fluorescence and Resonance of Sodium Vapour.\#151 ; II .
By the Hon. R. J. Strutt , Se .
D. , F.R.S. , Professor of Physics , Imperial College , South Kensington .
( Received June 12 , 1915 .
) [ Plate 8 .
] S 1 .
Introduction .
Prof. R. W. Wood has made many interesting observations on the fluorescence of sodium vapour .
They are conveniently summarised in his ' Physical Optics ' ( MacMillan , 1911 ) .
The fluorescent spectra he has obtained are apparently connected with the banded absorption spectrum of dense sodium vapour .
If white light is employed , this banded absorption spectrum is re-emitted completely as a fluorescent emission spectrum .
If monochromatic light is used , a portion only of the complete band spectrum is emitted , this portion consisting of a moderate number of lines approximately equally spaced along a normal spectrum , and including a line coincident with the exciting line .
These observations on the band spectrum are of great interest and importance , but observations on the line spectrum of sodium , in absorption and in fluorescence , are more within the range of theoretical discussion at the present time .
The line spectrum is observed in absorption and in fluorescence at a density of sodium vapour small compared with that needed for the band spectrum .
If a beam of white light traverses such vapour , the D line and the other lines of the same series in the ultra-violet are seen in absorption .
At the Hon. R. J. Strutt .
Observations on the same time there is a lateral re-emission of the D line , discovered by Wood , and called by him resonance radiation .
The first paper of the present series* * * S dealt with this resonance radiation .
It is excited most conveniently not by white light but by sodium light , which contains the only effective constituent of white light .
The D line is the first member of a series of lines known as the principal series of sodium .
The second line is at wave-length 3303 in the ultra-violet .
The lines of this series up to a very high number can be seen in absorption , and since , in the case of the D line , the whole of the absorbed light quantitatively reappears in resonance radiation , f it would seem at first sight very probable that resonance radiation would also be observed at wave-length 3303 , and at all the other lines of the Principal series .
The question arises also , would stimulation by a higher member of the series give rise to emission of a lower member ?
For instance would stimulation by \ 3303 give rise to D light ?
This question is not new .
* It has been proposed by Prof. R. W. Wood , and he has looked for such an effect , with negative results.^ There was no doubt , however , that if anything of the kind could be observed , the fact would be important for the theory of spectrum series .
For this reason I have made a fresh effort , which has had a successful issue .
S 2 .
Excitation of D Light by A , 3303 .
In planning the experiments , a source was looked for which would give a sharp and narrow line of great intensity at wave-length 3303 .
Preliminary experiments with a salted Meker flame showed that this source was extremely poor in the radiation desired .
An oxy-hydrogen sodium flame might have done better , but I had recourse to a sodium vacuum arc , in quartz , which gave the line 3303 in equal intensity to the D line , measuring the intensity by the action on ordinary ( not orthochromatic ) plates .
S The silica envelope of the lamp ( fig. 1 ) consists of two bulbs , , c , each of 50 c.c. capacity , joined by a tube b , about 13 mm. inside diameter .
The cathode is a pool of molten sodium d , and contact is made to it by an iron wire e , winch passes out through a narrow quartz tube into which it is * 'Roy .
Soc. Proc. , 'A , vol. 91 , p. 388 ( 1915 ) .
t Dunoyer and Wood , ' Phil. Mag. ' [ VI ] , vol. 27 , p. 1025 ( 1914 ) .
J * Phil. Mag. ' [ Vlj , vol. 18 , p. 533 ( 1909 ) .
In this paper it is shown that excitation of dense sodium vapour by the group of zinc lines in the neighbourhood of A 3303 gives rise to an ultra-violet band spectrum .
But no definite evidence is given of any re-emission of A 3303 , nor have I myself been able to observe this , as will appear .
S This measure of- -relative intensity has of course no scientific yalue .
It is merely used for practical convenience in comparing different sources .
An energy measure would be enormously more favourable tb the D line .
Fluorescence and Resonance of Sodium Vapour .
/ - C Fio .
1 .
cemented with sealing wax .
The anode is an iron wire f about 3 mm. in diameter .
It passes up the glass fitting gg , into which it is cemented ; gg is cemented into the silica tube at h. A stopcock h provides for exhaustion .
The constriction at the bottom of gg , where the wire f passes out , prevents too much distillation of sodium into the upper part of this tube .
This form of lamp , arrived at after repeated trials , is fairly satisfactory in use , lasting long enough for a considerable number of experiments .
The large bulbs are a most important feature .
The lower one allows of the effervescence of the molten sodium , which always occurs at first .
The upper one serves a different purpose .
The anode f gets red hot , and if space is not allowed round it , the surrounding silica gets so hot as to be rapidly acted on by the sodium , eventually cracking .
The lamp must be kept well exhausted , preferably by continuous action of a Gaede mercury pump .
The sodium gives off much hydrogen , and if this is not continually removed the lamp gets very hot , and the silica is rapidly blackened by reduction .
The current passed is about 5 amperes .
The lamp is started by warming it and connecting an induction coil to the sodium cathode , and to a wire twisted round the tube b. After prolonged use the silica gets brown .
The lamp can then be dismounted , cleaned out with alcohol and water , and then with dilute hydrofluoric acid , which readily removes the reduced silicon .
It can then be recharged with sodium , and is almost as good as new .
It may be mentioned that the lamp gave eight lines of the principal series of sodium with half an hour 's exposure on a small quartz spectrograph .
The D line was exceedingly brilliant , and the strongest salted flame looked a very pale object beside the lamp .
The lines of the two subordinate series were also shown very beautifully , the series relation being conspicuous to the eye .
Such lamps show the resonance radiation of D light 2 s VOL. xci.\#151 ; A. Hon. R. J. Strutt .
Observations on the incomparably better than any salted flame will do .
The advantage lies not only in the brilliancy , but also in the narrowness of the D line .
As Dunoyer has shown , only the central part of the broad line given by a flame is effective .
In studying the fluorescence produced by the line 3303 , it is necessary to suppress the light due to the visual lines , particularly the D line .
This was accomplished by a cell of cobalt blue uviol glass , filled with a dilute solution of nitrosodimethylaniline .
This combination is very transparent to \ 3303 , and suppresses everything in the visual region except a small part of the light of the red sodium line 6161 .
It is necessary to tolerate the latter , for if the nitroso solution is made strong enough to suppress it , serious loss of 3303 light is incurred .
In practice not enough red light came through to cause inconvenience .
The light coming through the filter was examined with a quartz spectrograph .
The only line on the plate was 3303 .
The visual spectrum showed only the red line 6161 , and this could only be seen by directing the spectroscope straight at the lamp through the absorption cell .
The arrangements are shown in plan in fig. 2 .
The lamp is at A. It is focussed by a quartz condenser B on the wall of the quartz flask E , the ultraviolet filter D intervening .
B is set in the wall C of a dark cupboard , the axis of the lenses being inclined at about 60 ' to the wall , whioh makes the apparatus more accessible to an observer .
The observations are made inside the cupboard .
E is a tound-bottomed quartz flask of 100 c.c. .capacity containing a little O A V/ Z/ // // // / c Fig. 2 .
Fluorescence and Resonance of Sodium Vapour .
515 sodium .
It is connected by rubber tubing to a Gaede mercury pump , which is kept running , and which serves in addition to keep the sodium lamp A exhausted .
Before starting observations , the eyes are well rested in the dark .
The bulb E is then well heated in a Bunsen flame , to nearly a red heat , so as to generate sodium vapour .
When the lamp is started , the front surface of the bulb is seen to emit visual light .
In the earlier experiments this was too faint for spectroscopic analysis , but it was examined by absorption methods .
First , a cell 1*2 cm .
thick filled with saturated potassium bichromate solution held in front of the eyes was found to transmit it undiminished .
This shows that the light must be in the yellow or red region of the spectrum .
Secondly , the light was entirely cut off by substituting for the bichromate a strong solution of prsesodymium nitrate .
The latter solution transmits the red , but has an absorption band extending from \ 5820 to X 6020 .
The D line at X 5890 lies in this narrow region , and considering that the emission takes place from sodium vapour , there was practically no doubt that it did consist of D light .
In later experiments , under improved experimental conditions , the light was bright enough for its orange colour to be very conspicuous .
Examined with a direct vision spectroscope it was found to be monochromatic , consisting entirely of D light .
So far I have supposed the bulb to be quite hot , say at 350 ' C. In this case the 3303 light is not able to penetrate far into the sodium vapour , and consequently the D light excited is confined to the surface of the mass of vapour .
As the bulb cools and the vapour diminishes in density , the excited D light gradually penetrates into the interior of the vessel , and fills it entirely .
The light then slowly fades away as the vessel becomes cold .
These effects are exactly the same as are observed when D light is used as the exciting light .
Possibly suspicion may arise that a trace of D light had been able to penetrate the ultra-violet filter and produced the observed effect .
A simple test experiment entirely negatived this possibility .
When a piece of ordinary plate glass , 1*2 cm .
thick , was interposed in the path of the exciting beam so as to cut off ultra-violet light , the excited D light disappeared altogether .
S 3 .
No Excitation of the D Lines by Other Kinds of TJltra-violet Light .
Another* doubt may possibly remain .
Granting that the excitation of D light is due to ultra-violet light , is it essential that this particular wave-length 3303 should be used ?
Would not any intense ultra-violet radiation serve ?
Hon. R. J. Strutt .
Observations on the To test this a mercury arc in quartz was substituted for the sodium arc .
It gave very strong radiation through the ultra-violet filter , lighting up a piece of uranium glass much more brightly than the sodium lamp had done .
It also caused the quartz wall of the bulb containing sodium to emit a little blue fluorescence , but when this was cut out by holding a bichromate solution before the eye , nothing remained : D light was not emitted .
The strong ultra-violet mercury lines present were probably the groups about X3650 and X3130 .
S 4 .
Search for Evidence of Resonance Radiation at X 3303 .
It appears , therefore , that light energy of wave-length 3303 absorbed by sodium vapour is , in part at any rate , re-emitted as D light .
Clearly then the relation found by Wood and Dunoyer for stimulation by D light , * that the whole of the absorbed energy reappears as energy of the same wavelength , cannot apply to the line 3303 .
It must be a peculiarity of the D line , distinguishing it from other members of the series .
The question arises , however , whether any part of the energy of X 3303 is re-emitted at the same wave-length ; whether , in other words , there is any resonance radiation of X 3303 .
An experiment was arranged as in fig. 3 .
In this case a cylindrical silica tube , about 2 cm .
in diameter , kept in connection with the pump , contains the sodium vapour .
Light of wave-length 3303 is incident perpendicularly upon it , as shown by the arrow .
Some ultra-violet light is found to proceed obliquely from the point of incidence .
It is focussed by a quartz lens B upon a fluorescent screen of uranium glass .
The image is at D , and is shown by the fluorescence .
This fluorescence must be viewed obliquely .
If viewed in the prolongation of AD , yellow D light from A , stimulated in the way already described , enters the eye , and masks the fluorescence on the screen at D. It is necessary to decide whether the ultra-violet light emitted from A is due to resonance radiation , or whether it is merely light scattered by the striae in the walls of the silica tube.*f A comparison fluorescent patch was obtained at E by forming there the image of a small smokeless gas flame F. E was adjusted to be of the same brightness as D when the tube A was cold , and contained no sodium vapour , and when the solid sodium in the tube was out of the way of the incident light .
On heating A so as to raise sodium vapour no increased brightness of the * ' Phil. Mag. , ' vol. 27 , p. 1025 ( 1914 ) .
+ The arrangement adopted excludes specular reflection from the silica tube , as will be evident from fig. 3 .
Fluorescence and Resonance of Sodium Vapour .
fluorescent patch at D could be observed .
E was still a match for it .
This proves that the resonance radiation of \ 3303 , if any , is but a small fraction of the light of this wave-length scattered by the walls of the vessel .
A similar experiment was made with the same vessel but with D light a6 the exciting light .
The ultra-violet filter was removed , a sheet of ordinary ground glass was substituted for the uranium glass at C , and a salted spirit flame for the smokeless gas flame at F. Starting with the sodium tube A cold , the yellow image at E was adjusted to equality with that at D. On heating the tube A , so as to raise sodium vapour , D became D E C Fig. 3 .
many times brighter than E , owing to the resonance radiation , which entirely outshone the scattered light .
There is no reason to suppose that the fraction of the incident light scattered by the striae in the quartz tube would be very different , whether this light consisted of D light or of X3303 .
Assuming that the same fraction is scattered by the walls of the tube in each case , it follows from the experiments described that the resonance radiation is a very much smaller fraction of the exciting radiation for X 3303 than for D light.* * -X tube with a window of clear optically worked quartz fused on would make it possible to push further the search for resonance radiation of X 3303 .
Hon. R. J. Strutt .
Observations on the As already mentioned , the experiments of Dunoyer and Wood indicate that the whole of the absorbed D light is re-emitted as D light .
My own experiments prove that this is not true for light of \ 3303 .
The interesting possibility remains for future investigation that not only a part but the whole of the absorbed energy of \ 3303 is re-emitted as D light .
Such a result would , howevbr , be difficult to reconcile with the quantum theory .
S 5 .
Effect of One Component only of the Ultra-violet Doublet \ 3303 .
The first ultra-violet sodium line , though hitherto spoken of as single , is in a fact a doublet like the J ) line .
The components have wave-lengths , on the International system , of 3302 96 and 3302*35.* There are reasons for regarding these lines as belonging to different series : in fact , for regarding the principal series of sodium as really including two series .
The series including Di and 3302*96 , the less refrangible members of the respective doublets , are each split into four components in a magnetic field , while 3302*35 and D2 , the more refrangible members , are each split into six components .
This point of view is strengthened by the observation of Wood and Dunoyerf that if sodium vapour is stimulated by the D2 line , Di does not appear in the fluorescent radiation , which consists of D2 light only .
It thus appeared of considerable interest to determine whether stimulation by the line 3302*96 would give rise to Di only , or whether it would give rise to D2 ( which may be regarded as belonging to a different series ) as well .
An accidental circumstance , to which attention has been drawn by Wood , made it possible to attack the question .
This is the extreme nearness of certain zinc lines to wave-length 3303 .
The zinc arc spectrum shows a doublet which lies inside the sodium doublet .
The wave-lengths given by Kayser stand thus : Intervals .
Sodium 3303*101 0*05 Zinc . .
, 3303*05 J Zinc 3302*701 0*21 Sodium 3302*49J Kayser 's table has been compiled by critical collation of the data given by different observers .
These observers have not of course felt any special interest in the exact relative position of the zinc and sodium lines mentioned , -* which has no importance except for the technique of the present investigation .
It was thought therefore that direct comparison would give greater certainty * I quote these wave-lengths from the Table given at the end of Kayser 's ' Spectroscopy , ' vol. 6 .
'm t ''Phil .
Mag. ' [ VI ] , vol. 27 , p. 1018 ( 1914 ) .
Strutt .
Roy .
Soc. Proc. , , vol. 91 , PI .
8 .
Fig. 4 .
Fluorescence and Resonance of Sodium Vapour .
as to the exact intervals .
The spectra were compared in the third order of a 10-foot Rowland grating , using a quartz vacuum arc both for zinc and sodium .
With short exposures the lines , especially in the case of sodium , were very fine and sharp .
The intervals above mentioned were measured as 0 043 Angstrom and 0*198 Angstrom , in good agreement with the numbers adopted by Kayser .
In all the photographs there was some overlap of the images of 3303*10 ( sodium ) and 3303*05 ( zinc ) .
On the other hand there was definite separation of 3302*70 ( sodium ) and 3302*49 ( zinc ) by a narrow interval of clear glass .
When there is separation , it is definite proof that the lines themselves do not overlap , but on the other hand an overlap of the photographic images is no proof of overlap of the lines themselves , for the images may be , and with any but the shortest exposures certainly are , broadened by irradiation .
For this reason 1 have not been able to definitely establish from the spectrograms whether , and to what extent , 3303*05 ( zinc ) overlaps 3303*10 ( sodium).* It is scarcely doubtful that , as is known to be the case with mercury , the zinc lines broaden with increase of current .
If therefore the zinc line 3303*05 does not overlap its sodium neighbour for small currents , an increase of the current will probably make it do so ; on the other hand , up to 30 amperes at all events , the spectrograms still showed that there was no overlap of 3302*70 ( zinc ) and 3302*49 ( sodium ) .
Fig. 4 ( Plate 8 ) shows an enlargement of a photograph taken with 30 amperes passed through the zinc lamp .
The closer doublet in the middle is of course the zinc one , the sodium doublet appearing above and below .
The net result of this study of the spectra is to show that there is a zinc line in practical coincidence with the less refrangible member of the sodium doublet , but no zinc line in coincidence with the more refrangible member .
If we use a zinc arc to excite sodium vapour , we apply excitation at one line only of the doublet 3303 .
The form of lamp which has been found useful for zinc vapour is shown in fig. 5 .
It is a slight modification of that used for sodium .
The envelope of the lamp consists of two lengths of rough silica tube each about 13 mm. inside diameter and 30 cm .
long , united by a short piece of clear silica tubing about 8 mm. inside diameter .
The cathode is a layer of molten zinc d resting on an iron plug e , which of course must not fit the silica tube too tightly .
A mica washer at f prevents the molten zinc running down below e. Connection is made to e by an iron wire g passing out through a glass fitting A , * Probably this could be done if the spectrograph were arranged with a suitable lens to form an enlarged image on the plate of the original grating image of the group 3303 .
Hon. R. J. Strutt .
Observations on the -a cemented with sealing wax .
The anode h is also a loose iron plug , with a pointed end , as shown .
The connection is brought out in the same way .
A side tube l in the glass fitting provides for exhaustion .
V 's .
The arrangements for the experiment are seen in plan in fig. 6 .
The zinc lamp is shown in section at A. The rays from it pass through the quartz condenser B set obliquely in the wall as before , then through the ultra-violet filter D , coti- ' verging at E on to the wall of a quartz bulb containing soditun vapour .
The rays impinge on the quartz bulb almost at grazing incidence , and set up a fluorescence of D light , as when the , , sodium lamp is used as a source of 3303 light .
The intensity of this light depends very much on the current through the zinc lamp . .
This is no doubt due to the fact that at small currents the zinc line is too narrow for any overlap with the sodium line .
With larger currents such overlapping begins , and the vapour is stimulated .
With currents of 4 amperes no D light is seen .
Increasing the current to 6 amperes it can be seen , and identified by the absorption methods before described .
At 15 amperes it is bright enough for spectroscopic examination .
The current may be further increased up to 100 amperes , with a great increase in the fluorescent light , which is now , perhaps , as bright as a slightly salted flame .
The zinc lamp , however , will only stand these currents for a few seconds .
It has been found convenient to start up the lamp , and run it at , say , 6 amperes , by means of a regulating resistance .
When all is ready for observation this resistance is shunted by a smaller one , so as to pass a heavy current for a short time .
For the heaviest currents a fuse wire without other resistance is used in the shunt circuit , and allows the heavy current to pass for a few seconds only ; enough , however , for observation .
The lamp is not extinguished when the fuse melts in the shunt circuit , thus the observation can easily be repeated after replacing the fuse .
In order to decide whether one or both D lines were present , a special spectroscope was employed , consisting of slit , direct vision prism , and telescope .
The slit , 1 mm. broad , is a fixed one , made in a brass sheet F. The slit itself is horizontal , and is in the plane of the diagram ( fig. 6 ) .
A vertical strip of brass G divides the length of the slit into two parts .
One of these parts ( that towards the top of the page on the diagram ) is backed by Jihe fluorescent light of the sodium vapour in E. The other , part Fluorescence and Resonance of Sodium Vapour .
521 is backed by a minute soda flame H , which affords a comparison spectrum .
This flame is simply a coal-gas flame burning from a drawn-out soda glass " , pA Fiq .
6 .
jet , and turned down " to the blue .
" Its spectrum shows the D line superposed upon the Swan spectrum .
The prism used ( indicated at J ) is a powerful combination designed by Lord Rayleigh , * to whom I am indebted for the loan of it .
Ten right-angled flint glass prisms , with their refracting edges horizontal , are immersed in carbon disulphide , containing enough benzol to exactly compensate the deviation for D light .
The combination is 20 inches long .
It was mounted with its nearest end 48 inches from the slit , though represented much nearer in the figure , for convenience .
Under these conditions the D lines in the comparison spectrum were seen well separated with the naked eye , but in the experiment a telescope K was used .
It consisted of single convex lenses , object glass 5 inches and eyepiece inches focal length , giving rather more than three-fold magnification .
With this amount of magnification the images lose nothing in brightness , while they gain in angular magnitude\#151 ; always an advantage in dealing with very faint objects .
The telescope tube was covered with phosphorescent paint near the eyepiece , which proved a convenience for quickly finding one 's way to it in the dark .
The spectroscope thus arranged proved most satisfactory for resolving the D lines from a very faint source , and I do not think that it could be improved on for this purpose .
The great advantage of the large dispersion is that a wide slit is admissible .
In making the observations the zinc lamp was started with a small current , the quartz bulb was heated , and the observer at the spectroscope * See his ' Collected Scientific Works , ' vol. 1 , p. 459 , and vol. 4 , p. 394 .
VOL. XCI.\#151 ; A. 2 T Hon. R. J. Strutt .
Observations on the got his eye rightly directed and focussed so as to see the D lines well in the comparison spectrum .
He then knew exactly where to look for these lines in the usually fainter fluorescence spectrum , during the short time it was on .
This use of a comparison spectrum is practically essential .
It is strongly to be recommended in all spectroscopy of faint sources .
At the first test , 100 amperes were passed for a moment , and both D lines were seen in equal intensity , as bright as the comparison spectrum , if not more so .
In subsequent tests the current was reduced by successive stages down to 15 amperes .
At this point the result was still the same , quite definite and distinct .
With smaller currents than 15 amperes the fluorescent light was too faint for spectroscopy .
In all not less than a dozen observations were made , not all on the same day , and each one of them separately was conclusive as to the general result .
I was not able to decide definitely which , if either , of the D lines was the brighter .
In a flame Da is somewhat brighter than Di , but in the spark no definite difference is recorded .
As already shown , stimulation is confined to the component 3303*10 at 30 amperes , and possibly for much larger currents still .
Both the D lines appear in equal intensity at 15 amperes .
There is , therefore , an ample margin of safety in saying that stimulation applied at one member only of the first ultra-violet doublet gives rise to emission of both the D lines .
S S 6 .
Search for Fluorescent Emission of the Subordinate Series Lines .
As stimulation at 3303 had proved capable of bringing out the D lines it seemed possible that it might also bring out the subordinate series lines .
To look for these a zinc lamp was first used , loaded momentarily with 100 amperes .
The arrangements were as in fig. 6 , except that instead of using the prism J and the telescope K , the slit was viewed without a telescope , through a much less dispersive direct vision bisulphide prism , the eye being only about 8 inches from the slit .
The spectrum obtained in this way was short and bright .
The swan spectrum of the little gas jet H served as an approximate guide for the eye , and the lines 5685 and 6157 of the first and second subordinate series specially looked for .
No trace of them , or of any other line except the D line , could be seen in the fluorescent spectrum .
A second attempt was made , using the sodium lamp as a source of A 3303 .
A quartz tube , 2 cm .
diameter , was used to contain the vapour , and examined with an ordinary pocket spectroscope .
In this case the brightness was " ^perhaps somewhat less , but the observations could be made at leisure because the^odium lamp does not need to be heavily overloaded in order to Fluorescence and Resonance of Sodium Vapour .
523 bring out the fluorescence .
No trace of the subordinate series lines could be seen .
The green one , 5685 , at all events , could have been seen if it had had the same intensity relative to the D line as it had in the original sodium lamp .
My colleague , Prof. Fowler , very kindly made these observations with me .
S 7 .
Summary* ( 1 ) Sodium vapour , illuminated by the second line of the principal series at wave-length 3303 in the ultra-violet emits the D line , which is the first member of that series , in fluorescence .
( 2 ) Stimulation by ultra-violet light in general does not cause emission of the D line .
( 3 ) If one member only of the ultra-violet doublet 3303 is stimulated , not one only , but both of the D lines are emitted , in about equal intensity .
This is an unexpected result , in view of the work of Wood and D unoyer , who found that stimulation by Da light was unable to excite Di light .
( 4 ) Stimulation at X 3303 was not found to give rise to any observable resonance radiation of the same wave-length , nor to any observable emission of the subordinate series lines .
I have much pleasure in thanking my assistant , Mr. P. Thompson , for valuable help in carrying out the experiments .
* The chief results of this investigation were indicated in preliminary .communications to * Nature , ' May 13 and June 3 , 1915 .
VOL. XOI.\#151 ; A.
|
rspa_1915_0045 | 0950-1207 | Obituary notices of fellows deceased. | 0 | 0 | 1,915 | 91 | Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character | P. A. M.|H. F. B. |F. W. D.|G. T. B. |F. D. A. |R. A. S. |F. W. D. |E. W. B. |C. R. M. |A. E. S. |G. C. F. |S. Y. |E. B. E. | biography | 6.0.4 | http://dx.doi.org/10.1098/rspa.1915.0045 | en | rspa | 1,910 | 1,900 | 1,900 | 4 | 1,385 | 39,833 | http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1915_0045 | 10.1098/rspa.1915.0045 | null | null | null | Biography | 57.593807 | Astronomy | 12.082639 | Biography | [
32.7570915222168,
80.58267974853516
] | ]\gt ; ROBERT HARLEY , 1828-1910 .
THE Harleys can be traced back to a Norse stock of Harlas .
liobert Harley 's family was settled in Dunfermline for dreds of years .
His father , Robert Harley of Dunfermline , began life as a merchcmt with property bequeathed to him by his uncle , Sir William Mitchell ( a Vice-Admiral who fought with Nelson ) , but he gave up a good business in Scotland to become a Wesleyan minister in England .
His mother Mary Stevensou , nlece of General Stevenson of Air .
They were at Seacombe , near Liverpool , when Robert Harley was born ( January 23 , .
1828 ) .
When a small boy he was devoted to swimming but found arithmetic the most irksome of his studies .
He was in this respect backward , but seems suddenly to have developed talent and enthusiasm while at school at Blackburn , which led to his accepting a post as mathematical lster at a Seacombe school when he was only 16 .
Shortly after this he was attracted by the mathematical problems which were appearing in The Lady 's and Gentleman 's Diary .
' His interest in the solutions had one very important result , for it brought him into contact with a young barrister , nine years his senior\mdash ; James Cockle\mdash ; who later became a distinguished mathematician , a knight , a Fellow of the Royal Society , and Chief Justice of Quccnsland .
Thev became life-long friends , and there is no doubt that his scientific work was more influenced by Sir James Cockle than by any other single individual who could be named .
When Sir James died in ) Mr. Harley wrote the obituary notice for the Royal Society 's ' At the of 17 he returned , as head assistant-master , to his old school at Blackburn .
This was kept by William Hoole , J.P. , a well-remembered lnayor of the town , by whom Viscount Morley of Blackburn and many others who have since risen to distiuction educated .
At the of 23 he determined to be a minister , and becanle a divinity student at Airedale College , Bradford , and on completing his course accepted a call to become minister of the Independent Chapel at house , in the West iding of Yorkshire .
When he was 26 he lnarried Sara Shoyan , niece of Mr. Hoole , and daughter of James Shoyan of , also of Scottish extraction , and lived happily with her for fifty-one years .
He served at Brighouse for fourteen years .
His four children , two sons and two hters , were all born there .
His congregation built a comfortable manse and a much larger chapel .
He laboured strenuously for the good of the growing village , preaching in the open air with his frisnd William Booth , afterwards famous as the Father of the Salvation Army .
He started Penny Readings for the poor , and himself took part in them every Saturday night .
He was much beloved by the people , and Harley Street , Harley Court and Place remain to link his memory with the now prosperous town .
During ths last four years of his Pastorate at Brighouse he was VOL. XCL\mdash ; A. Comlnittee ; was honorary Curator of the Museum , and President of the Literary and Philosophical Society .
In the latter capacity he introduced to a Leicester audience as lecturers many of the foremost scientific men of the day , including Huxley , Tyndall and Spottiswoode .
He himself lectured on " " The Moon " " Meteoric Showers and many other subjects .
In the summer of 187 he ited Mill Hill with the object of entering his eldest son at the now well-known school .
The Head Master\mdash ; .
Weymouth\mdash ; was so with his energy and capacity that he offered there and then to create for him a position as Vice Master .
This was accepted , and Mr. Hal'ley moved from Leicester and built for himself a house\mdash ; Burton Bank , Mill Hill\mdash ; which became the first boarding house in connection ith the School .
The house speedily filled , and for nearly ten years he was Vice Master of Mill Hill and Minister of the Chapel .
his efforts the school imming bath was built , the pla ing fields improved , and a reco1d in the number of boys established .
Apart from the School he interested himself in the life of the village .
He erected a lecture hall , which was opened by his friend the late Earl Stanhope , and made a centre of instruction and entertainment .
In 1882 .
Harley retul'ned to as Principal of Huddersfield which post he filled with marked success until 1886 , when he a , ccepted a call to the principal Congregational church in Oxford .
Soon after his ar1ival the University of Oxford conferred upon him the of M.A. , on wluch occasion the ) Orator paid a tribute to his labours in the cause of religion and philanthropy as well as to his attainments as a mathematician .
He took a part in founding the Oxford Mathematical Society , and , in 1889 , lectured before the Ashmolean Society on " " George Boole and his Method He was compelled to take a lest in 1890 , and , at the instance of a Special Committee of the Union of and Wales , he accepted a cabled invitation to take tenIporary charge of the Mother of New South Wales ( Pitt Street , Sydney ) .
He stipulated beforehand for two months , but he remained for eight months and was Robert Harley .
invited to stay on permanently , but he had left his wife and in England and had no wish to settle down the Antipodes .
He made a host of i.riends in Australia , and lectured before the Royal Society of New South Vales and Queensland , the Union of Sydney University , and Inany other bodies .
On his return to England he , in 1892 , went once more back to Yorkshire , tl1is time as Minister of Heath Church , Halifa In 1895 he retired and bought a house at Forest Hill , S.E. , where he lived quietly and happily for the fifteen years of his life .
He preached and lectured frequently , and advocated total abstinence incessantly .
He was , in fact , one of the pioneers of the Temperance 1novement .
At the British tion he often presided at the Temperance breakfast .
He was a Vice-President of the National Temperance League tor -three years , and only fe wecks before died a reception given in his honour by a number } workers interested in temperance , at the Memorial Hall , Street , presided over by Sir John Thomas .
On this occasion he an address , entitled eminiscences of an Octogenarian\mdash ; Chiefly Temperance was ovel 82 he spoke much and eloquence , an intellectual vigour in his old age which anlazed his friends .
He was always a keen udent of astronomy , and Fellow of the Royal Society .
He had an obselvatory nilt in his rden for a fine telescope which was presented to him by personal friends .
He was a frielld of Herschell , Airy , gins , Ball , and other well astronomers .
On one occasion he visited Lord Rosse at Parsonstown .
He was a Life of the British Association , and acted Secretary of Section A in 1868 ( Norwich ) , and in ( Edinbnr ) .
He was President ( Bradford ) , 1888 ( Bath ) , and 1891 ( Cardiff ) .
Throughout his life Mr. Harley found recreation in investiThese may be said to have commenced with friendship wit1 Sir James Cockle .
His eal.liest paper was published in and bore ) title " " Impossible Equations A few years later he becanle on the problem of the finite solution of the general lation of the fifth which had occupied the minds of the most celebrated dvsts of the 18th and 19th centuries .
He and were in almost daily correspondence for several years , particularly to 1862 , on the .
He approached the problem by seeking to nine in an explicit a certain sextic equation\mdash ; termed a resol \mdash ; on the solution of which that of the general ( may be made to delJend .
It ftppeared ) quently that cobi earlier , and Malfatti evell earlier still , ) ) ounded the doctrine of sextic resolvents , but , merit mained in the work , for it was independent and lucid .
In particular he devised a new ybol and a new cyclical function which much simplified and facilitated laborious lculations .
He later extended his esearches on the theory of equations far beyond the limits at first proposed .
His results were published in the 'Manchester Memoirs , ' the 'Quarberly Journal of of papers .
, 'On Impossible Equations , ' 'On the Method of Producfs , ' 'On the Theory of Quinties , ' . .
' On Certain Circular Fnnctions , ' .
esearches on the Theory of the Transcendental Solutions of Algebraic quations , ' Among those who supported his candidature were Cayley , Sylvester , Hirst , H. J. S. Smith , Boole and Spottiswoode .
these investigations Harley next took up the subject of differential , and with the collaboration of B. Rawson and Cockle constructed a theory of " " Differential esolvents Cockle encountered a class of differential invariants which he named " " Criticoids These were examined by Harley in a masCerl mmner .
Harley 's friendship with Boole now had a determining effect upOn the trend of his mathematical thought .
By studying Harley 's results Boole led to a discovery in the Theory of ifferential Equations , which Harley subsequently generalised .
The last paper ever published by Boole was on this subject ( ' Phil. Trans and contains a of Harley 's 1esealches down to that date .
On Boole 's death the Editor of the 'British Quarterly eview ' applied to Harley to prepare an essay on Boole 's life and .
This was willingly undertaken , and an elaborate article appeared in the July number of the Beview for 1866 .
eceived much help from Spottiswoode ( later President of the Royal Society ) , who invited him to London that he might have ready access to the British Museum , the Royal Society , and other librax.ies .
The obituary llotice of Boole for the ' Proceedings of the Royal Society ' was also written by Harley .
He expounded Boole 's logical method before the British Association in ( Nottingham ) and in 1870 ( Liverpool ) .
He wrote and lectured on the subjects the " " Laws of Thought and occupied himself with the study of earlier efforts to f.acilitate the processes of formal logic by the use of mathematical operations .
He spent some time at Chevening , Sevenoaks , the of Lord Stanhope , studying the papers and inventious ( two machines ) of Charles , third Earl Stanhope , F.R. .
( elected in 1772 at the age of 19 ) .
In 1879 he wrote in the number of 'Mind ' an rticle about the Stanhope Demonstrator for operations ; in his will he bequeathed to the Museum the Stanhope Demonstrator and the Stanhope Arithmetioal Machine ( daGed 1780 ) , both of which had been presented to him by Arthur Philip , fifth Earl Stanhope ( ob .
1905 ) .
On his retirement Robert Harley .
he still pursued his nlathematical studies , but he never lived to complete the ' Treatise on ' which he had begum .
He sat for some years on the Council of the London Mathematical Society , of which he was a member for forty-five years .
When over 80 he would come in every day from Forest Hill to spend his time in the library of the Athenaeum Club , of which be was a member for a long period .
He preached on Sunday , July 17 , 1910 , with no that it was to be his last sermon .
He went off to Cromer for a holiday but had to be brought back to his home on Monday , July 25 ; he passed peacefully the next day , July 26 .
1910 .
He was buried in Ladywell Cemetery .
The Rev. Sylvester Horne , M.P. for Ipswich , and Chairlnan of the Congregational Union of Englanld and Wales , delivered a memorial address 1 which he dwelt on his " " lovable and striking personality\ldquo ; ; he also read letter from Sir James to his daughter , in which was said : father had a very wide cilcle of { riends ; very few men ever had so many .
In the religious world , in the world of science , the total abstinence movement and in the sphere of national politics he was widely known and as widely held esteem .
His annual visit to his beloved Yorkshire to preach Sunday School sermons was almost like a progress as friends gathered from and near to hear see him Politicians will remember him as an unflinching friend of liberty and equality of opportunity , of unsectarian education and social , a 1nan of supreme moral who was never afraid to be on the which .
was for the moment that of the minority .
He lived a full and an ] lonoured life It may be added that Mr. Harley 's life was also happy .
He and Mrs. Barley celebrated their golden at Forest Hill in 1904 , when all their four children were seated round the dinner-table .
For fifty years they had been spared a single bereavement ; but the next yettl the eldest daughter died , and within a few weeks Mrs. Harley followed her .
He was a man of overflowing spirits and merry tlon , and was able to a remarkable degree to inspire confidence and win affection .
He was always a delightt.ul person lio meet .
Those who knew him impressed with the beauty of his disposition .
He showed the kindest and most generous appreciation of the work of others .
If there was a thing to be said the .
was not missed .
He was one of the most remarkable and most versatile men which the Congregational Ministry has ever produced .
P. A. M. JULES POINCABE , 1854-1912 .
JULES born at Nancy , April 29 , 1854 .
His father was a medical man who is spoken of as enjoying , in an especial degree , the respect of his fellow-townsmen .
His uncle was the father of the President of the French Republic .
The boy was at the Lycee at Nancy from October , 1862 , until ) , 1873 , leaving with the Prix d'Honneur au Concours General en Mathe'matiques Spe'ciales .
At the age of five he had from a severe illness , and is described as a delicate boy , preferring the society of his sistel to the games of his schoolmates .
But any tendency to devote himself too exclusively to a contemplative view of life must , ons feels , have received a rude shock from the experience which came to him at the age of sixteen .
Nancy is about thirty miles south of Metz ; his father was called upon in 1870 , as a medical man , to help with the wounded , and the , Poincare ' attended him as secretary .
So anxious was he to read the only newsI ) apers that were obtainable that he learned to read German for the purpose , so it said .
In later life he was one of the closesb ties between the mathematical world of Germany and that of Frarice .
In 1873 he was first among candidates for the Ecole Polytechnique at Paris .
ving this in October , , for the School of Mines , he was thence transferred as ineer to Vesoul , about 80 miles south of Nancy , from April to December , 1879 .
During this year , in August , 1879 , he became Doctor of Mathematical Science in the University of Paris .
In Decenlber of the same year he was in charge of the Cours d'Analyse \amp ; la Faculte des Sciences de Caen .
In March , 1881 , at the of nearly twentyseven , he was honourably mentioned as a competitor for the Grand Prix des Sciences matiques awarded by the Academy of Scienees of Paris .
In October , 1881 , he became Maitre dc Confe'rences d'Ana]yse a la Faculte ' des Sciences de l'Universite de .
In 1886 he was Professeur de Physique matiquc et de Calcul des Probabilite 's at the University of Paris , and in 1896 Professeur d'Astronomie Mathe'matique et de Mecanique Celeste .
He was chosen Member of the AcadelIly of Sciences the Section of Geometry in January , 1887 , served as President in 1906 , and was elected to the French Academy in 1908 .
He became a Member of the Royal Society in 1894 , and on the inauguration of the Sylvester Medal for Mathematics in 1901 , he received the first award .
He died at his house in Paris in July , 1912 , during the celebration by the Royal Society of its fifth jubilee .
At the funeral ceremony the Society was esented by the Senior Secretary and the Astronomer Royal .
Such , in briefest are the facts of his public career .
To give any * A fairly complele bibliography , with a portrait and various appreciations , is edited by Ernest Lebon ( Gauthier Villars , July 1 , 1909 ) .
To this the writer is much indebted for dates and references .
Jutes complete account of his work is a task well impossible on account of its vast ran , .
His writings deal with nearly every branch of analysis , with every part of theoretical astronomy , and with most of the issues of modern mathematical ysics .
To whatever he deals with he a breadth of outlook , a wide ality of conception , which the ination , though it may puzzle the mind .
Of the final value of his applications of mathematics to physics , time will pronounce ; of the importance of the influence which his wide enabled him to exert , especially in his own conntry , there can be no question .
His contributions to pure analysis may be classed under differential equations , automorphic functions , general theory of functions , Abelian functions , Analysis Situs , arithmetic .
The work on differential equations includes studies in extension of the eneral existence theorems by Cauchy , and consideration , on the lines of Riemann Fuchs , of the theory of linear differential equations .
Also a systematic considel'ation of the utility , as solutions of differential equations , of series which are , and yet asymptotic ; this last , forced upon Poincar 's attention , presumably , by his astronomical studies , has had a wide developnlent .
It is , however , the eneral consideration of an infiniGe discontinuous group , in connection with which he refers explicitly to Fuchs , and the associated phic functions , which are the best known results of his study of differential equations .
Historically an automorphic function arises among the formula for elliptic functions which are found in Jacobi 's undamenta Nova .
' Jacobi obtains a series whereby the square of the lnodulus , , can be expressed as a single-valued function of the ratio of the two so-called quarter periods .
These are solutions of a linear differential equation of the second order whose independent variable is .
Putting , and , it is then natural to consider of of the form , in which are constants .
uore sinlply and precisely , the facts are thus : Let 2 be two arbitrary quantities whose ratio is not real , but has its imaginary part positive .
Let be Weierstrass 's doubly periodic function with these quantities as periods .
Then the function which is the ratio of to is evidently a } -valued function of .
It is in unaltered by substituting in it , in place of , the quantity ; or by substituting ; or more generally by replacing by in which ) , are any integers of which and .
are even , such that , so and are odd .
There is number of substitutions of this form : any two of them performed in succession give rise to a substitution of the same form , so that the of them constitutes a group of substitutions .
Starting from an arbitrary value of whose imaginary is positive , all the values of arising by these substitutions have their part positive ; representing such values of on the upper half of a plane , the usual way , a fundamental of this half-plane can be named which is analogous to the fundamental viii Notices of Fellows used in the discussion of doubly periodic functions .
Namely , every point of the upper half-plane which does not lie in his funda .
: can be obtained from one , and only one , point of this region by one , and only one , substitution of the group above described .
If , we may take for such a fundamental the part lying betlveen the lines and above the semicircles inear substitutions , btain soinc , tudy teneral properties onfinite functions of the independent variable unaltered when this variable undergoes any substitution of group .
In both respects he obtained a brilliant success .
It is not easy in a few sentences to give an account of his general theory of the groups ; but it may be possible to clear the way in which he constructs functions unaltered by a given roup .
Let be any one of the substitutions of this group , the constants being chosen so that .
Denote the denominator by .
Let be a rational function of , and a constant such that ; let be an integer .
Consider the sum which is to contain a term corresponding to every substitution of the group .
It is then easy to prove that if for we substitute , any one of the transformations of arising in the group , we obtain .
The proof requires the assumption that the original series converges irrespective of the order in which the terms are taken ; when we consider the generality of the ideas involved , Poincare 's proof that this may be so for proper values of is one of the most striking portions of the work .
Taking now another such sum as , having , however , in place of rational function , we shall have a similar equation .
Thus the quotient of the two functions is unaltered when the independent variable is changed by any substitution of the group .
But now arises another consideration .
Reverting to the function before considered , for purposes of illustration , we may regard 7- , or as the quotient of two independent solutions of a linear differential equation of the second order whose independent variable is .
This is , in fact , a hypergeometric equation with singular points only at .
If we have any function of the unrestricted complex variable , of which every existing branch is expressible , in the neighbourhood of any value other than , or 1 , or , as a power series in , then it can be proved that , by regarding as that function of the new independent variable which is Jules Poincare ' .
ix given by the function above , the function under consideration becomes a single-valued function of .
A particular case of this result is that the dependent variable of any hypergeometric differential equation is a singlevalued function of , if the independent variable be ified with .
These are evidently results of scope .
Quite early formulated a demonstration that every analytical function , ?
, of an independent variable , is such that both and may be valued functions of an independent variable .
And both Klein ( in 1882 ) and he ( in 1883 ) have to make it clear that any rational algebraic equation , connecting and / ?
, can be satisfied by and as functions of another yariable , the snggestion of particular cases being that the functions can be taken to be autom morphic functions in the sense already explained .
To enunciate such a eorem , even though its exhaustive proof is a matter for subsequent investimation as it was in this case , may be to exert a great stimulus to the development of a theory .
It ought , however , perhaps , to be mentioned that unless the equation is capable of being satisfied by fun ctions , or by elliptic functions , of a parameter , the functions of the new parameter , which are contemplated by the theorem , must possess number of essential singularities .
The deductions to be drawn from the Rult must then , it would seem , be of a general character , and independent of the precise form of the functions .
Poincare himself returned to the matte1 ' in a paper on the uniformisation of analytic functions as late as vol. 31 ) , and the proof of the theorem has called forth an extensive literature .
There is one matter of subsidiary importance to which a word may be iven in connection with Poincare 's theory of automorphic functions .
The division of the upper half of the plane of the complex variable into ions corresponding to the substitutions of a group may be made , as it in the particular case previously taken for illustration , by means of circles their centres on the real axis .
Such circles have obviously at least some of the properties of straight lines in a plane ; two such circles intersect in one point ( in the upper half-plane ) ; one such circle can be drawn two given points .
As straight lines are the curves which render the stationary , taken between two given points , where , so the circles in question are the curves which render the integral statio1lary , being the ordinate to the real axis and the abscissa parallel to this axis .
The relations of these circles are , in fact , those of the so-called straight .
lines in the geometry of Lobatchewski , the integral , which we may call the separation of its two extreme points , replacing the distance of the Euclidian geometry .
Similarly the integral , which may call the extent of the zegion over which it is taken , may be used of the area .
Every one of these elements , the circles with centres on the axis , the separation , and the extent is unaltered by trahsformations , Notices of Fellows in which are real , just as straight lines , lengths and areas are !
tered movements in Euclidian geometry .
It is thus convenient to make use of these elements in discussing the roups of such linear substitutions .
It is in this Poincare ' employed -Euclidian geometry discussion of these substituCions .
In addition to the systematic development of the theory of automo1phic , of which we iven some account , Poincare wrote several papers dealing with questions of Abelian functions .
One of the briefest is of Kronecker 's theory of characteristics to ermine the nunlber of pairs of variables for which ) two theta functions of two lave each .
The sams is used also by in his greaC paper on the equilibrium of a rotating fluid mass ( Acta Math. , vol. 7 , p. 268 , 1885-6 ) .
In Kronecker 's hands the theory becomes an extension of Cauchy 's theorem for integrals of functions of one complex variable to integrals of functions of several ] variables , and is into connection with the theory of potential in any number of dimensions .
It is interesting , then , to find papers of Poincare ' dealing with exCenSlOUS of Cauchy 's theorem to functions of several complex variables , to see the heory of potential in any number of dimensions applied to the theoly of functions of several variables , and to note how exterlsive and ersistent were 's attempts to grapple with the problems of Annlysls Situs in space .
One of the problems to which Weierstrass de ote 1 much consideration was to generalise the expression , as a quotient of t functions , of a -valued analytic function of one variable whose only finite are poles .
Consider a single-valued analytic nctio of two variables ; assume that about every finite pair of values of these function is expressible , generally as a power series , but , if not , then as a quotient of two power series , with presumably only a limited of .
The question is whether there exist power series , each convergent for all finite values of the variables , as the quotient of which the function can be represented for all values of the varinbles .
A difficulty arlses from the fact that there are points at which the function has no definite value at all , the expressions which represent it different limits according l the path by which the variables approach the point\mdash ; it is rable that the representation of the function as the quotient of two functions should be such hat these integl'al functions do not slmultaneously vanish except at poihts for which the function is actually indeterminate .
Poincare 's papers in regard to the connection of the theory .
of potential with the theory of integral functions furnish a proof that such a representation is possible , and give rise incidentally to a splendid eneralisation of Weierstrass 's factor expression for an integral function of one variable .
The real part of the logarithm of the factor , wherein hich is introduced for convergence , may , for the oses of our statement , be out of account , is the potential of a mass at the point .
We may thus say that , save for a correction JnlesHem.i Poincare ' .
xi necessary to secure convergence , the real part of the arithm of the integral function is built np from the potential of masses situated the zero points of the integral function .
When we come to an integral function two variables , its zero points form a continulun .
The integral the potential of this continuum is the portion of the real part of the arithm of the integral function .
The application of this tion to Weierstrass 's problem requires the establishment of the notion of a definite continuum upon which iven function vanishes , and of another continuum lpon which the function becomes infinite , and so furnishes a further incitement to the study of hyperspace .
The ideas of which we have attempted to crive some ccount are applicable another ) of connected problems .
One result of the manifold study of Abelian functions in the nineteenth century was the ence of certain inteD functions of several iables , known as theta functions , and , intimately connected , of sinlultaneously periodic functions .
A func , tion of yariables ?
may be such that if })riate constants ) , , be simultaneously added to the variables ?
, , ?
, the valne of the function is unaltered .
Aud there may be sets of quantities , , for which this is true .
The theta functions are not so periodic ; are functions say of , , , associated with sets of constants such as , , , so that for the yalues , , the function is multiplied by the exponential of a linear function like For the theta fnnctions and for the multiply periodic functions which can be them , the quantities such as , , are con nected etber by certain bilinear relations of equality and inequality .
The quesbion then arises hither these relations are necessary for every possible multiply periodic function , and , a connected enquiry , whether the periodic function is expressible by theta functions .
Even though , as is now the case , these questions have been given affirmative answers , there remains a need of some comprehensive and direct method of at the result .
And the esti o that this will be associated with some reater insight the possibilities of Analysis Sitlls ( in space of real dimensions ) seelns inevitable .
Various lines of enquiry are thus opened ; there is evidence that Poincare ' attention to many of these .
With Picsrd he published a note with the bilinear relations among the periods of a multiply periodic function ; to the properties of integral functions whose second coefficients are periodic functions , and to the problem of sets of integrals whose periods are expressible linearlv by less than sets , he devoted a long paper .
his stndy of the Analysis Situs in any number of dimensions several laborious memoirs bear witness .
The surf.ace imagined by Biemann , it is well known , serves the purpose of representing an algebraic fnnction which is capable of several , say of , values , as a single-valued function of upon an -sheeted surface .
When , , we seek to apply Cauchy 's contour integral theorem to integrals of algebraic functions Xll Obituary Notices of Fellows deceased .
considered on this surface , we are at once met by the fact that it is in genera ?
possible to draw closed curves upon the surface which are not capable of being continuously deformed to evanescence , and do not form the complete boundary of any portion of the surface .
Such a circumstance arises also , evidently , for many surfaces ; as for instance for the surface of an anchor ring .
The questi.on arises for such a surface , what is theleast number of irreducible closed curves by means of which all others can be represented .
In the case of a surface ubilised in 's manner for the representation of an algebraic function , the nnmber so arising has the greatest importance for the theory , and is the most fundamental of the characters used to discriminate between ebraic functions of different individualities .
When we pass from a surface of two dimensions to a closed space of dimensions , and therein consider closed spaces of dimensions , there is a similar question .
Let two such closed spaces of order be regarded as equivalent when can be continuously deformed into the other within the given space of dimensions ; there will be a least .
mber , , of closed spaces of order in terms of which other such space can be replesented in the form wherein , are integers .
And there will be such a number for each value of which is less than .
These so-called numbers of Betti are in fact equal in pairs , the number for any being equal to the number for This theorem requires , evidently enough , much greater precision in defining the meaning of equivalence than we can attempt here .
For instance in the closed imensional space interior to an anchor closed .
curve is clearly representable in terms of one such curve ( unless itself deformable to evanescence ) ; and every closed surface in this three-dimensional space , if not itself deformable to evanescence , is deformable to one surface , whose shape is that of an anchor ring interior to the given anchor ring , so , that the two numbers of Betti are each equal to unity .
It is obvious that two spaces which are capable of being put into point to point correspondence with one another must h - the same numbers of Betti .
Conversely , .
however , it was shown by Poincare ' that the equalities of these nbers are not the only descriptive similarities necessary in order that two spaces should be capable of such correspondence .
The theory just referred to is suggested by the discussion of Riemann 's surface .
Riemann 's own theory of the functions arising for such a was based upon a theorem of existence of potential functions , for which the evidence was , in the of subsequenb scrutiny , undoubtedly The theorem in question , which the physical suggestion is extremely cogent , has thence become the centre of a wide literature .
To this Poincare contributed , with an extensive paper a method of his own , in addition to which he wrote long papers dealing in ooeneral with the , differential equations of mathematical physics .
In this sur-vey we have left aside many of Poincare 's discoveries , for Jules Henri Poinc ?
e. Xlll instance , his brilliant additions to Laguerre 's theory of the class df functions , or to Weierstrass 's theory of enic functions .
We have expounded instead some matters wherein is well seen the great generality and abstractness of much of his work .
If his had been limited to his contributions to theory of functions , they would have left an enduring mark- .
, however , now consider in a few hnes extensive publicatious in the field of Astronomy and Dynamics .
As has been said , Poincarc was .
of 1896 , and , in addition to pure mathematics , he was probably interested from the first in physical questions .
As early as 1881 , while yet Mines , in 'Liouville 's Journal ' ( vol. 7 , p. 376 ) , in a " " uolre S les Courbes Definies par un Equation rentielle , \ldquo ; we find the vords:\mdash ; " " Prenons pour exemple le problem des trois corps ; no pent on pas se demander si l'un des corps restera toujours dttls un certalne ciel These words would seem to the key to Poincar 's work in Astronomy and Dynamics ; to whether the theory leads us to expect stability of motion and periodical recurrence of may be said to have been his constant preoccupation .
The publication of G. .
Hill 's Researches in the Lunar Theory , ' in America , in 1877-8 , seems to reatly impressed him .
In vol. 1 of the Astronomiqne 1884 ) he published a paper , " " Sir Certaines Solutions Problem des Trois Corps which generalised Hill 's idea of a pel.lodlc orbit for the Moon .
And in the to vol. ( lS92 ) of his odes Nouvelles de la Mecanique ea1t of Hill 's cont iions t the theory , he says : " " Dans cette oeuvre il est permis d'apercevoir le erme de la plupart des progres que ] science a fait depuis Many of the leading ideas of his theory of orbits were expounded in his essay " " Sir Problem des Trois Corps et les Equalions de la Dynannque which obtained the prize offered by the of Sweden .
This was finished in lS88 , and published in revised form in 1890 .
In addition ) are to be mentioned the 'Methodes Nouvelles , ' already referred to ( vol. 1 , 1892 ; vol. 2 , 1894 ; vol. , 1899 ) , and the Sorbonne Lectures on Celestial Mechanics ( vol. 1 , 1905 ; vol. 2 , 1907-9 ) .
The idea of the work is the possibility of the existence of , solutions of theoretical exactness and of periodic character .
the case of the Earth and Sun and Moon , the Sun as moving with constant angular velocity in a circle about the Earth and the Moon as in the same plane , G. W. Hill obtained , by actual computation , an orbit of the Moon relatively to the uniformly rotating line joining the Earth to the which is both -entrant and symmetrical .
Poincare ' a generalisation of this for any dynamical system in which the differeutial equations have an appropriate form , of wide generality , b reasoni is quite eneral and quite simple ; but this reasoning requires an appreciation of Cauchy 's theorems of existence for the solutions of differential equatious ; and it is a characteristic property of the series which express the periodic solutions that Obituary Notices .
Fellows deceased . .
From the periodic orbit of the Moon Hill obtained , by tion of the equations , an equation for the motion of the Moon 's perigee .
] In order to calculate the frequency of its oscillations without solving the tiou , introduced the use of determinants of indefinitely great order .
That oincar should investigate the convergence of the method , and so set new of analysis , as an incident to his astronomical work , is stic of him .
He further considers in much detail the general llethod of variation and the quantities which generalise the frequency considered by Hill , and their e , xpansion as power series , as part of his theory of characteristic exponents .
In another direction , also , he adopts the idea , gested by Hill , of making the periodic solution the centre of the theory , by considering solutions which coincide with the periodic solutions after an infnllte time , or did so coincide an infinite time before the .
These the so-called asymptotic solutions .
Both the periodic solutions and the asymptotic solutions are particular solutions of the equations , not containing the full number of arbitrary constantsWhereas the for1ner converge , the latter , when expanded in terms of the snrall quantities , do not ; they are , however , definitely and formally shown to be capable of use for approximations , in the mannel of 's selies for the function .
The interplay between the original equations and the equations deduced by iation is again exemplified in 's consideration of integral invariants .
In the motion of an incompressible fluid the ralc which expresses the volume of any pottion of the fluid is unaltered by the motion , if always taken over the same particles of the fluid .
He obtains other integrals the same prop erty , and considers their relations in many aspects .
That a quantity should contain in its sion a term 01 the form is rendered by him as a statement that the quantity , though not for all time of limited itude , does yet return infinitely often to within arbitrary nearness of its original value .
This becomes a text for the consideration of dynanlical systems with such a property\mdash ; stable la .
In particular , a proof is given , as oetrating the theory of integral invariants , that for incompressible fluid in a closed vessel , if we consider the particles occupying at any stant a particular small volnme , these particles returll infinitely often to volume .
This theol.y of invariants real)pears in 's recelit ( Journ. de Physique , January , written ) of Planck ' Theory of Quanta .
But it is impossible not to consider the relation of Poincare periodic solutions with the expansions used by practical astronomers , and a parc of his deals with this matter .
Series had gradually been introduced containing only and cosines\mdash ; that is terms A , but no terms as , or such as , in which the time occurs outside the iodic f evident intention being to obtain series which might serve to express the circunnstances for all time .
Apparently possibility of series may have been recognised by d'Alembert Jules Henri Poincare .
( cf. E. W. Brown , 'Lunar Theory , ' p. 239 ) .
Poincare ' attributes the series to Newcomb Smithsonian Contributions ecember , 1874 ) , who used them for the motion of the planets , and after to Lindstedt .
For the case of the Moon Delaunay 's series are to be rel'erred to ( 1860 ) .
Poincarc ' investigates Lindstedt 's series again , and extends their scope ; but he proves that they are not as rule convergent .
His lnethod of proof is extremely simple , if wholly convincing for all possible cases .
It may be said to be part of his theory of periodic solutions .
It is related also to his general theorem as to the existence of uniform rals of the astrononlical equations .
He proves , however , that the Lindstedt serics are asymptotic , in the sense in which Stirling.s serics for the gamma function are asympbotic ; they give a rule for writing down a finite number of teruts approximating very closely to the fumctious sought , but the nation cannot be made arbitrarily close .
To the consideration of these sel.ies and the related investigations of Delaunay , of Bohlin , and of yldo'n , a part of the second volume of the 'Me'thodes Nouvelles ' is devoted .
the Sorbonne lectures a different plan of exposition is followed .
's tnethod of successive approximation is first to obtain ) ansions whelein the time occurs explicitly outside the periodic functions .
A proof is then given that the terms in which the time enters in this way may be absorbed ; if they be omitted they can be re-found from ) terms which renlftin , by a change of bsequent expansion ( ' de este , ' vol. 1 , 1905 , pp. , 198 , .
, is a furCher of ) ance which , like the } ) .
of the di ence of Lindstedt 's selies , in Poitlcar 's prize essay .
The problem of three bodies has the classical integrals , which belong to any dynamical system , known as those of and nlomentum .
It was proved by Bruns that , fro1n and indel ) endent of these , the problenl allows no other algebraic integral .
To this Poincare adds the theorem that the problem possesses no single-valued integral .
The statement is for certain cted values of the ) arameters ; upon these restrictions we need not now enter .
This account leaves tside ) matters dealing the theory of to which Poincare devotes attelllion , and it does not represent his whole tion to Astronomy .
very after the publication of the p , aper with periodic bits ( Bnll .
Astr .
, vol. 1 , 1884 ) Poincaro was ) investigations issuing in 1880 in a to.reat paper Acta ) with the of rotaking masi ) of fluid and their .
As his investigations in regard to periodic orbits ments to G. W. Hill , so this paper begins by quoting the results announced ) Thomson and Tait in the ' Philosophy , ' Without into precise mathematics it would seem to be impossible to here any competent account of Poincar 's work ; the questions of stability involved are still matrer of controversy .
Poincare considers a series of ) relative equilibrium , bestowing especial care upon the critical values of the parameters .
He is thus led to consider the possibility of Jacobi 's ellipsoid of tion of mastery for which he had the profoundest respect .
Besides this work there remains , however , also Poincare 's work in regard to tides .
It may be sufficient , perhaps , to refer to Sir Darwin 's ief indication of his concurrence , this matter , with what is undoubtedly a very comtlon feeling in oard to much of Poincare 's applied mathematics , nanlely , that the great generality of his methods is apt to militate ainst any quite immediate application .
Undoubtedly he has no scruple in bringing the most advanced and the most modern theot'ies of pure mathematics into service .
and where such theor is not already in existence he invents it .
When we turn from Poincare 's astronomical work to his work in Physics , we enter upon ground which has already been much trodden .
It may be sufficient to call attention to the number of volumes of Sorbonne lectures , edited by his pupils , dealing freshly with the whole field of recent discoverv and discussion in electricity , optics , thermodynamics , beside those with matters already referred to .
But in addition to all this mathematical and physical work , Poincare was also a prolific writer on ( eneral questions of ) hilosophic interest .
How far his contribntion to these matters was , and how far he stated in a brilliant way the critical conclusions which are common to many to-day , it must be for others to decide .
At least , while taking up humblest and simplest attitude in face of immensity of the universe , he preached in no uncertain way the dignity of the pursuit of truth .
" " Thought is the htning flash between two nities of blackness .
But it is the which matters\ldquo ; His writings on such matters are accessible to all and of general interest .
It is mnecessary to expound them here .
H. F. B. XVII SIR OBERT STAWELL BALL , 1840-1913 , .
ROBERT STAWELL BALL was born at Dublin on July 1 , 1840 .
His father , Dr. Robert Ball , was born Cove , co .
Cork , in 1802 , from whence he migrated to Dublin in 1827 upon his appointment to a post at the Castle .
Dr. Ball took a keen interest in Natural History , and the Dublin Gardens are largely due to his and unstinted labours .
He died at a connparatively early in 1857 , leaving a witiow and seven children , three sons and four daughters .
Robert Stawell was the eldest of the sons , who all became uished citizens of Dublin , Dr. Valentine Ball becoming the Director of the Science and Museum , and Sir Charles Ball the well known After some years at a preparatory school in DubliIl , Robert was sent in to Dr. Brindley 's school at Tarvin , near Chester , where he received his early training in Mathematics from the Rev. Tbeophilus .
Row , afterwards lnaster of Tonbridge School .
He remained at Tarvin till his father 's death .
In October , 1857 , he was entered as a student at Trinil ) College , Dublin .
He soon showed his aptitude for Mathematics won nmmerous prizeH .
In obtained a scholarship and the Lloyd xhibition .
1861 he was Gold Medallist in Mathematics , first Gold tedallist in Experimental and Naturffi Sciences , and University Student .
He competed three times for a Fellowship at Trinity College , but was not successful , the successful candidates on two of the occasions being W. S. Bnrnside and H. S. Tarleton .
Ball 's interest in Astronomy was awakened by Mitchell 's 'Orbs of Heaven , ' a book he read at school at a time when he should have been asleep .
At college he studied Brinkley 's ' Astronomy , ' ' rincipia , ' and the canique Celeste .
' In 1865 , at the instance of Dr. JohnstoIle Stony , was invited to become tutor to the sons of Lord Rosse rsonstown .
He accepted the post on the condition that he should access to the Observatory the privilege of using the great telescope .
He worked with the 6-foot reflector from , 1866 , to , making neter observations of the positions of small .
It is pointed out by ) that he was the first observer with the instrument to correct observed position for the error due to the instrument not , equatorially mounted , but supported at its lower end by a universal joint , the fixed axis of which was horizontal , in the east and west directiolL TlIis procedure , which materially improved the observations , was a natural outcome of Ball 's geometrical instincts .
About this time the application of the spectroscope to the problems of Astronomy was making great headway .
Sir Robert Ball took no active part in this , he was keenly interested in it , an interest quickened by a visit to Sir William servatory at Dnlwich .
VOL. XCI.\mdash ; A. of Fellous X I I In the College of Science was foundsd in Dublin , and Ball left Castle to become the firsl Professor of Applied Mathematics and .
He was well fitted for this post by his mathematical knowledge and ability skill , but especially by his for lucid exposition .
He was one of the first in Great Britain to introduce the system of C.G.S. units in his class teaching .
addition to his class lectnres he gave some evenJng lectures of a more elementary character , and here showed and developed his genius as a popular lecturer .
In 1871 he published a work on ' rimental Mechanics , ' the outcome of his evening lectures .
This was the first of the many popular books he wrote .
In 1870 Ball read a paper before the loyal Irish Academy on " " Small Oscillations of a Body moving about a Fixed Point under no Forces This was the first of many memoirs on the theory of screws .
The whole sPries was published in a volume by the University Press in 1900 .
A critical account of this important contribution to Mathematics is given at the end of this notice .
In 1874 Ball was appointed successor to Brunnow as Royal Astronomer of Ireland and Professor of Astronomy in the University of Dublin .
The tory , sitnated at Dunsink , a few miles from blin , possessed an excellenl -inch telescope , the of Sir James South .
This been elnployed by ultnow in the ation of stellar parallax , a ) ranch of Brinckley had attempted half a century previously .
Jecided to purse this important but difficult research , and collmen with tar Cl Cygni , for which obtained alesult in good reement with the deterlnination by Bessel .
1876 to 1881 prosecuted an active search for stars of large parallax .
In all , 368 stars were exami1led and the results in the Dunsink Observations .
In the preface to this memoir he states : " " It is , of course , well known that up to the present 110 of a beeIl detected which exceeds one second of arc ) .
In the majority of case } , the parallax is much less , even if it is preciable .
But when we reflect that not one sbar out of every 10,000 has yet been regularly examined for parallax , it is obvious that it would be rash to conclude that there are no to us than any of those of which aheady know the distance The results he obtained were fative , but it was nevertheless of to demonstrate that none of the stars presumably near the solar system so close as to have a parallax as great as one second .
, refined observatious of the eliometer and the raphic refractor were shown to be ecessary for the rement of the small displacc1ne1lts of even the nearest stars .
In , 1892 , Sir Robert Ball succeeded Prof. Adams in the Lowndean Chair of Astronomy and GeometIy and the Directorship of the University Observatory at Calnbridge .
directorate the valuable catalogue of stars , commenced in Adams ' time , was completed and published by Mr. Graham .
A telescope , mounted on a llovel to a design by erected for the purpose of on researches in stellar Robert Stawell xix parallax .
This instrument was put to very efficient use by Mr. Hinks in observations of the planet Eros in 1900 and 1901 for the determination of the solar parallax , and by Mr. Hinks and Prof. H. N. lssell ( then an advanced stude1lt of the Universit.y ) for observations of stellar parallax .
Sir liobert Ball maintained an interest in these parallax researches , but left their to Mr. Hinks and Mr. Russell .
As a lecturer on Mathematical Astronomy , Sir Robert Ball gave pupils a lucid exposition of the classical writers on celestial mechanics .
He wrote a text-book on 'Spherical Astronomy , ' intended for the use of Uuiversity students .
This book contains a chapter on the theory of astronomical instruments , which is of special interest , as showing the geometrical bent of mathematical interests .
Sir Robert Ball rendered reat service by his popular books and lectures .
These awakened an interest in astronomy among a very wide circle of eaders and hearers .
A lecture which he delivered at the Midland Institute at in 1881 attracted particular attention and established his fame as a popular expositor of science .
This lecture , entitled , " " A Glimpse through the Corridol .
S of Time in popular uage an outline of Sir George Darwin 's theory of the tidal evolution of ths Moon .
As a lecturer he possessed great lucidity and brought abstruse subjects within the comprehension of his audiences .
His gift of humour was always at hand to enliven any dull parts of a lecture and retain the attention of his hearers .
He lectured in most of the large towns in Great Britain and in many cities of the United States and in Canada .
Probably more than a million people have heard him lecture .
Among his many popular books , ' The ttory of Heavens , ' ) lished in 1886 ; The Story of the Sun , ' ] nblished in 1893 ; and reat Astrollomers , ' published in 1896 , may be specially mentiorled .
They are written in a very pleasant style , and the lives of Astronomers , including those of Hamilton and dams , his predecessors at Dunsink and Cambridge , are told in a delightful manner .
In 1884 , Ball became Scientific Adviser to the Commission of Irish Lights , in succession to Tyndall , and always took the greatest in the annual cruise of the Commissionel .
S round Ireland to inspect the hthouses .
In 1886 the honour of knighthood was conferred upon him .
He was elected a Fellow of the Royal Society in 1873 and served on the Council ill lS97-8 .
He was President of the Royal Astronomical ociety , 1897-9 : In 1868 he married rances Elizabeth , .
of the late ] .
W. Steelc , Director of the Science and Art Museum , Dublin .
He leaves four sons and two hters .
Sir Robert Ball died at Cambridge on November 25 , 1913 , after an illness which lingered for over two years .
He was a most warm-hearted and kindly man and had a large circle .
friends attracted by his genial manner , ready sympathy , and delightful humour .
xx Obituary Notices of Fellows deceased .
Ball 's 'Theory of Screws ' gives a very complete geometrical treatment of the of small movements in rigid dynamics , and in that respect is unique among English books .
The small first edition appeared in 1876 .
Ten years later was published the German ' Theoretische Mechanik Starrer Systems ' of Gravelius , founded mainly upon Ball 's memoirs .
The " " twelfth and concluding\ldquo ; memoir in the Proceedings of the Royal Irish Academy was dated 1898 , and the large and comprehensive work on the ' Theory of Screws ' was published in 1900 .
The keynote to the whole method consists in the use of the " " screw consisting of a line in space together with an associated length .
This geometric entity has a double use .
It gives the axis and the pitch of either " " wrench representing any system of forces , or of a " " twist representing the most general small displacement of a rigid body .
The derivative relationships of which the method is bui16 may be brielly described .
Two screws are defined as " " reciprocal\ldquo ; when a wrench on one screw does no work for a twist on the other , and so also conversely .
" " screw of inertia\ldquo ; is such that an impulsive wrench on it produces instantaneous twist on the same screw .
" " Conjugate screws of \ldquo ; are such that a twist on either is produced by an impulsive wrench on a screw to the other .
Similarly for the forces of restitution : " " screw of potenlial\ldquo ; is such that a twist on it evokes a wre1lch on the same screw , and " " conjugate screws of potential\ldquo ; are such that a twist on either evokes a wrench on a screw reciprocal to the other .
" " harmonic screw\ldquo ; is such that a twist on it evokes a wrench which produces a twist on the screw itself .
A harmonic twist on such a screw is thus one of the normal modes of oscillation of the body about its position of equilibrium .
These relationships are intimately connected with the " " kinetic screw complex consisting of the screws for twists on which the kinetic energy is zero , and the " " potential screw complex\ldquo ; for which the potential energy is constant .
With this apparatus a yation is made of the behaviour of a rigid body with any number of rees of freedom from one to six .
In the case of two degrees of freedom the notable " " cylindroid\ldquo ; presents itself , as the cubic surface locus of the screw-axes of all possible twists .
But the cylindroid is used fundamentally through the whole work , and a perspective view of the surface figures naturally as a frontispiece to the volume .
Though not the actual discoverer of the surface ( Hamilton and Plucker had found its chief property earlier ) , Ball certainly counts as its chief patron .
He took always a lively interest in any development of its properties , and a beautifully made model placed in the collection of Cambridge University serves as a memento of its former owner .
If the geometry of the linear complex had developed earlier , its immediate application to infinitesimal rigid dynamics should have followed as a consequence ; but the subject was in its infancy , and Ball had to investigate much of the geometry for himself as he progressed .
This he was well able to do , and he seems to have made independent of some of Sir Robert Stawell the theorems of line-geometry .
The conciseneffi and elegance , in particular , of the treatment of the case of two degrees of freedom by a circular diagram lepresents evidently his native geometric faculty .
Perhaps some of the later developments seem less natural .
Any general system of bodies is dealt with under the description of a " " screw-chain " " ; but the arbitrary assignment of a definite sequence to the bodies the chain seems artificial as a mode of treatment .
In the case of the so-called " " permanent screws\ldquo ; the terminology at least seems inapt , for the " " permanence\ldquo ; is only transient .
For a most admirable and appreciative survey of the scope of Ball 's work 011 screws , reference may be made to a review by Henrici ( ' Nature , ' June 5 , 1890 , pp. 127-132 ) of the German treatise above mentioned .
An excellent account was given by Ball himself in his presidential to the Mathematical Section of the British Association in 1887 .
He there tlses some geometrical ) stractions , quaintly personified , as speakers in a dission ; and , under this whimsical yarb , reveals the essenco of nethods very pertinently and clearly .
Through all Ball 's there shows a fine enthusiasm for his subject and a most of the of others .
the year 1879 the Irish Academy awarded him the Gold Medal , and his name thus occurs in a list which clndos also those of Casey , , Hamilton , Jellett , altd .
By his many and excellent contributions the geometry of kinematics and dynamics , Robert Stawell Ball assuredly takes an honourable place on the roll of Irish mathematicians .
F. W. 1 ) .
and G. T. B. xxii LORD STRATHCONA AND MOUNT ROYAL , 1820-1914 .
SIR ALExANDEli , Baron Strathcona and Mount , died on January 21 last in the 94th year of his age .
He was a man of very personality , who wrought out for himself a striking and remarkable career , achieving success in many different paths , but having ever in view the welfare and progress of the Empire as a whole .
He was born at Forres , in the Scotch Highlands , on August 6 , 1820 , and was the second son of AIexander Smith , a merchant of Archiestown , and Barbara Stewarb , whose brother , John Stewart , was a well known fur trader in the North-West Company , having its headquarters in Montreal .
After receiving a good elementary education at the school at Forres , it happened that on one occasion he visited Manchester in company with a friend of the rising young London novelist , Charles Dickens , and made the acquaintance of a wealthy and highly esteemed family of merchants named Grant , who were cousins of the Smith family .
These two warm-hearted men have been introduced to the world under the name of the Brothers by Dickens .
He was about to enter the office of this firm when his uncle , John Stewart , returned to Scotland , and through his influence Donald Smith was appointed to a junior clerkship in the renowr ed Hudson 's Bay Company , which at that time controlled the greatel of what has Hincc become the Dominion of Canada .
He was 18 years of at this time .
The passage out to Canada occupied rather more han six weeks , while his relurn passage to England on the " " Mauletania\ldquo ; ortly beforc his death occupied approximately six days .
Upon arrival he was sent to Labrador , one of the most remote and inaccessible districts occupied by the Company , where he remained for 13 years at one or other of the Company 's posts , in trading with the Indians and such skimos as inhabited or visited that most inhospitable coast .
He then promoted to the osition of Chief Tradel in the Company 's servlce , and after 10 years more spent on the shores of Hudson Bay he became a Chief Factor of the Company , and in 1868 became Chief Executive Officer of the Company , with his headquarters in Montreal , where he took up his residence , being now 48 years of age .
The fact that the great prairies of Central and Western Canada were suitable for settlement was becoming enerally recognised by the people of Canada at time , and negotiations were opened up in this year for the surrender of the lands of the Hudson Bay Company to the Government of the minion of Canada .
When , however , the Deed of Surrender was and the agents of the meant proceeded to Fort arry ( now Winnipeg ) , Lord Mouht xxiii the norant half-breeds , who with the Indians were the only residents of the eastern prairies at that time , thinking that the Government intended to deprive them of their lands , rose in revolt under a half-breed named Louis Riel , purposing either to establish an independent government or to take steps to have the countrv amlexed , to the United .
Donald Smith was sent to the scene of trouble with a view to explairl the situation to the halfbreeds and allay their fears .
Upon his arrival at ForC Garry , he was seized by Biel and held as a prisoner for about two months .
He was , lowever , so far successful in carrying out his commission that , while the Government found it advisable to send a expedition under ( afterwards ir Garnet ) Wolseley to the scene of the disturbance .
upon the arrival of the troops Riel fled to the United States and the revolt came to an end without a blow having been struck .
Upon the collapse of the rebellion , Donald Smith was to represent the constituency of Selkirk , one of the electoral divisions of new territory , in the Dominion House of Parliament .
About this time , in the early seventies , the necessity of building a transconti1lental railway to open up this ooreat western country and especially to open up communication between British mbia and the rest of the Dominion became evident .
Tn fact , one of the conditions under which this came into the Canadian Confederation was a railway be built within a period of 10 years after the agreenlenl ] been ratified .
At the inceptio1l of this great enterprise Slnith s advocated the policy that the road should be built by the of Canada and not by a private company .
But when both parties who came successively into power failed to make any substantial with the wor he recognised that unless some company with the requisite initiative and capital took the work in hand , the project would not be realised within any reasonable time .
In fact , the failure of the Government to carry through this reat undertaking which they had commenced left nitoba and the other prairie provinces without any means of communication by with the outside world , and order to immediately supply this Donald Smith associated with himself a few other far-seeing men and secured the control of the bankrupt and abandoned St. Paul and Pacific ailway which had been built from St. Paul in the State of Minnesota to a point far from the Canadian boundary .
Ihis been done , the road , under the nanlc of the St. Paul , Minneapolis and Manitoba Bailway , was completed to Winnipeg , thus giving the needed outlet .
great develop1nent of road subsequently very large financial retur1ls to the gentlemen who had essed the foresight to construct it .
In 1880 a syndicate was formed to take over the Canadian Pacific from the Government , who had barely commenced the road , and to complete it .
Although Mr. Smith 's name did not appear as one of the contracting parties , it was largely his energy , determination , and linancial assisCance times of great difficulty that carried the enterp1ise to a successful conclusion .
xxiv Obituary Notices of Fellows deceased .
( We had he writes , " " of course , a good deal of anxiety while the work was going on , but we were sustained by the knowledge that it was approved rand ross fmpire Hding omeans oementing together tarious parts obeing taken.oping tesources oountry , Canada.that amportant sasrd f\ldquo ; the last spike on November 7 , 1885 .
the peerage as Baron Strathcona and Mount Upon the outbreak of the Boer War Lord Strathcona raised in Canada a regiment of mounted infantry , numbering about 600 and recrnited largely from the North-West Mounted Police , known as the Strathcona Horse , which was equipped and transported to Africa at his own expense .
They were attached to Lord Dundonald 's brigade .
Lord Strathcona 's enerosity knew no bounds .
His benefactions were widespread not only in Canada but also in Great Britain .
Montreal , which was Lord Strathcona 's place of residence during most of his later years in anada and one constituency of which ( Montreal West ) he represented during two Parliaments in the Dominion House , was the especial object of his munificence .
In conjunction with Lord Mount Stephen he erected and endowed the oyal Victoria Hospital iu that city in comnlemoration of Quee. .
nVictox.ia 's Jubilee , which institution has by his will received a additional endowment .
His .benefactions to McGill University , of which he was Chancellor , were numerous .
Among these may be mentioned the Royal Victoria College for Women , the new building which has just been erected for the Faculty of Medicine , and the endowment of the Strathcona essorship of Zoology .
Lord Strathcona received the degree of .D .
from the University of Camblidge iu 1887 , from Yale University in 1892 , from the University of Toronto in 1903 , from the University of Durham in 1910 , and from St. Andrew 's in 1911 .
In the year 1900 he was appointed Lord Rector of the IJniversity of Aberdeen .
He was elected a Fellow of the Boyal Society in 1904 , and was Honorar ) Vice-President of the Royal Society of Canada .
He was also well known as a lover of the Arts , his picture containing well known by many of the great masters .
Together with Lord Mount Stephen he Ildowed a Canadian Scholarship in the Boyal College of Music , London , and he subsequently endowed a second Scholarship on his own account .
From the year 1896 until his decease , Lord Strathcona , as High Comsioner for Canada , represented the inion in London , a position which he filled with .
dignity and honour .
His age , his talents , his princely Earl of Crawford .
benefactions , his wide sympathies , his wise and kindly philanthropies , his charming personality , and the admirable manner in which he represented Canada in Great Britain , endeared Lord Strathcona to the Canadian people in a very especial manner , and no one in the Dominion was ever so beloved by all .
He a long life to the enlargement of the Empire and the knitting together of its strength .
F. D. A. EABL OF CRAWFORD , K.T. , 1847-1913 .
LUDOVIC LINDSAY , Earl of Crawford , was born in 1847 .
Amollg his many scientific and bibliographical interests , Astronomy took the foremost place during his most active years .
He established and maintained at Dunecht , near Aberdeen , an observatory and an astronomical librilry that call have had few parallels for completeness .
In this , which in Lord Lindsay , as he then was , worked in fortunate association and rival enthusiasm with David Gill , the son of an Aberdeen merchant , who had then already made his mark upon the science .
The chief instruments were an -inch transit circle , by Simms , a 15-inch equatorial , by Grubb ( at that date a ( aperture ) , many spectroscopes , and other physical apparatus .
The library contained many treasures , and bibliographical notes in many of the books testify to Lord Lindsay 's intimacy with them .
One feature of the Dunecht observatory was the issue of circulars in which early informario of astronomical events , the places of comets , and so forth , was conveyed to a number of other observers .
In 1874 Lord Lindsay , with Gill , organised an expedition to Mauritius to observe the transit of Venus .
The results of the transit were but incidentally a large amount of valuable longitude work was performed .
In 1876 , Gill was succeeded in the charge of the observatory by Dr. Ralph Copeland .
In 1880 , Lord Lindsay succeeded to the earldom , and shortly after decided to part with his estate at Dunecht and remove his observatory to Balcarres in Fife .
Circumstances arose which divel.ted his intention .
On the tion of C. Piazzi Smyth , the Royal Observatory at Edinburgh , then miserably housed on the Calton Hill , was in of extinction .
Lord Crawford saved the situation by offering the whole of his magnificent collection , instruments , printed books , and manuscripts , to the nation , provided that a proper establishment was maintained .
The gift was accepted , and the new observatory on the Blackford Hill was opened in 1896 .
VOL. XCI .
xxvi Obituary otices of Fellows This terminated Lord Crawford 's connection with Astronomy , but he was always a lover of books , and continued to make other bibliographical ] collections until his death .
He was also well known as a yachtsman , and , in 1906 , made an extended voyage in the South Atlantic and Indian Oceans 2 : specimens of natural history .
Lord Crawford was president of the Royal Astronomical Society in 1878 and 1879 .
In the former year he was elected a Fellow of our Society .
As Baron Wigan he took an active part in the management of the Public Library at Wigan and enriched it by many valuable gifts .
He died on January 31 , 1913 , and is succeeded by his son . .
A. SIR DAVID GILL , K.C.B. , 1843-1914 .
DAVID GILL , son of David Gill , J.P. , of Blairythan , Aberdeenshire , was born at Aberdeen on June 12 , 1843 .
He attended the Bellevue Academy in that city till he reached the age of 14 , when he was sent to the Dollar Academy , where the teaching of Dr. Lindsay imparted to him a love of Mathematics , Physics , and Chemistry .
He proceeded to Marischal College and University , Aberdeen , where his love of science was developed under the inspiring influence of Clerk Maxwell .
In the 'History of the Cape Observatory , ' published only a few months before his death , Gill tells of the pleasure he derived from Maxwell 's teaching .
After lectures , only perhaps partially understood , Maxwell would stay for hours in his lecture room with a few of the best students and disouss points which occurred to him or to them , or show them experiments he was making at the time .
These conversations with Maxwell profoundly influenced Gill , and implanted in him a deep desire for a life of scientific investigation .
This was not , however , realised at first .
Gill 's father , who had a prosperous old-established business in clocks , was anxious that his son should succeed him .
Gill reluctantly consented and entered his father 's business , of which after a few years he took complete .
He consoled himself by devoting all his spare time to Physics and Chemistry in a small laboratory he had established in his father 's house .
With characteristic hness , however , he mastered all the details of his business , and to the end of his life kept on his study mantelpiece a beautiful clock made with his own hands .
His special interest in Astronomy began in 1863 .
It occurred to him that a time service in Aberdeen such as Piazzi Smyth had established in Edinburgh would be of great value to the city .
He discussed the matter with David Sir David Gill .
xxvii Thomson , Professor of Natural Philosophy in 's College , Aberdeen .
Thomson gave him an introduction to Piazzi Smyth , whom he visited at Edinburgh .
Here he was shown not only the arrangements for the timegun and ball , but all the instruments of the Observatory on the Calton Hill .
From that day he took a new interest in Astronomy , and , on his return to Aberdeen , proceeded with Prof. Thomson to re-establish the disused " " Observatory\ldquo ; of 's College .
A small portable transit-instrument was unearthed , mounted on its piers and adjusted .
The Observatory possessed a good sidereal clock .
A mean solar clock was added , with arrangements for altering its rate , so that it could be kept within a fraction of a second of Greenwich time .
Contact springs were fitted to it so that electric currents were sent each second , and in this way the turret clock of the college and other clocks in the town were controlled .
When the time service had been got into working order , a Dallmeyer telescope of inches aperture and 4 feet focus was obtained for the College , and Gill made some micrometric observations of double stars .
Although the ob.iect glass was good , the mounting was too weak for the observations to be quite satisfactory .
Gill therefore purchased for himself , from the Rev. Henry Cooper-Key , a speculum of 12 inches aperture and 10 feet focus .
He designed an equatorial mounting himself , and had the parts of the instruments made to his own working drawings by a firm of shipbuilders in Aberdeen .
The driving circle , its tangent screw , and slow motion , as well as the declination circle , were made by Messrs. Cooke , of York .
The driving clock , which he made with his own hands , was on the same general ) as Airy 's raph at Greenwich .
This was his first experiment in the and construction of astronomical instruments , and it is interesting to note that in the course of life he never came across a driving clock which worked more satisfactorily .
The strument was employed in the observations of double stars and nebulae .
and in photographs of the Moon .
One of the latter , which he presented to Sir W. Huggins , has recently come into the possession of the Astronomical Society and is of great excellence .
he married Isobel , second daughter of Mr. John Black , Linhead , Aberdeenshire .
They settled in the town of Aberdeen , near the Observatory .
Shortly after their marriage Gill was faced with the alternative of continuing in a prosperous business and working at Astronomy as an amateur after business hours , or of following his own inclinations , and giving this up for a much smaller income and the opportunity of devoting his time exclusively to science .
The decision he took with Mrs. Gill 's full approval and support , and which they never regretted , was to make the pecuniary sacrifice so that Gill 's deep interest in Astronomy might be fully gratified .
The occasion of this change in Gill 's position arose through a friendship which had grown up between him and Lord Lindsay , who was interested in Gill 's aphs of the Moon and afterwards attracted by his scientific enthusiasm .
Lord Lindsay was an enthusiastic amateur astronomer and XXVIII Obituary Notices of Fellows proposed to erect a private observatory at Dunecht .
In 1872 , his father , the Earl of Crawford and Balcarres , wrote to Gill offering him the charge of Ghis observatory .
Gill gratefully accepted the offer , and , when his business affairs were wound up , moved to Dunecht .
Here he was soon engaged on the congenial task of the design and erection of the fine private observatory which Lord Lindsay projected .
The years ] were busily employed in the equipment of the observatory .
This comprised a 15-inch refractor by Grubb , an 8-inch reversible transit circle by Troughton and Simms , a 12-inch which Gill had at Aberdeen , a 4-inch heliometer by epsold , and a number of smaller instruments .
Preparations were also made for an expedition to MRnritius to observe the transit of Venus in 1874 .
In connection with this expedition and the building of the observatory at Dunecht , Gill paid visits to most of the Europear ] Observatories .
Thus acquaintanceships were made which ripened in several cases to a lifelong friendship .
In view of the possibility the British station at Mauritius becoming a central one to which the of stations would be referred , Lord Lindsay decided that the longitude of Mauritius should be determined with as much accuracy as possible .
He and Gill proposed to determine the longitude Greenwich-Aden telegraphically , and Aden-Mauritius the transportation of chronometers .
The section Greenwich-Aden was com- pleted by the chain Greenwich-Berlin-Malta-Alexandria-Suez-Aden .
The time determinations at the intermediate stations had to be made between the arrival and departure of steamers .
A theodolite mounted on a tripod was employed by Gill , and subsequent determinations have shown the great accuracy of the results he obtained with this small instrument .
The carriage of the chronometers was a matter of some difficulty , especially their embarkation and landing at ports where only coloured labour was available .
No less than fifty were hired from the leading makers , very carefully packed and mounted , compared before starting , and then carried with incessant watchfulness from Greenwich-Aden , Aden-Mauritius , and back The main interest of the expedition to Mauritius centres in the heliometer observations of the minor planet Juno , which were made for the determination of the solar parallax .
As Lord Lindsay 's arrival with the heliometer was delayed by unfavourable winds , the observations could not be begun till a week after opposition .
Nevertheless , after a series of observations extending over 12 evenings and 11 , the value seconds was obtained for the solar parallax with a probable error sec. The discussion of these observations gave Gill a profound conviction of the possibilities of the heliometer for measurements of great refinement , and influenced his future work very materially .
Thus , the observations of the transit of Venus failed in their direct object , this expedition became the starting point of a method by which the Sun 's distance has since been determined with the highest accuracy .
On the return journey from this expedition Gill obtained his first experiSir Gill .
xxix ence in geodetic work .
While he was at Mauritius , he was invited by General Stone , Chief of the Military Staff of the Khedive , to return through Egypt and measure the base line for the survey which was projected .
With Lord Lindsay 's ready assent , Gill undertook this task , and , with the assistance of the American astronomer , Prof. Watson , who happened to be at Cairo , laid down a line near the Sphinx , using a base-measuring apparatus belonging to the yptian Government constructed by Brunner , of Paris .
The next great piece of work which engaged Gill 's attention was the determination of the solar parallax from the exceptionally favourable opposition of Mars in 1877 .
He was aware of the advantage which a minor planet possessed for this purpose , owing to its no perceptible disc , but the geometrical conditions of the opposition of 1877 were so favourable that he considered that the opportunity of utilising it was not to be missed .
had left Dunecht in 1876 , he had obtained from Lord Lindsay the loan of his heliometer , conditionally upon his obtaining the means to undertake this expedition .
The sum of f500 was provided , half by the Royal Astronomical Society and half by the Government Grant Fund of the Royal Society .
The Island of Ascension was chosen as the station observation , as its latitude ( south of the equator ) made the base line obtained from evening and morning observations of Mars a large one , and on account of the south declination of Mars .
Lady Gill accompanied her husband and wrote a delightful account of the expedition , *which gives a picture of its incidents and anxieties .
They were on the island for seven months .
At first the Observatory was set up at Garrison .
Lady Gill writes:\mdash ; Fearful of losing one hour of starlight we watched alternately for moments of break in the cloud , sometimes with partial success , but more frequently with no result but utter disappointment , and the mental and physical strain , increasing every night , grew almost beyond our strength when one day David spoke and took away my breath .
He said , " " Let us prove how far this cloud extsnds and find out whether there is any accessible part of the island not covered by it The clouds only came up at night , and Gill could not leave the Observatory at a time so near opposition .
He yielded to his wife 's wish that she should make the necessary exploration .
Lady Gill found a spot in the south-west corner of the island much freer from cloud .
But this was difficult of access .
The surf made from the sea only possible now and then , and the transport of instruments which could not be repaired , if injured , ovel rocky country without roads was not to be lightly undertaken .
On the one hand my husband felt , If I stay here and fail , I shall have failed also in my duty , not having done my utmost .
On the other hand , every night is now of portance , and a week is lost tainly , if I pull down the Observatory , while the slightest accident to an instrument here , with no one to repair it , will be fatal to the \mdash ; - ' Six Months in Ascension : An Unscientific Account of a Scientific Expedition , by Mrs. Gill .
John Murray , London , 1878 .
xxx Obituary Notices of Fellows expedition .
Yes !
both " " \ldquo ; were unpleasant , but the first was intolerable , and after a day of anxious thought David made uP his mind that an attempt to reach South Poimt must be made .
The Observatory was moved without accident to the new site , which they called Mars Bay , and only five days elapsed before successful mornlng and evening observations were made .
This laborious and difficult enterprise was crowned with success .
The solar parallax was determined as seconds , with a probable error of second , a considerable advance on previous determluatlons ; but Crill 's experience convinced him that for a definitive determination a mlnor planet must be , as it was impossible to set a star on the limb of the planet without danger of systematic personal error .
A second imp.ortant result of the investigation was the clear evidence afforded by comparison of the positions of the reference stars obtained by transit circle observations with their relative positions given by the heliometric measurements that there was among meridian observers a personal equation depending on the magnitude of the star , whose general vendency was to make faint stars late relatively to bright ones .
This " " magnitude equation suspected by Bessel and investigated to a certain extent by Argelander , is of special importance wherever meridian observations are used in conjunction with others , whether heliometric or photographic .
Its serious consideration dates from this time , modifications have since been introduced into methods of observing for the purpose of its elimination .
In 1879 Gill was appointed H.M. Astronomer at the Cape .
He possessed unrivalled skill as an observer , was never satisfied with anything less than the most accurate work , and spared no pains to avoid all errors of systematic character .
His engineering and mechanical skill added greatly to his qualifications for the directorship of an observatory which needed to be re-equipped .
But the qualities which marked him out for success in this new post were his abounding and enthusiasm and his resolute perseverance .
Immediately after his appointment he visited the observatories at Paris , Leiden , Groningen , Hamburg , Copenhagen , Helsingfors , Poulkova , and Strassburg , learning the aims and methods of different astronomers and coming into touch with them .
He was particularly impressed by Winnecke at Strassburg , whom he regarded as the greatest astronomical teacher of the day , and by the earnest band of students whom he had gathered around him .
The Cape Observatory had been founded in 1820 by the Lords Commissioners of the Admiralty on the recommendation of the Board of Longitude .
Fallows , the first of His 's Astronomers , established the Observatory on a bare , rocky hill , within sight of Table Bay , and commenced meridian observations of the positions of stars and planets .
He died in 1831 , and was succeeded by Henderson , who in one year made a large number of valuable observations of stars , and whose name is associated with his discovery of the distance of Centauri .
Henderson was succeeded Sir David xXXi by Maclear , whose directorate lasted from 1833 to i870 ; Maclear added magnetic , meteorological , and tidal observations to the work of the Observatory and commenced the geodetic survey of South Africa .
Stone devoted his attention ( 1870-1879 ) mainly to a great catalogue of 12,441 stars , in which he -observed all the stars observed by Lacaille in 1763 .
The national character of the Observatory made the continuance and improvement of meridian observations an essential part of the work of the Cape Observatory .
The traditions left by Maclear and Henderson suggested that geodetic investigations and determinations of stellar parallax ought to be carried out .
Researches in both of these directions were in harmony with Gill 's tastes and previous experience .
During his stay at the Cape the whole of this programme was carried out .
Old meridian observations were reduced and published , a new instrument embodying new and most useful features was installed ; the geodetic survey of South Africa was co-ordinated , and a work of fundamental importance towards the determination of the size and shape of the Earth initiated ; the distances of the Sun and a number of stars were determined with unexampled precision .
In addition , at least three very valuable projects were executed , which were not foreseen in 1879 , the 'Cape Photographic Durchmusterung , ' the ' International Photographic Chart of the Heavens , ' and the establishment of a large telescope for spectroscopic and other work .
To these projects Gill gave both guidance and driving force .
Soon after his appointment to the Cape , Gill bought from Lord Crawford the 4-inch heliometer with a view of commencing forthwith researches on stellar parallax .
In this work he secured the assistance of a young American astronomer , Mr. W. L. Elkin , a pupil of Winnecke 's , who had selected The Parallax of Centauri ' as the subject of his dissertation for his Doctor 's degree .
Elkin went to the Cape in January , 1881 , and stayed there 18 months as a guest of Dr. and Mrs. Gill .
Nine stars were chosen as suitable for parallax determinations on account of their ness or large proper motion .
Gill and Elkin decided that three of these stars , Centauri , Sirius , and Indi , should be observed by both of them , but using different comparison stars , in order to furnish a check on possible systematic errors .
The results obtained from this arduous and very skilful observing were very valuable .
The distances of Centauri and Sirius were determined to within a small percentage of the total amount , and Canopus , the brightest star in the sky except Sirius , was found to be at a great distance , not less than a hundred times that of .
The accuracy obtained with this small telescope is very remarkable , but its use wss found by experience to be hampered by the small field , which limited the choice of comparison stars .
Gill therefore urged upon the Admiralty the desirability of a larger instrument , and the purchase of a 7-inch heliometer was sanctioned .
This was constructed by Messrs. Repsold , of Hamburg , who embodied in their design a numbel of improvements and refinements suggested by Gill 's experience .
The instrument was completed xxxii Obituary Notices of Fellows deceased .
in 1887 and housed in an observatory specially built for it .
The programme which Gill set before himself was not so much to determine the parallax of individual stars as to find out what general relationships existed between the parallaxes of stars and their magnitudes and the amount of their proper motions .
Work was therefore first directed on the brightest stars the Southern Hemisphere .
The actual observations , involving much painstaking and trying work for some hours after sunset and before sunrise , were carried out by Gill himself .
One star was wholly observed by Mr. Finlay , Chief Assistant at the Observatory , and two stars were observed by both Gill and Finlay .
In 1897 , Mr. W. de Sitter , a pupil of Prof. Kapteyn 's , joined the staff of the Cape Observatory for a short time , and , among other observations with the heliometer , determined the parallaxes of four stars of large proper motion .
The results of the researches on stellar parallax were published in a volume of the ' Cape Annals ' in 1900 .
This contains all the determinations of parallax of stars in the Southern Hemisphere , and comprises the 12 stars yhter than the second magnitude , and 10 stars selected on account of their large proper motions .
The 10 quick-moving stars all proved to be comparatively near , but the brightest stars were found to be at very great distances , except Centauri , Sirius , and Piscis Australis , all of which have considerable proper motions .
accuracy of the work may be said to mark an era in the determination of stellar parallax .
It is exceeded , but not bevreatly , by the best photographic determinations , but these made with very much larger telescopes , and , of course , with much less trouble .
This precision is , in part , due to Gill 's great personal skill as an observer , and , in part , to the admirable design of the instrument .
He was not content to make many observations with small apparent error , but investigated , or eliminated , all causes introducing error of systematic character .
The success which had attended the observations of Juno in Mauritius and Mars in Ascension made Gill desirous of the 7-inch heliometer at the first available opportunity to determine solar parallax by observations of a minor planet when in opposition .
The solar parallax enters as a coefficient into various terms in the theories of , Moon and planets , and may therefore be deduced from the observed values of these terms .
It is also derivable from the value of the constant of aberration , the velocity of light being obtained from laboratory measurements .
But it was of great importance to determine this fundamental constant by direct geometrical methods , and to show that the value agreed , or wherein and why it differed from , the value foumd in less direct ways .
The transit of Venus of 1874 , on which great hopes had been placed and on which very large sums of money had been spent in expeditions to all parts of the world , had proved very disappointing .
The various phases of the transit did not admit of sufficiently precise observation , a fact forcibly illustrated by the different results , seconds and seconds , derived by Airy and Stone respeotively from the same observations .
Looking folward to the available opportunities , Gill found that a opposition of Iris would occur in 1888 and of yictoria David Gill .
xxxiii and Sappho in 1889 .
The co-operation of the Yale Observatory was secured for observations of Iris , and suitable comparison stars were chosen so that simultaneous observations should be made in the evening at Yale and in the morning at the Cape .
This plan was slightly modified by the addition of the Radcliffe Observatory , Oxford , and the Leipzig Observatory to the schemes , and a number of observations were made at Yale for compal'ison with these .
Between October 10 and December 13 , 1888 , over 1000 measures were made of the distance of the planet from various comparison stars at the four observatories , and were utilised for the determination of the solar parallax .
The resulting value from a discussion by Dr. Elkin was seconds , with a probable error of second .
For the observations of Victoria a very complete ramme was devised , involving the co-operation of many ories .
It was desired to obtain the relative positions of the comparison stars with such accuracy that the error in the resulting parallax arising from the uncertainties in the framework of reference points should be negligible .
Thus the errors would be confined to those of the heliometer measures of the distance of the planet from the sbars and to errors in the ephemeris .
Meridian observations of the stars were secured at no less than 20 observatories .
These were combined by Dr. Auwers so as to give the best positions of the stars .
The declinations were sufficiently good , but the right ascensions showed somewhat large discrepancies .
Accorda heliometric ulation of the stars was made by Gill , Elkin and Schur in 1890 .
By this means the weight of the position of the reference stars was largely increased , and the probable error of the final results reduced to second .
The actual observations of Victoria were made at the Cape by Gill and Auwers , at Yale by Elkin and Hall , at .
by Peter , at Gottingen by Schur , and at Bamberg by Hartwig .
A preliminary discussion of the observations showed that the errors of the ephemeris computed by the aid of arithms from Leverrier 's tables of the Sun were greater than those of the observations .
A new ephemeris was constructed at the office of the ' Berliner Jahrbuch , ' using 8-figure logarithms , and paying special attention to the accuracy of the terms depending on the position of the Moon .
The value of the solar parallax derived from the observations of Victoria was seconds second , and it is of interest to note that the Cape observations alone gave an identical result , seconds , with the but still very small probable error seconds .
The observations of Sappho did not form ) so complete a series as those of Victoria , nor was the ephemeris constructed with the same care .
Nevertheless a very accordant series of observations at the Cape and the four Northern observatories gave the result seconds , in satisfactory reement with those obtained from Victoria and Iris , and with a probable error of second .
The final result for the solar parallax found from the three planets was seconds , with a probable error slightly less than second .
xxxiv Obituary Notices of Fellows Only one criticism has been urged against the acceptance of this probable error as a measure of the real accuracy of this result .
It was urged by Prof. Newcomb that if the mean wave-length of the light of a minor planet were somewhat different from that of the comparison stars , then atmospheric dispersion would introduce a systematic error into the result .
Gin met this by the assertion that an observer with the heliometer unconsciously matched the different colours of the very small spectra into which the images were dispersed , when he superposed one image over the other .
In support of this contention he chose the very red star , Sagittarii , and had its distance measured from comparison stars when it was at different altitudes by Mr. de Sitter and Mr. Lowinger .
No perceptible effect arising from atmospheric dispersion was detected , and he therefore concluded that the etfect must be igible in the case of Victoria and Iris , which were to the eyes shable in colour from their comparison stars .
Gill 's value of the solar parallax has been confirmed by the observations of Eros and by a determination made at the Cape from spectroscopic observations of the velocity of the Earth in its orbit .
When the observations of Iris , Victoria , and Sappho were being discussed , it appeared that the residuals showed a period of about 27 days .
This was traced to the lunar inequality of the Earth 's motion round the Sun .
Each month the Earth describes an orbit about the centre of gravity of the Earth and the Moon .
The dimensions of this orbit are determinable from the inequalities in the positions of Victoria , Iris , and Sappho ; and from the dimensions of the orbit the ratio of the masses of the Earth and Moon may be calculated .
In this way Gill found for the mass of the Moon value confirmed by Mr. Hinks ' discussion of the observations of Although not of the same importance as the solar parallax , this is a more difficult quantity to determine .
The excellence of the determination of the positions of the stars which served as .
the reference points is the secret of Gill 's success in this work .
There was a thoroughness and completeness which made his research a model , and one which was , in fact , closely followed in the later investigation .
The determination of the mass of Jupiter is a third important research made with the 7-inch heliometer .
This was partly the observational work of Gill himself , and in part resulted from the younger astronomers whose enthusiasm he had kindled .
Before Gill had taken up his appointment at the Cape , Adams had urged o11 him the need for observations to give the latitudes of the satellites of Jupiter , the longitudes alone determined satisfactorily from eclipses .
it is not possible to obtain sufficient precision by the positions of the satellites relatively to the planet , Gill adopted a method employed by Hermann Struve and obtained their positions relatively to one another .
In 1891 he made a considerable series of observations and a smaller series was obtained by Finlay .
The most interesting feature of this research is the care employed on the scale value of the heliometer , so that the observations be employed to give the mass of Jupiter .
Gill .
xxxv pair of standard stars whose position-angle agreed nearly with the plane of the satellites was selected , and the scale value of the heliometer corrected by constant reference to these stars .
Their absolute distance apalt was derived by relating them to the Victoria triangulation , and found with a probable error of 1 in 100,000 .
The observations were not reduced till de Sitter 's visit to the Cape , when he discussed them , and obtained a very accurate value for the mass of Jupiter , and also determined corrections to the of the planes of the four satellites .
The subject was pursued further by Bryan Cookson , who visited the Cape in 1901-2 and again in 1905 , and made a series of observations with the heliometer , while photographs were taken with the astrographic telescope .
In this and subsequent work of de Sitter Gill took great interest , and was anxious that work on these satellites should be continued with large photographic telescopes .
The mass of Jupiter found by de Sitter reed closely with that derived by Newcomb from the perturbations produced in Saturn and the minor planets Themis Polyhymnia by the action of Jupiter .
The introduction of the heliometer was a new departure in the history of the Cape Observatory .
Following procedure establlshed by Airy at Greenwich , the work of the Observatory had till the bime of Gill been mainly devoted to meridian observations .
In consonance with the practical aim of being of service to navigation , Airy had made it his first business to determine the positions of Sun , Moon , planets and the htest stars with all accuracy possible .
This had resulted in a very full knowledge of the movements of the members of the Solar system and served as the basis of tables for the National Ephemerides .
This work is of great importance .
but the observations require to be carefully organised and constantly carried on .
There is , however , no finality about it , and it tends to become of a somewhat routine character .
By directing attention to other problems of Astronomy , and at the same time introducing a class of observations which demanded the'greatest skill and care on the parC of the observer , Gill gave new life to the Cape Observatory and new stimulus to British Astronomy .
He did not , however , fail to recognise the imporbance of meridian work .
He had in mind , from the time of his appointment , the improvement and development of Fundamental Astronomy .
In particular , he desired to introduce a reversible transit circle , but this proposal did not meet with any encouragement from Airy and was postponed for a time .
Observations with the non-reversible instrument were continued .
A list of 303 fundamental stars , selected by his friend Prof. Auwers , were fully observed between 1879 and 1885 , as well as Zodiacal stars , reference stars for heliometer and other observations , and stars which , in conjunction with observations at Greenwich , would serve to determine astronomical refraction .
This formed the Cape Catalogue of 1713 Stars for the Epoch 1885 .
The stars observed between 1885 and 1895 were of a similar class ; the results are contained in the Cape .
3007 Stars for the Epoch 1890 .
The next work with this instrument consisted in the observations of the xxxvi Obituary Notices of Fellows deceased .
positions of 8560 stars between and -5 declination , intended to serve as points of reference for the photographs , taken at the Cape , for the International Astrographic Survey .
After this had been completed observalions were begun towards a catalogue of Zodiacal stars , for use in heliometric and other observations iu which the differential positions of the Moon or planets are obtained .
For this work the co-operation of a number of other observatories was secured .
the results of several of these observa- tories have been published , the co-ordination of the whole series of observations into a Standard Catalogue has not as yet been made .
During Gill 's directorate the reduction and publication of Maclear 's observations was completed .
Maclear had left a large amount of valuable material with which he had been unable to reduce , but which his successors Stone and Gill have now discussed , thus iving the positions of a large number of southern stars at the middle of the nineteenth century .
While carrying out observations with the old transit circle , Gill kept constantly in mind his scheme for a new reversible transit circle , and steadily worked towards this end and lost no opportunity of advancing it .
The necessary expenditure was sanctioned in 1897 , and Gill devoted his thought to the and construction of an instrument which should be , as far as possible , free from the systematic errors which are the bane of Fundamental Astronomy .
His reat experience and his mechanical and engineering skill fitted him admirably for this difficult task .
The difficulties which have to be faced arise from want of stability of the instrument , due movements of the from changes caused by temperature in the atmosphere of the observing room and the positions of reading microscopes or the divisions of the circle , from uncertainties in the flexurs of the telescope , and from personal errors inherent in the methods of observation .
The instrument was designed so as to be reversible on its pivots , thus providing a check on the collimation , and with the eye-end and the object glass interchangeable , so that in the mean of the two positions the astronomical flexure should be eliminated .
Temperature changes were minimised by making the instrument of iron or steel , which had a coeflicient of expansion nearly equal to that of glass , and by carefully covering it with insulating material and so protecting it from the heat of the observer 's body and other ular radiations .
The piers carrying the microscope were iron tanks containing water , so that constancy of temperature was preserved particularly in horizontal layers .
But the most interesting and novel feature of this transit circle is found in the meridian marks .
Permanent marks were obtained at depths of 30-40 feet in the Archaic rock .
Marks on the surface vertically above these were deter- mined optically on the principle of Bohnenberger 's eyepiece , and this provided long focus collimators both north and south of the circle , by means of which its shift in azimuth may be readily determined at all times .
This ingenious plan proved very successful and has been copied by several observatories .
For the elimination of personal errors of the observer , he adopted the principle of travelling wire , and developed the method of employing a David xxxvii motor to make the wire move at approximately the rate of the star , the observer only to keep the image bisected by means of slow motions .
The instrument was not brought into full use till after Gill 's retirement , but the excellent results which were obtained under his successor 's direction were a source of great satisfaction to him .
A remarkable proof of the value of the underground marks was shown by the detection of the movement of the Earth 's pole in azimuth corresponding to the well-known variation of latitude .
In the development of stellar raphy Gill took a considerable share : In 1882 , the comet discovered by Mr. Finlay at the Cape Observatory was photographed by several people with ordinary cameras and without adequate means for following the diurnal motion .
Gill strapped a camera with a -inch Dallmeyer lens of 11 inches focus on the counterpoise of an equatorial telescope , and obtained a series of photographs , interesting as representations of the comet , but specially remarkable for the large number of stars shown on the plate .
The images were in excellent definition over a considerable field and the practicability of constructing star maps by photographic means was clearly indicated .
Gill obtained from Mr. J. H. Dallmeyer a " " rapid rectilinear lens\ldquo ; of 6 inches focus and inches focal , and , with the assistance of a grant from the Royal Society , commenced in February , , a raphic survey of the southern sky .
In December of the same year he received from Prof. Kapteyn , of , a proposal to undertake the measurement of these photographs and the formation of a ' Durchmusterung ' or catalogue of the approximate positions and nitudes of the stars .
Gill welcomed this offer of co-operation very heartily .
The methods to the pursued were discussed and the plates forwarded to Groningen .
The work was completed most successfully by Kapteyn , who began the measurement in Octobcr , 1886 , and completed it in February , 1898 .
The results are contained in three large volumes of the ' Annals of the Cape Observatory , ' and comprise a complete survey of the southern sky between -18declination and the South Pole .
The positions and raphic magnitudes of more than 400,000 stars were determined ; the Durchmusterung has been of the greatest service to astronomers in the southern hemisphere , and has served as a basis of important cosmical discussions by Kapteyn and others .
In December , 1882 , Gill forwarded to Admiral Mouchez a short paper , for communication to the French Academy of Sciences , accompanied by of Finlay 's Comet , expressing his views on the practicability of charting the stars by means of photography .
At this time Messrs. Paul and Prosper Henry , at the Paris Observatory , were engaged in charting the Zodiac .
As they approached the Milky Way the difficulty of the task caused them to consider the possibility of employing photographic methods .
Gill 's communication came at an opportune moment , and they were encouraged by Admiral Mouchez to proceed with the construction of object glasses suitable for this purpose .
Their constructive ability , combined with xxxviii Obituary Notices of Fellows the administrative skill of Mouchez and the persistence and enthusiasm of Gill , were the foundation of the great international enterprise for cataloguin and charting the whole sky by photographs on the large scale of 1 mm. to one minute of arc .
From its inception in 1887 to the time of his death Gill assisted this scheme in many ways .
He took an important share in the elaboration of the many details of the work itself , and in the correlated me1idian observations necessary to give the photographs their ooreatest value .
He clearly recognised that the 'International raphic Catalogue ' was a topographical survey which needed to be strongly connected with the principal triangulation furnished by meridian observations .
In this and other particulars the conference held at Paris for the execution of the international chart and catalogue were largely guided by his views .
Gill 's great power of getting a comprehensive scheme carried through is nowhere better shown than in the geodetic survey of South Africa .
But for his influence it is probable that the different States of South Africa would have been content with small local surveys unconnected or at least very weakly connected with one another .
Gill impressed on the Governments of the different States the value of an accurate survey based upon a principal triangulation of such accuracy that it would be defimtive for all future time .
Very soon after his appointment at the Cape he outlined a scheme for a Nidiron system of chains of principal triangulation extending over the Cape Colony , the Orange Free State , Natal , and the Transvaal .
A commencemeIIt was made in 1883 by the decision of the Governments of Cape Colony and Natal to make a principal triangulation of these countries as a joint work .
The observing in the field was placed under the direction of two officers of the Royal Engineers , Captain Morris ( now Sir William Morris ) and Lieutenant Laffan ( now Colonel Laffan ) who entered heartily into Gill 's plans , and amidst difficulties carried out a survey of the highest precision .
The results of this work were published in vol. 1 of the ' Geodetic Survey of South Africa ' in 1896 .
Gill saw that these operations be made the commencement of a still more comprehensive work of the greatest geodetic importance .
In his own words ( ' Geodetic Survey , ' p. 157 ) : Looking ward to the practical and possible progress of geodesy , the question may be asked , Should not the progress made in geodetic survey in South Africa be regarded as the first step in a chain of triangulation which , approximately travsrsing the 30th meridian of east longitude , shall extend continuously to the mouth of the Nile The amplitude of such an arc is , and by triangulation through the Levant and the islands of Greece , it may be connected with the Roumanian and Russian arc , so as to form a chain 10 amplitude extending from Cape Agulhas to the North Cape .
This great project Gill kept constantly in mind and forwarded at every mity .
The next stage of the geodetic survey was in a different .
It became necessary to delimit part of the boundary between German and British South Africa , which had been fixed by treaty in 1890 , as the David Gill .
xxxix 20th meridian , from the Orange River ( latitude ) to latitude .
It by Gill that the chain of triangles , which passed main was through German territory in order to avoid the Kaliharl desert should start from Rietfontein , the northern limit of an exce en survey llent surve oi South Bechuanaland by Mr. Bosman , and that the latter should be connecte at its eastern and western ends with the surveys of the Cape and Natal .
This was completed in 1899 .
The interest of Mr. Cecil Rhodes was secured in the measurement the reat arc along the 30th meridian , and in 1897 the Administrator of Rhodesia sanctioned the commencement .
It was carried forward by Mr. Alexan er Alexand Simms in Southern Rhodesia as far as the Zambesi .
The outbreak of the compelled a suspension of the work during 1902 .
In 1 903 the work was continued by Dr. Rubin , under Gill 's direct on , direction , and was carried forward by 1906 to within 70 miles of Lake Tanganyika , when it was suspen ded Soon after the close of South African War the geo detic survey of the Transvaal and Orange River Colony was proceeded with .
On Gill 's adv ce Colonel Morris put in charge of these operations , his own posltlon eng be .
that of Scientific Adviser to the overnmenls of the two Colonies , so that unity of purpose might be preserved in these surveys and that they hold form part of a harmonious whole .
These surveys were comp .
leted by the be ( yinning of 1906 and the chain on the 30th meridian was continued northas far as the Limpopo River .
Thanks to Gill 's efforts the surveypartyAf was kept together , and funds obtained , half the British South Afr ca Company and half from scientific societies in Englan , ena arc land which enabled the connection to be made with the chain in Southern , The great Ph desia , The on the 30th meridian was thus carried from latitude 31 36 to .
As a result of these measurements , utilising 571atitude stations , Dr. Ba as Bahn shown that the terrestrial spheroid is somewhat greater than that are Clarke in agreement with a determination by Hayford from the eo Geodetic Survey of North America .
When Gill went to the Cape in 1879 , the Observatory staff was sma , an 11 and the only inslruments were the transit circle , a 7-inch equatorial , and a a hoto- heliograph .
The grounds , buildings , and water supply vere n a a very unsatisfactory state , and after heavy rains the road to the Observatory was nearly impassable , so that computers who were not in residence on the hill had to be there in carts .
In consequence of Gill 's persistent sentations these were gradually remedisd , and sufficient provision made for the suita table of the grounds and buildings .
The swamp at the bottom the hill was drained , trees were planted , fences erected , were repa re red and extended , so that when Gill left , the Observatory and its surroun lngs were not unworthy of a scientific institution of its great mportance .
To the instrumental equipment were added the reversible trans crc circl the 7-inch heliometer and an astrographic equatorial , and the Victoria inch)photographic refractor .
The last of these instruments was a generous gift from Mr. Frank McClean , and was a to Gill 's great achievements xl Notices of Fellows deceased .
as an astronomer .
Coupled with the 24-inch is an 18-inch visual refractor .
Objective prisms and a powerful slit spectroscope were included in the gift .
This munificent gift was intended to be in commemoration of Queen Victoria 's Jubilee in 1897 , and although the Observatory and telescope were not completed till a few years later , this date is inscribed on a tablet inserted in the front of the Observatory , which was unveiled by the Governor , Sir Walter Hely Hutchinson , in September , 1901 .
Valual ) spectroscopic work has been done with the instrument .
Gill was particularly delighted by the determination of the solar parallax from the chailges in the apparent velocities of stars to or from the earth at different times of the year in consequence of the earth 's orbital motion obtained from observations with the instrument by Dr. Halm umder the direction of Mr. Hough .
The staff of the Observatory was increased in correspondence with the larger equipment , so that when Gill left the Cape the Observatory was qualitied to carry out work of the highest order in many different directions , and was one of the finest Obselvatories in the world , and of additional importance from its siGuaGion in the southern hemisphere .
In 1905 , the year before Gill left the Cape , the British Association visited South Africa .
The invitation to the Cape was largely the result of Gill 's efforts , and his unremitting labour as General Secretary contributed greatly to its success .
He was ghted to welcome so many of his friends to South Africa , among others Sir George Darwin , Admiral Wharton , .
Backlund , Prof. Kapteyn and several younger astronomers from England and the Continent .
The meeting in South Africa was signalised by Kapteyn 's announcement of his discovery of star-streams .
Acting on his doctor 's advice that a more bracing climate would be benefi- cial to him , Gill intimated to the Admiralty his desire to retire in February , 1907 , after 28 years of service , and was granted leave of absence from October , 1906 .
He settled in London and was soon busily engaged in its scientific activities .
He was President of the British Association at the Leicester meeting in1907 .
He on the Council of the Royal Society 1908-9 , and again 1910-11 ; on that of the Royal Astronomical Society 1907-1913 , being President 1910-12 and succeeding Huggins as Foreign Secretary in 1912 ; and on the Council of the Royal Geographical Society , 1908-10 and 1911-12 .
He also served on the Council of the British Science Guild , and succeeded Lord Cromer as President of the Research Defence Society .
After he had settled in London a large part of his time was devoted to a History of the Cape Observatory with a full and technical description of the new instruments .
This admirable work was happily completed and published a few months before his death .
Gill thoroughly enjoyed the opportunities of seeing his many friends which his residence in London afforded him .
He was constantly consulted astronomers , particularly as to the design of instruments .
His interests embraced not only the practical branches of Astronomy and Geodesy with which his own work had been more particularly concerned .
He followed with interest the ourrent researches of astronomers in lunar theory , solar and Sir David Gill .
xli stellar spectroscopy , and especially those bearing on the extent and movements of the sidereal system .
Another subject in which he was keenly interested was manufacture of optical glass for large telescopes .
Nothing gave Gill greater pleasure than to invite his astronomical friends to his house , especially if an occasion was provided by the visit of a distinguished foreign af ; tronomer , and to have a talk about Astronomy .
He found a similar pleasure in the Astronomical conferences he attended , particularly those at Paris in connection with the national Photographic Chart of the Heavens and kindred subjects .
These conferences were a source of great delight to him , because of the opportunities they furnished of personal intercourse with his friends , of finding out what they were doing , and how their work pg.essed , and in return telling them what he had hand .
They benefited by his advice and the results of experiences , but still more by the enthusiasm he communicated to them .
's influence is shown by the number of astronomers who worked in co-operation with him or were guided by him in their choice of work .
Reference has already been made to Auwers , who undertook the discussion of the meridian observations in connection with the solar parallax , to Kapteyn 's co-operaLion the Photographic 'Durchmusterung , and the parts the arts taken by Elkin , Cookson , and de Sitter in heliometer and raphic observations .
To these may be added Jacoby 's work on the ulation of the Victoria stars , and that of Innes on the revision of the Cape raphic 'Durchmusterung McClean 's spectra of the bright Southern Stars were obtained by hinl with the astrographic equatorial while he was a guest at the Cape .
The valuable photographic survey of the sky made by Franklin-Adams was largely due to Gill 's encourag meant .
In the introduction to his ' History of the Cape Observatory , ' Gill tells of the delight with which he read Struve 's 'History of the kova Observatory ' : is inspiration to be found in neally every page of it , for authol had the true genius and spirit of the practical ash.onomer\mdash ; the love of refiued and precise methods of observation and the inverltive and capacity .
These words are as applicable to Gill as to Strtlve .
He loved to make an instrument capable of the most refined ) easurements , and the pleasure of making observations as as possible counterbalanced the tedium of aking similar observations night after night .
His force of acter enabled hinl to triumph over culties and carry out great projects .
His enthusiasm and tenacity of purpose communicated themselves to his colleagues and assistants , ctnd his kindness of heart them devoted to him .
received ] ) onoul 's in recognition of his ) sel.vices to Astronomy .
He oreated Companiou of the in 1896 , and Knight Commander in created Commander of ths Legion of Honour ( France ) in 1908 , and Kuight of ths Prussian Order " " Pour le MoriCe\ldquo ; in 1910 .
He was an Hon. .D .
of Aberdeen and Edinburgb , and Hon. D.Sc .
V0L .
lii Obituary Notices of Fellows deceased .
S of Oxford , Cambridge , Dublin , and the Cape of Hope .
He was elected Amer.edal ooyal Astronomical Society wwardeda ostronomical Society oacific iatson Medalto hgain ioyal Medal ooyal Society iedal onstitute orance iruce .
Medal of the National Academy of the United States in 1900 .
Since his return to London Gill 's health had been excellent , and he thoroughly enjoyed an occasional day 's golf or .
In December , 1913 , he was suddenly ssized with pneunlonia , and passed away on January 24 , 1914 , after an illness of six weeks .
F. W. D. G. W. HILL , 1838-1914 .
GEORGE WILLIAM HILL was the son of John William Hill and Catherine Smlth , and was born in New York City on March 3 , 1838 .
Both his father and grandfather were artists , and he himself was of English and Huguenot descent .
His early education , like that of most of the men of his time in Amcrica , gave him few advantages .
In 1846 , when his father moved from New York to the farm at West Nyack , the country was too busy with material development to produce many teachers who could give any but the most elementary instruction , and the country school which he attended must have been inferior in this respect to those of the larger cities .
Even at Rutger 's in New Jersey , to which Hill was sent owing to the exhibition of capacity and from which he took his degree in 1859 , the course probably went but little beyond that now found secondaly schools .
There , however , he came under the influence of a man whose ideas on education were unusual .
Dr. Strong , according to Hill 's evidence , believed only in the classic treatises ; but the published after 1840 was admitted to library .
Hill 's sound of the fundamentals of his subject is donbtless due to this course of reading .
Hill 's first paper , published in 1859 when he was but 21 years of and before he had taken his degree at college , is a half-page note on the curve of a drawbridge .
Two years later he showed his capacity in the essay which gained a prize offered by Runkle 's ' Mathematical Monthly ' for the best solution of a problem connected with the constitution of the Earth .
President R. S. Woodward , who has himself worked much at this subject , says that memoir is still worthy of careful readincr .
G. W. Hill .
xliii In the year 1861 he joined the staff of the Nautical Almanac ' office , which then had its headquarters in Cambridge , Mass .
, and for a year 01 two he worked there and thus had an opportunity for association with some of the ablest men of the time in astronomical sciencs .
But he soon obtained permission to do his work at the home in West Nyack which he never seemed to leave willingly during the rest of his life .
It was there that nearly all his best work was done .
In fact , he was only away from ib for one considerable period , and this is covered by his residence Washington from about the year 1882 until 189 ; even during that time the smmmers were generally spent in West In the first ten years after college , Hill only published papers , and none of them deal with celestial mechanics in the modern sense term .
But from his output after that time it is evident that he had been reading and digesting the newer treatises and memoirs as they appeared .
Delaunay 's two magnificent volumes on the lunar theor.y were published in 1860 and 1869 respectively , and the methods of that lnvestigator exercised a tion over .
Hill for the rest of his life .
The other great lunar theorist of the period , P. A. Hansen , had been explaining his methods for many years before this time , and Hill was probably one of the few men of his time who understood them thoroughly .
He does not seem to have been particularly drawn to them , although they are in his theories of Jupiter and Saturn with but little alCerarion .
It is difficult to find many traces of other influences in his work .
His most celebrated memoir , it is lrue , is based on one of Euler 's numerous methods , as he himself tells , but after the start he proceeds entirely on lines of his own devising .
The publications which follow his first attempts this early period exhibit knowledge of theoretical astronomy and the power to handle large masses of numbers rather than amy unusual mathematical ability .
In his discussion of the observations of the great Comet of 1858 , which was undertaken to obtain a satisfactory orbit ( 1867 ) , he has to deal with 363 places gathered from many sources .
As usual with Hill , he does not confine himself to the main point but discusses systematic errors between different observatories and those due to the size of telescope used .
His final conclusion is that there is no evidence of any force other than tion influencing the motion of the comet .
It is probable that his work on this body was rssponsible for the next three papers : on the reduction of star places , the detelmlnatlon of the elements of a cular orbit , and the conversion of latitudes and longitudes into right ascensions and declinations , or , at auy rate , that it drew his attention to these fundamental problems .
But he was soon to lay them in the background for more original investigations in celestial mechanics proper .
One can see in his published work the gradual approach to this subject .
His tenth memoir is a correction to the elements of the orbit of Venus from observations extending over 33 years .
It is followed by a xliv Obituary Notices of deceased .
derivation of the mass of Jupiter from the perturbations of certain asteroids , and the calculation of an inequality of very period in the motion of Saturn .
Shortly before , however , he had been assisting in the campaign which ] had started some years earlier to get the utmost out of the transits of Venus in 1874 and 1882 .
II of the Papers of the United States Commission relating to the transits is by his hand : consists of charts and tables for facilitating predictions of the several phases at any place on the globe .
The active period of Hill 's work in celestial mechanics in 1872 .
Between that year and 1877 , when his two chief memoirs appeared , he published eleven papers on various phases of the subject , besides seven others in pure and applied mathematics and the long transit of Venus calculations already mentioned .
Most of them are quite brief and call for no special mention .
In order Chat the value of Hill 's contributions to celestial mechanics and more particularly to the lunar theory may be made clear , it is necessary to say a few words as to the condition of the subject at the time they were published .
For 200 years mathematical astronomers , many of them of the first rank , had been devoting their to furnishing a complete demonstration of the power of the law of gravitation to account for the motions of all the bodies in the solar system within the degree of accuracy of the observations .
In the third quarter of the nineteenth century it was evident that this demonstration would soon be made .
Leverrier was publishing tables for the positions of the great planets , while Hansen and Delaunay had completed their work on the Moon .
For the purposes of navigation all needed accuracy had been obtained , and from the scientific side there seemed to be but few matters which needed explanation ; the final polish which a few industrious workels might give was the last step .
There was thus danger that the subject of celestial mechanics might encounter a blank prospect .
The number of ators began to dwindle .
At the same time , pure mathematics and physics were showing vast territories to be explored , while the discovery of spectrum analysis and the use of the photographic plate attracted many astronomers who earlier would have devoted themselves to the mathematical side of the subject .
From the old point of view this attibude on the part of astronomers was justifiable .
But Hill saw that there were problems other than the mere verification of the law of gravitation by comparisons of theory and observation of the chief bodies in the solar system , which would demand solution .
He also saw , partly from the industrious work of Newcomb on the old and modern observations of the Moon , that even the enormous labours of Hansen and Delaunay on the theory of its motion would demand extension and verification if a test of the Newtonian law to the yree of accuracy of the observations were required .
For the former object , a new set of problems must be formulated and a start made towards their solution ; for the latter , a new method of procedure was practically necessary , for it was almost certain tlIat no one G. W. Hill .
xlv would repeat the calculations , which appeared to have been pushed as far as was humanly possible with the adopted methods .
These two sides of Hill 's work are quite distinct , even though they both start from the same memoir .
The older lunar theorists had taken the ellipse as a first approximation , that is , at the start the action of the sun was neglected .
Hill proposed a first approximation in which a portion of the sun 's action should be taken into account .
If an examination of Delaunay 's final expressions for the longitude , latitude , and parallax be made , it is seen that the infinite series proceed along powers five parameters , and that the rate of convergence along powers of one of these , the ratio of the mean motions of the Sun and Moon , is fat more slow than along powers of the others , owing to the presence of large numerical factors .
Hill conceived the idea of neglecting all these other ameGers and then finding the series in powers of this ratio with all needed accuracy .
He set up the equations of motion , solved and gave formulae of recurrsnce which enabled him to avoid the slow approxlmation methods which genel.ally advanced the degree of accuracy by only one or two powers of the ratio at ch step ; in his method it advances by four powers of this ratio .
The expressions are worked out both literally and numerically , the latter being taken to even significant figures , a number not very much in excess of what is actually required .
As obtained , the co-ordinates are referred to axes which move with the mean velocity of the Sun round the Earth , and in this form the expressions involve the time through its presence in multiples of a single angle .
In the transformotions which are necessary to convert rectal ) gular co-ordinates to polars , Hm makes full use of the method of " " special \ldquo ; or , as it is now called , of harmonic analysis and synthesis .
He was always very fond of this kind of transformation , using it much in later years and even attempting to sysrematise its use when many hundreds of terms were present .
It would be unjust in this connecbion to mention the indebtedness of Hill to Leonard Euler , probably the greatest of lunar theorists since Newton .
Euler , as Hill remarks , had had the idea of .
the theory in the same way with moving rectangular axes , and with the same first .
approximation , and had carried it out to a considerable extent in his theory published in 1772 and in a later memoir .
The further steps outlined by Euler , and quoted by Hill , consist of the determination , step by step , of the terms arranged in powers of the parameters which had been neglected .
Each step is to consist of the complete calculation with all needed accuracy of the function of the tims and the ratio of the mean motions whioh multiplies each combination of powers of the remaining parameters .
There are several difficulties in following this process .
The chief one , which Hill solved in the memoir on the of the Moon , is the determination of the firsC new angle containing the time which arises in the second approximation .
later approximations this angle also involves all the parameters , and othsr methods are needed to find the new porb ons depending on them .
Euler possibly foresaw this ; Hill certainly did , but he xlvi Obituary Notices of Fello deceased .
never carried his work to the degree of approximation which would need them .
The method has been used by the writer for the construction of a complete theory of the Moon 's motion .
The expressions for the co-ordinates , referred to the moving rectangular axes , have another property : they form Fourier series and are therefore periodic .
The resulting orbit in this moving plane is consequently closed .
Recognising this fact , Hill draws the curve .
But he saw that the orbit was of interest apart from its application to the lunar problem , for he immediately to trace , with some care , orbits for values of the ratio of the mean motions other than that which holds for the actual Moon and Sun .
He thus obtains a family of such orbits .
It is Hill 's idea of periodic orbit which , developed chiefly by Poincare and G. H. Darwin , has given new life to the whole subject of celestial mechanics and has induced many mathematicians to investigate on these lines .
The treatise of the fo1mer , ' Les Nouvelles Methodes de la Me'canique Ce'leste , ' is based mainly on the idea .
Darwin actually traced many such orbits under varying conditions .
There is still another portion of this memoir which has been largely used as a foundation for investigations into the ] of celestial systems .
If the eccentricity of the Earth 's orbit round the Sun be neglected , it is possible to write the relative equation in a finite form .
eferred to the same axes , the square of the velocity can , in fact , be expressed as a finite algebraic function of the co-ordinates .
Since the square of the velocity can nsver be negative , this metion , equated to zero , gives the equation to a surface which the Moon cannot cross .
As the surface consists of various vals and folds , we can obtain certain limitations on the path of the Moon and therefore carry forward the question of the stabiliby of its motion o1le important step .
Hill draws the surfaces for a limited case .
Darwin made extensive use of a similar diagram for a more extended case , and many others have followed on the same lines .
Thus this memoir , of but 50 quarto pages , has become fundamental for the development of celestial mechanios in three different directions .
Poincare 's remark that in it we may perceive the germ of all the progress which has been made in celestial mechanics since its publication is doubtless folly justified .
It has sometimes been said that Hill did not appreciate at the time the importance of his work .
Hill was far too modest about his own achievements to lay any such stress on his productionls as has the scientific world .
But it does not require an extended study of his memoirs to see that his vision often went beyond the particular matter in hand .
The second memoir of 1877 , ' On the Part of the Motion of the Lunar igee which is a Function of the Mean Motions of the Sun and Moon , ' has already been referred to .
It is essentially a continuation of that part of the researches which deals directly with the lunar problem , although published a few months earliel. .
While not so far-reaching from the point of view of future developmenbs , it is even more remarkable as an exhibition of Hill 's powers of analysis .
In it , the determinant with an .
W. Hill .
xlvii infinite number of elements is raised from a nebulous possibility to an instrument of computation .
Hill 's periodic orbit contained only two of the four arbitrary constants which the complete solution of his differential equations requires .
He , therefore , proceeds to find an orbit\mdash ; no longer periodic\mdash ; differing slightly from the periodic orbit but still .the differential equations to the first power of the small variation .
The equat ons obtained are two of the second order and linear with respect to the two unknown dependent variables .
An able analysis with the use of known integrals enables him to reduce the solution to that of one of the second order in the normal form\mdash ; where is a known Fourier series depending on the time .
Knowing the form of the solution\mdash ; from previous work in the lunar theory and which he justifies by general considerations , Hill substitutes and obtains an infinite series of linear equat ons for the determination of the unknowns .
But is also unknown and it does not enter in a linear form .
The are eliminated by means of a determinant with an infinite number of rows and columns equated to zero ; this is therefore a determinantal equation to find , the main object of the investigation .
Then follows a remarkable series of operations .
The determinant is reduced to a convergent form ( though it was left to Poincare to furnish the proof of convergence ) by dividing each row by a suitable factor which reduced every element of the pri1lcipal diagonal to unity .
Next , the unknown , , must be isolated ; Hill achieves this by recognising that if be a root so must be also a root and that , thel.efore , all the roots can be expressed by a coslne function .
On the assumption that there are no other roots , he equates the determinant to the cosine function , obtaining the constant by comparing the highest ( infinite !
) power of on each side of the equation .
A partlcula value of ( not a root ) can be inserted in the identity thus obtained .
In this way , Hill reduced ths work to a computation of an infinite determlnant every element of which is known .
He ives a general ntebhod for this expansion which enables him to tell at once the order of the terms neglected when the series is cut off at any place .
Each term of this series , however , consists of singly , doubly , , infinite series which must be summed .
The labour at this stage was very great and it caused a liability to error .
Hill carried it through with complete success in its eneral form , afterwards substituting numbers and determining to 16 significant figures .
The principal part of the motion of the Moon 's perigee is immediately deducible from .
President Woodward relates that the determinant was solved one of two trips which Hill made to the north-west region of Canada ; I imagine , however , that this stat , ement refers to the method to be adopted rather than to the actual computation .
xlviii Obituary Notices of Fellows deceased .
The story of these two memoirs is incomplete without a notice of the work of J. C. Adams on somewhat similar lines .
Almost immediately after their publication , a brief paper by him appeared in the 'Monthly Notioes ' of the Royal Astronomical Society .
He had also taken up Euler 's idea and had obtained the variation orbit as a first approximation .
But he turned t.o motion of the node instead of to that of the perigee .
investigation here follows lines very similar to those of Hill , the solution of the infinite deberminant closely analogous .
It is convenient at this to take up Hill 's work rather by subject than in chronological order .
The periodic orbit used with such excellent results in the lunar theory is later ( 1887 ) on the motion of the satellite Hyperion as disturbed by Titan and the results applied in a following paper to obtain the mass of the latter .
These were written before the publication of Poincare 's researches .
Only on one occasion did hs make it the subject of a theoretical research , and it was then probably stimulated by Poincare 's ' Mecanique este .
' As the title , ' Illustlations of Periodic Solutions in the Problem of Three Bodies , ' indioates , it consists of applications to certain bodies in the solar system .
From time to time a paper was published advancing the applications to the lunar theory .
In one , the periodic orbit is extended so as to include the terms which depend on the ratio of the parallaxes of the Son and Moon as well as on the ratio of the mean motions .
In another the terms dependent on the latter ratio and on the first power of the solar eccentrioity are computed .
In still another paper he calculates the expression for the principal part of the motion of the moon 's perigee as far as literally in order to settle the correctness of Delaunay 's value , which had been questioned as to certain of the earlier powers of by Andoyer .
Beyond these , he seems to have made no effort to continue the work in this direction .
Possibly this was due to the heavy labour on the theories of Jupiter and Saturn which engaged him at least until 1892 .
In fact , as early as 1888 he stated in a letter to Sir George Darwin that he scarcely expected to proceed with the subject .
His fondness for Delaunay 's methods has already been mentioned .
One of his most valuable memoirs is an application of them to the calculation of the smaller perturbations of the Moon 's motion which arise from the action of the planets and the figure of the Earth .
Hill , using Delaunay 's methods and results , showed , in a short paper on the Jovian evection , that the whole action of the Earth and Sun on the Moon could be treated as known from the start , and that therefore only one approximation was needed in order to get the effect of any disturbance whose square could be neglected .
All later ators have used this method .
The formulae of Delaunay are literal , while Hill 's final equations for the calculation of the effect of any small disturbing force have the great advantage of well-determined numerical coefficients to.be multiplied by the constants which depend ] on the nature of the given force .
G. W. Hill .
xlix Tn an earlier paper he had also shown how the disturbing function for direct planetary action can be expressed as a series of prodncts , one factor in each product containing the co-ordinates of the Earth and Moon only , while the other contained Chose of the Earth and planet only .
The former could , therefore , be computed once for all ; it was the latter which required separate computations for each planet .
This paper has also formed the basis for all the complete calculations of the planetary disturbing forces which have been made since its publication in 1883 .
But Hill 's most extensive application of Delaunay 's theory is made in its original form to the calculation of the inequalities produced by the figure of the Earth .
While he carried these to the degree of accuracy needed for observation , the method appears to be somewhat long and complicated .
It has to be applied in a literal form , and this requires expansions which convery slowly .
As a matter of fact , a few days ' work with the methods which he adopted for the planetary termfi will furnish the inequalities with all needed accuracy .
In the first part of this paper Hill , not content with the values for the of the Earth which were then in use , duced one directly from a large number of pendulum observations all over the Earth .
The result , 1/ 288 , is considerably larger than most of the other determinations , and notably so than that of Helmert , 1/ 298 , deduced from the same class of observations .
The memoir occupies over 140 pages , and must have demanded an enormous amount of careful and accurate algebraic computation .
To complete the account of his work on the lunar theory , mention must be made of his calculation , by de 's method , of the principal inequalities produced by the motion of the ecliptic .
Hansen was the only writer who had found the term in longitude as well as in latitude , and nearly all his calculations of the small perturbations are doubtful .
Hill , of course , obtained correct results as far as he went in the matter .
Newcomb , who had taken charge of the American Ephemeris in 1877 , soon induced Hill to undertake the theories of Jupiter and Saturn , and so material assistance in his plan of forming new tables of the planets .
The method adopted is thaG of Hansen with only a slight moditication , which consisted in expressing the computations directly in terms of the time instead of using two auxiliary angles .
That he used an old method in prefelence to devising a new one is perl ) unfortunate , even though the result leaves little to be desired .
Had he taken more time over the preliminary stages we should probably have had something new and original , for Hill was then at the of his powers as a mathematician .
But he was doubtless nder some pressure from Newcomb , who wished to complete his great plan during his tenancy of the office of director , and Hill ] have desired to finish the calculations as soon as possible in order that he might to West Nyack .
However this may be , he completed the task successfully , ss may be judged from the small residuals which he obtains after a comparison with observations extending over 150 years .
The Tables which he formed from the theories of the two planets are now used in most of the national ephsmerides .
Obituary Notices of Fellows deceased .
In 1882 , Hill published a memoir of some length on method for computing the secular perturbations of the planets .
Gauss had outlined only the general idea .
Hill takes it up and develops in detail the formulae to be used , In the course of the work he finds that a considerable portion of the calculation depends on eiliptic integrals which may be needed for values of the argument up to .
Consequently , a large part of the paper consists of the tabulation of these to eight places of decimals at intervals of a tenth of a degree ; the first and second differences are also printed so that the Tables are in form ready for interpolation .
As an example , he computed the secuiar perturbations of Mercury by Venus with great accuracy .
Two further papers on the same )ject appeared in 1901 .
In these years Hill published a number of short papers in the ' Analyst , ' journal no longer in existence .
Sometimes they are merely solutions of wellknown problems , at other times simplifications of proofs of theorems which had evidently presented difliculties to him and which he felt needed elucidation or eJaboration\mdash ; two favourite words with him .
But Hill was not a g.reat expositor : even for those familiar wiCh the subject his work is often difficult and sometimes obscure .
Newcomb used to say that if Hill had only the faculty of explaining his own ideas he might have avoided many an error and saved much time .
Hill 's ability to assimilate and extend the work of his predecessors , at any rate in his earlier days , doubtless prevented him from appreciating the difficulties of others .
When the reader is used to Hill 's style of composition and his general plans in writing out what he had to say , his arguments are much more easily grasped , but he is rarely anything else than concise .
In his last years Hill still continued to publish , in spite of failing health .
Hs covered a variety of topics , several of them quite away from the region of celestial mechanics .
One of the most extensive of his papers is a memoir on dynamic eodesy , the last in the fourth volume of his collected works and not previously published elsewhere .
Some later papers on a variety of subjects will appear in a fiSth volume , to be ] ished , like the previous four volumes , by the Carnegie Institution of Washington .
If an attempt is made to regard Hill 's work as a whole and to try to find out point of view , one stands out clearly : a desire to obtain exact knowledge about natural phenomena , in however limited a field , which could be expressed in a numerical form .
He never seemed to hesitate about making long calculations , and apparently had a positive liking for obtaining his results to many places of .
But , unlike the tendencies of those who engage much in computation , his mind did not seem to get cramped by figures .
Not only could he see both trees and wood , to adopt a familiar simile , but could paths in the wood and keep his eyes open for roads which led in directions other than that he was .
He had remarkable ability for ebraic manipulation , which.reached its highest manifestation in the memoir on the perigee the moon .
The more modern sides of mathematics apYealed to him but little ; if a formula or a series could be G. W. Hill .
li reduced to numbers , such questions as conyergence did not trouble him much , a point of view which has later been fully justified by Poincare .
He seemed to take but little colour from the work of others .
Even when , as in many cases , he starts with the results of some previous investigator , his writing shows but little influence of the source of his ideas ; it is individual and carries the reflection and methods of his own mind .
Hill never married .
He lived much alone , but while ) in Washington would take long walks on @unday , often with one or two companions .
He was fond of botany withont being a collector of specimens and foumd his chief outdoor recreation in the study of nature .
He made two canoe trips in the north-west of Canada .
A carefully written diary , illustrated with photographs of the second expedition , which took him by rlvers and lakes from Lake Superior to Hudson 's Bay , is amongst the books which he left in his will to Columbia University .
He was President of the American Mathematical Society from 1894 to 1896 and served as lecturer on celestial mechanics in Columbia Universiby from 1898 to 1901 .
The manuscript of his lectures shows that they must have .
cost him much labour ; it contains long algebraic nents and is apparently intended to be a more or less complete accoullb of the methods by which the motions of the Moon and planets are calculated .
His numerous honours include membership in ths Royal Society , the Paris Academy , and the Belgian Acadenly .
He received the Schubert Prize ( Petrograd ) , the amoiseau Prize ( Paris ) , and the Gold Medal of the Royal Astronomical Society .
He was eleoted to membership in our Society in 1902 , and received the Copley Medal in 1909 .
His chief characteristic a single-minded devotion to the subject which he had made his own .
A sensitive conscience was always apparent in his dealings with the world : he refused to accept the salary of his lectureship at Columbia one year because no tudents then appeared to attend the course , and this in spite of the fact that the endowment allowed him absolute freedom to lecture or not as he chose .
In later years he rarely left West Nyack , owing to ill-health .
He died on April 16 , 1914 , from heart failure , and was near the graves of his ancestors not far from his home .
E. W. B. lii Votices of Fellows SIR GEORGE NARES , K.C.B. , F.R.S. , IN the death of Admiral Sir George Nares our Society has to regret the loss of a very meritorious officer who had been a Fellow for nearly 40 years .
George Nares came of a literary family , among its members AIchdeacon Nares , the author of the best life of Lord Burleigh .
Born in 1831 , young Nares entered the Navy in 1845 , and served first on board the " " Canopus when he saw some feats of seamanship in the Tagus , in the exchange of main yards with the " " Asia\ldquo ; flagship , bonnd for the Pacific .
His next service was on board the " " Havannah\ldquo ; in the Pacific , when his scientific training was commenced .
Nares was appointed to the " " Besolute u1lder Captain Kellett , in the Arctic Expedition of 1852 to 1854 .
He commanded the auxiliary sledge to Lieutenant Mecham , who , next to McClintock , was the oreatest of Arctic sledge travellers .
Nares performed this service admirably , going as far as Eglinton Island , where he made a collection of fossil wood , most interesting geological discovery .
On his return from Arctic service he was promoted to the rank of Lieutenant .
For the next ten years Nares was most employed in surveying and in the work of instruction .
In the Illustrious\ldquo ; he was in charge of the training of cadets , again in the Britannia and he had the " " Boscawen\ldquo ; training ship .
He wrote by far the best book on seamanship since the days of Darcy Lever , which went ) several edilions , and was translated into rench and Italian .
As a veyor , in command of the " " Salamander\ldquo ; and .
' Shearwater he surveyed , part of the coast of Australia , and the Gulf of Suez with reference to the Ction of the canal .
But his best known and Dlost important surveying work was on board the\ldquo ; Challenger\ldquo ; in the expedition which was dne to the representations of the Royal Society .
His labours extended over the Atlantic , Ocean , and far as the Antarctic regions , where he discoveled what appeared to be an which still remains to be explored .
Nares was recalled from the\ldquo ; Challenger\ldquo ; to command of a scientific Arctic Expedition , due to the strong representations of the loyal and Boyal Geographical Societies .
The SocieGies desired discovery and scientific esearch , the Admiralty an attempt to go as near the Pole as possible .
The Smith Sound route was selected as the best for discovel.y and scientific research , showed consummate seamanship iu forcing the " " Alert\ldquo ; ough the ice to N. The resuIts of the expedition were most valuable .
Commander ( now Admiral Sir Albert lIarkham , in his memorable ourney , reached a latitude of The them coasts of rant Land and Greenland were discovered for a distance of 300 miles .
A fossil flora of extraordinary interest was one reat eological result , and the .
and biology of the region were liv SIR JOHN , lf .
C.B. , SIR JOHN MURRAY was born on March 3 , 1841 , at Coburg , Ontario .
He came of one of those Scottish families that have done so much for Canada , and , indeed , throughout his life no one would have mistaken him for anything but a Scot : His father , Robert Murray , an accountant , had left Scotland seven years before and settled in Upper anada , where during the troublous of the Mackenzie Rebellion he took an active part in Canadian politics .
John was for a time at the Public School of London , Ontario , and later at Victoria College , Coburg .
When he was seventeen years old he left Canada and , as he has himself reminded us , he then for the first time saw the sea whose problems he was destined to make his own .
When he left that early home , he says , " " to find another amongst my relatives in Scotland , I had not yet seen the ocean .
The voyage across the Atlantic made a gleat impression on me , so different was the salt , rolling sea from the great fresh-water lakes with which I had up to that time been fatniliar , and I was fascinated by the operations of bhe officers on the bridge when taking the altitude of the stll at each mid-day.\ldquo ; On witnessing the rise and fall of the tide for the firsb time on the West Coast of Scotland , the impression was still more profound .
John Murray founa1 a new home amongst his Scottish relatives , ons of whom was John Macfarlane , his maternal grandfather at Coneyhill , shire .
He helped his grandfather in purchasing and collecting specimens for a museum , the remnants of which are still exhibited in the Macfarlane Institute at Bridge of Allan , many of the labels being in Murray 's handwriting .
Whilst living with his Scottish relatives attended the High School , Stirling , and here he showed great interest in science .
He used to pay especial attention to the teaching of Mr. Duncan Macdougall , from whom he learnt the principles of the sextant and how to construct an electric lamp and a battery of 80 Bunsen cells .
Murray remained for a long time at School and College .
In fact , as he himself records , he came to be known as a " " chronic student\ldquo ; at the University of Edinburgh .
One thing he would not do , he would not go in for examinations .
He learnt what he wanted to learn , and the mere was to him its own reward .
At the University , although in the main he followed the Science course , he was not infrequently to be seen in the lecture rooms of the lit , erary professors and from time to time in those of the theological professors .
Amongst his student friends more than one have made a mark on the theological thought of the last of the nineteenth century .
Occasionally * In writing this short memoir of my friend I have been greatly helped by Mr. Laurence Pullar , of Bridge of Allan and Bridge of Earn , by Dr. Hugh Roberb Mill , by Dr. J. Sutherland Black and by Mr. James Chumley , who for many years was Sir John Murray 's chief assistant .
John lv he even listened to Law .
His and Anatomy he studied under Goodsir and Turner , the present Principal , whilst he worked at Chemistry with Playfair and Crum Brown , and at Natural History with Allman .
But undoubtedlv the teacher who made most mark upon his mind was Prof. Tait , in whose laboratory he worked for several terms under William Ihomson ( afterwards Lord Kelvin ) , Clerk Maxwell , and with life-long friend , Robertson Smith , who at that time was Demonstrator to Tait and was writing more than one lnathematical paper of note .
Later Robertson Smith became a distinguished Semitic scholar , one of the rs of the 9th edition of the 'Encyclopaedia ' and after a controversy with the Free Church of Scotland a Professor of Arabic in the verSlty of Cambridge , and , finally , University Librrian .
Tait was then , perhaps , at of his reputation and students of various sorts were attracted to his laboratoty ; Sir John Jackson and Mr. Meik , the celebrated ineers , were the physicists , and curiously enough Robert Louis Stevenson was another .
last named , however , had no interest in science and used to beguile his demonstrator , Robertson Snlith , into theological disputes , so dear to all true Scots .
Murray was always a great individualist , and he worked at what ltlterested him with no eye to examinations or evrees , and although in later life he must been surfeited with degrees , as a student he passed by the examinations and the consequent degrees and never graduated .
In the year 1868 , in a spirit of adventure and on the of attended medical classes in , Murray accepted the post of on the whaler " " Jan Mayen He ] Peterhead in , and was away seven months .
He saw a good deal of the Arcbic ions , explored part of Spitzbergen , and landed at least.once on Jan Mayen .
During his absence his grandfather died , and Mnrray arlived home two days after the funeral to that\mdash ; unlike Loudon Dodd\mdash ; he had been cut out of his grandfather 's will with less than the proverbial .
It was the experience he gained on this Arctic voyage and his subsequent wor on the West Coast of Scotland in the years 1869 and 1870 which qualified him for his next post .
's great chance in life came when the Government decided , on the recommendation of the Royal Society , to equip a ship , the " " Challenger for research and to send her round the world .
" " The ' Challenger ' was a spar-decked oOI'vette of 2306 tons , with auxllial'y steam to 1234 horse-power , ) and was well adapted for the scientffic purposes to which she was devoted for four .
The scientific staff was under the direction of Prof. Sir Wyville Thomson , of Edinburgh University , and at first John Murray was not included on it ; but at the last moment , owing to the of one who had been chosen , on the earnest advice of Prof. Tait , John was selected for the vacant post .
Tait especially dwelt upon the fact of Murray 's resourcefulness and readixless , and considered he would be a very useful man to have at hand in case of any difficulties Obituary Notices of Fellows deceased .
with natives or other possible sources of trouble .
It was characteristic of Murra .
to embark on such an enterprise at a moment 's notice , when there was most no time to get togsther his sclentific or personal " " kit But the science of the depths of the sea and the science of oceanography were in these times inchoate .
The first great expedition to investigale the physical , the , the geological , and the biological conditions of the great ocean basins was out in 1872 by Government of this country , then undel Mr. Gladstone , and in that year H.M.S. " " Chalienger\ldquo ; left England with a staff of scientific observers to traverse the salt waters of the lobe .
From that date until the present time no such complete and a staff of scientific observers , helped in every way by the naval ofIicels ( for it was an Admiralty Expedition ) , has left any country for so exhaustive an investigation into the economics of the ocean .
The " " Challenger\ldquo ; Expedition set a standard\mdash ; in fact it practically established a new science , a science of which Sir John Murray was , in a way , the arch-priest .
The " " Challenger\ldquo ; Expedition had predecessors , though on a much smaller scale .
Maury had done a great deal in the way of the study of the ocean , especially in so far as concerrled its depth and the ocean currents .
Dr. Wallich on H.M.S. " " Bulldog surveying the route for the proposed Transatlantic cable , added much to and there were others .
The immediate precursors of the expedition of the " " Challengsr\ldquo ; were a series of voyages made by the " " Porcupine\ldquo ; and " " Lightning\ldquo ; under the scientific guidance of Dr. W. B. Carpenter , Mr. Gwyn Jeffries , and Prof. Wyville Thomson . .
W. B. Carpenter took an immense intel.est in the question of deep-sea temperatures , and read a number of papers to the Royal Society dealing with all exist.ing data accumulated down to 1870 , and he was ons of the leading spirits in stirring up that Society to urge the Admiralty to undertake the " " Challenger\ldquo ; Expedition .
At the Admiralty they were aided by the then hydrographer , Admiral G. H. Richards , who was extremely sympathetic with the work .
As the introduction to the narrative of " " Cruise of the 'Challenger ' " " recites : " " The vast ocean lay scientifically unexplored .
All the efforts of the previous decade had been ected to the strips of water round the coast , and to enclosed or partially enclosed seas .
Great things had certainly been done there , but cerCainly far yreater things remained to be done beyond .
This consideration led to the conception of the idea of a great exploring expedition which should circumavigate the globe , and , if possible , find out the conditions of life at the surface of the sea , at the intermediate depths , and also at the profound abysses of the ocean .
Sir John Murray 's main interest in the expedition was at first physical and geological rather than biological , though he soon acquired a real knowledge of animals , at any rate in so far as they affected.the problems which appealed more nearly to him He was an adept at criticising machines and instruments which plumb secrets of the deep , and as soon as the results of his researches on the Sir lvii bottom of the deep sea had appeared he was recognised at once , and as long as he lived , as the authority on the deposits the floor of the ocean .
Sir John was no specialist .
He had ever the widest point of view of the chenlistry , the physics , the geology , and the biology of ocean , and to him these sciences always had their full value the oblem which he had made his own .
He was constantly devising new lndlng apparatus for bringing up samples of the sea bottom , .
thermometers for testing the bottom temperature , instruments Sor rc the pressure at great depths , and other implements hich have made our kllowledge the depths of the sea accurate and even mlnute .
The ship sailed from , quite at the end of 1872 , with Jotm Murray on board as Naturalist at a of f200 per annum .
From the time of its arture Murray gave especial attention to the various oozes and other deposits which compose the floor of the ocean , and at an early period he came to the conclusion that Bailey , Johannes Muller , Count Pourtales , Krohn , Schultze and Haeckel were right when they attributed certain of the minute at the bottom of the ocean organisms which live nearer the surface .
correlated the contents of the surface tow-net with the results of and found a close relation to exist between the surface fauna of any locality and the deposit which lies be1leath it .
Amongst other anisms he paid much attention to the ious coccospheres and rhabdospheres , as Murray now for the first time called them .
He devised an ingenious method of abstracting these extremel minute organlsms from the sea-water by pieces of fine thread through a bucket of salt water and allowing it to stand for the night .
The examlnation of the threads ext es organ sms en ang ho these or anisms entangled among the strands .
Another unfailing source of supply of these curious , and still imperfectly understood , orgamsms was the stomachs of the Salps , whose pharynx , fine as its walls are , allowed these organisms to pass through its narrow-meshed sieve .
' The " " Challenger\ldquo ; Beport on Deep-Sea Deposits ' by Murray and Renard blished in 1891 .
It was the first attempt to deal with marine deposits was as a whole , became at once the standard book on this subject , a pos ton it occupies to the present day .
It was in sense of the word " " epochmaking The amonnt of research work entailed in the of this monograph was stupendous ; the detailed mlcroscoplc study and chemical examination of thousands of deposit-samples from all parts of the world and from all depths , and of the various constituents contained therein , involved the expenditure of much time and labour .
The terms applied to the various types of deposits , with the exception of Globigenna ooze already in use before the time of the\ldquo ; Challenger\ldquo ; Expedition , vere devised by on board the " " Challenger some of them being subsequently more or less modified in collaboration with llenard .
The nomenclature and classification finally adopted by them have stood ths test of time .
Notwithstanding the numerous contributions to the subject published in the interval , and the many attempts to improve upon either the divisions , lviii Obituary Notices of Fellows deceased .
the terms , or the methods originally employed , " " Challenger\ldquo ; Report renlains the model and upon which all studies of deep-sea deposits are and it appears to satisfy all the demands made upon it .
This is conclusive evidence of the abundant , care , and scientific precision brought to bear upon the study of the " " ChalleIJger\ldquo ; material and of material collected by other ships up to the time of publication .
Murray came to be recognised as authority all matters relating to the floor of the ocPan .
His reputation became world-wide , and his advice was solicited on all hands in connection with the fitting out of expsditions and with the scope of deep-sea researches of various kinds .
Needless to say his extensive owledge and practical experience were freely placed at the service of scientists , and many further additions to our knowledge of the sea and its laws are due to his initiative .
The bottom samples collected by nearly all the surveying ships , cable ships , and raphic expeditions of all nations , found their way to the " " Challenger\ldquo ; Office in for examination and report , and Murray was thus enabled to bring there a nificent collection of marine deposits , a collection which is unique in the world .
One may quote ) an appreciation of his work given by the retic explorer , General Greely .
two years ago in the 'National Geoglaphic zine of , U.S.A. , ' General Greely says : " " Nearly 40 years since , a uished scientist , born on the continent of th , Sir John Murray , of ' Challenger ' Expedition and fame , and one of the eight honorary menlbers of the National Geographic Sociely , considered the mooted extent of South Polar lands and finally outlined their continental form as the continent of Antarctica\mdash ; a fitting and largely accepted name .
This great feat of constructive geography depended on a few score handfuls of oceanic ooze from the South Polar seas and scanty bits of rocks from scattered lands .
Whatever doubts remained as to the accuracy of Murray 's deductions have isappeared since the cumulative discoveries of Amundsen , Borchgrevink , ruce , Drygalski , Gerlache , Larsen , Nordenskiold , Scott and Shackleton Secondly , Sir John did much to thro light upon the origin of coral reefs .
the time of the " " Challenger\ldquo ; Expedition Darwin 's theory of subsidence held the field , but Murray : who proved all thin.gs and held fast only to that which he cotlceived to be true , found occasion to doubt its universal applica .
Ihe boring at Funafuti , an island which was especially selected alike by the opponents and adherents of Darwin and ray respectively as a typical place for investigation , clearly proved that Darwin was in some places ; there is room enough in the world for some coral islands to have been formed by and others by the rising of the earth 's crust .
Darwin self always adnlitted , after the publication of Semper 's memoir , that his sidence t was not of universal applicatio1l .
At the time of Murray 's return from the ' Challenger\ldquo ; Expedition , Sir Archibald Geikie , O.M. , was Professor of Geology at the University of Sir John Murray .
lix Edinburgh , and Murray then attended his lectures .
Sir Archibald helped him in the preparation of the geological section of the " " Challenger\ldquo ; Reports and Murray took an active part in the many excursio1ls which are ever the delight of the student .
Sir Archibald has kindly written the following lines:\mdash ; " " During the preparation of the parts of 'Challenger ' Reports we had long talks over the problems suggested by the observations made on the voyage .
He was always an and estive thinker in connection with these problems .
Nowhere are his inality and acuteness more conspicuous than in his discussion of the origin of coral reefs .
Up to this time , Darwin 's explanation held the field , though a few observers had challenged its universal application .
But when Murray published his views , in which he combated the proofs of vast oceanic subsidence and held that all the types of coral reef could be accounted for without subsidence and even with local elevation , he effected one of the most striking revolutions in iheory which have taken place in our time .
When Alexander Agassiz took up the question and made a prolonged series of expeditions over the coral regions of the oceans he brought a vast mass of fresb material in support of Murray 's opinions .
While I think it quite possible that here and there Darwin 's explanation may be found to hold , I feel tolerably certain , after 's ample succession of explorations , that Murray is right for the general crin of coral reefs over the globe .
" " Then Murray 's laborious researches into the nature and distribution of the materials that are accumulating on the ocean floor and his classification of them broke entirely new ground in the Dynamical section of Geology .
Many a long discussion he , Rellard , and I had on this subject , and it was a delightful experience to watch how , bit by bit , out of the vast mass of materials collected by the ' ' there emerged the clear and impressive generalisations which were embodied in the ' Deep Sea Deposits .
' Murray and Renard , by this remarkable volume , rendered a noble service to Oceanography and to our knowledge of the geologioal processes now in action in the oceans .
" " Murray 's later work on the Scottish lakes is another example of his originality and thoroughness .
He not only plarlned this work with great skill and wide knowledge but , as it proceeded , he threw into the labours of his associates much of his own enthusiasm and devotion During the time that Murray was seeing the " " Challenger\ldquo ; Reports through the press he was engaged with his friend , the late Mr. Robert Irvine , and others , on a series of chemical investigations upon the secretion of carbonate of lime -water by marine organisms and on the part played in this by the waste products given off during their nutrition .
He also worked at the bacteriology of the deep-sea deposits , developing the work of the Russian oceanographers on the sulphuretted bacteria of the lx Obituary Notices of Fellows deceased .
Black Sea , The series of papers thess researches appeared in the Proceedings ' of the Royal Society of Edinburgh .
The third investigation , referred to by Sir Archibald , on which he embarked in his latter years was that of the bath.ymetric survey of the freshwater lochs of Scotland .
The Councils of the Royal Societies of London.and of Edinburgh had urged the Government to undertake this survey .
The Government did not feel that this erprise came within the province of the Ordnancs Survey Office nor within thab of the Hydrographic Department of the Admiralty , but when Murray wanted a thing done , in the long run it generally was done , and he and Mr. Frederick Pullar in 1896 commenced the work and had already published some papers of importance when by the accidental death of Mr. Frederick Pullar by an ice accident in 1901 , the work was interrupted .
His father , however , Mr. Laurencs Pullar , determined tc see the work through , and provided a large part of the funds used for tlns purpose , and in 1902 a staff of assistants was appointed to resume the survey .
For the next four years the surveying work was vigorously carried on , and some 60,000 were recorded from no less than 562 inland lakes .
and observations were also carried on during the two following years , and the results of this , the most careful survey ever out on the inland waters of any country , were published in six handsome volumes in 1910 .
One would have thought that three such problems as Deep-Sea Deposits , the Origin of Coral Islands , and the Fresh-Water Lochs of Scotland , would have exhausted the energies of any man , but Sir John seems to have been tireless in his activity .
Besides editing the 50 volumes of the " " Challenger\ldquo ; Reports , he was the author of the summary of the scientific results of the expedition in two large volumes .
As he records , " " The direction of the whole of the work connected with the publication of the scientific results passed unexpectedly into my hands , and I have done my best under the circumstances to place on permanent record a trustworthy account of the labours of this famous expedition .
It has been my earnest endeavour to complete the publication in a manner worthy of the naval position and the scientific reputation of this great Empire .
Notwithstanding troubles , personal sacrifices and regrets necessarily connected with the work , it has been a pleasure and an honour to have taken part in the explorations and esearches which mark the greatest advance of the ] of our planet since the celebrated hical discoveries of the and centuries He was never tired of exploring the sea , and in 1880 and 1882 he took part in two expeditions to explore the Faroe Channel in H.M.S. " " Knight Errant\ldquo ; and H.M.S. " " Triton He established marine laboratories first of all at Granton on the Firth of Forth , and later on the Clyde at Millport , Cumbrae .
Between 1883 and 1894 he was continuously sxploring the West coasl of Scotland in his small steam yacht " " Medusa which was specially fitted for on oceanographical investigations , and in these he was assisted by Mr. J.-T .
Cunningham , Dr. H. R. Mill , and many naturalists .
Sir John Murray .
lxi He never spared himself , and when he was approaching his birthday he embarked on the " " Michael arsc a steamer no bigger than an ordinary fishing trawler , with a gross tonnage of 226 and with bnt 300 .
engines , to cross the Atlantic on a scientific expedition , the profoundly important of which he published in collaboration with Dr. Johan Hjort in the well-known book , 'Ths Depths of the Ocean .
' He was very capable of getting on terms with sailor men , and had a thorough of the sailor 's mode of life and the sailor 's point of view , itnd , it may perhaps be mentioned , of the sailor 's vocabulary .
Although he became 73 a few days before the tragedy , he seemed , and was , in fact , a much younger man , " " good for at least another 10 years as a leading physician , who knew him well , remarked to me some ago .
He took a great interest in the project for establishing a meteolological on the top of Ben Nevis .
He was Secretary of the Comm ttee which raised the funds , and largely through his efforts Xo000 was soon collected .
He was one of the Directors of the tory until , , it was closed a few years .
For several years he was a scientific member of the Soottish Fishery Board , and he represented the British Government at the International Fisheries and Hydrographic Conferencs in Stockholm in 1899 , and he was President of the Geographical of the British Association in 1899 .
The same year hs delivered the Lowell Lectures at Boston , U.S.A. , and in 1911 he delivered a second lrse of lectures at the ] Institute .
For many years he ngly gave his services as one the Secretaries and Member of the Council and Vice-President of the Royal Society of Edinburgh , and the societies with which he was conl ) ecte are a are almost as numerous as the honours which in later days were showered upon him .
At the time of his death he was President-elect of the Meteorological Conference .
to be held in 1914 at Edinburgh , and was actually in arrangements for a meeting the day before his tragic end .
Sir John held strong views on Education .
He had little for the " " grand fortifying curriculum\ldquo ; of the Classics , but I shall never forget how indignant he was with me when a few years ago I was unable to produce at almost a moment 's notice a tutor for his son , who was to be at once " " a firstclass classic an a lassic and a thorou hl trairled oceanographsr was then reading for the Previous Examination and embarking on a round the world .
Apart from his science , which would have occupied the time of most men , Sir was latterly also interested in commerce .
A bit of material among a collection of deep-sea deposits from the neighbourhood of ClIristmas Island in the Indian Ocean enabled him to nlse that that remote islaYtd contained valuable phosphatic deposits .
The island was quite uninhabited , but obviously a source of wealtl ] , and be the Government to annex the island .
Ultimately they did so , and Sir John obtained a lease of it along with Mr. Ross , of the Cocos Islands .
company was formed to develop its resources , and Mr. C. W. Andrews , of lxii Obituary Notices of Fellows the Deparlment of the British , was granted leave of absence for a year , and in 1897-8 he visited and explored the island , Sir John paying all the expenses and presenting the specimens Mr. Andrews collected to the itish Museum .
The Trustees in 1900 published the resnlt of the researches in a monograph , which is a most interesting record of the ldigenous animals and plants of a lonely oceanic island both before the arrival of civilised man and after .
Sir John himself on several occasions visited Christmas IsJand , and crossed it end to eIld .
Valuable deposits of phosphates were found , water was discovered , clearings were made , a railway laid dowIl , waterworks and piers constructed , aerial haulage erected , and houses builb .
The island now maintains a population of about 1500 , composed of Europeans , Colonials , Chinese , bIalays , Sikhs , etc. , and a flourishing business is being carried on in the export of phosphates .
PIantations of rubber , hemp , .
coconuts , banaI ) , papaws , cotton , etc. , have been established with more or less success .
Sir John always looked upon this development as an indirect result of the scientiflc work of the " " Challenger\ldquo ; Expedition , and an excellent argument for such research work being carried on by the Government .
He knew that His Majesty 's Treasury had received in hard cash within the past 15 years , in the form of , royalties , and taxes , a sum greater than the cost to the mtry of the whole " " Challenger\ldquo ; Expedition , and he recalled how , during the time the money was being annually voted for the issue of the " " \ldquo ; publications , many Members of Parliament objected to public money voted for such a purpose .
To enumerate the various honorary degrees , honorary memberships of Societies , medals and decorations of all sorts that Sir John received would occupy too much space .
more important of them are set out in ' Who 's Who , ' but he always held that they were on the xpedition rather than upon hiinself .
In stature Sir John was short , broad shouldered , with a finely poised , uished head .
His complexion was fair and his blue eyes His was a personality that could not be overlooked in aIlycompaIly .
He was at brusquc , rather domineering , very confident of his own opimon , and he liked to have his own way , and , indeed , he generally got it , but he was most most helpful to his assistants , aItd he spent his wealth largely in promoting the advance of science .
He was ularly straightforward and at times almost blunt , but he did not understand or appreciate the methods of the politician .
If he was once your friend he remained your friend .
ather late in life he married in 1889 Isabel , onJy daughter of the late Mr. Thomas Henderson , of the well-known Anchor Line of Glasgow .
He was a devoted husband and father , and although he had unconventional ideas about the education of his children he was profoundly attached to them , and was never happy unless he had one or other with him .
Sir John Murray was instantaneously killed in a motor accident near on March 16 , 1914 .
A. E. S. lxiii WILLIAM GRYLLS ADAMS , 1836-1915 .
WILLIAM yLLs ADAMS was on ebruary 1 , 1836 , at Lidcot , Laneast , Cornwall , the youngest son of Thomas Adams , who had married Tabitha Knill Grylls , of Budharlick , the .
of a small estate .
Both families had been farmers in the as far back as records can be traced .
The marriage resulted in a of four sons three daughters , the eldest son , born in 1819 , being the renowned John Couch Adams , the discoverer of the planet Neptune .
William Grylls Adams was educated at a private school at Birkenhead , and afterwards at St. John 's he entered in 1855 .
He graduated as Twelfth Wrangler in 1859 , and was elected to a Fellowship at St. John 's in 1865 .
After leaving Cambl'idge he acted for about a year as Vice-Priucipal of the Peterborough Training College , and then , for three years , as a mathematical mastel at .
In 1863 he was appointed Lecturer in Natural Philosophy at King 's College , London , where the Professorship was then held by Ulerk Maxwell .
After Maxwell 's retirement , Adams was , Easter , ] , appointed to succeed him , and he retained the Chair for forty years , till the summer of 1900 Adams early nised the importance for studen ts of Natural Philosophy that they should have the opportunity of taking part in practical experimental wolk , and , as the result of his efforts , a Physical Laboratory opened for the instruction of students at King 's in October , 1868 , As a professor , Adams made teaching his nain occupation , but he by no means neglected original work .
In 1877 he published in the 'Philosophical Transactions , ' in conjunction with his pupil , Mr. B. .
Day , an importanr experimental investigation of the electrical effects } ) roduced by the acLion of on selenium .
And , in 1875 , a paper on the experimental determination of the lines of flow and equipotential surfaces in conductors of two three nensions was chosen as the Lecture before the Royal Society .
In this paper Adams followed up considerably extended the previous work in the same direction of Kirchhoff and Quincke .
He took an active part in the foundation of the Physical Society of London , of hich he was President for the years 1878-80 .
One of his communications to it was an account of a new measuring polariscope .
He was President of the Mathematical and Physical Section of the British Association at the Swansea meeting in 1880 , and was President of the Society of Telegraph Engineers and Electricians ( now the Institution of Electrical Enginesrs ) for the year 1884 .
In his Presidential Address he gave some valuable results of the experimental measulement of the efficiency.of dynamos , carried ont chiefly in cotlnection with the Electrical Exhibition held at the Crystal Palace in 1882 .
He also communicated to lxiv Notices of Fellows SocieCy a paper on the use of alternate current dynamos as motors , chiefiy founded on experimenffi carried out at the South Foreland Lighthouse .
In 1885 he carried out for the Trinity House , at the South Foreland , experimenGs on the comparative value for lighthouse purposes of oil and the electric light .
HG was for nlany years a mber of the Kew Observatory Committee of ths Society ( since amalgamated with the administration of the National Physical Laboratory ) , and was also a membsr of the Board of yiSiGorS of the Royal Observatory , Greenwich .
It was robably his connection with these bodies that led to his giving special attention to Terrestrial Magnetism .
He wrote several papers on the simultaneous disturbances of the netic elements at different parts of the earth 's surface .
In 1896 he issued a volume in which were collected all the scientific papers published by brother John , who had died in 1892 .
This was followed in 1901 by a second volume , edited in conjunction with Mr. R. A. Sampson , the papers , so as they could be made available which brobher had left in matluscripr .
He was elected a Fellow of the Society in 1872 , and served on the Council from 1882 to 1884 and from 1896 to 1898 .
As a young Adams was an enthusiastic mountaineer , and became a member of the Alpine Club as early as 1864 .
Personally , he was a man of the greatest geniality , and full of good-natured fun .
Many must have pleasant memories of the kindly hospitality and hearty welcome which he and Mrs. Adams offered to their many friends at their house in Campden Hill Square .
After resigning his Professorship he went in 1906 to live at Broadstone , Dorset , but continued for some time to come to town occasionally for Boyal Society and other meetings .
For the last few years , however , his failing memory him to give up more and more completely all public engagements .
He died at his at Broadstons on Apri110 of the present year ( 1915 ) .
In 1869 he married Mary Dingle , of Lewannick , who , with a daughter an two sons , snrvives him .
G. C. F. H. AMAGAT , 1841-1915 .
EMILE AMAGAT was born at Berri ( Saint Satur ) in 1841 .
After a sound preliminary education he studied physics for several years at the Sorbonne in preparation for the examinations for the higher teaching posts .
After acting some time as assistant at the College de France , he held ths Professorship of Physics at Fribourg in Switzerland for a few years ; he was then elected to the Chair of Physics at the Catholic University of Lyons , where he remained until lS92 .
He then returned to Paris , where at first he had no definite post , but he was aftel.wards made a teacher and , later , an examiner at the ]cole Polytechnique ; he carried out duties of the latter post until his death .
was a simple , modest , and unassuming man , but he possessed vigour and ellthusiasm for work , and his fearlessness in attacking the most serious experimental difficulties was rewarded by magnificent results .
He was not only a brilliant experlmenter , but a most ingenious and ) constructor , nearly all the apparatus he employed having been made either himself or by a skilled anic whom he had trained .
Amagat himself very lruly states that under no other conditions would it have been possible for him to cal.ry out his researches successfully .
Amagat 's great conscientiousness is well shown by incident , the parciculars of which have been furnished very kindly by Gtllllaume .
Iu the voce examination for entrance into the cole Polytechnique , two-thirds of the candidates are usually rejected , and a chano of exat1linels during the process of selection would be liable to produce unfair results .
While holding this examination Amagat had a slight apopleptic stroke , resulting in partial paralysis , he insisted on continuing the work , and had a bed placed near the examination hall , so that , when overcome by fatigue , he could retire and rest from time to time .
During his period of study at the Sorbonne Amagat made a study of 's celebrated memoirs , the importance of which greatly impressed him , and between 1867 and 1871 , as a preparation for his esis for doctorate , he carried out his first cotlsiderable research on the influe , nce of temperature on the deviations from Boyle 's law , and on the coefficient of expansion ases under normal pressure .
In the conrse of the next six years Amagat studied the of liquids at tsmperatures between and 10 C. and at pressurss from 1 to 40 atmospheres .
He realised , however , the importance of greatly sxtending the range of pressure in ating the properties of gases , and between 1876 and 1890 he carried out the wondsrful series of esearches with which his narne will always be associated .
The range of pressure was extended in both directions .
Between 1876 and 1882 , making use of a differential manometer , Amagat determined the lxvi Obituary Notices of )deceased .
compressibility of hydrogen carbon dioxide from the atmospheric pressure to 2 or 3 mm. of mercury , while with he made measurements down to mm. At these lowest pressures Amsgat concluded that the gases followed Boyle 's law within the limits of experimental err.or .
Determinations of the compressibility of rarefied are very ]iable to errors , the data obtained by a number of other investigators being highly dictory , but the accuracy of Amagat 's resuIts has been amply confirmed by those of Lord , who made a most remarkable extension of the range of low pressures .
As regards pressures , Amagat determined the compressibility of nitrogen up to 430 atmospheres at temperatures from to , with open steel manometer tubes containing merctlry .
In order to support these tubes , he first made use of a tower of the church of Fourviere at Lyons , and was thus able to take up to 80 atmospheres .
A much greater range , with greater consCancy of temperature , was afterwards attained by attaching the tubes to the side of a mine shaft in the SaintEtienne Colliery at Verpilleux .
The manometer consisted of of steel screwed together , terminating in a glass tube , to allow of the height of the mercury read directly .
Having now determined the deviations from Boyle 's law in the case of nitrogen , Amagat was ) to employ a nitrogen manometer in the laboratory , and to determine the compressibility of oxygen , air , methane , ethylene , carbon monoxide , and carbon dioxide up to a of 430 atmospheres .
But Amagat was not satisfied with this step in } , and in order to measure still pressures he constructed in 1886 a maIlometer on the principle of that of Gally-Cazalat .
It may be described as a reversed hydraulic press , the pressure being measured by a column of mercury , the of which bears same ratio to that of an open column corresponding to the actual pressure as the cross-section of the small piston does to that of the large one .
The original instrument was very but by the introduction of important modifications it was found possible to all leakage and to obtain sufficiently accurate measurements of pressures exceeding 3000 atmospheres .
The glass volume tubes were enclosed in strong blocks of metal and were subjeoted to pressure both externally and internally , so as to avoid rupture ; of volume were taken by the method of electrical contacts recommended by Tait .
This method was found unsuitable for temperatures than , and could not be when many readings close together had to be taken , as , for example , in the neighbourhood of the critical point .
A very genious method was , however , devised by which direct readings could be taken , and was elnployed for pressures up to 1000 atmospheres and for temperatures as as 26 C. The gases examined by means of these two forms of apparatus were oxygen , fiitrogen , air , carbon dioxide , and vlene , and the comE .
H. Arnagat .
lxvii pressibility of the following liquids was also determined : Water ; ethyl , methyl , propyl , and allyl alcohols ; acetone ; ethyl chloride , bromide , and iodide ; carbon disulphide and phosphorus trichloride .
The researches relating to the compressibility of fluids necessarily involve determinations of the deformation of the vessels and of the absolute compressibility of mercury .
Amagat first verified the formulae relating to elasticity in the case of circular cylin ders with plane bases , and determined the coefficient of Poisson and the coefficient of elasticity for glass , flint glass , steel , copper , brass , metal , and lead , and he then carried out determinations of the compressibility of glass and flint glass up to 2000 atmospheres at , and , by a method somewhat resembling that employed for the measurement of cubical dilatation by means of linear dilatation .
In ord.er to determine the absolute compressibility of meroury employed long tubes of glass and of flint oolass filled with mercury , which he compressed both internally and externally in order to ascertain the apparent compressibility .
The absolute compressibility was then calculated by difference .
The abnormal behaviour of water in many respects led Amagat to make a special investigation of this substance , and he found that the point of maximum density was lowered by the pressure , under a pressure of less than 200 atmospheres .
Amagat also made important investigations of the efl'ect of pressure on the freezing points liquids ; in the case of tetrachlorethylene the ezing point was raised from to by the pressure from 210 to 1160 atmospheres .
In tabulating his results Amagat does not give the volumes occupied by a gramme , but by such a mass of each substance as would occupy unit volume in the gastous state at normal temperature and pressure .
The general results are clearly shown by graphs in which the co-ordinates are and P. the more interesting points brought out by Amagat may be mentioned the following:\mdash ; 1 .
For hydrogen isotherms , at all the tempst.atures studied , are straight parallel lines ; hence , where and are constants .
2 .
For all the other substances the value of falls with increase of pressure to a minimum and then rises again , the fall becoming more and more abrupt as the temperature is lowered .
The form of the isotherm , starting from the minimum , is slightly curved .
3 .
Straight lines of equal volume are intersected at equal distances by the isothermals , drawn at intervals of , in the case of both carbon dioxide and ethylene .
In other words , temperatures as abscissa and pressures as ordinates , the isochors are straight lines , or .
This relation was discovered independently by Barus and by Ramsay and Young ; it is probably very nearly but not absolutely true .
lxviii Notices of Fellows deceased .
4 .
The locus of the values of is a parabola with respect to the horizontal axis .
The coefficients , and , were examined in great detail .
When retur1led to Paris in 1892 he was unable to obtain the use of a laboratory in which he could continue his experimental vestigations , and the last 21 years of his life were spent in compiling and co-ordinating the immense number of numerical data from his previous work .
The results were published in a brochure entitled , " " Notss sir la Physique et la Thermodynamique Among the more important subjects dealt wibh may be mentioned:\mdash ; ( l ) The specific heat ases , ( 2 ) the internal pressure of fluids , ( 3 ) the states of matter .
his own results with bhose of Prof. Joly on the specific heat of carbon dioxide at constant volums between and 10 under a pressurs of about 100 atmospheres , he was able to calculate the ratio of the specific heats for this substance and to show the great variation of the ratio for pressures between 50 and 100 atmospheres at .
Hs also proved the discontinuity of the specific heat during change of state from liquid to saturated vapour .
2 .
Amagat arrived at the conolusion that two functions and , starting from sufficiently great molecular distances ( greater in the latter case than in the former ) , are inversely proportional to the square of the volume .
and that when this law is followed the inte1molecular attraction proportional to the fourth power of the distance .
In the course of this research he was led to an exact and unexpected method of calculating the value of the absolute zero point .
3 .
By a simple and ingenious method of projection was abls to prove the approximate correctness of the law of corresponding states without the necessity of ascertaining the actual critical constants .
He ) rrived at the conclusion that , at any corresponding points atever , the value of is ( approximately ) the same for all substances .
The great value of was nised both in France and in this country .
On the death of Alfred Cornu , Amagat was elected to take his place in the Academy des Sciences , and he was awarded the Prix La Caze by that body .
He was at one Cime president of the Societe de Physique , and was afterwards made an honorary member of the Society .
He was a Foreign Member of the Royal Societies of both London and Edinburgh .
's work was inspired by that of Regnault , and he may be regarded as the great successor to that great physicist .
S. lxix HENRY WILLIAM LLOYD TANNER , 1851-1915 .
THE father of Henry William Lloyd Tanner was Prof. Henry Tanner , F.C.S. , .
a well-known writer on Agriculture and Agricultural Chemistry , who served on one or more Boyal Commissions .
The son was born at Burham Kent , on February 17 , 1851 .
He was t , alkative about himself , even at home , so that few facts are known about his .
His school was Bristol School , which has turned oul many an able mathematician , and has supplied Oxford in University\mdash ; with a considerable number of strong men in learning , education and affairb .
He must have left school young ; for when in October , 1868 , he came up to Jesus College , Oxford , as Natural Science Scholar he had already spent a year at the Royal School of Mines ( where he had formed a that was used against him later ) and had secured his diploma there .
At Oxford he soon showed his bent for Pure Mathematics , and research therein .
His mathematical tutor was Mr. John , an orlglnal writer on Elliptic unctions , who happily still lives , and one can how such a tutor welcomed and stimulated such a pupil .
Tanner obtain ined first class in Mathematical Moderations in 1870 , one in the Final School of Mathematics in 1872 , and one in Natural Science in 1873 .
It is a little surprising that he let others carry off the higher ) rizes open to nahcal students , Fellowships , and the Junior and Senior Mathematical Scholarships ; but the days were those of examination for everything , and his is not the only case one can remember of a man with a pass on an a gen us a enius for investigation who did not allow to himself tha that the circumstances of the moment called for patient application to uncongenial as well as congenla tasks , and for the cultivation of examination Moreover , he had strong interests outside Mathematics , being a keen muslclan , a reader of fine literary taste , a Union debater .
He was Librarian of the Union in Easter term , 1873 , ucceeding Mr. E. W. B. Nicholson , aflerwar ds Bodley 's Librarian , just between the times at which present Prime Minister was Treasurer and President .
After leaving Oxford he is bslieved to have been a schoolmaster for a little while , but was soon appointed Profe.ssor of Mathematics and Physical Scisnces at the Royal Agricultural Collegs , Cirencester .
While there , his fine work on Differential Equations proceeded vigorously , and it looked as he might long enjoy in the College congenial and not too burdensome with sufficient leisure for research .
But there seem to have been elements of unhappiness in the Institution .
' strike\ldquo ; of members of the staff connected with a case of alleged dismissal termiuated in a victory for the employers , and Tanner 's resignation was accepted .
Finding himself without secure means of livelihood even for one , he marked the occasion by taking.eryVOL X.small cottage for two , and a wife , Miss Helen Aliceh Edith lxx Notices of Fellows Saunders .
C'ommon may condenin the haste of this , but the results were vel.y happy .
He could protect others , but needed even more than most men a protector himself .
Mrs. Lloyd Tanner was musical like her husband , like him highly educated and widely read , yet altogether womanly , and she proved a most devoted wife .
Often joining her husband in attention to his responsibilities , she oontributed in no small measure to his later success .
Her death , in 1902 , after a long and painful illness , lefb him an exhausted and failing man .
After the fiasco at Cirencester he held for comparatively short periods masterships at Sherborne and at his own old school , Bristol .
But in 1883 University College of South Wales and Monmouthshire was fou.nded at Cardiff\mdash ; years had yet to elapse before it became a constituent of a new , and now flourishing , University of Wales\mdash ; and he was appointed to the Chair of Mathematics and Astronomy in it , thus entering on a settled life of vast usefulness .
While lasted , he retained the Chair .
During the last illness of Prof. J. Viriamu Jones , and the interregnum which followed its lamented termination in 1901 , he directed the College as Acting Principal with marked efficiency .
Finally , when all too soon , in 1909 , he could work no longer , the Council made him Emeritus Professor on retirement .
As he was taking possession at Cardiff painful incidents occurred .
The word went round among certain good Welshmen that he was a secularist , or friend of secularists , whose influence on students might be anti-religious ; and some effort was made to upset his appointment .
Tanner bore his sensitive- ness in private .
The man who at Cirencester , in wild indignation because of a real or fancied to another , had been insubordinate , and had suffered orJi it , now at Cardiff , threatened with a rrievous w himself , said nothing , but possessed his soul in patience the storm to pass .
And it did pass .
Very soon all knew that professor no firebrand , but the most lovable and sympathetic of men .
Testimony to the energy and foresight with whioh he set about the task of courses of study , and to the inspiring character of his own is abundant .
Equally abundant , and no less strong , is the testimony to his unfailing courtesy and good humour , to his happy faculty of securing affection from colleagues and generabions of students .
In the early days of the College\mdash ; before University dignity was secured\mdash ; there can have been little scope for the exercise of his gifts in higher study .
The requirements must have been for the systematisation of unambitious teaching and for methods suitable to new armies of raw recruits .
No exercise of patience was too great for him .
I could quote letters from those who worked with him full of warm admiration for his successful devotion , in class and out of it , to the interests of the college , of student life , and of the individual\mdash ; letters all free from a single word of disparagement .
I could give at length the resolution recently communicated by the Council of the to his family , in which it is shown how strong a sense prevailed in higher Henry Lloyd lxxi circles that he had been one of the most highly valued members of the Staff , that he had taken a very deep interest in the welfare of his students and in the general social life of the College , and that he was regarded with warm admiration by colleagues and students alike .
But the one appreciation which I choose to give verbatim is that of a peccant undergraduate , taken from comparative estimate clearly not intended , and not altogether suitable , for publication:\mdash ; ' ' But call on old Tanner about a cut lecture , and his smile fairly shouts , ' Well , if it my old pal Jack Owen , ' and he treats you as if you 'd just got a First , and never rags you about the lecture .
But somehow when he 's finished.you have interred a vow that whatever else you may cut in future it sha n't be Maths .
And it isn't.\ldquo ; The " " old Tanner\ldquo ; in the above is the " " old\ldquo ; of endearment ; and undoubtedly dons in general are looked upon as really old by raduates perhaps ten years younger than themselves .
All the same , Tanner never looked The light in the eye shone from an apparently care-worn face quite early ; and as care grew and strength failed that began to need kindling by the of a friend to be encouraged .
He was elected a Fellow of the Royal Society in 1899 ; and was also an Associate of the Royal College of Music , a Fellow of the Boyal Astronomical Society , and a member of the London Mathematical Society .
This last-named society published most of the more important among his mathematioal writings .
He was an early recipient of the degres of Doctor in Science at Oxford when rrees in recognition of eminence in research were instituted .
was an excellent man of business\mdash ; of public and altruistic businsss at any rate .
His mark has been left in the organisation of the mathematical icula of the Welsh University .
He did not go out of his way to seek administrative work , but when it came his way he undertook it cttnd did not spare himself in rying it out .
His valued services as Acting Principal of the College for a time have already been referred to .
In 1891 he earned golden opinions by his discharge of the onerous duties of a Local Secretary on the occasion of the meeting of the British tion at Cardiff .
His services to education\mdash ; as to the value of which he was an enthusiast\mdash ; were not confined to the College and University .
For several years he was on the Glamorganshire Governing Body for Intermediate Schools , working thereon with keen interest , and being greatly missed when he retired from it .
He was a Governor of the Penarth County Schools .
In another field mention must be made of his efforts for the encouragement of Music in Cardiff .
For many years he was a esident and active supporter of the Cardiff Musical Society .
Soon his wife 's death in 1902 it became that he had overGaxed his powers .
Failure in bodily strength began to be accompanied by lapses of and dazed intervals in the midst of effort .
His amazing power of concentration was gone , but not his devotion to duty .
He gled on , being with difficulty kept from the lecture room even when acutely ill ; but in 1909 lxxii Obituary Notices of Fellows deceased .
it became clear that his retirement from active work could no longer be postponed .
There were difficulties , financial as well as other , both for his family and for the College : the days of the Federated Superannuation scheme for Universities and University Colleges were not yet .
Self-denial had to be exercised all round ; and a small Civil List pension was secured for him .
Thus it was made possible for him to end his days in simple comfort .
His life in retirement was quiet and uneventful , with nothing pairlful about it but progressive decay .
On hlarch 6 , 1915 , hs passed away peacefully at Exeter .
He leaves two sons and a daughter .
The elder son , Evelyn Lloyd Tanner , 8th Wrangler 1903 , First Class Natural Science Tripos 1904 , has held important posts in the Indian Civil Service , and is , for the moment , .
trooper in the Bellar Light Horse , straining in vain for permission to go on active service .
( Tanner himself had been a keen volunteer in his , days , and was a fine " " shot The second , Percy Lloyd Tanner , who has adopted a business career , has my best thanks for much help given me in compiling these notes .
The daughter , Cicely Marguerite Lloyd Tanner , has inherited her parents ' love for music , and may make it her profession , though now she has devoted herself to " " Red Cross\ldquo ; work .
Prof. Lloyd Tanner 's contributions to mathematical science , omitting some that are comparatively trifling , form two distincC series .
There an early series on Differential Equations , more particularly on Partial Equations of the second and third orders with intermediate integrals , and a later series on the Theory of Numbers , more particularly on Problems of Cyclotomy .
Both series show vigorous penetration , and both artistic refinement .
The " " push and go\ldquo ; are , however , more marked in the former series , and the beauty and taste in the latter .
The papers on Differential Equations belong to the years 1875-80 , and are to be found in vols .
7-11 of the 'Proceedings of the London Mathematical Society , ' vol. 16 of the ' Journal , ' and vols .
5-7 of the ' Messenger of Mathematics .
' Some ( probably the least important ) deal with Pfaff 's Theorem and Pfaflian Expressions , but most of them with questions of Solution of Equations of the second and higher orders in two , and more than two , independent variables .
For a number of the more conspicuous results obtained , reference may be made to the sixth volume of Forsyth 's ' Theory of Differential Equations .
' One paper , " " On the Transformation of a Linear Differential Expression stands in somewhat close relation to earlier work of Grassmann 's , which was no doubt unknown to the writer ; but in general it may be said that Tanmer in this series of researches did pioneer work in a department of investigation which was neglected , not onJy in England , but mostly elsewhere at the time .
He makes some reference to very instructive work by Imschenetsky ou the theory of partial equations of the first and second orders ; but he went far beyond that work , opening up some new ways for equations of the second order , and proceeding to those of the third order .
For equations of the second order he obtained many results which , expressed in rent form , were much later included in a more complete Henry William Lloyd Tanner .
lxxiii investigation by Gosserat , for which see the fourth volume of Darboux 's ' Theory of Surfaces .
' There is no reason to think that Gosserat 's work was not completely independent of Tanner 's ; but men less self-effficing than the latter\mdash ; and perhaps the latter himself , had his full remained to him\mdash ; would hardly have refrained from pointing out a claim to priority .
As regards equations of the third order , which admit of integrals of lower order expressible in finite form , Tanner 's investigations were most valuable ; and some are standard even now .
It is very remarkable that a man who was producing work of such quality in steady stream should stop suddenly .
The advent of exciting times in his life , followed by imnlersion in absorbing duty , may have had to do with this .
But , as affording another explanation , I remember the importance which he attached to keeping in touch with the current thought of the day .
He had been applying , very brilliantly , the formal methods of the older analysis ; and meanwhile others were doing work with modern weapons .
Before further he must allow himself time for a profound study of modernism .
Once in congratulating me , with the most graceful kindliness , on a piece of formal work of my own , he was too naive to keep me from being aware that what he really meant was : " " Twenty years ago this would have been charmlIlg ; but ; it not rather late for the sort of thing now ?
\ldquo ; I am pretty sure thab he had once reasoned in this way with himself .
However , he never returned with new tools to the work of his old love .
During his first busy years at Cardiff his writings were infrequent and minor .
About 1886 the later period of his productive activiGy ; and the subjects attended to now were the purest of the in Mathematics , those studies about number whose difficulties and beauty enchain and fascinate an artistic intelligence when once they have allured it , but which leave unaffected except by wonder the man who pursues Mathemacics as knowledge for practical use .
His chisf papers of the new series are spread over vols .
lS-27 of the 'Proceedings of the London Mathematical Society .
' All have more or less bearing on what is known as Cyclotomy .
The nth roots of unity are arranged in sets or " " periods \ldquo ; -basic periods if is prime .
Tanner submits the properties of periods , mono-basic and other , to searching examination .
It is probably impossible in few words\mdash ; and I certainly have nob the necessary grasp on the theory\mdash ; to state clearly the nature and extent of this examination .
It is evident , however , that the group-notion was used with great cleverness , and that notable advance was made in methods for the formation of equations satisfied by of periods .
ious labour must have been required in the detailed analysis , as , for instance , reference to the paper ( ' Proc. Lond. Math. Soc vol. 24 ) on " " Complex Primes formed with Fifth Roots of Unity\ldquo ; will certify .
On p. 224 we read : " " To give some idea of the facility of the method from the calculator 's point of view it may be stated that the determination of the prime factors of two primes selected at random in the second million VOL. XCI.\mdash ; A. lxxiv Notices of Fellows 1562,051 and 1,671,781 ) was completed in three hours After this , ( viz. ' of results for about 310 primes , results pp. 256262 comes a full table of resu ts previously obtained by Reuschle of some service in respect of the first 40 .
He never finished all he had to say on these subjects .
Very stiortly befote his powers of concentration to fail he spo ke to me of surelegant and comprehensive conclusions at be ransacked hich he was arriving , putting aside the natural notion that the mono-basic must rst and the poly-basic thus led up to .
These conc us ons were lusions were to remain unrevealed to others .
E. B. E. \mdash ; .
|
rspa_1915_0046 | 0950-1207 | The influence of gases on the emission of electrons and ions from hot metals. | 524 | 535 | 1,915 | 91 | Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character | O. W. Richardson, M. A., D. Sc., F. R. S. | article | 6.0.4 | http://dx.doi.org/10.1098/rspa.1915.0046 | en | rspa | 1,910 | 1,900 | 1,900 | 3 | 141 | 3,738 | http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1915_0046 | 10.1098/rspa.1915.0046 | null | null | null | Tables | 34.192799 | Thermodynamics | 19.884278 | Tables | [
4.135152339935303,
-63.069217681884766
] | ]\gt ; The Influence of Gases on the mission of Electrons Ions from Hot Metals .
By O. W. DSON , D.Sc .
, , Wheatstone Professor of Physics , University of London , King 's College .
( Received April 22 , 1915 .
) As is well known , the saturation density of the electron currents from hot bodies can be represented accurately by the formula , ( 1 ) where is the absolute temperature and A and are constants characteristic of the substance .
An equation of type ( 1 ) has been found to represent the currents not only from pure metals in a good vacuum but also when a aseous atmosphere is present , provided the constants are given different values .
Thus in general A and are functions of the nature and pressure of the surrounding gas as well as of the hot metal .
They are independent of within the limits of temperature in which the formula is valid .
In the case of pure metals there is evidence that the formuIa is valid at all temperatures .
In certain cases the constants A and are very sensitive to minute changes in the nature and pressure of the surrounding gaseous atmosphere .
This is well shown by experiments on tungsten , where a slight lrace of hydrogen changed the value of A by a factor of about and that of from oC .
to oC .
In the case of platinum heated in an atmosphere of , H. A. Wilson has shown that A and are functions of the pressure of the hydrogen , and that the changed values of A and are subject to the relation , ( 2 ) where are oonStanLS .
In other words , the changes in the constants A and caused by the admission of hydrogen are always of such a character that the change in A divided by the change in is invariant .
In the present paper it is shown that a similar relation holds for the changes in the values of A and for sten which are caused by traces of various yases .
In fact it seems probable , in reneral , that when the emission of ions from metals is affected by the presence of gases , the changes in A and are subject to a linear relation between and A. There is evidence that the relation is independent of the particular gas used to ' Phys. Rev vol. 2 , p. 460 ( 1913 ) .
'Phil .
Trans , vol. 208 , p. 247 ( 1908 ) .
Influence of Gases on Emission of Electrons Ions .
525 effect the changes , and that the law applies to the emission of positive ions as well as electrons from hot metals .
In view of the complexity of the phenomena which may occur when metals at a high temperature are immersed in a gaseous atmosphere it seems unlikely that such a simple law will be exact for all the small changes in A and which may arise ; but the evidence is strong that it covers the main features of the phenomenon .
Let us consider the case of tungsten first .
Langmuir ( loc. cit. ) has measured values of A and from this substance both in the best attainable vacuum , similar to that in a Coolidge tube , and in a vacuum to which small amounts of various gases have been added .
The data obtained are shown in the following Table:\mdash ; The conditions were with the time in some of the experiments , so that in such cases the data are only oproximate .
It is clear from a glance at the fures for hydrogen that A and are not definite functions of the pressure of this gas .
The in the constants apparently caused by hydrogen are probably caused by some other substance introduced with it .
Langmuir , who takes this standpoint , attributes them to traces of water vapour .
Although there is no relation between the values of either A or and the pressure of the gas which appears to determine these values , there is definite relation between all the values of A and given in the Table .
It will be noticed that the corresponding values of A and always diminish or increase together .
Thus a high value of A always corresponds to a high value of , and vice versed .
In fact , no matter which of the gases tested determines the values of the constants A is a linear function of .
This is clearly shown in fig. 1 , in which A is plotted against the corresponding value of .
The figure contains all the data given in the Table , and some others in addition .
In fact , it contains all the Prof. O. W. Richardson .
Th - Influence of Gases on Considering all the points simply as they stand , the divergence from the line drawn is considerably greater than the corresponding.deviation of the slen points shown in fig. 1 .
The agreement is , however , very much improved if the conditions affecting the different determinations , which are by no means of equal value , are ently considered .
Thus Nos. 10 and 11 are believed to be affected by the occurrence of ionisation by collision .
This makes A too big without .
Again No. 13 is believed to be cted by lack of saturation .
If the currents are fairly small fractions of the saturation ] A will be too small and unaltered .
These objections to Nos. 10 , 11 , and 13 were pointed out when the original data were published .
On these grounds we should expect Nos. 10 and 11 to be above and No. 13 below the line , as in fact is the case .
No. 9 is a very old observation and its distance from the line might be due to a number of causes .
No. 5 is deduced from a small number of determinations of very small currents which extend over a short stretch of temperature ; so that the possible error of measurein this case must be quite considerable .
No. 12 is given by Langmuir as only a preliminary determination , and further investigation may change its position considerably .
As ards Nos. 7 and 8 there does not seem to be any obvious criticism one can offer ; but they are not very far from the line , and it is possible that the true position of this should be a little to the right of that in which it has been drawn .
We see then that in platinum as well as tungsten there is a correspondence between the values of A and , so that large values of A correspond to values of , and conversely .
There is , however , one important difference between the two metals .
In tungsten the pure metal has small values of the constants , which are increased by gaseous contaminants , whereas pure platinum appears to be characterised by high values of the constants , which are reduced by the presence of gases .
It is possible that traces of are responsible for all the changes observed with platinum , but that is a point which I do not wish to discuss in the present paper , the object of which is to consider corresponding changes in A and without reference to the processes causing them .
Since the changes observed with platinum and tungsten are similar , but in opposite directions , it is natural to try to attribute them to similar causes in opposite senses in the two metals .
of the Effect of Gases on the Emission stants .
The theory of the efflct of hydrogen on electron emission from platinum has been considered at by H. A. Wilson .
* In the present paper I * 'Phil .
Trans , vol. 208 , p. 247 ( 1908 ) .
the Emission of Electrons and Ions Hot Metals .
529 shall consider the effect of contamination on the emission constants general from a somewhat different standpoint .
It has been found empirically that the emission from pure metals either in a vacuum or in equilibrium with a gaseous atmosphere can be represented by the formula .
( 1 ) There is a certain amount of doubt about the exact value of the index of in the factor in this formula , as the particular value may be replaced by any number between and without appreciably affecting the agreement of the formula with the experimental numbers , provided somewhat different values of the constants A and are taken .
We shall , however , disregard this point and assume ( 1 ) to hold , as the values of the constants we are dealing with are based on the assumption that ( 1 ) is valid .
In addition to equation ( 1 ) there are a number of related equations*which may be deduced by the application of the principles of thermodynamics to electron emission .
In considering these it is more convenient to deal with the number of electrons per cubic centimetre of the space outside the body which are in equilibrium with it at the temperature , instead of the saturation current .
These quantities are related by the equation , ( 3 ) where is the charge and ?
the mass of an electron and is Boltzmann 's constant .
The only assumptions involved in the relations referred to are ( 1 ) the reversibility of the phenomena , ( 2 ) the two laws of thermodynamics , and the applicability of the law of a perfect gas to very attenuated electron atmospheres .
The results must , therefore , possess a very high degree of certainty .
The proofs of these relations hitherto given only apply to the case in which gases are absent .
It is thus necessary to modify them somewhat in order to obtain results which will be valid when gases are present and may affect the emissions either by reacting with the electrons or the surfaces .
For purposes of calculation a contaminated surface may be regarded as a pure surface covered with a contaminated layer of composition to a small but finite thickness .
This will probably give a fair representation of the unless the layer of actual contamination is excessively thin .
In that case the superficial properties of the contaminated material might become somewhat indefinite .
The proposed treatment practically amOunts to considering the pure metal as being covered with a thin layer of another metal having the properties of the contaminated *Cf .
The Electron Theory of Matter , ' Chap. XVIII , Cambridge University Press , 1914 .
space outside .
In carrying out the calculation a virtual displacement may be imagined to be produced in a closed cyiinder filled with the gas under consideration by a piston permeable to the gas but not to the electrons .
The base of the cylinder consists of the emitting material .
With this arrangement the only work done is caused by the partial pressure of the electrons on the piston .
On account of the integral in the exponent of in ( 4 ) this relation does not appear to be ] adapted to a discussion of the changes , in A and in equation ( 1 ) , which are caused by gases .
Another disadvantage of ( 4 ) is that it give in terms of the value of for the contaminated material , and this quantity is not directly accessible to experiment .
Another relation involving the specific heat of electricity in the metal is given in the 'Electron Theory of Matter , ' p. 448 .
The proof may be extended to cover the case when gases are present by covering the bodies A and with a definite layer of the contaminated material in equilibrium with the gas , as already outlined .
The difference of potential now includes the contact potential between the two contaminated surfaces .
Before equalising the potentials in the manner described in the calculations referred to , the electrons are separated from the gas by drawing them through a semi-permeable membrane which stops the gas .
A loss of energy , per electron , may be posed to be involved in process without affecting the final results , which are thus valid even if the electrons enter into combination with the gas molecules .
The only other change in the calculation is the introduction of the change in the energy of an electron on passing the interface between the contaminated and the pure surfaces , which corresponds to the Peltier effect .
Proceeding , except for these changes , in the manner of the calculation referred to , , ( 5 ) where is a universal constant , is the ratio of the two specific heats for Ghe electron gas , is the energy change at libsration of an electron from the material , is the energy change when an electron passes the Emission of Electrons and Ions from Hot .
531 from the pure to the contaminated material and corresponds to the Peltier effect , is the electronic charge , and is the specific heat of electricity for the pure material .
If we consider another temperature , , for which the values of the corresponding quantities are denoted by dashes , ( 6 ) so that .
( 7 ) But by a known thermo-electric result , ( 8 ) where is the specific heat of electricity for the contaminated material .
Thus .
( 9 ) From hence , by comparison with ( 9 ) , It appears from this that if for a contaminated material ries considerably with temperature , the specific heat of electricity in such a material may be expected to have abnormally large values .
If and are the values of these quantities for the pure material at temperature , ( 12 ) is obviously zero , but the equations are more symmetrical if it is retained .
By comparison with ( 11 ) , ( 13 ) By a known result , is equal to where is the contact potential difference between the pure and contaminated stlrfaces .
Thus , if and are the saturation currents corresponding to and .
( 14 ) This result may be obtained more directly by considering the equilibrium of electrons in an enclosure containing a rod of the metal in question whose sides are protected by an .
insulated covering , the ends only being free .
The enclosure is divided into two halves by a semi-permeable membrane , which stops the gas but not the electrons , one of the two free ends being in each half of the chamber .
The method which has been 'Electron Theory of MatteI ; ' p. 456 .
532 Prof O. W. Richardson .
The Influence of Gases on adopted , however , brings out a number of additional relations that the whole treatment is self-consistent .
Since we know from experim that is expressed accurately by we have lvhere , is half the number of calories which are equivalent to the work if is the number of molecules per gramme-molecule .
In ( 15 ) A and are constants , but , which is proportional to the change in the contact potential difference caused by the gas , may in general be a function of the temperature as well as of the pressure of the'gas .
Suppose that in the of temperature under consideration is represented by , ( 16 ) where the coefficients are functions of the pressure of the gas , then But since is still of the form , where and are constants , it follows that all the coefficients and are negligible ; so that If and denote the values of A and when gas is present , or , ( 19 ) and or .
( 20 ) To satisfy the linear relation demanded by figs. 1 and 2 it is necessary that should be a positive quantity which is independent of the pressure of the gas .
If , as appears on the surface , this ratio is independent of the nature of the as well as the pressure , the generality of the constancy of is still further extended ; but it is possible that all the effects with a iven nletal which are apparently caused- by various gases are really due to traces of some particular which is present as an impurity .
This does not seem probable in the case of tungsten but it cannot be denied that it is possible .
Thus and have opposite and for a given metal are in a constant ratio .
This ratio is nearly the same , and may be exactly the same , for both metals .
The values of given by figs. and 2 are : for tungsten , and for platinum .
.If we denote the value of this ratio by we may write equation ( 18 ) .
( 21 ) For the temperatures at which the experiments have been made is less than 1 for both metals ; so that the of is that of .
For tungsten the Emission of Etectrons and Ions from Hot .
533 is positive ; so that is positive at these temperatures , and the effect of gaseous amination should be to make the metal electronegative to pure tungsten .
The actual change in the contact potential difference , compared with the pure metal , should be given by : volts .
( 22 ) The data taken from fig. 1 on substitution in the formula make the extreme value of at 2000o K. , corresponding to and , equal to volt .
For platinum is negative ; so that contamination with should make the pure nletal more electropositive , as is known to be the case .
The magnitude of the should be comparable with that for tungsten .
The calculated contact potentials are those which would be observed at the high temperatures of the experiments ; so that they are not strictly comparable with those given by experiments at ordinary temperatures .
Emission of Positire Ions .
There is some evidence that the linear relation between the constants A and in the emission temperature formula holds for the emission of positive ions as well as of electrons , although the data available in this case are nruch less extensive .
The writer*has measured the values of A and for the positive emission from an old platinum wire in the eraseous aeres : \mdash ; ( 1 ) Oxygen at 2 mm. , ( 2 ) hydrogen at mm. , ( 3 ) air at 760 mm. , ( 4 ) at 226 mm. and ( 5 ) nitrogen at mm. These appear to include the known data .
The values of are plotted against the Corresp n values of in fig. 3 , the points being numbered in accordance with the foregoing enumeration .
It seems hardly likely that the observed linearity is due to a coincidence , although there was evidence the experiments with hydrogen that complete equilibrium between the 1netal and the gas was not attained .
Thus too much reliance should not be placed on the points numbered ( 2 ) and ( 4 ) .
The whole question , of course , calls for further investigation .
It is interesting to note that the value of , or is of the same order as that for the negative emission .
Data taken fro1ll fig. 3 give If the change in the negative emission constants is so intimately connected with the contact difference of potential as we have supposed , one might * Phil. Trans , vol. 207 , p. 60 1906 ) .
for the of Dibasic Acids .
535 case of these two metals .
In this connection it is interesting to notice that the effect of hydrogen on the constant for the positive emission from platinum is opposite to that for the negative emission for this metal , and is in the same sense as that for the ative emission from tungsten .
These differences are to be expected if it is a question of of dissolved or adsorbed ions .
In concluding , the writer ventures to hope that the considerations have been forward will help to introduce some degree of derliness into the experimental values of the elnission constants , which , it must be admitted , are at present somewhat incoherent .
General Equations the No olisation of Acids , their Use to Calculate the Acidity of Dilute Carbonate Solutions .
By E. ( Communicated by Prof. F. G. Donnan , F.R.S. Received May 26 , 1915 .
) The numerous equations which have been proposed to express the equilibrium of acids , bases , salts , and their ions are generally convenient to apply , since in each particular case different simplifying assumptions can be 1nade .
The subject has now a stage , however , at which these can be replaced by equations of a more ature .
Practically the most important cases are those of the mono-and poly-basic acids combined with monacid bases , which furnish the bulk of those mixtures of balanced hydrion concentration which are used in physiological chemistry and also effect the physical ulation of the physiological fluids themselves .
The relation between the stage of neutralisation and the hydrion concentration of these acids is such that , usually , only two dissociation constants need to be considered .
Thus the constants of a tribasic acid , such as orthophosphoric , are each one of a higher order of magnitude than that which precedes it , and at the of neutralisation at which the third begins to have an effect , that of the first is inappreciable .
The eneral equation for a weak dibasic acid will alone be considered in what follows .
This will dissociate in steps\mdash ; , ( ) .
|
rspa_1915_0047 | 0950-1207 | General equations for the neutralisation of dibasic acids, and their use to calculate the acidity of dilute carbonate solutions. | 535 | 543 | 1,915 | 91 | Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character | E. B. R. Prideaux|Prof. F. G. Donnan, F. R. S. | article | 6.0.4 | http://dx.doi.org/10.1098/rspa.1915.0047 | en | rspa | 1,910 | 1,900 | 1,900 | 5 | 107 | 2,426 | http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1915_0047 | 10.1098/rspa.1915.0047 | null | null | null | Tables | 48.634531 | Biochemistry | 32.201162 | Tables | [
-23.510780334472656,
-59.15363693237305
] | ]\gt ; General Equations for the lisation of Dibasic Acids .
535 case of these two metals .
In this connection it is interesting to notice that the effect of hydrogen on the constant for the positive emission from platinum is opposite to that for the negative emission for this metal , and is in the same sense as that for the ative emission from tungsten .
These differences are to be expected if it is a question of sign of dissolved or adsorbed ions .
In concluding , the wliter ventures to hope that the considerations have been forward will help to introduce some degree of orderliness into the experimental values of the elmission constants , which , it must be admitted , are at present somewhat incoherent .
Equations for the lisation of their Use to the of Dilute Carbonate Solutio By E. ( Communicated by Prof. F. G. Donnan , F.R.S. Received May 26 , 1915 .
) The numerous equations which have been proposed to express the equilibrium of acids , bases , salts , and their ions are generally convenient to appl since in each particular case different simplifying assumptions can be made .
The subject has now reached a stage , however , at which these can be replaced by equations of a more general nature .
Practically the most important cases are those of the mono-and poly-basic acids combined with strong monacid bases , which furnish the bulk of those mixtures of balanced hydrion concentration which are used in physiological chemistry and also effect the physical ulation of the physiological fluid , themselves .
The relation between the stage of neutralisation and the hydrion concentration of these acids is such that , usually , only two dissociation constants need to be considered .
Thus the constants of a tribasic acid , such as orthophosphoric , are each one of a higher order of magnitude than that which precedes it , and at the stage of neutralisation at which the third constant begins to have an effect , that of the first is inappreciable .
The general equation for a weak dibasic acid will alone be considered in what follows .
This will dissociate in the steps\mdash ; , ( ) .
If the total acid concentration is , then the ionised part is , etc. , and the number of equivalents of ionised acid are equal to the added base .
} Hence And the expression above may be transformed into .
( 1 ) This formula does not give quite accurate results when the total concentration is , and especially at alkalinities .
It fails altogether at very low concentrations .
In order to include these cases also , an extension may be made of the method applied by the author to the correction of the third dissociation constant of orthophosphoric acid .
The ratio of equivalents alkali to .
of acid is equal to NaHA)NaOH ) ( 2 ) Also NaHA NaOH ) in which now stand for the fractions dissociated , not of the total acid , but of the primary and secondary salt .
By the help of these , and of the ionic equations ( HA ' ) , ( HA ' ) , 'Die Wasserstoffionen Konzentration , ' p. 30 .
the terms of equation ( above , except t the May be transformed into terms containing either NaHA ) alone or lone .
By the first method By the second method Or dividing through by NaHA ) , or If the third terms of the numerators are omitted , and the simplifying assumptions of p. 536 are introduced , it may easily be shown that either of these equations becomes identical withr the transformed lfichaelis ' equation ( 1 ) .
If the equations and are used as they stand , the former is suitable for solutions containing only small proportions of alkali , the latter solutions containing small proportions of acid .
The two give identical results for solutions containing moderate proportions both of HA ' and of If the total concentration is moderate , and the third terms may be obtained with sufficient accuracy from the atnounts of acid and alkali taken .
Dilute Solutions.\mdash ; At higher dilutions , the hydrolysis appreciably affects the amounts of primary and secondary salt .
The third terms of the numerators must then be expressed differently .
Let , as before , be the total concentration and its ions .
Then either or will be vanishingly small in comparison to the other two forms of combination .
Which form may be neglected is easily to be determined by means of the and equations on p. 536 combined with the value of chosen .
In the more acid solntions .
And , since ionisation is practically complete , NaHA ) .
Mr. E. B. R. Prideaux .
Equations for Or , substituting for its value , it follows that NaHA ) Similarly , it may be shown that in the more alkaline solutions The complete equations for high dilutions become and These equations are the quantitative expression of the fact that extreme dilution increases the amount of alkali required to produce a given value of ( OH ' ) .
The third term of the numerator is a measure of the extent to which the hydrion concentration of a given partly neutralised ) acid varies with the dilution .
Application to Carbonic Acid.\mdash ; The carbonate equilibrium is the chief physical agent which regulates ) hydrion concentration , not only of fluids , but also of the hard waters , fresh and salt , the acidity of which has so intimate a connection with the growth of plaukton and other simple organisms .
This acidity may in most cases be directly determined , but the determination is sometimes inconvenient .
In an important research , e.g. by Bronsted and Lund* on the physical and biological conditions of Danish lakes , the amount of and of has been determined in each case , but not the acidity of the water .
The use of the equations will , it is hoped , enable the atum to be supplied in such as these .
The acidities of carbonic acid at different stages of neutralisation as determined by Auerbach and Pick and others , may now be compared with those calculated by the different formulae given above , using Walker and Cormack , and , Shields , Koelichen , McCoy , Auerbach and Pick ( loc. cit Experimental Values at mol .
per litre .
1.60 9 .
10.35 ll ll69 'Chem .
Phys. Untel.suchungen der Danischen Gewasser , ' 1912 .
' Arb .
aus .
Kais .
Gesundheitsamt , ' vol. 38 , ( 4 ) , p. 562 ( 1912 ) .
the Neutralisation of sic The first Table given below has been calculated from formulae and p. 537 , using and in a molar solution .
The second Table is from the simplified formula 1 , p. 536 .
The two almost identical results in the middle of the neutralisation curve at .
But in the more alkaline solutions the introduction of the third term makes a considerable difference .
Thus by interpolation on the curves , from the , eneral formula , and from the simplified formula at .
The former thus gives a better reement with the experimental values of Auerbach at than the latter .
Table I. ( H ) Table II .
Dilute Carbonate Solutions.\mdash ; The calculation of the acidity of solutions , of which the total concentrations are lower than those of , etc. , in presence of the specified amounts of , are , of course , equally applicable to carbonates of the calcium group as to those of the sodium roup .
There are a few experimental values of the of hard waters which will serve to check the accuracy of the values in Tables III and , which are based equations and 4 Table III .
mol .
per litre .
Table In a molar solution of Auerbach loc. found The solubility of ( calcite ) is , according to Schloesing*and Kohlrausch 'Comptes Rendus , ' vols .
74 , 75 and 90 ( 1872 and VOL. XCL\mdash ; A. second in conjunction with Mr. J. Twomey .
The nity of filtered solution ( without chloride ) was also measured by the colorimetric method ( using phenolphthalein ) , both in deep Nessler glasses and in a Donnan colorimeter .
The comparison solution was an alkaline phosphate of which .
The mean of five measurements the carbonate solution An unsteadiness in the results is to be expected , both on account of the slowness of the eneous equilibrium , and on account of the extreme sensitiveness of the alkalinity to traces of in this part of the curve , which is accentuated by the dilution .
A discrepancy between the observed and calculated alkalinities of sodium acetate has accounted for by Walpole on similar grounds .
S The acid part of the curve may be tested by the help of the measurements of Walker and Kay Waters of diHerent ' : degrees of hardness\ldquo ; made from standard lime-watel were brought into equilibrium with the of the air , and the acidities were measured by a colorimetric ethod : ation orbonntc e molecules ation orbonntc e molecules ation orbonntc e molecules ation orbonntc e molecules ation orbonntc e molecules ation orbonntc e molecules ation orbonntc e molecules ation orbonntc e molecules ation orbonntc e molecules ation orbonntc e molecules ation orbonntc e molecules ation orbonntc e molecules ation orbonntc e molecules ation orbonntc e molecules ation orbonntc e molecules ation orbonntc e molecules ation orbonntc e molecules ation orbonntc e molecules ation orbonntc e molecules ation orbonntc e molecules ation orbonntc e molecules ation orbonntc e molecules ation orbonntc e molecules ation orbonntc e molecules ation orbonntc e molecules ation orbonntc e molecules ation orbonntc e molecules ( H ) .
'Zeitsch . .
phys .
' vols .
12 , 44 , 64 ( 1893-1903 ) .
' J. Amel .
Chem. Soc vol. 33 , p. 468 ( 1911 ) .
'Phil .
Mag I , p. 958 ( 1912 ) .
S 'Trans .
Chem. Soc vol. 105 , pp. 2502 , ( 1914 ) .
'J .
Soc. Chem. vol. 31 , p. 1014 ( 1912 ) .
the Neutratisation of Acids .
541 These figures suffice for a calculation of the degree of neutralisation , for the total alkali ( in equivalents ) is and the same figure represents the bicarbonate ion concentration , since it can be shown that the fraction of original forming is ible at the hydrion and total concentrations given .
The excess of carbonic acid , should be that which is in equilibrium with the pressure of the air , i.e. by and Bock 's results It may , however , be derived with more certainty from the constant of the eneous equilibrium This gives in the first case and in the second case Introducing these values , the ratio is found to be in the first case and in the second case The values of the ratio from the general equation at the given acidities and , are and respectively .
If , however is calculated from the absorption coefficient of the gas-liquid equilibrium as above , the calculated value of the second case falls right off the The observation that calculated from the homogeneous is slightly greater than calculated from the heterogeneous equilibriu1ll has been made by several investigators and has not yet been adequately explained .
It is clear from all the evidence has come under the author 's view that the data of the eneous equilibria , i.e. pressure of and solubility of , can only be used with great caution to calculate by means of the and solubility product ) which are supposed to be in eqnilibrium with the gas and solid phase respectively .
On other hand , the analytical data , total concentration of and of alkali in a homogeneous solution , can be so used with considerable confidence .
easiest of employing the equations is evidently to plot a section of the curve corresponding to the known carbonic acid concentration , choosing values of above and below that which is to be expected .
The from of found then gives the correct figure .
Volatihsation of Extremely Deposits .
543 NOTES ON DIAGRAM .
Ordinates .
Left-hand numbers refer to upper curves , right-hand to lower .
Abscissoe ratio alkali to acid .
Upper numbers refer to upper curves , lower numbers to lower curves .
Upper Curves .
plain line\mdash ; values calculated by formulae and at and dotted alues calculated by formula 1 Auerbach 's values at oken \mdash ; values calculated by formulae and Curves\mdash ; Dilute carbonate 011 larger scale .
plain line\mdash ; values at broken line\mdash ; values at experimental values as quoted .
third points in Tables I and II have been erroneously plotted as of Extremely Radioactive Deposits .
By A. B. WOOD , M.Sc .
, Oliver Fellow and Assistant Lecturer in Physics , University of Liverpool .
( Communicated by Prof. Sir E. Rutherford , F.R.S. Received July 1 , 1915 .
) Introduction .
Within the last few years papers dealing with the volatilisation of radioactive substances have been published by various authors .
The principal aims of the experiments described in these papers may be classified under three heads:\mdash ; ( a ) To determine the telnperatures of volatilisation of the various members of the active deposits of radium , thorium , and actinium ; in some cases with a view to the assification of these substances in the periodic system .
( b ) To prove that these extremely small quantities of matter form definite chemical compounds in a manner similar to that of the commoner elements .
( c ) To separate the various members of the series from one another .
Other interesting results , throw light on the phenomena of volatilisation , have also been reported , but these have always formed a subsidiary part of the researches described .
Makower* determined the * Makower , Manch .
Lit. and Phil. Soc vol. 53 , Part II 1909 ) , and 'Le Radium , ' vol. 6 , p. .
|
rspa_1915_0048 | 0950-1207 | Volatilisation of extremely thin radioactive deposits. | 543 | 560 | 1,915 | 91 | Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character | A. B. Wood, M. Sc.|Prof. Sir E. Rutherford, F. R. S. | article | 6.0.4 | http://dx.doi.org/10.1098/rspa.1915.0048 | en | rspa | 1,910 | 1,900 | 1,900 | 9 | 272 | 6,418 | http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1915_0048 | 10.1098/rspa.1915.0048 | null | null | null | Thermodynamics | 41.040295 | Tables | 25.863243 | Thermodynamics | [
1.9889140129089355,
-82.6473159790039
] | ]\gt ; sation of Extremely Deposits .
543 NOTES ON DIAGRAIsI .
Ordinates .
Left-hand numbers refer to upper curves , right-hand to lower .
Abscissoeratio alkali to acid .
Upper numbers to upper curves , lowel numbers to lower curves .
Upper plain line\mdash ; values calculated by formulae and at and dotted alues calculated by formula 1 Auerbach 's values at oken line\mdash ; values calculated by formulae owerO.upper .
Lower Curves\mdash ; Dilute carbonate 011 larger scale .
plain line\mdash ; values broken line\mdash ; values at experimental values as quoted .
N.B.\mdash ; The third points in Tables I and II have been erroneously plotted as and of Extremely Thin Radioactive Deposits .
By A. B. WOOD , M.Sc .
, Oliver Fellow and Assistant Lecturer in Physics , University of Liverpool .
( Communicated by Prof. Sir E. Rutherford , F.R.S. Received July 1 , 1915 .
) Introduction .
Within the last few years papers dealing with the volatilisation of radioactive substances have been published by various authors .
The principal aims of the experiments described in these papers may be classified under three heads : \mdash ; ( a ) To determine the temperatures of volatilisation of the various members of the active deposits of radium , thori , and actinium ; in some cases with a view to the ciassification of these substances in the periodic system .
( b ) To prove that these extremely small quantities of matter form definite chemical compounds in a manner similar to that of the commoner elements .
( c ) To separate the various members of the series from one another .
Other interesting results , throw light on the phenomena of volatilisation , have also been reported , but these have always formed a subsidiary part of the researches described .
Makower* determined the *Makower , Manch .
Lit. and Phil. Soc vol. 53 , Part II 1909 ) , and 'Le Badium , ' vol. 6 , p. .
Wood , more recently by the author .
S These authors have also shown the possibility of separatinCro radioactive substances which have not yet been separated by other methods .
possible sources of error in the determination of volatilisation temperatures .
facto.hich mnfluence tisation othese eyHence iddition tehaviour oubstance mubstance whose behaviour weated tarious hemperaturesbe there substances oharacter Barratt andOne fcommon txperiments mentioned , eference tecessary , nvestigation oature jentioned , hoose rhin films was desirable .
Wood , in studying the volatilisation of thorium and thorium , showed thatthecurveconnectingquitesimpleinthecaseofthoriumB , whereasthecurveforthoriumCwastheamountvolatilisedwithtemperaturewas more complex .
The author has also shown that the volatilisation curve for thorium is similar to that for thorium B. We may thus reasonably assume that the volatilisation curve of thorium is typical of that for any single constituent in the active deposits of radium , thorium , or actinium .
Consequently thorium is the substance employed in present experiments for an investigation of the various influences which aflect the volatilisation of the active deposits .
: : * Schrader , ' Phil. Mag vol. 24 , p. 125 ( 1912 ) .
Wood , Phil MDecember , Barratt aPhys .
Proc. JuneRussell , Phil. ' Extremely Thin Deposits .
Apparatus and Experimental Procedure .
The apparatus employed is shown diagrammatically in .
An electric furnace*whose temperature coul be measured accurately by means of a platinum thermometer and Callendar-Griffiths , was used to heat the active material .
The furnace and thermometer have been described in detail in a previous paper .
* aa .
Porcelain lining of furnace .
tinum thermometer .
bb .
Fused silica tube . .
Light nickel spoon . .
Tap connecting to pump and pressure gauge .
Temperatures above 1100o C. were estimated ) extrapolation of the curve connecting temperature and current through the furnace .
The active substance was placed inside a tube of fused silica , closed at one end , arranged centrally in the furnace and symmetrically with regard to the platinum thermometer see .
By means of a long nickel spoon , fixed to a ground glass joint which closed the cold end of the tube , the active material could be introduced or removed quickly from the silica tube .
The nickel spoon was of very small heat capacity , and attained the temperature of the furnace in a very short time .
This point is of importance , and will be referred to later ( see Section 3 ) .
The silica tube was connected by means of a side tube to a vacuum pump and pressure gauge , thus making it possible to heat the active substance at any desired pressure .
This arrangement also proved extremely useful in evacuating the tube between successive experiments , in order to remove any volatilised active material which would necessarily be present in the tube .
A strongly emanating source of radio-thorium ( equivalent in activity to 1 mgrn ] .
of radium bromide ) was used as a supply of active deposit .
By a simple arrangement this could be obtained ou one side only of the plate exposed to the emanation , and by varying the conditions of exposure a considerable range of activity could be obtained .
In all experiments , except a few of those described in Section 2 , exposures were made without electric field , a thin layer of tissue paper separating the radio-thorium from the metal foil , so that the possibility of thorium X being deposited on the foil was reduced to a minimum .
The active deposit * A. B. Wood , the activity were taken and the mean time of observation noted .
The deposit was then placed in the nickel spoon introduced into the furnace for the desired interval .
When a period of not less than six hours had elapsed after the removal of the active deposit from the furnace , the -activity was measured and at the end of this time the atilised portion of the deposit had again attained .
equilibrium .
* From the observed and calculated values of the activity at the time of the second set of measurements the percentage volatilised is easily deduced .
At the end of every experiment similar to the one just outlined , the silica tube was evacuated to a pressure of about 2 cm .
of mercury in order to free it as far as possible from the volatilised portion of the deposit .
Factors Irlflu arlier experiments have shown that the qation of a thin of radioactive matter ries enormously with the conditions to which it is exposed .
For example , the kind of surface on which the film is deposited has a 1narked effect , whilst several experi nenters have recorded notable variations with different ases on the furnace tube .
It is unnecessary at this stage to ellter into a discussion of numerous other sources of influence on this phenomenon , but the following list will serve as a guide to some of the principal factors wlrich have been investigated in detail .
The effects of variation on the ving conditions have been studied:\mdash ; 1 .
Nature of the surface on which the active substance is deposited .
2 .
Thickness of the layer of active material .
3 .
Period of heating .
4 .
Temperature .
5 .
Pressure of the surrounding .
gas .
6 .
Nature of the surrounding gas .
The first five of these factors will be considered in the order given above .
The consideration of the sixth , i.e. the influence of the nature of the gas surrounding the active material , will be discussed in a later communication .
* See paper by Barratt and Wood , loc. Extremely Thin Deposits .
1 .
fluence of Surface.\mdash ; Before investigating the other factors which may the volatilisation of the thorium , it is necessary to choose a suitable surface as a " " support\ldquo ; or base\ldquo ; for the deposit .
Barratt and Wood showed the necessity for a perfectly clean surface , since a film of grease , or other substance hich easily volatilises , will carry away the active material with it .
It is essential then to use some substance as " " base\ldquo ; which can be cleaned easily and thoroughly , either by heating or by treatment with acids .
Platinum and quartz are both ideal in these respects .
It is interesting , however , to examine other substances as to their suitability .
Substances whose melting points are below 1000o C. can at once be missed ; , all substances the volatilisation of which is detectable below this tenlperature are unsuitable .
* in his work on volatilisation of radium from surfaces of nickel , platinum , and quartz has shown that volatilisaLoion of the active substance is appreciable in all cases between and C. All the radium was driven off nickel and platinum at 1200o C. bnt not from the quartz till a temperature of 1300o C. was reached .
Barratt and Wood , using thorium active deposit , confirmed this observation of Makower that the initial temperature of volatilisation was the same whether the active substance was deposited on quartz or platinum : but found it impossible to volatilise the whole of the deposit from either quartz or platinum even after heating at 130 C. These conclusions are supported by the results of the present experiments .
It was found that after heating the active deposit on platinum for 10 minutes at a white heat ( temperature estimated at C. in the blowpipe flame there still remains an appreciable amount of thorium unvolatilised .
A similar result was obtained wfien quartz was used as the base .
With to unvolatilised portion of thorium , the experiment is instructive .
A platinum foil coated with thorium active deposit was heated for about 60 minutes at 120 C. and approxinlately 99 per cent. of the thorium volatilised .
The portion remaining on the platinum foil , i.e. the 1 per cent. , was allowed to attain equilibrium , when it was heated for the same lime at 120 C. It was now that o1lly 18 per oent .
of this remaining portion of the original deposit was volatilised .
These observations seem to indicate that a certain fraction of the molecules of the active deposit are held to the surface of the platinum by forces of cohesion due to the molecules of platinum in their immediate neighbourhood .
Possibly this small percentage of the active deposit has penetrated below the * A list of elements with their melting points , boiling points , and temperatul.es of initial volatilisation is given in a table in Kaye 's ' ) Makower , ' Manch .
Lit. and Phil. Soc vol. 53 , Part II 1909 ) .
quite probable that a small portion of the active deposit is carried off by this means , in addition to the normal volatilisation .
When the active material was heated on a nickel surface , the effects observed were very conflicting .
The temperature at which volatilisation colnmenced reed fairly well with the temperatures noted when platinum and quartz surfaces were used .
At temperatures , however , divergences were sometimes observed\mdash ; the results seeming to depend on the condition of the nickel surface before exposure to .
the emanation .
Thus it was noticed that the results were more consistent when the nickel surface , , before exposure to the emanation , was oxidised by heating strongly in blowpipe flame .
The following shows the result of a series of experiments using nickel and platinum surfaces:\mdash ; ( 1 ) First Heating at 1200o C. quite that a small portion of the active deposit is carried off by this means , in addition to the normal volatilisation .
When the active material was heated on a nickel surface , the effects observed were very conflicting .
The temperature at which volatilisation colnmenced reed fairly well with the temperatures noted when platinum and quartz surfaces were used .
At temperatures , however , divergences were sometimes resulffi seeming to depend on the condition of the nickel surface before exposure to .
the emanation .
Thus it was noticed that the results were more consistent when the nickel surface , , before exposure to the emanation , was oxidised by heating strongly in blowpipe The following shows the result of a series of experiments using nickel and platinum surfaces:\mdash ; ( 1 ) First Heating at 1200o C. quite that a small portion of the active deposit is carried off by this means , in addition to the normal volatilisation .
When the active material was heated on a nickel surface , the effects observed were very conflicting .
The temperature at which volatilisation colnmenced reed fairly well with the temperatures noted when platinum and quartz surfaces were used .
At temperatures , however , divergences were sometimes resulffi seeming to depend on the condition of the nickel surface before exposure to .
the emanation .
Thus it was noticed that the results were more consistent when the nickel surface , , before exposure to the emanation , was oxidised by heating strongly in blowpipe The following shows the result of a series of experiments using nickel and platinum surfaces:\mdash ; ( 1 ) First Heating at 1200o C. quite that a small portion of the active deposit is carried off by this means , in addition to the normal volatilisation .
When the active material was heated on a nickel surface , the effects observed were very conflicting .
The temperature at which volatilisation colnmenced reed fairly well with the temperatures noted when platinum and quartz surfaces were used .
At temperatures , however , divergences were sometimes resulffi seeming to depend on the condition of the nickel surface before exposure to .
the emanation .
Thus it was noticed that the results were more consistent when the nickel surface , , before exposure to the emanation , was oxidised by heating strongly in blowpipe The following shows the result of a series of experiments using nickel and platinum surfaces:\mdash ; ( 1 ) First Heating at 1200o C. ; After equilibrium had again been attained , the foils were reheated .
Boberts , ' Phil. Mag. , ' 6 , vol. 25 , p. 270 ( February , 1913 ) .
Extremely Thin Radioactive Deposits .
( 2 ) Second Heating at 1200o C. A third heating in the blowpipe flame ( temperature between 1500o C. and 1600o C. ) showed that there was a of the active deposit left from ( 2 ) , still unvolatilised .
It will be clear from these results that it is with only very great difficulty that the last 2 or 3 per cent. of the active deposit can be volatilised .
Again , it is more difficult to remove the active deposit from nickel than from platinum .
As one would expect , the nickel , on removal from the furnace at these high temperatures , is always coated with a thin film of black oxide , which renders this substance unsuitable as a base for several reasons\mdash ; in particular , the complication of the -ray measurements due to the absorption in the oxide film .
Again , volatilisation of this film might introduce serious errors in the measurements .
A surface of iron or steel is objectionable for similar reasons .
Using copper and brass surfaces this trouble of oxidation was still further increased , the comparatively low point of copper ( 1084o being another serious objection to its use at temperatures .
The metals osmium , iridium , and tungsten would be excellent for the purpose , since volatilisation of these elements has not been detected below 1400o C. in account of .
expensive nature , however , they were not used in the investigation .
From the above considerations it is clear that platinum and quartz are the most suitable materials to employin a research of this kind .
On account of the ease with which it can be cleaned and manipulated platinum has been used as base for the active substance in all experiments subsequently described .
2 .
Density of the Deposit.\mdash ; When referring to such minute quantities of substance as the active deposits from the various radioactive emanations we cannot use strictly the term " " thickness Assuming a uniform distribution of particles , a simple calculation of the thickness of a very active layer of thorium active deposit , equivalent in -activity to mgrm .
of radium per square centimetre of platinum , shows that only one thousandth of the platinum surface is covered by a layer one molecule deep , i.e. for every now considering .
It ] be shown later that the amount volatilised is not a linear function of the time of There are twc methods open to us for varying the density of the deposit : ( a ) by the time of exposure to the etnanation , without employing an electric field ; ( b ) by exposing for different times with an electric field .
( a ) By comparing the -activity of the active deposit with that of a standard source of radium , a simple calculation gives us the approximate number of active deposit molecules per square centimetre .
Variations of exposure from 1 tc 40 hours have been made Yvithout electric field , representing a range of density from to active deposit molecules per square centimetre\mdash ; the number of platinum molecules in a surface layer being of the order No regular variations in the amount volatilised with change of density of the deposit were observed , all diHerences being well within the experimental error .
Hence , under these conditions , the volatilisation is independent of the time of exposure to the emanation .
( b ) If an electric field is used when exposing to the emanation , the density of the deposit can be increased to about one hundred times the maximum possible by method , i.e. to a density of about molecules per square centimetre .
, however , fairly large and almost unaccountable variations occur .
Several explanations of these variations can be suggested .
They may be due ( 1 ) to the collection of dust particles or other nuclei , coated with active deposit , ( 2 ) to the formation of charged aCes of active deposit , and to the non-uniformity of the layer of active deposit collected by this method , as compared with that obtained by the ordinary process of sion .
In all cases , however , the amount volatilised from a plate exposed , till equilibrium is reached , by method ( b ) is greater for short periods of than that volatilised from a plate exposed by method ( a ) .
Extremely Thin Radioactive Deposits .
This gives strong support to the view that dust particles or other nuclei coated with the active deposit have been collected on the plate by the electric field used in consequently , when such a plate is introduced into the furnace , the dust burns rapidly , and carries away the actiye deposit with it .
This question will be discussed ] ater ( see Section 3 ) .
The Table gives a comparison of a series of results obtained by the two methods just outlined:\mdash ; Percentage thorium voIntilised nt of heating .
electric field .
ctric { ield .
Time Platinum foil exposed to emnnation ithou to ation 2 hours ' exposure .
) ' exposure .
24 hours ' exposure .
The above remarks must be modified , of course , when we are considering the volatilisation of the portion which remains after the platinum and active deposit have been once heated to temperatures over 1000o C.\mdash ; this has been explained in Section 1 .
For experiments of this character 1he results are always the same , whatever the density of the original deposit .
It appears , then , that the most consistent results are obtained when the platinum foil is exposed to the emanation without electric field , the volatilisation in that case being practically independent of the time of exposure .
In all subsequent experiments the active deposit was collected by exposure to the emanation for six hours without electric field .
3 .
Variation of Pcriod of Heating.\mdash ; A point of great ) ortance in the study of the problem of volatilisation is to determine the rate at which the active material is removed from the surface .
The experimental procedure was as follows : After the furnace had attained a steady state ( usually after about 2 hours ' preliminary heating the active deposit , previously measured , was introduced into the furnace for a definite period , by means of the nickel spoon .
On removal its activity was measured as explained above .
The silica tube was then evacuated to remove volatilised active deposit , and a second source of active deposit introduced for another different period .
This process was repeated u1ltil a series of observations had been made the relation between the time of The result of such a series of observations is shown in fig. 2 .
Time of heating ( minutes ) .
prominent features of these curves will be noticed at once .
( 1 ) The a1nount volatilised increases at first rapidly , then more and more slowly as eating is continued , .
the rate of volatllisation decreases rapidly time of heating , particularly at high temperatures .
( 2 ) The initial rate of volatilisation increases very rapidly with small increases of temperature .
This point is shown more clearly in fig. 4 , which will be discussed in Section 4 .
Another , perhaps less tant , feature of these curves will be oticed from a consideration of the rate when a large percentage has bee volatilised .
A decided flattening of the curves becomes evident as the ioned iection 1amount viQthe turve ( hown iigure)Cruns pwith 9dinate.eriod oeating temov.traces ofThe first ation ourves wests isExtremdy Teposits .
that they are exponential .
It seems quite reasonable to suppose .the rate of volatilisation is proportional to the amount of active substance present on the platinum foil at any particular time , i.e. we are dealing , as in this case , with a comparatively small number of molecules .
The facts do not support this view , however , and it becomes necessary to look for some other explanation .
Of course , it is quite probable that several factors are nvolved in the complex behaviour of the active deposit ; hence a ) sideration of the following hypothetical case may throw some cvht on the problem .
Suppose we could obtain on a platinum surface a layer of active deposit of measurable thickness ( sa .
mm Let us consider what happens this layer is heated .
Up to a certain critical poit , in fig. 3 , Thickness of layer ( diminishing ) .
Maximum less at .
Infinitesimally small thickness at Zero thickness at would ) the rate of volatilisation to be constant , .
the amount volatilised is proportional to the time of heating , but when ) depth of the layer had decreased to one or two molecules the rate of volatilisation vould begin to decrease , at first slowly , then more rapidly , until only those molecules of the active deposit which are intermingled with molecules are left .
At this stage , in fig. :3 , the rate of volatilisation decreases more slowly , since the remaining nzolecules are subject to a different law of foroe\mdash ; the cohesion of the platinum molecules\mdash ; from that of the active deposit molecules volatilised in the earlier stages .
is a diagrammatic represeutatiom of the process just outlilled The latter portion Mr. A. B. Wood .
Volatilisation of of the curve , between the points and , represents the result of an actual experiment similar to the one described at the beginning of this seccion .
As was made clear in Section 2 , the thickness of the active deposits is correct wxpect , gating whick 1ayers octive depositto iortion ourve 1ying between tisation iever constant ibove suggestions a points and .
Unfortunately , we have no sources of thorium emanation at .
3 present available , from which we can collect such thick layers of active deposit by diffusion .
to the disturbing action of dust particles , when an electric field is used to increase the density of the deposit , the results obtained.in such cases cannot itimately be compared with those obtained by the diffusion method used in the above experiments .
We now come to the second and , perhaps , more important feature of the curves shown in .
the influence of temperature on the rate of volatilisation .
The problem bears a close similarity to that of the emission of ioDS from a hot metal .
Thus if we assume that the volatilised particles like a perfect gas , the calculation of the rate of volatilisation is analogous in practically all respects to that in the case just mentioned .
egarding the steady state as the result of a dynamical equilibrium between the molecules going from the layer of active deposit to the air and those going from the air to the deposit , we obtain the well-known relation connecting the rate with the absolute temperature Rate where A nd are constants which.can be determined experimentally .
The expression for the rate , just given , was first deduced by Richardson in his researches on emission of ions from hot bodies , and was subject to the condition that the number of free electrons per unit volume of the metal is independent of the temperature .
He has since modified his views* by assuming that the number of free electrons in the metal is proportional to , whence Rate The assumption just mentioned was made in order to explain the observed values of the specific heat of electricity .
More recently hasgiven another deduction of the second formula based on the quantum theory. .
* Richardson , 'Phil .
Mag vol. 23 , p. 604 Richardson , ' Phil. Mag vol. 28 , p. 633 ( 1914 ) .
Extremely Thin Radioactive Deposits .
Planck* also has obtained the relation by consideration of the vapour pressure of a solid at very low temperatures , using the assumption that the entropy of the solid at these temperature will be practically independent of the temperature , while that of the vapour can be considered like that of a perfect gas .
It seems very doubtful , however , whether the assumptions used by Planck will apply to the case under consideration , i.e. to the evaporation of a metal at high temperatures .
In this case , a lower power of the factor would be expected .
Both the relations just given require that the rate should be constant when the temperature is constant , but , as we have already seen , this is far from being the case , the rate varying considerably with the amount of material volatilised .
Consequently we must introduce a factor into the expression for rate , in order to make this quantity in agreement with observations\mdash ; the function expressing the rate as a function of the number of thorium molecules volatilised .
We now have Rate , ( 3 ) where or 2 .
The form of the function has already been discussed from the physical standpoint , hence we need only concern ourselves with a consideration of the remaining factor .
From observations of the initial rate of volatilisation at two different temperatures the values of A and in equation can be calculated , and the rates at any other temperatures deduced .
The following Table provides a comparison between the observed and calculated values of the initial rates at different temperatures .
*The observed rates at these temperatures were used in the calculation of the constants A and in the expressions for the rate .
PIanck , " " Die gegenwartige Bedeutung der Quantenhypothese fur die tische Gastheorie 'Vortrage uber die kinetische Theory der Iaterie der Electricitat \mdash ; Mathematische Vorlesungen an der Universitat Gottiugen , ' VI .
VOL. XCL\mdash ; A. 2 Mr. A. B. Wood .
sation of Considering the extreme sensibility of the expressions and to small changes of temperature , the reement between observed and calculated values is good .
It will be noticed , however , that the factor or has practically no effect on the value of the expression for the rate until the temperature reaches a high value\mdash ; thus both sions for the initial rate of yolatilisation agree equally well .
It is only possible , experimentally , to distinguish between the two forms when the temperature is in the neighbourhood of 1000o C. ; unfortunately at this temperature it is practically impossible to measure the initial rate .
Similar results are found if , instead of using the initial rates , we consider the rates of volatilisation at a later stage of the process .
Thus the rates of volatilisation at different temperatures whetJ 40 per cent. of the active material has been removed are in the same relative proportion as the initial rates at the same temperatures .
This only holds , however , up to a point where about 80 or 90 per cent. of the thorium is volatilised .
Beyond this point , the whole process is changed on account of the effects previously discussed .
The results of the experiments on the rate of volatilisation of the active deposit thus seem to support the view that the volatilisation proceeds on similar lines to the emission of ions ( positive or negative ) from a heated metal .
Other experimenters have shown*that there is a close si1mlarity between the laws of disintegration of a heated wire and the leak of positive electricity from it .
The present experiments support this view , although the only safe conclusion which can be given at present is that the formula for the volatilisation\mdash ; besides containing terms more slowly\mdash ; may be expected to contain the factor or , where is the gas constant and the latent heat of vaporisation : this result , of course , is well known from ordinary thermodynamical considerations .
4 .
Variation of the Temperature.\mdash ; From the poin of view of interest this factor should have been considered earlier , for several reasons it seemed advisable to defcr ib until the questions raised in Section 3 had been discussed .
Barratt and Wood ( loc. cit. ) the question by heating thorium active deposit for a constant time ( 15 minutes ) at various accurately measured temperatures .
Their work led to a result C. as the temperature of volatilisation of thorium B. In the experiments the procedure adopted was exactly the same\mdash ; the constant period of heating in this case again being 15 minutes .
Curve , fig. 4 , is a combination of the results obtained in the present work with those obtained in a previous research by Barratt and the author .
The observations made in the present research are indicated in the figure by * See J. J. TAomson 's ' Conduction of Electricity through Gases , ' p. 213 , Chap. VIII .
Extremely Deposits .
a circle\mdash ; those in previous work by Barratt and Wood by a combination of a circle and a cross .
It will be seen that the two sets of observations are in excellent agreement .
One important difference , however , should be noted .
Temperature ( degrees Curve A. At 760 mm. Curve B. At 3 mm. pressure .
Present paper .
Barratt and Woo Mr. A. B. Wood .
of The temperature of volatilisation , as given by Barratt and Wood , was slightly lower than 75 C.\ldquo ; \mdash ; it is evident from the figure that if the main portion of the curve is produced to cut the axis at , the temperature obtained , 74 C. , agrees very well with the value just given .
This temperature , C. , is that at which the thorium begin to volatilise very rapidly .
Below this temperature , however , a small amount of volatilisation is observed , but this quickly falls to a quantity too small for detection at about 68 C. Of course , the lowest temperature at which it is possible to detect yolatilisation is even lower than this , but in that case the time of heatir-g must be considerably increased .
The following observations at temperatures below 68 will illustrate this point:\mdash ; The form of the curve , is interesting .
It will be that the amount volatilised increases at first slowly , then much more rapidly as the temperature increases .
When a fairly large percentage has been removed , however , the rate of volatilisation rapidly falls off with further heating at higher temperatures .
Of course , a series of curves similar to the one just described could be constructed from fig. 2 directly .
If the form of the function in equation ( 3 ) , Section 3 , were accurately known it would be possible to calculate the total amount volatilised in a yiven time at desired temperature .
5 .
Vctriation of Pressure of the \mdash ; All the experiments described up to this stage have been carried out with the air at atmospheric pressure in the silica tube .
We shall now consider the effects observed when the active deposit was heated at pressures considerably lower than this .
After its -activity had been measured the active deposit on the platinum foil was placed on the nickel spoon and introduced into the silica tube .
The air in the tube was immediately expanded into a bottle of large volume exhausted to the required pressure .
Hence it was possible to obtain almost instantaneously any desired pressure in the tube by that the volume of the receiver was very large compared with the volume of the silica tube .
A series of observations of this kind , keeping Extremely Thin Radioactive Deposits .
the time of heating constant ( 15 minutes ) , was made at different temperatures and pressures .
The result of such a series of observations at a pressure of 3 mm. is shown in curve , fig. 4 .
Comparing the two curves it is evident that the process of volatilisation takes place on very much } same lines in each case .
Thus the slow initial rise , followed by the much steeper pol.tion and ended by another slow increase , is characteristic of both curves .
In the " " low pressure\ldquo ; curve , however , the central portion is considerably steeper than the portion of the " " atmospheric pressure\ldquo ; curve , indicating that volatilisation is much more rapid in the former case .
Another ence b the curves is the lowering ( about C. ) of the initial temperature of volatilisation at low pressures .
It should be noticed , too , that at low pressures it is still found practically impossible to volatilise the last tlaces of the active deposit .
The following Table gives a few of the results of a series of experiments carried out on the variation of the amount volatilised at different temperatures , the pressures from 7 mm. to 3 mm. of mercury:\mdash ; The more important factors which influence the volatilisation of extremely thin films of the radioactive deposits have been ated experimentally .
Each of these sources of influence has been considered separately by eliminating , as far as possible , the disturbing effects of the others .
for reasons given in the earlier part of the paper , has been chosen as typical of all similar constituents of the active deposits of radium , thorium , and actillium .
560 tilisation of Extremely Thin Radioactive Deposits .
been examined:\mdash ; ( 1 ) The surface on which the active substance is deposited .
collected on the surface .
ised \ldquo ; withtimeofheating\ldquo ; series oifferent temperatures aVariation oeriod oeating .
Curves connecting percentageThe ience oowing factors oroce , olatilisation hVariationoftheamountpersquarecentimetre\ldquo ; oftheactivedeposit ( 4 ) Variation of temperature\mdash ; the time of heating remaining constant .
( 5 ) Variation of the pressure of the surrounding gas .
It has been shown to be extremely difficult to remove , by heatin , alone , the last traces of the active deposit from surfaces of quartz , nickel , or platinum .
A suggested explanation of this is given and verified experimentally .
The most consistent results are obtained when the surface is exposed to the emanation without electric field , in which case the volatilisation is independent of the time of exposure to the emanation .
The volatilisation is shown to obey practically ) same law as the rate of emission of ions from a hot body , this expression\mdash ; Rate \mdash ; being modified by the introduction of a factor which depends on the amount of active deposit which has been volatilised .
The function is considered from a physical standpoint , the mathematical relation being extremely complex .
A comparison of the volatilisation curves at pressures of 760 mm. and 3 mm. is given , a lowering of the initial temperature of volatilisation at low pressure being observed .
The volatilisation curve at atmospheric pressure rrees extremely well with that given in a previous paper by Barratt and Wood ( loc. cit In conclusion , I should like to express my warmest thanks to Prof. L. B. Wilberforce for his interest and encouragement , and to Prof. Sir E. Rutherford and Dr. N. Bohr for kind help and criticism .
|
rspa_1915_0049 | 0950-1207 | On the longitudinal strength of cylinders closed by screw plugs. | 1 | 8 | 1,915 | 92 | Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character | Lieut.-Colonel A. G. Hadcock|Sir George Greenhill, F. R. S. | article | 6.0.4 | http://dx.doi.org/10.1098/rspa.1915.0049 | en | rspa | 1,910 | 1,900 | 1,900 | 7 | 58 | 1,886 | http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1915_0049 | 10.1098/rspa.1915.0049 | null | null | null | Measurement | 48.988702 | Fluid Dynamics | 38.702349 | Measurement | [
47.053497314453125,
-50.8703498840332
] | ]\gt ; PROCEEDINGS OF HE ROYAL SOCIETY .
SECTION A.\mdash ; MATHEMATICAL AND PEYSICAL SCIENCBS .
On the Longitudinal Strength of closed by Screw Plugs .
By ieut.-Colonel A. G. HADCOCK .
( Communicated by Sir George Greenhill , F.R.S. Received May 28 , 1915 .
) When designing the breech end of a ooun , or the screwed end of a hydraulic cylinder , it has been customary to assume that the longitudinal stress due to the powder pressure in a gun , or to the water pressure in a cylinder , is uniformly distributed over the cross-section of the gun tube or of the cylinder , as the case may be .
This , however , is seldom the case , because in practice the stress can rarely be applied uniformly over the section , and , therefore , almost always acts either on the inner or on the outer circumferential surface .
The stress on the material is consequently greatest on the surface where the force is applied ; thence , owing to the fibres stretching and sliding longitudinally over each other , the stress is partly transmitted throughout the thickness of the cylinder .
We shall show that in a cylinder there is , on the screwed end , a bending moment exerted on the material , in addition to the ordinary uniform longitudinal stress .
To reduce the investigation to its simplest case : Suppose that we have a cylinder closed by means of a screwed plug and subjected to an internal pressure exerted within the cylinder .
We desire to ascertain the greatest stress on the screwed part of the cylinder .
Let the screw thread be of V form , of which the thrust side makes an angle with the axis of the cylinder .
VOL. XCIL\mdash ; A. Lieut.-Colonel A. G. Hadcock .
On the Longitudinal Let be the total area ( square inches ) of the thrust surface of the few thread , the length in inches of the screwed portion , the internal pressure ( tons per square inch ) , the internal radius of the cylinder to which the pressure is co1lfined , the radius of the screwed part at the root of the thread , the mean radius of the screw thread , the external radius of the cylinder , the angle of friction of the screwed surfaces .
The total longitudinal pressure , in tons , on the screw plug is Then if the depth EA of the screw thread ABD ( fig. 1 ) is taken instead of the inclined surface AB , we can put where is the total helical surface formed by the line The pressure acts on the thrust side AB of the thread , giving rise to a reaction and an outward thrust Q. If is the pressure per quare inch corresponding to and and the pressures per square inch corresponding to and respectively , then we have AB Q. Now and , or and the curious result is obtained that if Strength of Cylinders closed by Screw Plugs .
As aots on AC or on only half of the width of the root of the may , by halving , consider it to act on the whole depth .
Thus the thrust outwards becomes per square inch on the inner surface of the cylinder of radius but as the outward thrust is : ( !
) This will manifest itself as a bursting stress on the threaded part AB , fig. 2 , of the cylinder .
If the screw thread is of the buttress type becomes , and as the Lieut.-Colonel A. G. Hadcock .
On the Longitudinal longitudinal force is normal to its surface there is no tendency to : consequently the outward stress vanishes .
The total pressure on the screw plug is taken on the wall of the cylinder at the root of the screw thread .
Here , the surface exposed to this longitudinal force is , and there will , consequently , be an uniformly distributed but cumulative longitudinal stress of tons per square inch .
At ( fig. 2 ) this stress is , but at A it has an intensity tons per square inch .
In order to examine the stress on the cylinder divide it longitudinally into an infinite number of elementary segments EFGH , and consider the forces acting on one segment embraced by two radial planes at an angular distance apart .
Then the width of this beam at radius is : and as the longitudinal force is uniformly increasing over the screwed internal surface , it is zero at ( fig. 2 ) and has its greatest value , tons per square inch , at A. The total longitudinal force on the width of the beam at any cross-section distant from A is therefore This force tends to stretch the material longitudinally ; it will also tend to bend the beam about its neutral surface , and as can be made indefinitely small , the neutral surface may , for each elementary beam , be considered a plane surface .
If denotes the radius of this neutral surface the force acts at a distance from it .
The tension , or positive , stress on the material of the beam , at any radius of the section is , therefore , the uniformly distributed stress on the section due to the load plus the stress due to the bending moment on the section .
Thus where resultant bending moment on the beam about the neutral axis of the section under consideration , and I the moment of inertia of the section .
Note , however , that when is greater than , the last term becomes Strength of Cytinders dosed by Screw Plugs .
5 negative , and a compressive may result on the outer circumferential fibres .
The resultant bending moment , .
( 3 ) The first term on the right is the moment of the longitudinal force , acting at radius , about the neutral axis at radius ; the second term is the sum of the moments of the bursting stress due to the thrust component of the screw threads .
This thrust is uniform throughout the length and acts about the point ( fig. 2 ) ; its magnitude , on the mean width of the screw thread and for a length of the beam , is for any distance from A the leverage about is , consequently the moment is : and the sum of the moments from to is that shown in the second term .
The third term , acting in the contrary direction , is the sum of the moments of the hoop tension resolved parallel to the central plane of the segmental beam ; it is greatest at and vanishes at , where the deflection of the beam outwards is least .
The total tension effort , for a thin strip across one of the bounding radial planes , is , suppose , and we may assume that the distribution of the tension through the thickness of the cylinder follows the usual laws for thick tubes .
This is , however , only strictly correct when the longitudinal stress is uniform throughout the section .
is , therefore , the sum of the circumferential tensions through the thickness of the cylinder .
It should be noted that can be replaced by , and that when has its greatest value ; and that when , i.e. at the extreme end of the cylinder .
Again , from elementary principles , we have for the deflection of the beam EI Therefore from equation ( 2 ) , putting in the last term for the greatest stress , EI , ( 4 ) Lieut.-Colonel A. G. Hadcock .
On the changing into and integrating As when , there is no constant .
Integrating again E .
( 5 ) Here at the neutral surface the deflection when , and , therefore , there is no constant ; also is grea when , in which case For the greatest deflection put , then equation 5 becomes E , ( 6 ) the negative sign indicating the direction of the deflection .
From the usual formulas for thick cylinders where is the circumferential tension at radius the radial pressure ( a negative value ) , the longitudinal stress , both at radius When , a constant , so that the ordinary gun formulas hold at this point .
From the ordinary gun formulas for the interior layers of metal in a thick cylinder , viz. , and In our case as we are considering a cylinder only , as there is no external pressure .
If , however , an outer strengthening cylinder is shrunk on to the main cylinder and Consequently in ( 7 ) , Strength of Cytinders closed by Screw Plugs .
where is the circumferential tension of the inner layer at the extreme end of the cylinder .
From equations ( 6 ) and ( 7 ) we obtain\mdash ; by putting Poisson 's ratio inserting the values just found for and so that .
( 8 ) In order to find the value of ( when ) in equations ( 2 ) and ( 3 ) , some law must be assumed for the variation of in the expression If the ordinary formulas for thick cylinders be adopted as the most convenient , although not perhaps absolutely exact , then , since there is no external pressure , and where is the internal pressure which , acting on a diameter , would be required , at each section considered : to produce the total tension From the form of equations ( 5 ) and ( 8 ) it is reasonable to assume that the inner rircumferential tension increases , proportionally to .
from zero at A to at B. If this be assumed , then at any section distant from And when , I or , and there is therefore no constant .
Inserting the limits .
( 9 ) At , where , the expression assumes its greatest value , viz. :\mdash ; and when it becomes zero .
The value of cau now be found at any point from equations ( 2 ) and ( 3 ) by replacing the various terms by their proper values ; it is only 8 Longitudinal Strength of Cylinders closed by Screw Plugs .
necessary to know the greatest stress the material has to support .
Thus when and the greatest is found , i.e. When is very small it will be found that ( 10 ) and replacing by its value in equation ( 8 ) we finally obtain tons/ inch2 .
( 11 ) It follows that the length should be so proportioned that .
( 12 ) The expression equals 1 when , but for all ordinary values of up to or it is a little less than 1 ; if , therefore , we suppose it to be 1 a slightly larger value for the bursting moment will be obtained .
The formula will then be simplified to tons/ inch2 .
13 )
|
rspa_1915_0050 | 0950-1207 | The reaction between gas and pole in the electrical ignition of gaseous mixtures. | 9 | 22 | 1,915 | 92 | Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character | Prof. W. M. Thornton, D. Sc., D. Eng.|Sir Charles Parsons, K. C. B., F. R. S. | article | 6.0.4 | http://dx.doi.org/10.1098/rspa.1915.0050 | en | rspa | 1,910 | 1,900 | 1,900 | 7 | 208 | 3,827 | http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1915_0050 | 10.1098/rspa.1915.0050 | null | null | null | Thermodynamics | 44.186132 | Electricity | 37.842275 | Thermodynamics | [
3.932511329650879,
-51.93400573730469
] | 9 The Reaction between Gas and Pole in the Electrical Ignition of Gaseous Mixtures .
By Prof. W. M. Thoknton , D.Sc .
, D.Eng .
, Armstrong College , Newcastle-upon-Tyne .
( Communicated by Sir Charles Parsons , K.C.B. , F.R.S. Received June 21 , 1915 .
) 1 .
Introduction .
Every inflammable gaseous mixture has a definite lower electrical limit , of current or voltage or capacity , at which ignition fails .
Previous measurements on this have been confined to the observation of least sparking distance or lowest gas pressure at which inflammation ceases to be possible , and in almost every case the sparks used have been disruptive discharge between platinum or aluminium points .
The results of Emich * who made the first systematic observations , led to the view that ignition is independent , or nearly so , of the metal of the poles between which the igniting spark is produced , and this is generally accepted .
There appear to be no previous observations of ignition by low voltage condenser discharge , or by break-sparks , as being affected by the metals of the poles .
The present paper is an examination of typical reactions : in the case of break-sparks , at atmospheric pressure and with the percentage of combustible gas in air varied ; in the case of long and short jump-sparks , with a constant mixture and varied gas pressure .
The two gases chosen for the purpose , using break-sparks , were ethane and carbon monoxide , both of which could be obtained pure .
Ethane is a better representative of the paraffins than methane , which appears to be in some respects abnormally difficult to ignite .
Carbon monoxide was chosen because of the relative simplicity of its combustion .
The limits of inflammability of ethane are 3*1 and 10*7 per cent , in air , of carbon monoxide about 14 and 71 .
The latter have not been worked out closely , for it is in the intermediate mixtures that most difference is observed .
2 .
Continuous Current .
The results of the trials of different metals using .continuous current are given in fig. 1 for ethane .
The curves have the same relative positions in * F. Emich , Vienna , 'Akad .
Wiss .
Sitzber .
, ' vol. 106 ( Abth .
2b ) , p. 10 ( 1897 ) ; 'Naturw .
Rundsch .
, ' vol. 12 , p. 575 ( 1897 ) ; ' Monatshefte Chem. , ' vol. 18 , p. 6 ( 1897 ) ; vol. 19 , p. 299 ( 1898 ) ; vol. 21 , p. 1061 ( 1900 ) .
10 Prof. W. M. Thornton .
The Reaction between Gas and weak and rich mixtures , and are inclined to the horizontal in the manner previously found for continuous current ignition of the paraffins.* Ignition is most difficult with platinum poles , then with copper , nickel , iron , and aluminium in this order , f S 4 5 6 7 8 9 IO II 12 13 14 PER CENT OF GAS IN AIR Fig. 1- Least igniting currents in mixtures of ethane and air .
Continuous current , .
100 volts .
Break-sparks .
( 1914)Tte EleCtrlCal Ignition of G~ Mixtures , " ' Roy .
Soc. Proc. , ' A , vol. 90 , p. 272 .
+ See ^'^bs !
\lt ; PbiL MaS- ' ( 6)\gt ; voL P- 617 , 1905 , or J. J. Thomson , The Conduction of Electricity through Gases , ' 2nd edit .
, fig. 127 , p. 459 .
I amperes Pole in the Electrical Ignition of Gaseous Mixtures .
11 In carbon monoxide ( fig. 2 ) the curves are more of the horizontal type observed with condenser spark-ignition , * which is atomic in the sense that ignition is determined by difficulty of choice between atoms free to combine .
The order of difficulty in weak mixtures is platinum , copper , nickel , iron , and aluminium , the same as in ethane .
In the rich mixtures copper and platinum change places .
10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 PERCENT OF GAS IN AIR .
Fig. 2.\#151 ; Least igniting currents in mixtures of carbon monoxide and air .
Continuous current , 100 volts .
Break-sparks .
3 .
Alternating Currents .
With ethane ( fig. 3 ) the usual rounded type of curve is found , though the lower cuives are flattened .
The order of difficulty is now copper , iron , nickel , aluminium , and platinum , and the same order is found in carbon monoxide ( fig. 4 ) .
The Ignition of Gases by Condenser Discharge Sparks , " vol. 91 , p. 17 ( 1914 ) .
1 Roy .
Soc. Proc. , ' A , 12 Prof. W. M. Thornton .
T Reaction betiveen Gas and 9 10 II 12 3 1 PERCENT OF GAS IN AIR .
Fig. 3 .
Least igniting currents in mixtures of ethane and air .
Alternating current , 200 volts , 40 ~ .
Break-sparks .
i AMPERE Pole in the Electrical Ignition of Gaseous Mixtures .
to 15 20 25 30 35 40 45 50 55 60 65 70 75 80 PERCENT OF GAS IN AIR Fig. 4 .
Least igniting currents in mixtures of carbon monoxide and air .
Alternating current , 200 volts , 40 ~ .
Break-sparks .
Comparing continuous and alternating values , the currents for platinum are much the same in both , but the others have changed greatly .
Taking the midway mixtures , that is , 7 per cent , in ethane , 42*5 per cent , in carbon monoxide , we have the following ( Table I ) , the currents being in amperes:\#151 ; Prof. W. M. Thornton .
The Reaction between Gas and Table I. Continuous current , 100 volts .
Alternating current , 200 volts , 40 ~ .
Metal .
Ethane , 7 per cent. Metal .
CO , 42 * 5 per cent. Metal .
Ethane , 7 per cent. Metal .
CO , 42 *5 per cent. Pt 1 -98 Pt 0*90 Cu 9*7 Cu 9 *7 Cu 1 *65 m 1*05 Fe 7*5 Fe 7*5 Mi 1-47 Cu 1 TO Ni 3*7 Ni 4*7 Fe 1 -33 Fe 0*85 A1 2-9 A1 3 2 A1 1T5 A1 0*82 Pt 2*5 Pt 2*6 0 With alternating pressures the magnitudes of the least igniting currents are little different in the two gases , and it is therefore necessary to qualify a previous conclusion* that " ignition by alternating current break-sparks appears to depend more upon the nature of the gas , that by continuous current on the nature of the poles " The reaction is too intimate for this to be true for all gases .
It applies to the paraffins when ignition is made with iron poles .
4 .
Jump-sparks .
This name describes the single disruptive discharge through a gas , from condensers or from the secondary of an induction coil the primary circuit of which is made or broken with the trembler locked .
The latter spark is sometimes called in chemical papers a " break-spark , " but this may be confused with the extra current arc formed at the point where any circuit is broken , which has been always called a break-spark .
In the present case the spark-gap was fixed in the explosion vessel at a length of 1^ mm. If the current broken is below a certain value no secondary spark passes , and in most inflammable gaseous mixtures even when a jump-spark is first obtained it does not cause ignition .
There is , for every mixture , pressure , and coil , a least primary current which , when broken , causes ignition by the single secondary spark .
The disruptive discharge in this case lasts longer than condenser discharge and is at atmospheric pressure a thin spark .
At lower pressures it spreads to a much larger volume .
Most work on the electric strength of gases has dealt with sparks of this nature , a full discussion of which , from the point of view of ionisation by collision , is given by Prof. J. S. Townsend , in 'Electricity in Gases/ Chapters 9 and 10 .
It is shown there that in general the sparking potential is a linear function of the product of gas pressure and sparking distance , which means , as shown by de la Rue and * The Ignition of Coal Gas and Methane by Momentary Electric Arcs/ ' 4 Trans. Inst. Min .
Eng./ Part I , vol. 44 , p. 173 .
i Pole in the Electrical Ignition of Gaseous Mixtures .
15 Muller , that the passage of the spark depends on the number of molecules of gas between the poles.* 3 Under this head may be also classed the exceedingly short sparks obtained at the discharge of a condenser , charged at a low pressure , from 50 to 250 volts , by bringing together a platinum wire and rod .
Just before metallic contact a spark passes , a few thousandths of a centimetre long , sometimes with large sparks welding the poles together .
Ignition by this very rapid discharge has features quite distinct from that by break-sparks .
The most definite of these is that at certain mixtures there is a sudden increase in difficulty of ignition as the percentage of combustible gas is raised .
A series of steps is formed , the lowest starting from the lower limit of inflammability , each having a flat tread , the last at the upper limit having an infinite rise .
In order to examine the electrical conditions of ignition by jump-sparks under conditions comparable with those for which the laws of sparking potential have been worked out , mixtures of constant proportion were used and the gas pressure varied .
In this case the heat of combustion q of the gas per unit volume is proportional to the pressure .
The relation between voltage Y , pressure p , and spark length s , is of the form Y = aps + b , where both a and b differ with the kind of gas.f Writing q = Cp , the voltage required to produce a spark of constant length which will liberate unit quantity of heat in the gas is Y/ q = A + B/ jp .
If this is the critical igniting voltage there should be a relation of the form ( y \#151 ; A)p = a constant , where y is the electrical ordinate .
This is sometimes found with jump-sparks , but more usually with break-sparks , when the pressure is varied .
On account of the large volume of gas required for these observations it was only possible to work with coal-gas used for lighting .
The mixture to give perfect combustion was 11 per cent , of gas in air .
This was made up in a gasholder , and the same used throughout .
The results are given in figs. 5 to 7 , and show that the material of the poles has a great influence on ignition both in magnitude and type of variation , even with jump-sparks .
To distinguish between the two kinds used single induction coil discharge has been called a jump-spark J , a condenser discharge spark being called a condenser spark K. In the latter case the capacity was varied , the voltage maintained constant .
The same number of molecules was , therefore , acted upon in every trial .
In the former the secondary voltage is proportional to the primary current , the energy of the secondary spark to the square of the current .
There is evidence that it is the voltage and not * W. de la Rue and H. W. Muller , 'Phil .
Trans. , ' vol. 171 , p. 109 ( 1880 ) .
+ See Townsend , loc. cit. , p. 357 .
16 Prof. W. M. Thornton .
The Reaction between Gas and energy of the spark that determines ignition in certain cases .
The ordinates of the J or long jump-spark curves are the primary currents which when broken cause ignition by the single secondary spark .
Those of the K or condenser discharge curves are the capacities which when charged to 100 volts just cause ignition by discharge between points a few thousandths of a centimetre apart .
amperes microfarads ATMOSPHERES NICKEL ATMOSPHERES r _ I RON ig .
, ) .
Ignition by disruptive discharge .
Gas pressure varied .
Mixture , 11 per cent. of illuminating gas in air .
i * Pole in the Electrical Ignition of Gaseous Mixtures .
ATMOSPHERES ALUMINIUM VOL. XCII.\#151 ; A , C 18 Prof. W. M. Thornton .
The Reaction between Gas and * MICROFARADS 1-4 O atmospheres COPPER 8 10 12 14 O CARBON Fig. 7 .
ATM05PHERES 5 .
Ignition by Jump-sparks .
The material of the poles has here as much influence on ignition as the nature of the gas .
The following Table gives the relative order of difficulty of ignition , with the break-spark results for comparison .
Pole in the Electrical Ignition of Gaseous Mixtures .
Table II .
Coal-gas .
Ethane .
Carbon monoxide .
Jump .
Condenser .
C.C. break .
A.C. break .
C.C. break .
A.C. break .
Ni Cu Pt Cu Pt Cu Fe Fe Cu Fe Cu Fe Al Ni Ni Ni Ni Ni Pt Al Fe Al Fe ah Cu Pt Al Pt Al pt| Condenser and alternating break-sparks have the same order of metals .
In all three cases ignition is easiest with platinum poles .
With jump-sparks copper is lowest , and the inversion of copper in the first two columns and of platinum in the next pairs shows that the mechanism is profoundly different .
6 .
Causes of Difference .
The physical properties of the poles which may influence ignition are density , specific heat , melting point , thermal conductivity , and , for jump-sparks , tenacity .
The following values are taken for these .
Table III .
Metal .
Density , A. ' Specific heat , \lt ; r. Melting point , M. Thermal conductivity , d. Tenacity .
xl0'- M0 Aluminium 2*61 0*212 ' C. 625 0*344 1 *75 x 109 2*5 Copper 8*9 0*093 1084 0*918 2*9 8*3 Iron 7*8 0*110 1515 0*115 4*6 4*9 Nickel 8*6 0T09 1435 0*142 5*3 4*6 Platinum ... 21 *5 0*032 1900 0*166 3*3 2 *1 The order of difficulty of ignition by continuous-current break-sparks is that of density of the poles , and would appear to arise from difficulty of accelerating bodies of atomic dimensions set free at the cathode .
Continuous-current ignition has been previously observed to have features of ionisation , * by a-rays , for example .
The difference between continuous and alternating break-spark ignition depends mainly upon time , that is , upon the relative rates of reaching a state at which there is discharge from the poles .
It is therefore directly proportional to density and specific heat , and inversely to thermal conductivity .
If , however , the surface liquefies at a relatively low temperature * ' The Electrical Ignition of Gaseous Mixtures , ' loc. cit. , p. 279 .
20 Prof. W. M. Thornton .
The Reaction between Gas and there is both an absorption of heat from the spark and a lower temperature available for corpuscular discharge .
The lower the melting point the greater the difficulty of ignition by radiation from the poles .
We take , then , the ratio Aa/ M0 as a measure of the difficulty of ignition when it is affected most by rate of heating .
The order of magnitude of the figures in the last column is copper , iron , nickel , aluminium , and platinum , which is that of the metals in condenser and alternating break-spark ignition .
This kind of ignition can thus be said to have a thermal origin , * in the sense that it is proportional to the rate of heating of the poles .
The rate and its influence are the same in ethane and carbon monoxide at the mid-point chosen , but not elsewhere .
No direct comparison can be made with condenser ignition , but the relative positions of the curves are the same .
Disruptive discharge , apart from ignition , has been shown to depend upon the rates of ionisation by collision in the gas .
When , however , there is chemical combination , the spark may be accelerated or retarded in its igniting power ; there is evidence of both .
Aluminium and carbon ignitions are very sensitive to change in collision frequency in the gas , and no two materials give the same curves .
The order of the metals in Column 1 of Table II is that at half an atmosphere pressure , the currents at atmospheric pressure being too small for discrimination .
The magnitudes are as follows:\#151 ; Table IV .
Jump-sparks .
Condenser discharge .
Metal .
Primary current .
Metal .
Capacity .
amperes .
microfarads .
Ni 11 Cu 6 Fe 7 Fe 6 Al 4*5 Ni 5 Pt 2-4 Al 2 Cu 1*5 Pt 0*9 Carbon 1*9 Carbon 0*45 The spectrum of spark discharge shows that atoms are torn from the poles and carried over in the disruptive rush .
Difficulty of starting a spark might therefore be expected to depend upon the tenacity of the material.f * * " The Least Energy required to Start a Gaseous Explosion , " ' Phil. Mag. , ' vol. 28 , p. 737 ( November , 1914 ) .
t See also J. J. Thomson , loc. cit. , p. 457 .
) Pole in the Electrical Ignition of Gaseous Mixtures .
21 With the exception of aluminium and carbon , the order in the first column is that of tenacity .
Both of these substances offer more difficulty than might be expected from their sensitiveness to gas conditions .
Carbon atoms in gases are difficult to ionise , and the pioneering ionisation before the spark passes may be retarded by this .
The influence of the metal and state of the poles on disruptive discharge in different gases requires fuller examination .
7 .
Carbon Poles .
In many observations it has been found that when the limit was approached ignition took place not at the first spark but after a few had passed , with a wait of several seconds between each .
To account for this the surface must be changed .
Under the microscope it appears slightly roughened , and when working with carbon compounds and most metal poles a faint deposit of carbon was made around the point of contact , which after many sparks had been passed formed a regular ring .
It became necessary , therefore , to examine whether carbon helps ignition .
For this purpose graphite B drawing pencils were used , one sharpened to a point , the other rounded , with results given in fig. 7 .
Ignition by condenser spark discharge with carbon poles is about twice as easy as with platinum .
It has a very well-defined curve , a curious medley of steps and cusps .
That by jump-sparks has an equally singular shape not unlike that of aluminium .
In both carbon cases the first increase of difficulty begins about 0*8 atmosphere .
At 0'7 there is a sharp rise which with jump-sparks ends in a step with a further rise at 0*62 , reaching a maximum at 0*55 .
It then falls to an ill-defined minimum which appears to be an attempt to renew the stepped formation , and proceeds to a lower limit at about 0T8 atmosphere .
In the condenser curve , after the rise at 0*7 there is a fall to a minimum at 0*55 , from which the curve goes by steps to a lower limit a little above 0*2 atmosphere .
The magnitudes of the latter curve are about midway between copper , the lowest , and platinum .
The steps at 0'6 and 0*7 are found in methane but not in hydrogen .
There is a fall at 0*55 in hydrogen and 0*5 in methane .
Steps are found in methane more than in any other gas ; the rise at 0*35 is peculiar to carbon monoxide .
As might be expected , all the constituent gases take part in the reaction , carbon monoxide carrying it on below pressures at which , in both methane and hydrogen , ignition fails .
The condenser curve follows hydrogen in type , the jump-spark curve methane .
Thus when , as in condenser discharge , we see from SS 5 and 6 that the order of ignition depends on the rate of heating of the poles , hydrogen carries on the action of the spark ; when , as in jump-sparks , ionisation by collision is the decisive feature , methane is Electrical Ignition of Gaseous Mixtures .
first affected .
These are pre-combustion conditions , and the above conclusions do not bear upon the question of preferential combustion m an established inflammation .
The influence of carbon as an accelerator may have bearing on ignition in internal combustion engines .
So long as the deposit does not short-circuit the spark-gap it would appear to be beneficial .
The fact that with condenser discharge carbon gives easiest ignition of all the materials tried may help to explain why carbonisation of the sparking plug does not hinder and may even help the efficient working of the Lodge condenser system of gas-engine ignition .
8 .
Summary .
It is shown that the metal of the sparking points has a great influence upon ignition , at pressures up to an atmosphere , whether the sparks are disruptive or formed by separation of the poles .
The order of difficulty of ignition by continuous-current break-sparks is that of the density of the poles .
That by alternating or condenser discharge sparks is proportional to the rate of heating of the points of contact .
That by jump or long disruptive discharge sparks varies with the tenacity of the material of the poles .
With carbon poles condenser discharge in coal gas has most effect upon the hydrogen , longer disruptive discharge upon the methane .
|
rspa_1915_0051 | 0950-1207 | On the conditions under which the \quot;probable errors\quot; of frequency distributions have a real significance. | 23 | 41 | 1,915 | 92 | Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character | L. Isserlis, B. A.|Prof. Karl Pearson, F. R. S. | article | 6.0.4 | http://dx.doi.org/10.1098/rspa.1915.0051 | en | rspa | 1,910 | 1,900 | 1,900 | 10 | 129 | 4,094 | http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1915_0051 | 10.1098/rspa.1915.0051 | null | null | null | Tables | 77.206495 | Formulae | 8.96028 | Tables | [
59.12885284423828,
-45.71897888183594
] | ]\gt ; On the Conditions under which the " " Probable Errors\ldquo ; of Frequency Distributions Real Significance .
By L. ISSERLIS , B.A. ( Communicated by Prof. Karl Pearson , F.R.S. Received June 21 , 1915 .
) When we seek the value of a statistical constant , we may either consider the whole aggregate of individuals pessinl characteristics of which the constant in question is a function , or we may limit ourselves , from choice or necessity , to the consideration of a random sample of the whole population .
The mean height of of military , at a given instant , is a constant which could be determined by considering the whole population , but , in practice , would be determined from a random sample .
On the other hand , the mean weight of adult frequenting the North Sea is necessarily to be determined only by a consideration of a sample of the whole population .
Statistical constants calculated from a sample give us little information unless we know , at the same time , the manner in which the values may be expected to vary from random sample to random sample , i.e. the frequency distribution of the constant in many samples .
The universal custonl is to state the " " probable error \ldquo ; the constant , which is equivalent to giving the parameter of the normal curve of errors representing the frequencies of the deviations of the values of the constant , calculated from the various samples , from the value of the constant in the population as a whole .
The parameter\mdash ; the standard deviation of the frequency distribution\mdash ; therefore ceases to provide an adequate description of the facts if the frequency distribution differs sensibly from the normal .
Now any statistical constant may be determined by means of the moment coefficients of its frequency distribution , and it is well known that the mean and the standard deviation , i.e. the first and second momeut coefficients of a frequency distribution , themselves have frequency distributions which rapidly approach normality with the increase in the size of the sample , at any rate , when the sample is itself of small size compared with the size of the whole population .
When a frequency distribution ceases to be norma ] , it can , in the * The statement that a statistical constant has a value with a " " probable error \ldquo ; means that if the constant be determined many times from random samples of the relevant material , the value obtained will differ from by less than , in half the number of cases .
is always taken equal to times the standard deviation .
this is based on the assumption of normal distribution , and it is this value of that ceases to have real significance if the distribution be not normal .
24 Mr. L. Isserlis .
Conditions which " " Probable Errors\ldquo ; overwhelming majority of cases , be represented by one of Pearson 's well known frequency curves , the constants of such a curve requiring in addition to the mean and standard deviation , a of the -coefficients and , where , are the third and fourth moment coefficients .
For a Gaussian distribution is zero and is three .
I propose , in the present paper , to discuss the values of these -coefficients for a moment coefficient of order in the case of a sample of size ?
extracted out of a finite population of size N. It will appear thaC in the case of moment coefficients of moderate order , and approximate to their normal values as the size of sample increases , especially if the sample is itself small compared to the general population .
For coefficients of however , the sample has to an inconveniently fraction of the popnlation itself if and are to approach even approximately to their Gaussian values .
The usual " " probable error\ldquo ; ceases for such moment coefficients to have Gaussian significance and statistical constants , founded on such moments , cease to be of valne , unless they are accompanied by the constants of their skew frequency oution .
It t.o be hoped that the values of , which are here given without approximation , for moments of any order , ma prove useful in applications in which is not small and moments of order necessarily occur .
The results of the present paper suggest , howevel , that there is little value in graduation which , thanks to the employment of high moments , represent a iven sample with raphic accuracy .
Now the moment coefficient of order obtained from a ) of drawn a population of is given by the formula where is the frequency of the roup of character in the sample , being measured from some fixed origin .
The mean value of or will clearly be the value of for the population , or where is the frequency of the group of character in the whole populatiou where deviation in the sample .
We have now to find the monlentsM , of the distribution of to ascertain the values of and and ascertain how these approach the values zero and three , wluch would accord with normality as the value of is increased .
It is clear that we shall * For moments of odd tends to zero , howe high the order may be .
of Frequency Distrributions require for this purpose a knowledge of the mean values of , as well as the mean values of various products of the deviations of type , and in general of products of type , of yree not higher than the fourth .
In the next place when the moment coefficients are taken about the mean of the sample , so that and we shall require for the determination of the moments of the deviation , a of the mean values of products ( of not higher than the fourth ) of type We proceed in the next two sections to a systematic ation of the mean values of products of these two types .
2 ( i ) .
The Moment of the Frequencics.\mdash ; If a sample of be extracted from a population of containing Np with and Nq without a given characteristic , then the moment coefficients are the moments of the terms of the hypergeometrical series , ( 1 ) where The moments of this series are known to be as follows:* In the case of a character occurring in a group of and , whence by substitution in the above values we obtain the moment coefficients of occurring in the sample / Let us write , ( 3 ) 'Phil .
Mag 1899 , pp. 236-246 , Prof. Karl Pearson , " " On Certnin Properties of the Hypergeometrical Series Mr. L. Isserlis .
Conditions under which " " Probable Errors\ldquo ; and When the sample is small compared with ] the total population , so that is ible , we have and Then the mean value of is .
Or Mean to the best of our knowledge , as is the besb value we can put for Similarly Mean value of , ( 7 ) Mean value of ( ii ) The of the Frequencies.\mdash ; Let a populatiou co1ltain dividuals of type 1 , N2individuals of type 2 and others .
A sample of size being taken , the probability that it contains individuals of type 1 , individuals of type 2 , others , is clearly : where , , while Thus the product moment coefficients are those of the tel.ms of the double hypergeometrical series The sno1nents of this series have been calculated by the author* 'Phil .
Mag 1914 , pp. 386-387 , L. Isserlis , ' Application of Solid Hypergeometrical Serics to Frequency Distributions in Space of Frequency butions hSigni.ficance .
and the values required in the present paper can be obtained by replacing the quantities , and of the ' Phil. Mag. ' article by and respectively .
We thus obtain the additional mean values\mdash ; Mean value of Mean value of .
( 10 ) It was unnecessary for the purpose of fitting the double hypergeometrical series to calculate the product moments and , but as the mean values of and are required in the present investigation , we will indicate briefly the methods by which these product moments are obtained .
The notation is that employed in the ' Phil. Mag. ' article previonsly quoted .
Operate on Equations ( 11 ) and ( 12 ) with and respectively and we obtain , ( A ) and Divide by and put , then equation ( B ) becomes or replacing the raw moments by their equivalents in terms of moments about the mean If we now use the moments already found , we obtain on reduction .
If we treat ( A ) in the same way , it becomes 'Phil .
Mag 1914 , p. 380 .
28 Mr. L. Isserlis .
Conditions under tnhach " " Probable Errors\ldquo ; A similar equation will hold in which the suftixes and accents are interchanged , is replaced by by and by .
Let second equation be subtracted from the one last written ; the factor will cancel , and , after considerable reduction , we find ( D ) From ( C ) and ( D ) , we iind Mean value of ( 11 ) Mean value of .
( 12 ) ( iii ) We shall require also the values of , and Now , for given values of and , the mean value of be iven by the regression plane Mean Now from ( 6 ) and ( 9 ) and .
Hence mean for constant and mean mealt mean d .
( 13 ) The mean value of similarly seen to be mean mean d , and by the use of ( 11 ) and ( 12 ) we , after some reduction , Mean value of .
( 14 ) inally , to find the meall value of , we use the regression equation Mean for constant ' Phil. Trans , vol. 18 p. 302 .
of Frequency Distributions have Real Significance .
where denotes the minor with its proper sign ) of in the determinant Using the values of the 's and 's as above , we find mean value of ( mean mean dmean d ) , and with the aid of ( 14 ) this reduces to mean value of When the total population is infinite , the frequency distributions can be represented by binomial series in place of the hypergeometrical series employed above .
If , in addition , we suppose the sample to be so large that may be neglected , we get the case considered by Mr. H. E. Soper* in his discussion of the probable error of the correlation coefficient , and we may vote , as a check on the results ( 6 ) to , that when we put , snd neglect terms in , they agree with the values in equations ( xviii ) to ( xxvii ) of his paper .
For the special case of a normal distribution .
Ghe mean value of can be from a esult published by Prof. Karl Pearson leading to , reeing with our equation ( 12 ) .
We may note also that the methods of the latter part of this section may also be employed to obtain the mean values of and directly from the single series , but fail to give mean value of .
This necessitates the employment of the double series .
3 .
We are now in a position to calculate the exact values of the moments and the coefficients of the distribution of , the characteristics , , being measured from some fixed origin 'Biometrika , ' vol. 9 , p. 95 ( 1913 ) , H. E. Soper , M.A. , " " On the Probable Error of the Correlation Coefficient to a Second Approximation .
' Drapers ' Company Research Memoirs , ' XIV , " " the General Theory of Skew Correlation p. 20 , footnote .
30 Mr. L. Isserlis .
under which " " Probable Errors\ldquo ; and meall value for all samples of or mean value of using ( 6 ) and ( 9 ) , or .
( 16 ) For the third moment coefficient about a fixed origin , we have mean value of mean value of using ( 7 ) , ( 10 ) , and ( 13 ) , this becomes reducing to Thus .
( 18 ) If the population out of which the sample is compared to the sample , we may put , and ( 18 ) may be put in the form ( 19 ) The fourth momeltt about a fixed origin is mean)alue of mean value of value of insert this expression the mean values of the fourth order moments and product 1noments of the frequency deviations given by ( 8 ) , ( 11 ) , ( 12 ) , ( 14 ) , and ( 15 ) , and find of Distributions Real Significance .
' or This be reWl.itten in the form But we have already shown that , ( 16 ) therefore the " " second \ldquo ; of the distribution of the mcment of order about a fixed Origin is given by the elegant formula Now for an infinite population and .
For such a population , therefore , Let us put in equations ( 19 ) and ( 23 ) and we obtain vell known result : If , B2 be th constants of the of the of of drawn at ra , ndom , corrcsponding to in the original f ) ibntion ( uith infinite population ) , In other words the and tend to the normal values and 3 respectively as the size of the sample increases .
* Henderson , R. , JourlL Inst. of Actuaries , ' , pp. 429-442 ; cf. also " " Student ' Biometrika , ' vol. 7 , p. 210 . .
Isserlis .
Conditions under which " " Probable Errors\ldquo ; 4 .
With a view to their use in values of the moments , and t , he -coefficients B2 of the moment coefficients , no about a fixed ; but about the mean of the sample , we proceed in this section to the calculation of the products of various powers of the deviations in the frequencies of one or more of the characters and various verse o the deviation in the rneaIl .
, meall , by ( 6 ) and ( 9 ) , or mean .
( 24 ) When this reduces to the well known formula for the probable error of a mean : Of course the result in ( 24 ) can be obtained directly by putting in equation ( 16 ) .
In the same way we obtain directly from ( 17 ) and ( 21 ) the esults : Mean value of .
( 25 ) Mean value of .
( 26 ) Mean of mean value of by ( 6 ) and ( 9 ) We shall find it convenient , and an aid to brevity to denote , etc. , by , , hence mean value of .
( 27 ) Mean value of mean value of by and ( 10 ) ( 28 ) of Frequency Distri utions have Mean value of mean value of mean of Using ( 7 ) and ( 10 ) and ( 13 ) , this reduces to .
( 29 ) The mean value of mean of and using ( 10 ) and ( 1:3 ) this reduces to .
( 30 ) For the mean value of we use ( 8 ) and ( 11 ) and find mean of or Mean .
( 31 ) The mean value of mean of using equations ( 11 ) , ( 12 ) , and ( 14 ) , we VOL. XCIL\mdash ; A. 34 Mr. L. Isserlis .
Conditions under which " " Probable Errors\ldquo ; and obtain after a further reduction Mean .
( 32 ) The mean value of mean of by ( 14 ) and ( 15 ) , reducing to Mean .
( 33 ) The mean value of mean of With the aid of equations ( 8 ) , ( 11 ) , ( 12 ) , and ( 14 ) this can be reduced to - - so that Mean value of ( 34 ) The mean value of mean of of Frequency ibutions have To reduce this we use ( 11 ) , ( 12 ) , ( 14 ) , and ( 15 ) , obtaining from which we deduce Mean value of Finally we shall require the mean value of , i.e. of This can be reduced by means of equations ( 8 ) , ( 11 ) , , and ( 15 ) .
We give the-final result Mean value of .
( 36 ) 5 .
We proceed to apply the results of the preceding section to the calculation of the constants of the distribution of a moment coefficient when it is taken not about a fixed origin , but about the mean of the sample .
We have , or .
( 37 ) mean value of mean of 36 Mr. L. Isserlis .
Conditions under ?
which Errors\ldquo ; Substituting the meall values found above , of and we get .
( 38 ) Secondly value of , and by ( 37 ) . .
Thus .
( 40 ) For we have again , from ( 37 ) , of Frequency Distnbutions have ignifican c and mean value of for all samples .
Now the mean value of the first term is clearly obtained by dropping the accents in ( 20 ) , and so equals The mean value of the second term is The third term has for mean value The fourth term has a mean value whilst the mean value of the last term is given by ( 26 ) and equals On adding the various terms together , we find that can be written in the form , ( 41 ) where , ( 42 ) ( 43 ) 38 Mr. L. Isserlis .
Conditions under which " " Probable Errors\ldquo ; From equation ( 38 ) we see that P. ( 44 ) Hence .
( 45 ) Also ( 40 ) may be written , ( 46 ) where .
( 47 ) 6 .
When is small compared with so that ( 46 ) and ( 45 ) become , and rapidly approach normal values zero and three as increases , provided and do not become large .
Now we cannot calculate either of these expressions unless we know the actual distribution , but , for large samples , they occur as coefficients of the small quantity and we may get a good idea of their order of magnitude by considering their values for the case of a normal distribution .
Now for such distributions , ( 48 ) and , ( 49 ) Hence for odd values of , ( 50 ) .
( 51 ) For even values of , ( 52 ) , ( 53 ) .
( 54 ) of Frequency Distributions .
39 To calculate these values in numerical cases , we use , when is odd , the formula : and when is even both being simple consequences of equation ( 49 ) .
In practice moments of higher order than the fourth are rarely employed .
The following Tables give the values of , for the moments up to the sixth order and the resulting values of Tabl I. 'Probable \ldquo ; .
Frequency Distributions .
It must be remembered that when the ratio of to , i.e. size of sample to total population , is small , the quantities and all approach unity .
The deviation from normality of the fifth and sixth moment coefficients is considerable , even for samples of 10,000 , and the of the fourth moment differs very significantly from three for samples of 1000 .
The size of the salnple is more influential than the ratio of the sample to the popnlation .
Consider a sample of 1000 , extracted from a population of 1,000,000 , to six places of decimals : , so that to three and For such a saml ) the -coefficients of the first four moments are given in the following Table:\mdash ; Table III.\mdash ; Approximate Valnes of for Samples of 1000 out of a Population of 1,000,000 .
To three places of decimals , values in this Table agree with the values we should obtain by ptltting , or , for a sample of 1000 , population of 1,000,000 may be considered infinite as far as its influence on the first four moments is concerned .
The first four moments are those most frequently employed and a sample of 1000 is not unusually small\mdash ; it is , therefore , of great importance to notice that for such a sample the frequency distribution of the fourth moment is decidedly skew .
7 .
Finally , it is interesting to examine the values we obtained in ( 19 ) and ( 22 ) for the and and of moment coefficient about a fixed , for the case of crtn infinite population .
They may obviously be written:\mdash ; , ( 58 ) where , and are the -coefficients of a frequency curve obtained by Some on the Properties of electrics .
distorting the frequency curve of the original distribution , the distortion consisting in raising each ordinate to the power It seems probable that the values and B2\mdash ; which are given by ( 45 ) and ( 46 ) for an infinite population admit of a similar interpretation .
In fact ( 52 ) , ( 53 ) , and ( 54 ) show that this is the case for even , when the original distribution is normal , but the general case appears at present to be intractable .
Some Experiments on the Properties of Dielectr.ics .
By SPENCER W. RICHARDSON , ( Camb .
) , D.Sc .
( Lond. ) , formerly Principal of , and Professor of Physics at , the University , Southampton .
( Communicated by Sir Joseph J. Thomson , O.M. , F.R.S. Received July 19 , 1915 .
Introdnction.\mdash ; The phenomenon of the residual discharge has attracted the attention of many eminent physicists , and a large number of papers on this subject have been published .
In 1854 Kohlrausch* showed that the instantaneous discharge apparently independent of the residual discharge and that , for a given jar left to self for a given time after charging , the residual discharge was proportional to the initial potential ; and in 1873 Maxwell put forward the view that the existence of the residual discharge could be explained by the assumption that it was due to the heterogeneity of the medium exhibiting it .
In 1881 and asserted that Iceland Spar did not exhibit the phenonlenon of the residual discharge , and claimed that its absence was a confirmation of Maxwell 's view .
I , however , having performed a considerable number of experiments on Iceland Spar , have found evidence of the phenomenon in this case .
The specimen I have studied was a carefully polished slice\mdash ; cut parallel to a cleavage \mdash ; in which no flaw of any kind could be detected by eye .
This specimen was silvered on both surfaces and round the edge\mdash ; a gap being left between the silvered part of each surface and the edge for insulation see .
The charge , as it appeared on one of the surfaces , was conducted away to a subsidiary condenser of much greater capacity than the specimen , and the 'Poggendorff 's Annalen , ' 1854 .
'Treatise , ' vol. 1 , 1873 .
'Phil .
Mag 1881 .
|
rspa_1915_0052 | 0950-1207 | Some experiments on the properties of dielectrics. | 41 | 57 | 1,915 | 92 | Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character | Spencer W. Richardson, M. A. (Camb.), D. Sc. (Lond.)|Sir Joseph J. Thomson, O. M., F. R. S. | experiment | 6.0.4 | http://dx.doi.org/10.1098/rspa.1915.0052 | en | rspa | 1,910 | 1,900 | 1,900 | 10 | 136 | 3,284 | http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1915_0052 | 10.1098/rspa.1915.0052 | null | null | null | Electricity | 38.30399 | Tables | 21.086077 | Electricity | [
16.715755462646484,
-72.25037384033203
] | ]\gt ; Some on the Properties of electrics .
distorting the frequency curve of the original distribution , the distortion consisting in raising each ordinate to the power It seems probable that the values and B2\mdash ; which are given by ( 45 ) and ( 46 ) for an infinite population admit of a similar interpretation .
In fact ( 52 ) , ( 53 ) , and ( 54 ) show that this is the case for even , when the original distribution is normal , but the general case appears at present to be intractable .
Some Experiments on the Properties of Dielectr.ics .
By SPENCER W. RICHARDSON , ( Camb .
) , D.Sc .
( Lond. ) , formerly Principal of , and Professor of Physics at , the University , Southampton .
( Communicated by Sir Joseph J. Thomson , O.M. , F.R.S. Received July 19 , 1915 .
Introdnction.\mdash ; The phenomenon of the residual discharge has attracted the attention of many eminent physicists , and a large number of papers on this subject have been published .
In 1854 Kohlrausch* showed that the instantaneous discharge apparently independent of the residual discharge and that , for a given jar left to self for a given time after charging , the residual discharge was proportional to the initial potential ; and in 1873 Maxwell put forward the view that the existence of the residual discharge could be explained by the assumption that it was due to the heterogeneity of the medium exhibiting it .
In 1881 and asserted that Iceland Spar did not exhibit the phenonlenon of the residual discharge , and claimed that its absence was a confirmation of Maxwell 's view .
I , however , having performed a considerable number of experiments on Iceland Spar , have found evidence of the phenomenon in this case .
The specimen I have studied was a carefully polished slice\mdash ; cut parallel to a cleavage \mdash ; in which no flaw of any kind could be detected by eye .
This specimen was silvered on both surfaces and round the edge\mdash ; a gap being left between the silvered part of each surface and the edge for insulation see .
The charge , as it appeared on one of the surfaces , was conducted away to a subsidiary condenser of much greater capacity than the specimen , and the 'Poggendorff 's Annalen , ' 1854 .
'Treatise , ' vol. 1 , 1873 .
'Phil .
Mag 1881 .
Dr. S. W. Richardson .
Some Experiments difference of potential between this surface and the permanent earth in no case exceeded of a volt .
The whole apparatus , including the specimen and the keys , etc. , was placed in a metal-lined , earth-connected case , containing calcium chloride , and was maintained at a constant temperature night and day .
It was anticipated that in the above conditions any error due to surface conductivity would be small .
That the charge which escaped from the specimen ( after it had been charged and instantaneously discharged ) , in any given case , may be considered to be directly proportional to the area of the conducting surface and inversely proportional to the thickness of the specimen can be seen from the following Table :\mdash ; The results given in the Table were obtained as follows .
One surface of the specimen was connected to the earth .
The other surface was maintained at a voltage for 2 minutes .
It was then connected to the earth , and the quantity that subsequently escaped from the specimen during the first and second succeeding minutes was measured .
The values of given in Column A were obtained on November 14 , 1913 .
The gap ( by which is meant the space required for insulation ) between the permanent earth and the silvered surface through which the charge escaped was cm .
, the area of the surface sq .
cm .
, and the thickness of the specimen cm .
The values given in Column were obtained on March 9 , 1914 .
The specimen had been cleaned and re-silvered .
The gap measured cm .
, but the area and thickness were the same as in the previous case .
The values given in Column were obtained on December 24 , 1914 .
The on the Properties of Dielectrics .
specimen had been re-cut , re-polished , and re-silvered .
The gap now measured 0.3 cm .
, the area sq .
cm .
and the thickness cm .
The values given in Column were obtained by multiplying the values in Column by .
An extensive series of experiments on the apparent conductivity of quartz and other crystals has been performed ) Curi has shown , inter that a specimen of quartz cut perpendicular to the optical axis behaves vety differently from one cut parallel to i6 .
He has also suggested that an electromotive force of polarisation may be set up in the specimen when the external field is applied .
I propose , in a subsequent paper , to give an account of some measurements of this electromotive force of polarisation made by me .
NOTE : has shown that the apparent specific inductive capacity of crystallised sulphur has different values in diffel'ent directions in the crystals .
I have performed a great many experiments on a specimen of quartz , cut perpendicular to the optical axis , and silvered in the same way as the specimen of Iceland spar .
The results of some of these experiments are given below .
I have also performed some experiments on a specimen of rock salt , cut parallel to a cleavage plane .
This specimen , being soluble in water , could not be silvered , but it was found that if tin foil , moistened with distilled water , wa , pressed firmly on the surfaces and edge it adhered to the specimen when dry .
The specimen was set up in an air-tight metal box , containing phosphorus pentoxide , which was kept closed for about six weeks before , and during , the experiments .
Boltzmann ( loc. cit , and other observers , have that the apparent specific inductive capacity of a dielectric depends upon the time of charging , or , in the case of the alternating current method , .upon the frequency , e.g. , J. J. ThomsonS has found for glass\mdash ; Frequency , , 100 per , 9 to 11 , per sec. , where is the apparent specific inductive capacity .
The experiments performed by me ( commenced in Southampton in 1906 'Annales de Chimie , ' 1889 .
'Vienna K. Akad .
Sitzungsber 1872 , 1873 , 1874 .
'Phil .
Trans 1876 , ; 'Roy .
Soc. Proc 1876 , 1897 .
S 'Roy .
Soc. Proc 1889 .
I desire to place on record my indebtedness to Prof. E. L. Watkin , of University College , Southampton , who co-operated with me in the earher experiments performed at Southampton .
44 Dr. S. W. Richardson .
Some Experiments have been continued in the Davy Faraday Laboratory from October , 1912 , up to the present time .
The conclusions arrived at by me include the ollowing : 1 .
When a dielectric is subjected to an electromotive difference of potential it becomes polarised .
If the difference of potential is suddenly removed the polarieation dies rapidly at first , but more slowly afterwards .
It is the decay of this polarisation that gives rise to the so-called and of a condenser .
2 .
Let one surface of a dielectric ( in the form of a plate or cylinder , etc. , and originally unpolarised ) be permanently connected to the earth and the other surface be maintained at a potential for a time T. If this second surface is now connected to the earth , after a very short time , , both surfaces are at zero potential and the charge of electricity that has been set free may be represented by where is a constant depending on the size and arrangement of the surfaces , and is , in general , sensibly independent of both and T. 3 .
There is a charge remaining in the dielectric , which slowly dies away , and this charge can at any time , , from the commencement of the discharge , be represented by In this paper is called the Specific Inductive Capacity , and the Specific Inductive Residual of the dielectric , and the total initial charge in the dielectric is represented by 4 .
If the dielectric is charged for any given time diminishes according to the law , ( since is small compared with t ) and In these equations are constants .
This , however , is only true for a given time of charging .
A careful examination of the of a specimen of , cut perpendicular to the optical axis , and a specimen of Iceland spar , cut ] to a cleavage plane , has shown that in the case of.each of these specimens , vary continuously with the time of charging , but that A is proportional to and , therefore , on the Properties of Dielectrics .
where is a constant independent of the time of charging .
In general , within the limits of experimental error , it is possible to write After the discha1ge has taken place for some time this equation reduces to all the above conclusions it is assumed that the temperature of the speoimen is maintained constant .
Jfethod.\mdash ; The experimental results were obtained in the following way : Both surfaces of the specimen to be examined were connected to the earth ( see fig. 2 ) and the specimen was intained at a constant temperature for some days .
One surface was then connected to the main battery by operating the key and the specimen was charged for a given time .
This surface was them reconnected to the earth .
At a subsequent time , , the other surface ( and the subsidiary condenser and one pair of quadrants of the electrometer to which it is attached ) was qconnected from the earth by operating the key .
At a later time , the specimen was separated from the subsidiary condenser and the electrometer by operating the key , and one minute afterwards the deflection of the line of light on the electrometer was observed and a correction for " " leak\ldquo ; was made .
After a sufficient time had elapsed to allow all trace of the previous charging of the dielectric to disappear , the main battery was reversed and the Dr. S. W. Richardson .
Some Experiments experiment was repeated .
The mean of the two deflections is represented below by .
The electrometer was then standardised .
During the time the charge that escaped from the specimen accumulated mainly in the subsidiary condenser , whose capacity is large compared with the other capacities concerned , and if represents the capacity of the subsidiary condenser , , , , , standardising potential , the deflection of the line of light when one pair of quadrants is raised to the standardising potential , the other pair being to earth , the charge that has escaped from the specimen can be calculated from the relation We also have , if represents the electromotive force of the main battery , , , , , area of the conducting surface of the specimen connected to the electrometer for the time , , , , , thickness of the specimen , Finally we get In the above equations it is assumed that the capacity of the subsidiary condenser is sufficiently great to allow the difference of potential set up by the accumulated charge to be neglected in comparison with the electromotive force of polarisation of the dielectric , and that may be taken to represent approximately the charge that would have escaped from the specimen in the time if both surfaces had been permanently connected to the earth .
The capacities of the subsidiary condensers used were carefully determined in conditions approximating to those that obtained in the actual experiments one minute after charging .
Their values were : Microfarad .
Microfarad .
No. I No. No. II 00274 No. 0:00182 No. No. VII No. \mdash ; The specimen Sp , Dolezalek electrometer , subsidiary condensers , etc. , were all contained in a wooden case ( see fig. 3 ) , lined Dr. S. W. Richardson .
Some xperiments with felt and earth-connected 1netal , and maintained night and day at a constant temperature by means of the following automatic arrangement ( see fig. 4 ) .
A battery was connected in series with an adjustable resistance ( outside the case ) , and two heating resistances , ( inside the case ) , through a mercury contact When the temperature of the case reached a certain value , the mercury in a long vertical tube ( inside the case ) made contact with a platinum po nt thus completing a subsidiary circuit and a small electromagnet As soon as this took place the mercury contact was broken and the heating current was reduced owing to the inclusion of the adjustable esistance in the hearing circuit .
The temperature of the case then fell until the mercury in the tube sepal.ated from the platinum point .
This caused the exclusion of the resistance , and the ture of the case rose .
It was thus found possible to maintain the temperature of the case constant to within 0 .
C. Three keys , , of the type shown in 5 ; were contained in a metal-lined , earth-connected box , attached to the case A. Leads passed from these keys through holes into the case A. The key shown in the consisted of an ebonitc strip , to the extremities of which two metal points ( joined by a wire ) were attached .
The strip could be turned round a horizontal axis by exciting a small electromagnet .
One of the keys was used for connecting one surface of the specimen to the battery or to the earth , one for connecting the other surface to the electrometer ( and attached subsidiary condenser ) or to the earth , and one for and disconnecting the electrometer ( and attached subsidiary condenser ) and the earth .
on the Properties of Dielectrics .
During an experiment the box was kept closed .
The bserver excited the electromagnets , and thus produced the necessary nges in the positions of the ebonite strips , by oompleting the exciting circuits .
This was effected by means of the sliders see , which could be moved separately or moved clamped together .
Efperime tal fiesults.\mdash ; The data given below relate to expel.iments performed at the following temperatures:\mdash ; Tenlperature .
I. Quartz : specimen cut perpendicular to the optical C. II .
Iceland Spar : specimen cut parallel to a cleavage plane C. .
Rock Salt : specimen cut to a ] plane C. The following values have been obtained for In the-equation the values have been calculated for I. Quartz II .
eland Spar III .
Bock Salt A series of ements of , under varying conditions as to , etc. , have been made , and from these the following data have been compiled .
In the first column of the Tables are shown times measured from the instant at which both surfaces of specimen were brought into contact with the earth , and in the columns the corresponding values of for different times of chargiIJg are given , the last value in each column being computed and not derived from an experiment .
From these data the curves plotted as figs. 6-9 ( Quartz ) , figs. 12-14 ( Iceland Spar ) and fig. 17 ( Rock Salt ) were obtained .
Above the curves the logarithms , to the base 10 , of the various values of VOL. XCIL\mdash ; A. Dr. S. W. Richardson .
Some III .
Rock Salt .
Curves connecting the values of and the times of are shown I. Quartz II .
Iceland Spar 16 .
III .
Rock Salt , , 19 .
If the curves shown as figs. 6-9 ( Quartz ) , and 12-14 ( Iceland Spar ) are examined analytically it will be found that can be represented imately by , and that vary continuously with the time of charging .
A curve connecting and the time of , or and the time of charging , is of the same general type as th connecting and the time of .
As , however , the relation is only approxintely true , definite values have not been to Addendum.\mdash ; The following results were obtained from experiments on a large oolass test-tube , a sheet of paraffin and an ebonite tube : On Waves .
In each case the time of was two minutes .
The results are given in terms of the total charge in electromagnetic units contained in the specimen when the original difference of potential between the surfaces was unity .
In the first column times measured from the instant at which both surfaces are connected to the earth are given .
These results are plotted as figs. 20-22 .
For these spec imens the values of are ( after two minutes charging ) Glass ( test-tube ) .
Paraffin .
Ebonite .
The author 's thanks are due to the Managers of the Royal Institution for placing the resources of the Davy Faraday Laboratory at his disposal , and to the Director , Prof. Sir James Dewar , for much helpful kindness and consideration .
On Water Waves by a Local on or beneath the By K. TERAZAWA , Ri-Gakushi in the Imperial University of Tokyo .
( Communicated by Sir Joseph Larmor , F.R.S. Received June 28 , 1915 .
) The classical problem of waves produced in deep-sea water by a local disturbance of the free surface has been investigated by Prof. H. Lamb* in a very able manner .
He completed the theory of wave propagation in one dimension and in two horizontal dimensions when the initial disturbance is concentrated in the immediate neighbourhood of a line or a point , assuming that Fourier 's double integral theorem can be applied in ) a case .
In this paper I venture to discuss the same problem , especially the oscillations at the centre of the disturbance , following Prof. Lamb 's method , in cases where the initial disturbance is spread over a certain ext , ent of the free surface ; and , as an application of the general solution , I propose to treat the case in which the initial disturbing source is situated at a finite depth from the free surface , where the surface wave is produced by an explosion like that of a mine under water .
S1 .
Supposing the water to extend to infinity , horizontally and downwards , and taking the axes of and on the undisturbed free surface and that of ' Lond. Math. Soc. Proc vol. 2 ( 2 ) , p. 371 ( 1904 ) , or ' Hydrodynamics , ' third edition , SS236-239 , 251-262 .
VOL. XCIL\mdash ; A.
|
rspa_1915_0053 | 0950-1207 | On deep-sea water waves caused by a local disturbance on or beneath the surface. | 57 | 81 | 1,915 | 92 | Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character | K. Terazawa|Sir Joseph Larmor, F. R. S. | article | 6.0.4 | http://dx.doi.org/10.1098/rspa.1915.0053 | en | rspa | 1,910 | 1,900 | 1,900 | 24 | 205 | 5,258 | http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1915_0053 | 10.1098/rspa.1915.0053 | null | null | null | Fluid Dynamics | 49.042646 | Tables | 25.308331 | Fluid Dynamics | [
43.4381217956543,
-39.86262893676758
] | ]\gt ; On Waves .
In each case the time of was two minutes .
The results are given in terms of the total charge in electromagnetic units contained in the specimen when the original difference of potential between the surfaces was unity .
In the first column times measured from the instant at which both surfaces are connected to the earth are given .
These results are plotted as figs. 20-22 .
For these spec imens the values of are ( after two minutes charging ) Glass ( test-tube ) .
Paraffin .
Ebonite .
The author 's thanks are due to the Managers of the Royal Institution for placing the resources of the Davy Faraday Laboratory at his disposal , and to the Director , Prof. Sir James Dewar , for much helpful kindness and consideration .
On Water Waves by a Local on or beneath the By K. TERAZAWA , Ri-Gakushi in the Imperial University of Tokyo .
( Communicated by Sir Joseph Larmor , F.R.S. Received June 28 , 1915 .
) The classical problem of waves produced in deep-sea water by a local disturbance of the free surface has been investigated by Prof. H. Lamb* in a very able manner .
He completed the theory of wave propagation in one dimension and in two horizontal dimensions when the initial disturbance is concentrated in the immediate neighbourhood of a line or a point , assuming that Fourier 's double integral theorem can be applied in ) a case .
In this paper I venture to discuss the same problem , especially the oscillations at the centre of the disturbance , following Prof. Lamb 's method , in cases where the initial disturbance is spread over a certain ext , ent of the free surface ; and , as an application of the general solution , I propose to treat the case in which the initial disturbing source is situated at a finite depth from the free surface , where the surface wave is produced by an explosion like that of a mine under water .
S1 .
Supposing the water to extend to infinity , horizontally and downwards , and taking the axes of and on the undisturbed free surface and that of ' Lond. Math. Soc. Proc vol. 2 ( 2 ) , p. 371 ( 1904 ) , or ' Hydrodynamics , ' third edition , SS236-239 , 251-262 .
VOL. XCIL\mdash ; A. Mr. K. Terazawa .
On Water vertically downwards , we have , on the assumption that the motion is infinitely small and irrotational , , ( 1 ) where denotes the pressure , the density of water , the constant of gravity and the velocity-potential which satisfies the equation .
( 2 ) If ' denotes the depression of water-level at the point and at time below undisturbed surface , then the pressure condition to be satisfied at the free surface , to be small , is , ( 3 ) and the kinematical condition is .
( 4 ) Hence , for , we must have or , if the time factor be .
( 5 ) The solution of equation ( 2 ) , which makes when , is , in cylindrical co-ordinates , , ( 6 ) where is Bessel 's of th order and is any positive number .
From equations ( 5 ) and ( 6 ) we get .
( 7 ) The modes of irrotational motion of water by surface disturbance present themselves , as Prof. Lamb points out , in two forms : ( 1 ) by an initial displacement of the surface , without initial velocity ; ( 2 ) by an initial impulse applied on the surface , without initial surface displacement .
The most general case is a combination of these two .
I. S2 .
As the typical solution for the case of initial rest we take .
( 9 ) caused by Local Disturbance .
The water is supposed to be unlimited in extent , and hence there is no limitation to the length of waves , but the motion will be the result of the superposition of waves of infinite variety of length .
Therefore to obtain the general expression which embraces the superposition of all such solutions we must make use of the double integral theorem of Fourier 's type , ( 10 ) with some conditions concerning the function .
Thus , corresponding to the initial conditions , , ( 11 ) we have , ( 12 ) , ( 13 ) where ; ( 14 ) for these expressions clearly satisfy the conditions specified above .
As to the disturbing function , we can snme its form in several ways , under the condition that the theorem ( 10 ) must rernain valid .
Now we consider the case where the initial elevation of the surface is spread over the whole surface according to the law .
( 15 ) This is the simplest form which satisfies the ouble integral theorem .
By taking the value of A sufficiently small , we may consider that it approaches , when , to the case where the initial displacement of reat amount is confined to the neighbourhood of the origin .
* It been kindly pointed out to me by a referee that this statement requires correction and precision .
However small A may be taken , the initial elevation is spread niformly along the radius , but is not concentrated in the sense of Cauchy and Poisson , though it is to be expected that only the central part when the height is considerable can ntribute sensibly to the amplitudes of the waves .
It might appear that the total initial elevated volume , which is expressed by the integral when should be finite .
But it seems to me that this condition is not a necessary one for the validity of the integral theorsm ( 10 ) .
This remark applies to both the initial distribution and that is treated in S4 .
But for the initial distribution that is treated on p. 69 there can be no doubt , for it is of finite total amount ; Mr. K. Terazawa .
On Deep-Sea Put the expression ( 15 ) into ( 14 ) , then it appears , by a well known formula , that ( ) ( 16 ) Whence the eneralised expressions for and will become \ldquo ; ( 17 ) Acos ' ( 18 ) By expanding and into series , we , ( 19 ) Acos ; here is eliminated by the relation The definite integral contained in ( 19 ) and ( 20 ) can be evaluated as follows:\mdash ; By using Hansen 's form of Bessel 's function and the integral formula , we hnd that If we put then we have and when b vanishes it is concentrated at a point , the result )eing then the well known form of Cauchy and Poisson .
A main object of this paper is , as stated , to trace the effect on the waves propagated to a distance , and especially on the course of the disturbance at the centre , of a broadening of initial disturbance from a mere point to a wider region .
This has also the advantage that we do not have to proceed to a Iimit .
] * Gray and Mathews , ' Treatise on Bessel Functions , ' p. 79 .
caused by Now , define the function by being the zonal harmonic of nth order , then the integral expression oi , which corresponds to Laplace 's integral for , will be Therefore the required integral becomes .
( 22 ) The result of this , in the case of , was found by Prof. .
W. Hobson .
* In this case , if we remember that , where is the associated function defined by we have ( 23 ) in agreement with his result .
Hereafter we will use ( 22 ) for and ( 23 ) for Hence , putting these values ( 22 ) and ( 23 ) into equations ( 19 ) and ( 20 ) , we get and .
( 25 ) 'Lond .
Math. Soc. Proc vol. 25 , p. Mr. K. Terazawa .
On Water The values of and are as follows:\mdash ; ' ( 26 ) , For the case of symmetry about the origin , i.e. , the first summations in ( 24 ) and ( 25 ) disappear , and therefore we have simply , ( 27 ) , ( 28 ) similar expressions to those which were found by Prof. Lamb for the case of complete concentration of the source .
The next simplest case is that of , though it may not be very important in practice .
In this case we obtain , ( 29 ) ( 30 ) These solutions do not give any information as to what takes place at the immediate neighbourhood of the origin .
Not only the initial data but the displacement at any time will be infirlite at the origin ; such a point is excluded in our fundamental assumption .
The appropriate initial data and the solutions to illustrate this point will be given presently ( S4 ) .
S3 .
The series ( 25 ) is not convenient when we deal with the case in which has large values , since it converges rather slowly in such a case .
The suitable expressions in this case , at least when and , can be obtained by a similar method to that employed by Prof. Lamb for the case of complete concentration of the source .
If we put , ( 31 ) then ning to ( 18 ) we have -A .
( 32 ) Waves caused by Local Disturbance .
By using the integral expression for and putting with ; we get .
( 33 ) Now expanding into a s.eries and using the formula ( 34 ) where , and ; we find corresponds to .
Hence where The functions and a , re closely connected with Fresnel 's integral as is well known .
If we put ( 36 ) Mr. K. Terazawa .
, On then we shall have* sirl If is a large quantity , then is plso large , and the functions and can be expressed as semi-convergeuC series of the form ( 38 ) If we neglect and higher powers of it.in these series , we have , from ( 36 ) , approximately Putting , or , ( 39 ) and , ( 40 ) can be written iu the form .
( 41 ) From ( 40 ) it that when is an odd number , and when is an even number .
If we find the values of and V in proper form , we can obtain the expression for by ( 41 ) and ( 32 ) .
The special case was discussed by Prof. Lamb and it was found approximately that , ( 42 ) Lamh , ' Hydrodynamios , ' p. 366 .
Lord Rayleigb , 'Scientific Papers , ' III , p. 129 .
Waves caused by Disturbance .
and therefore we get .
( 43 ) For the case and ( 44 ) The value of the integral contained in the expression of cannot he found very easily .
Since we see that and similarly ; and if we remember that then we can evaluaGe these integrals , following the method which is fully explained by N. Nielsen in his book on Cylinder-Functions .
* I calculated these rals after this method , and found that For large values of we can use the asymptotic expansions of Bessel 's functions , and , to the degree of approximation above mentioned , it is sufficient to retain only the first term of them .
Thus we may take .
Putting these values in the above formulae ( 45 ) , then by ( 44 ) , after simplifying , we have .
( 46 ) Substituting this for in ( 32 ) , we obtain .
( 47 ) 'Handbuch .
Cylinderfunktionen , ' SS 77 , 81 , 82 .
Mr. K. Terazawa .
On Though we have been considering in the above only the terms involving , it must be understood that the same analysis could be applied to the terms containing , if the initial data be so given .
a proper assumption to illustrate what occurs at the origin , take the disturbing function of such a form as instead of ( 15 ) .
This function does not violate the double integral theorem ( 10 ) .
Supposing the value of to be sufficiently small , this approaches , at a distance from the origin , to the function assigned in S2 , and yet it is finite at the origin .
Therefore we might take , even in this modified assumption , the solutions in S2 as those for the point at which has a moderately large value .
For the case of symmetry the function defined by ( 14 ) becomes This integral can be effected by using the double integral theorem ( 10 ) in a special case , and is found easily to be ( 49 ) supposing to be positive .
Hence we have the expressions for and from ( 17 ) , ( 18 ) , ( 50 ) .
( 51 ) Making use of the integral formula ( 23 ) , we get the following solutions , in place of ( 27 ) and ( 28 ) , ( 52 ) with and with , At the origin , we have The is valid for only when Or , as a special case of the integral of N. Sonine ( ' Math. Ann vol. 16 , p. 50 ) , we get the above result , putting in his formula Waves caused by Disturbance .
and since ) , the equation ( 53 ) gives .
( 54 ) If we put , for the present , then the above expression can , referring to , ( 36 ) , be put in the form and , therefore , using the integral expressions ( 37 ) for the functions and we have Or , putting again , for the sake of simplicity , , ( 55 ) it follows that .
( 56 ) The expressions ( 54 ) and ( 56 ) for the displacement of the point which was initially situated at the origin are equally inconvenient to discuss its subsequent motion , but it is not very difficult to obtain the general feature of it from the latter form .
For the small value of the value of the function can be obtained by expanding the exponential function in the integral sign and integrating it term by term .
For the large value of the asymptotic expression for the function is ( 57 ) Therefore the course of the ordinate at the origin tends approximately to . .
the ( 5S ) when is great .
* E. T. Whittaker , 'Modern Analysis , ' ; A. E. H. Love , 'Phil .
Trans vol. 207 ( 1907 ) , p. 196 .
Waves caused by a Local Disturbance .
The highest point in the curve corresponds to the initial prescribed tion at the origin .
As increases from zero the elevation decreases and reaches once to the value nil ; and then begins the depression of the surface at the point under consideration .
After that there is only one maximum of the depression , the amount of which is smaller than that of the initial elevation .
Then it decreases more and more , very slowly , until , after an infinitely long time , it takes the limiting value zero .
The number of zero-point and maximum-point can be determined without using the above We can assi several assumptions to the disturbing function to illustrate the movement at the origin .
For example , if we take the form ( 59 ) instead of ( 48 ) , then it appears that , ( 60 ) which can be found in a similar way as before .
In this case and , performing the integration , we have ( 61 ) where and are defined in ( 53 ) .
At the origin this becomes ( 62 ) Concerning this series and also as to the motion at the origin , we can make a similar interpretation to the former case .
II .
S5 .
Quite analogous treatments can be employed in the case where the initial condition is an impulse applied on the free surface .
The typical solution is , ( 63 ) .
( 64 ) This formula gives , in fact , the Cauchy-Poisson series as a lirst pproximation when is taken very small ( Lamb 's 'Hydrodynamics , ' p. 408 , equation 20 ) .
See the footnote on p. 69 .
] Mr. K. Terazawa .
On Water Corresponding to the initial conditions at the free surface , the general solution is ( 66 ) ; ( 67 ) where .
( 68 ) At we assume the initial impulse is given by , ( 69 ) then the value of becomes corresponding to ( 16 ) in the former case .
The explicit form for the solution can be obtained by performing the operation upon that of the former case .
Thus from and ( 25 ) we get , ( 70 ) where , ; and .
( 71 ) Specially for , from ( 27 ) and ( 28 ) , , ( 72 ) .
( 73 ) and for , from ( 29 ) and ( 30 ) , Waves caused by a Local Disturbance .
Now , when is a large quantity , we can make use of the function defined .
Thus A .
Referring to the expressions for and found in ( 42 ) and ( 46 ) , we get ( 76 ) for ; and ( 77 ) for S6 .
As in S4 , we take the function expressing the initial impulse of the form ( 78 ) to illustrate the history of the point which was situated initially at the origin .
For the case of symmetry about the origin , the function becomes Thus we have , ( 79 ) .
( 80 ) Or , performing the operation upon ( 52 ) and ( 53 ) , we obtain ' ( 81 ) , ( 82 ) .
in which as before .
At the origin , becomes .
( 83 ) .
K. erazawa .
On This series call be put in a similar form to that ill S4 ; or rather directly from ( 56 ) it follows that , ( S4 ) , for simplicity , it is ) .
( S5 ) large values of , using ( 57 ) , we can take for its asymptotic expansion of the form ( 86 ) From these expressions we can make out the general feature of the movement of the point under consideration .
By the aid of the Table I we can draw the approximate diagram which represents the isplacement at the origin , units of scales being modified by ( 85 ) .
For , we have and as soon the impulse is applied on the free surface the point at the origin gains suddenly a finite velocity and to move downwards .
It will be seen , from the above figure , that at about the depression becomes nlaximum , at about it takes the value zero and then begins the elevation of the surface , and it takes the maximum value at about , after that it decreases slowly until it tends to its linliting value zero , and the point comes to If we assign another assumption to the initial impulse like that expressed Waves caused by a Local Disturbance .
in , it will probably take place by a similar mode of motion , but in a somewhat complicated form .
III .
S7 .
Now we come to the problem of surface waves caused by an explosion which takes place at a finite depth from the free surface .
* In this case , we might take the value of the impulse , i.e. that of , given by the explosion as .
the initial datum , but the mathematics would be complicated and it might not give any concrete results .
The following consideration , however , may serve to treat the problem without touching on the difficulties .
Suppose that an explosion under water sends out a pressural pulse of the of a wave of sound , propagated by compression at speed , and leaving unruffled water in its wake .
As each ray reaches the free surface it is reflected totally , as required by the condition that the impulse is null at the surface , while a surface normal velocity caused by the pulse remains and determines a hydrodynamic flow throughout the water .
We may take the velocity of the propagation of the pressural pulse to be infinite , then the ima , method in will be applichle as follows .
Let the point which the explosion occurs be at the depth from the free surface and on the axis of .
Suppose the initial value of due to the source at .
to be , where is the distance of any point in the water from , then we must consider a fictitious negative source of equal strength at the image of with regard to the surface , to fulfil the condition that the initial impulse is zero at the free surface .
The initial value of should then be , where This value of gives the initial normal elocity ( 87 ) over the free surface and it dies away of itself .
Thus the problem is , transformed to one of the surface motion , being given the initial surface normal velocity ( 87 ) .
If we take * This problem and the next following were undertaken mainly to illustrate in a general way the nature of the tidal waves produced by a bmarine earthquake , with its source at a point or on a long straight fault in the strata .
The source of the explosion is supposed to be so deep or its force so gentle that the surface of the water is not broken by the ejection of a column of water .
VOL. XCII.\mdash ; A. Mr. K. Terazawa .
On Water as the typical solution , then the general solution corresponding to the initial data ( 87 ) will be ( 88 ) with .
Since , by ( 60 ) , we have ( 89 ) and accordingly .
( 90 ) These are the same essions as ( 79 ) and ( SO ) up to the constant factor .
Therefore putting we get , ( 91 ) and .
( 92 ) At the point just above the explosion , that is at the origin , , ( 93 ) we have ) ( 94 ) Comparing ( 94 ) with ( 84 ) , we see that the curve representing the displacement at the is quite the same as in .
( 2 ) , only inverted in form and the unit of ordinate being different .
If we take as the values of which give the maximum , zero and the minimum of the displacement , and , then the times at which they occur will be given by respectively , in which , and t3 are expressed in seconds and in feet .
Conversely , ?
we can measure any of them , then the depth can be calculated approximately by using the above relations .
Waves by a Local Disturbance .
S8 .
We will conclude this paper by discussing the explosion problem in a horizontal canal of infinite depth and infinite length .
Take the axis of along the canal and on the undisturbed free surface of water , and that of vertical downwards as before .
If we suppose that all the circumstances are independent of , we must consider the initial value of iven by the explosion to be of the form .
Therefore , considering the image as before , we have the effective initial normal velocity at the free surface ( 95 ) in place of ( 87 ) .
Corresponding to this initial velocity , the general solution wiIl be in which .
By a well known formula we get and consequently kx .
( 96 ) Expanding and then making use of the integral formulae , it may be , ( 97 ) where , .
At the point just above the explosion , i.e. along the axis of This series can be put in the form , ( 98 ) in which is defined by ( 93 ) .
* Since this work was finished my attention has been called to a paper by Prof. Lamb in the 'Annali di Matematica , ' vol. 21 , p. 237 1913 ) , where the surface waves that accompany a cylinder travelling uniformly transverse to its length under water are investigated .
H. Weber , ' Die part .
Diff.-Gleich .
, ' vol. 1 , p. 43 .
Mr. K. Terazawa .
On Deep-Sea Water For large values of , if we use the asymptotic expansion ( 57 ) , then Making use of Table I we can trace the curve for In this figure the units of length and time are modified by From this figure it will be seen that the line which was initially situated .
the axis of is suddenly put in motion and there begins an elevation of the free surface , and that after a certain time ( about ) there is the one only maximum of the elevation , and then it decreases more and more until the surface takes the original plane form .
If we take for the value of which ives the maximum of the elevation , then the time at which it occurs is given by , in which is reckoned from the time of explosion in seconds and is measured by feet .
Lastly , at a point very far from the source of disturbance , if we neglect compared with , we may put and in .
Then we ilave ( 99 ) This formula and those that follow are applicable only when is moderately small , this being the only range of values which matters in the physical problem , each phase of the physical disturbance travelling , as is well known , with constant acceleration .
When is large , the most essential terms of the series ( 99 ) are situated far along it , and in deducing them from ( 97 ) we must not replace by unity .
Thus the impossible physical feature of persistence of the amplitude for all time with period diminishing randly without limit , which is indicated in ( 100 ) and in fig. 4 , would not occur in an exact solution : it can be cut away while the earlier undulations of the curve remain applicable .
caused by Local Disturbance .
or referring to ( 35 ) and ( 36 ) this can be put in the form with For large values of , from ( 38 ) , we get ( 100 ) Further , if we put , then .
( 101 ) Again , if we put then we have .
( 102 ) The function has been tabulated by E. Lommel in his memoir on the diffraction problem , and the other functions needed are deduced in Table II , so that the forms of the few waves can be traced without difficulty .
* The first term corresponds to the known Cauchy-Poisson expression for the disturbance at a distance due to a point source , and the second is the modiIication in it that is produced by the finite extent of the source : it represents a gradual fall of the surface to the general level .
' Abh . .
Bayer .
Akad . .
Wiss .
, Cl vol. 15 ( 1886 ) , Tafel Waves caused by a Local Disturbance .
The figure 4 , which belongs to equation ( 101 ) , shows the rise and fall of the surface at various times and at a particular place of a great distance from the , the unit of time being modified by .
For moderately small values of , which alone are applicable , the curve is unsymmetrical with regard to the axis of time and as the time increases the rise and fall becomes more and more symmetrical and , on the other hand , the tions follow .one another with ever decreasing period .
For larger values of , the course of the curve ceases to represent the motion , which really dies away , for reasons explained already ( foot note supra ) .
As a practical application , the earlier part of this curve serve to determine the distance of the point under observation from the source of the explosion , if we measure the time of any zero-point of the displacement or the interval ( i.e. period ) between any two adjacent ones .
For example , if we take , as the values of of the zero-points , and if we measure the :actual time between them : then the distance will be given by in the foot-second-unit system .
It will be noticed that the period in this formula would be a large quantity of the order The figure 5 , which belongs to the formula ( 102 ) , shows the wave profile at a particular time at various distances from the origin , the unit of horizontal scale being modified by .
The second part of the diagram is condensed along- the axis of to 1/ 10 scale of the first part .
As we advance farther and farther towards the infinite distant point from the origin , the essential groups of the waves are found to increase continually in length and to dimlnish continually in , in such a manner that remains constant in each phase .
This figure applies only at great distances from the origin , i.e. when is large , so that has to for the earlier part to be applicable ; e.g. , gives in the foot-second-unit system .
In the region some distance away where equation ( 102 ) holds , and therefore the fig. 5 is applicable , the wave-length can be determined by the . .
values of of the earlier in this diagram .
In conclusion I wish to express my sincere thanks to Prof. ciir J. Larmor his kind advice during the progress of this work .
|
rspa_1915_0054 | 0950-1207 | An application of the principle of dynamical similitude to molecular physics. | 82 | 100 | 1,915 | 92 | Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character | W. B. Hardy, F. R. S. | article | 6.0.4 | http://dx.doi.org/10.1098/rspa.1915.0054 | en | rspa | 1,910 | 1,900 | 1,900 | 15 | 230 | 5,742 | http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1915_0054 | 10.1098/rspa.1915.0054 | null | null | null | Fluid Dynamics | 51.912323 | Tables | 19.168661 | Fluid Dynamics | [
35.5620231628418,
-34.44145202636719
] | ]\gt ; An Application of tl , Principle of Dynamical Similitude .
Molecular Physics .
* By W. B. HARDY , F.B.S. ( Received May 14 , 1915 .
) 1 .
Consider a molecular system subject to the condition of stationary motion , and let ths forces acting between or within the molecules be tive .
A statistical specification of the energy content of such a system can be obtained either by considering a mass containing a large number of molecules , and the energy as the sum of the energies of individual molecules at an instant of time , or by averaging the energy of individual molecules over a sufficiently long time , and expressing the whole energy as the sum of these time averages .
Let us choose the former method .
At any instant of time some of the nlolecules will be in material contact , some free , and , if the molecules are not all alike and some are formed by the more or less complete fusion of others there will be molecules in process of combination to form a distinct type , and molecules of this type in process of up into constituent molecules .
Material contact between molecules is to mean any encounter in which forces of mntual repulsion come into operation .
This definition is exact so long as radiation between the molecules is excluded ( as it is by the imposition of the condition of conservatism ) .
For the term repulsive forces\ldquo ; is here to refer to those forces which confer upon the individual molecules the property of extension in space .
It is not necessary for the moment to enquire whether these forces arise wholly or in part from the variation of the kinetic of internal degrees of freedom .
As the molecules are the moving parts , it is necessary to specify the energy in terms of their number and kind .
The molecules may be classified in two ways , which yield totally different results , namely , according to their chemical structure or to their dynamical characters , , the number of degrees of freedom .
The latter is more general ; it includes the former , and it is necessary to follow it in this paper .
We can recognise three conditions : free molecules , molecules in contact , and transition stages .
The free molecules will include any multiple from unity * A reference to a paper by Kammer ] ingh Onnes ( ' Verh . .
K. Akad . .
Wet .
3 , ' Amsterdam , vol. 21 , 1881 ) first drew my attention to this principle .
ning to the paper I found be in Dutcl ] , and therefore sealed from my comprehension .
This communication gives the results of an entirely independent research , which will , I hope , be found to cover fresh ground .
Principle of Similitude in Molecular Physics .
83 upwards of the chemical molecule or molecules which form the system .
Lt the free molecules be divided into classes in any convenient manner : the transition then are stages of combination or breaking apart of molecules of some of these classes to form molecules of other classes .
Stages in the combination of single chemical molecules to form complexes would come within this category .
Obviously , in order to avoid statistical ambiguity , the classes must be so defined as to exclude transition stages , which then form a class apart .
A sufficient definition is that molecules of the classes are structures in stable equilibrium ; transition states , on the contrary , are in process of internal change , and are therefore labile states .
Lt the word \ldquo ; encounter\ldquo ; refer to molecules which are merely in material contact .
Such molecules can be enumerated as members of the classes , for during an encounter they do not lose their individual dynamical characters .
If is the whole energy of the mass , and , etc. , that of the molecular species , , etc. where is the energy of transition states .
Since in a steady state the distribution of the energy amongst the different molecular species is constant , we can write constant , the constancy being supposed to refer to averages taken over masses of the same chemical fluid each containing a very large number of molecules and each in- the same state as defined by temperature , pressure and specific volume .
The kinetic energy of any one molecule of a species , say species , is , where is the number of degrees of freedom .
The potential energy similarly may be farded as the sum of a number of terms enting respectively the potential energy due to the attraction of the other molecules and the elastic forces within the molecule , including repulsive forces , that is to say those forces which confer extension in space upon the molecule .
, Since the forces are conservative the potential energy is a pure function of the co-ordinates which specify position , thel.efore each term in the potential energy will have the form where are the resolved forces .
Averaging over all the molecules of class , we have as the total energy : , ( 3 ) Mr. W. B. Hardy .
Application of the Principle of is the average ki1letic energy of a degree of freedom , and the average potential energy of any one system of forces .
If denote number of distinct species of molecules , the energy of the mass is .
( 4 ) The quantity includes both kinetic and potential energy .
It is the energy of molecular states which are not in stable equilibrium\mdash ; that is of labile states .
It is a familiar fact that molecular reactions involving the fornlation of new species often can take place only when molecules which do not form part of the new species assist .
An extreme instance of this is found in ferment-actions .
In general a reaction between two molecules leading to structural changes may be supposed to be possible only in certain special local states of the general internal field of force as regards intensity and , especially if the forces are electrical , orientation .
Thus from whatever aspect the energy is regarded it is seen to be energy which cannot be considered as belonging to the chemical molecule or to molecules formed by association of chemical molecules , for these are molecules which are in stable equilibrium .
It is obvious that vanishes when the system is expanded to the state of an , and incleases on the whole as it is condensed , until the crystalline state is reached , when the gas molecule as such ceases to exist .
Let there be two distinguished by the suffixes 1 and 2 , which differ only in their linear dimensions .
There will be two equations similar to equation 4 .
, ( 5 ) .
( 6 ) The limits of summation will be the same in both , and The one equation will be changed into the other if ( 8 ) etc. etc. ( 9 ) etc. ( 11 ) etc. ( 12 ) and .
( 13 ) Similitude to Molecular Physics .
On comparing equations 7-13 with equations 5 and 6 it is seen that .
( 14 ) 2 .
Equation 8 practically limits the application of the principle of dynamic similitude to molecular systems composed of one single chemical substance , and to chemical series such as the paraffins , alcohols , etc. For such a series the parameter may be identified with the ratio of the molecular weights , or if is the gramme-molecule The parameter offers greater difficulties .
is the ratio of corresponding linear velocities in the two systems .
The theorem of equipartition of kinetic states that or the mean energy absorbed by each degree of freedom is the same .
is a constant having the dimensions of energy , and may be taken to be a pure number .
We now have for two systems in which is the mass of the chemical molecules , and a component of the velocity of the centre of ravity of the molecule .
If the units of energy are the saule in both numerator and denominator , and we get from ( 9 ) and ( 17 ) , ( 18 ) where are the temperatures of the two systems when dynamically similar , that is to say when they are in corresponding states .
The propriety of extending the law of equipartition of energy to condensed systems is , however , still open to debate .
* But the statement that the temperature of a substance is proportional to the mean kinetic energy of translation of the molecule , taken in conjunction with equations 8 and 9 , gives relation 18 independently of the distribution of the amongst the degrees of freedom .
I do not think it can be maintained that there is any proof of this statement .
It is founded upon two facts of experience : ( 1 ) that if a number of systems are placed in material contact , that is to say in a relation such that mutual repulsive forces come into play , they reach equality of temperature in the sense that if the physical state of any other system , say a column of mercury , be fixed upon as an indicator , and placed in contact with each of the systems in turn , it will indicate the same temperature for each ; and ( 2 ) that potemial energy of one system cannot be directly converted into the potenlial energy of another system .
The *Cf .
for instance Burberry , ' Kinetic Theory of Gases .
' Mr. W. B. Hardy .
ication of the Principle of fact that one of the uous systems may be a permanent gas enables us to identify the temperature scale with the kinetic scale .
The parameter offers no difficulties , for corresponding volumes will be the volumes occupied by corresponding masses .
If is the specific volume , will be a volume , namely , the volume occupied by a grammemolecule .
We then have .
( 19 ) 3 .
The real difficulty in the application of the principle of dynamical similitude to actual substances lies in the identification of corresponding states .
Equation 4 may be written ( 20 ) the various coefficients being less than unity .
In a stead-y state the coefficients are constant and states are such that etc. Theoretically , therefore , any physical property such as temperature , pressure , specific volume , or magnetic susceptibility which can be used to measure the ratio of any one of the terms on the left say can be used to identify corresponding states , since and will bear the same ratio , and these are quantities which in certain cases are subject to actual measurement .
equations 8 , 9 , and 18 , we get .
( 21 ) NI here is the mass of a molecule of any one of the molecular species and the velocity of progressive motion .
There is no difficulty in upon certain states , namely , that at the absolute zero , that of the ideal gas , and , with less certainty , the crirical state .
for the critical temperature , , ( 22 ) and for two systems in states .
( 23 ) We may also write .
( 24 ) herefore , when , the systems 1 and 2 are not only dynamically similar at the corresponding temperature , but there is also mWualdynamical similarity along the temperature scale at temperatures defined by constant ences in the value of It is to notice the affords no for the that when there is no molecular association .
It shows only that Sirnilitude to Molecular Physics .
whatever degree of association there in the one stem be reprodnce in the other whn there In different systems it is , of course , necessary to compare masses composed of the same number of molecules .
The gramme-molecule may be taken , for if two systems are dynamically ilar the number of moving , that is the number of molecules including transition states , will then be the same in both , irrespective of the degree of association of the chemical molecules to form complex molecules .
4 .
The limitation of conservatism does not make the theory inapplicable to actual substances .
A mass of fluid is in a steady state when its temperature , pressure , and volume are constant .
It is then receiving energy from without by conduction or radiation on the average as fast as it is losing energy .
In this sense the system is conservative , and when two steady states are compared as to their energy content that portion of the to forces whose potential energy is not a single valued function of position may be dealt with as the quantity was dealt with .
It may be put constant for each steady state , and , therefore , as bearing a constant ratio to the whole energy content .
5 .
Internal Latent Heats.\mdash ; At colTesponding temperatures such that we have for each substance two conjugate states , that of the fluid and that of its vapour .
The work done in from the one state to the other against the forces of cohesion may be identified with the product of .
the internal latent heat and the total mass .
For this heat is the total energy required to convert unit mass of fluid into vapour less energy absorbed by surface forces such as an external pressure .
Let be the energy of a gramme-molecule of the substance as fluid , and as vapour , both at the same temperature .
Then , if be the internal latent heat of unit mass , we have and From equations 14 , 15 , and 18 we get , since .
( 25 ) Equation 25 follows directly from the law of equipartition of kinetic energy if this assumed .
Let be the total number of degrees of freedom of the system , then , if all the equations apply to corresponding states , we have and , and for two states of the same substance Mr. W. B. Hardy .
Application of the Principle of Let one state be fluid and the other vapour in equilibrium with it , then ' and LM but for systems in the term in square brackets is equal .
6 .
The equation for corresponding states , therefore , is where is a function only of in equation 22 .
Since dynamical similarity between molecules of different chemical types is not to be expected , this relation cannot be a general one .
A chain compound is as little likely to correspond dynamically to a compound as is a reciprocating engine to a turbine .
If dynamical correspondence is to be found it must be looked for in members of the same chemical series .
The difficulty mentioned in raph 3 now confronts us .
Two courses are open , we may either make some assulnption as to corresponding temperatures and develop the consequences , or identify corl.esponding temperaturea by equations 25 and 26 .
I propose in this paper to confine myself to the first alternative , and to examine the consequences of the assumption that corresponding temperatures are identified by the relation , etc. That is to say corresponding states are those whose temperatures are equal fractions of the critical temperature .
Since van der Waals ' time such states so defined have been called corresponding states , , so far as I know , the properly of dynamical similitude has been ttributed to them only by Onnes.* Ample excuse the examination of this assumption in detail is to be found in the immense superstructure of theory as to molecular association , , which has been based upon it .
7 .
has calculated the internal latent heats of a number of compounds .
His figures furnish data for four chemical series : ( 1 ) the benzene series , namely , benzene , cyclohexane , and the four substitution products of benzene : ( 2 ) the paraffins , including from pentane to octane of the normal series and the isomers isopentane , diisopropyl , and diisobutyi ( 3 ) the esters ; and ( 4 ) the alcohols .
The internal latent heats were calculated in order to test the truth of the formula constant , where is as before internal latent heat and and are the densities of the fluid and vapoul1 respectively , and published in 1904 and Since then Mills has recalculated the values and improved them .
The altered values are not *Cf .
van der Waals , ' Zeits . .
Phys. Chem vol. 13 , p. , Appendix 2 .
Journ. Phys. Chem vol. 8 , p. 383 ( 1904 ) .
' Journ. Phys. Chem. ' vol. 13 , p. 512 ( 1909 ) .
militude to Physics .
available , but in all cases they are said to make the approximation to the formula closer .
rtainly Mills ' formuIa is closely followed by the benzene series and paraffins , and where his figures lie off my curves the value given by the curve fits his equation more closely than do his own values .
Thus as an example the values for brombenzene to are below the curve and give values for Mills ' constant which are too low .
For this reason the value for pentane at is too high , and those from to 313 are too low .
Therefore the point for pentane on the curve for is flxed where it ia Mills thoroughly criticises the accuracy of his calculations .
The great care he took is revealed in his papers and his relation given above is so close an approximation as to have led to corrections being made in Young 's data .
It is assumed that when in equation , the bstanc s are in corresponding states .
8 .
Benzene Series.\mdash ; Below are given the values of in equation 26 .
According to theory they should be constant for corresponding temperatures The agreement with theory is more exact than that usually accepted as being satisfactory in papers dealing with molecular physics , but in spite of this it would be wrong to conclude that equation 26 is complied with .
In fig. 1 the molecular latent heats are plotted against absolute temperature .
On each curve certain points surrounded by a ring are at corresponding temperatures , namely , , etc. The oblique lines which pass through certain of these points , therefore , by assumption , pass through corresponding points , and they are the curves of equation 26 .
They satisfy the equation in that they are straight lines , but they do not satisfy it in that when produced they do not pass through the origin at absolute zero .
The curve for does within the limits of error pass through the origin .
The concordance between theory and fact is close , but the equation of corresponding states , instead of , is .
It will be noticed that the equation applies only to the halogen derivatives , that is to say , these substances form a similar series to which neither benzene nor cyclohexane belong .
* Mills ' figures for di-isobutyl I found intractable .
They would not fall into any regular curve , therefore I do not give them .
The specimen Young used seems to have been inipure .
VOL. XCIL\mdash ; A. 9 .
The Paraffin ( Fig. ) \mdash ; The normal paraffins form a series whose equation for corresponding temperatures again is , but is numerically larger , and is always positive .
Of the isomers isopentane is indistinguishable from the series , but di-isopropyl clearly falls out of it .
The benzene derivatives and normal paraffins thus form two series , the members of each of which are in dynamical similarity , but at each corresponding temperature the series is displaced uniformly .
The degree of displacement is measured by the parameter , and is much greater in the paraffins than in the ring compounds .
10 .
The Methyl Esters ( Fig. ) \mdash ; The curves for corresponding temperatures now are no longer linear , therefore the series is no longer dynamically similar .
This follows at once from the form of the equations .
11 .
The Alcohols ( Fig. ) \mdash ; The curves also are no longer linear .
The degree of curvature is maximal at , vanishes at the critical point , and is at .
Where the curvature is greatest the molecular internal latent heat at corresponding temperatures diminishes with molecular weight .
12 .
The parameter is of great interest .
The argument developed in paragraphs 1 and 2 may be reduced to three propositions : ( 1 ) that the kinetic energy of a system is a linear function of its temperature , ( 2 ) that in similar states the kinetic and potential energies stand to each other in a constant ratio , and therefore ( 3 ) that the potential energy of systems when dynamically similar is also a linear function of their temperatures .
In raic form these propositions reduce to .
( 27 ) Dynamical Sir nilitude to Molecular Physics .
to comply with equation 13 .
Two guns may be dynamically similar even when firing shells with different bursting charges .
Thus , there may be present reserves of potential energy not referred to in 27 , but which may be upon when certain changes take place .
If the assumption that etc. is a criterion of dynamically similar states be valid , the relation shows that the energy is made up of the quantity received from without as heat , and the quantity drawn from some reserve of energy within the fluid .
is not necessarily the whole of the energy drawn from this store .
Some , for instance , may be oonverted into kinetic energy of progressive motion of the molecules of the vapour , in which case it is necessarily included in the temperature term It is merely that portion of the reserve of energy absorbed in increasing the kinetic energy and the potential energy of the forces of attraction which is not a linear .
function of temperature .
The reserve in question must be intramolecular energy .
Calling , as before , the forces which confer on the molecules the property of extension in space repulsive forces , the reserve is potential energy of repulsive forces .
It is not suggested by anyone that the mutual attraction of molecules vanishes at the absolute zero ; therefore , except in the single case of rigid molecules , the potential energy of repulsive forces vanishes only in the state of an ideal gas , increases on the whole as the system becomes more condensed , and is probably maximal at the absolute zero .
The quantity in general decreases as the absolute temperature rises , and vanishes at the critical point .
The variation is shown in fig. 5 , where both and are plotted against .
It is easy to see that this must be so .
If it were possible to convert fluid into vapour at a temperature just above the absolute zero , we should pass at once from the state of maximal condensation to maximal expansion , and the whole potential energy of repulsive forces would be converted into kinetic energy and the potential energy of attractive forces .
Passing up the temperature scale the fluid is more expanded and the vapour less expanded , with the result that the reserve of energy is less in the former and greater in the latter , until they finally become equal at the critical point .
Since is the whole or part of the difference , it will , on the whole , decrease as temperature rises to the critical point .
In order to include the small negative values of , which the derivatives of benzene seem to show , it is necessary to drop the narrow conception of simple repulsive forces , or , rather , to enquire what is meant by Tepulsive forces .
We may conclude from what is known of the structure of matter that the property of extension in space of individual molecules , even at the absolute zero , is due to the possession of kinetic energy by internal Dynamical Similitude to Molecular Physics .
In the present state of the controversy as to the structure of matter and energy it is of interest to note that the equation can be derived directly from the theory of quanta .
Let it be supposed that the kinetic energy of a fluid is distributed between ( 1 ) the movements of progressive motion of the molecuIes , ( 2 ) the rotation of the molecuIes , and ( 3 ) the vibrations of an indefinite number of vibrators within the molecuIes .
If 1 and 2 between them have degrees of freedom , we may , without violating the quantum theory , put their energy as sensibly equaI to .
The energy of each vibrator is whers is Planck 's constant and the frequency .
As a first approximation when is not too large\mdash ; that is in fluids at ordinary this is equal to Therefore , in the absorption of an amount of energy from without by a fluid , the distribution of the energy amongst the degrees of freedom would be given by an equation of the form The frequencies of the vibrators will depend upon configuration since they are determined by the damping effect of the fields of neighbouring molecules .
The number oi vibrators will depend upon the chemical ucture of the molecule , that is to say , upon the number and nature of the atoms and their spatial arrangement .
It will also depend upon the configuration of the system as a whole , as Weiss 's work on the magneton shows .
We may , therefore , suppose that for corresponding states of systems whose molecules belong to the same chemical series , the last term in this equation either is constant or varies from substance to substance in the series by some multiple of a .
constant 13 .
Obviously , it is important to settle whether really is constant .
In compiling the following Table , the method of interpolation adopted was not sufficiently accurate to give the units in the values of the internal latent Within the degree of accuracy aimed at , is seen to be a trus Mr. W. B. Hardy .
of Principle of constant for the paraffins .
It is only approximately constant for the benzene derivatives .
Knowing the immense taken by Mr. Mills to secure accuracy in his calculation of the internal latent heats , it is almost ungracious to suggest that the consistent negative values found for and are within the limits of error .
Yet a glance at the curves shows that in region the values refuse to plot to a curve which can be made to include the values between and .
It is therefore possible that really never is negative .
14 .
The dynamical similarity of the benzene derivatives is not to be expected from priori considerations .
When an atom of hydrogen is replaced by a atom the symmetry of the benzene ring is destroyed .
The loading would introduce an additional degree of freedom , and therefore , since the loaded molecules are corresponding masses , the loading must be such as to keep the centre of mass of the whole molecule in geometrically corresponding points .
It is clear therefore that the halogen atom cannot simply replace a hydrogen atom so that the centre of mass of the former occupies the same position as the latter .
This follows from the fact that the mass is constant whilst the load varies from Fl to .
The load must either be at the centre , or the ring must be distorted proportionately to it .
Neither benzene nor cyclohexane belong to the series , since they are symmetrical unloaded molecules , probably with fewer degrees of freedom .
15 .
The esters and alcohols do not exhibit dynamical similitude because they do not conform to the narrow assumption that corresponding states are to be identified by the relation When this holds we have ( equation 24 ) .
( 27 ) Choosing any two corresponding temperatures and , ( 28 ) and therefore 29 ) It is with the last relation that esters and alcohols probably fail to comply .
J. J. Thomson has given reasons for concluding that the molecules of alcohols are polarised electrically , the study of the tension of interfaces gives reason to believe that the molecules of esters if not actually polarised very readily acquire that property .
Let us asgume that the molecules in both cases contain electric doublets .
MagSoc .
Proc. , ' , vol. 88 , p. 303 ( 1913 ) .
to Molecular Physics .
There will then be attractions and repulsions between the molecules due to their electrification , and there will also be mutual induction leading to clustering of the molecules.* The distribution of the energy amongst the molecules must be very complex , little likely to have the simple relation to temperature denoted by equations 26 and 29 .
Sutherland , who was the first to suggest that cohesion might be of electric rigin , has calculated the foroes between molecules holding electric doublets .
His argument briefly is as The sum of the attractions and repulsions over a space containing a large number of doublets equally spaoed tends to zero .
Therefore such a system would have no cohesion .
But when the doublets are in motion there is a preponderance of attraction over repulsion because when two doublets are approaching they tend to pull one another 's axes into the straight line joining their centres .
This follows from the fact that the force which one doublet exerts on another forms a couple , and while the attractions and repulsions vary inversely as the fourth power of the distance separating the centres , the couples vary inversely as the third power .
When a pair are near together the couple is thus much more potent than either attraction or repulsion , therefore orientation of the axes of approaching molecules in the stable end-on position tends to occur before the latter forces are very great .
Now , if two doul ) lets are approaching with the pxes similarly directed , the attractive force increases to a maximum at ision , while repulsive forces arrest approach before a maximum is obtained .
In general there is the same tendency for attractive forces to increase as for repulsive forces to decrease .
Sutherland draws attention to a property of such a system of doublets which has apparently been entirely overlooked , namely , that the range of the force is a function of the violence of the molecular agitation .
For though the range of the force between two doublets has no upper limit the movement of neighbouring molecules tends to fix a limit , since , as the distance from the centre of any doublet increases , the end-on orientation , on which the excess of .attraction over repulsion depends , will be diminished by the influence of other doublets until at a distance which can be only some small multiple of the average distance between the molecules , the disposition of the axis of any particular doublet considered with respect to the axes of surrounding doublets *Cf .
Thomson , ' Phil. Mag. ' [ 6 ] , vol. 4 , p. 625 ( 1902 ) .
There is no abrupt change at the fusion point of glasses in any physical property .
Hence one may conclude that a random disposition of molecules persists in glasses .
Therefore electric cohesion of glasses should vanish at the absolute zero .
100 inciple of Dynamical ilitude in Molecular Physics .
becomes purely random and the sum of the attractive and repulsive forces on it vanishes .
In this way the form of this force becomes a function of emperature , of the angular moment of the molecule , and of the density of the fluid .
The linear relation of equation 27 is then not likely to hold .
Summary .
The principle of dynamical similitude is developed and applied to the case of the internal latent heat of evaporation .
It is found that if temperature be proportional to the mean energy of progressive motion of the molecules , the internal latent heats of dynamically corresponding states should be given by the equation , where is the latent heat , the grammemolecular weight , a constant , and the temperature .
This equation may be used either to identify corresponding temperatures or to test some assumption as to corresponding .
In this paper the assumption made is that the critical states are dynamically corresponding states and that corresponding temperatures are equal fractions of the critical temperature .
The equation for internal latent heats is then found to have the form for normal paraffins and for certain halogen derivatives of benzene .
The conclusion is drawn that , subject to the assunlption being correct , the potential of repulsive forces acting between the molecules contributes Go the process of evaporation .
An examination of the alternative view that corresponding temperatures may be identified by the relation is deferred for the present .
|
rspa_1915_0055 | 0950-1207 | The flow of electricity through dielectrics. | 101 | 107 | 1,915 | 92 | Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character | Spencer W. Richardson, M. A. (Camb.), D. Sc. (Lond.)|Prof. A. Schuster, Sec. R. S | article | 6.0.4 | http://dx.doi.org/10.1098/rspa.1915.0055 | en | rspa | 1,910 | 1,900 | 1,900 | 6 | 63 | 1,196 | http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1915_0055 | 10.1098/rspa.1915.0055 | null | null | null | Electricity | 43.882003 | Fluid Dynamics | 20.623061 | Electricity | [
37.053985595703125,
-49.3646240234375
] | ]\gt ; Thae Flow of Electricity through Dielectrics .
By SPENCER W. RICHARDSON , .
( Camb .
) , D.Sc .
( Lond. ) , formerly Principal of , and Professor of Physics at , the University College , Southampton .
( Communicated by Prof. A. Schuster , Sec. R.S. Received September 4 , 1915 .
( From the Davy Faraday Laboratory of the Royal Institution .
) Curie , * Hopkinson , and other observers have shown that when a condenser is charged by means of a battery of constant electromotive force the charging current diminishes as the time of charging increases .
Results obtained by me when the dielectric consisted of glass , paraffin , ebonite , quartz and Iceland spar are in agreement with this conclusion .
I have also found that if ( during charging ) the applied electromotive force , , is suddenly reduced to ( say ) , then , provided that is greater than a certain value , a current flows through the specimen in the same direction as the original charging current , but that if is less than a current flows for some time ) in the opposite direction to the charging current .
I have taken to be a measure of the electromotive force of polarisation of the dielectric in the given conditions .
increases with the time of charging , very rapidly at first , but more slowly afterwards .
I have calculated the rate at which the charge is ttccumulating in a specimen of quartz , cut perpendicular to the optical axis , and a specimen of Iceland spar , cut parallel to a cleavage plane ( of known areas and thicknesses ) , from the data iven by me in a paper entitled ' ' Some Experiments on the Properties of Dielectrics published in the ' Proceedings of the Royal Society ' of October , 1915 .
A relation between these various quantities can be obtained which enables Ihe true electrical resistance of the specimens to be determined .
For if\mdash ; charging current , applied electromotive force , electromotive force of polarisation of the dielectric , rate at which the charge is accumulating in the dielectric , then we have .
where is the true electrical resistance of the specimen .
* ' Annalea de Chimie et de Physique ' ( 1889 ) .
'Phil .
Trans. ' ( 1897 ) .
Dr. S. W. Richardson .
In the case of the specimen of quartz the values of obtained in this way , for times of charging varying from 10.seconds to 20 minutes .
are in general agreement .
The results for Iceland spar seem to indicate a diminution in the value of as the time of increases .
This apparent diminution , however , may be due to inaccuracies in one or more of the series of results upon which the calculations are based .
In the paper referred to above I have shown how small quantities of electricity escaping from a dielectric during discharge can be measured .
To measure the charging current the same apparatus has been used .
On6 surface of the specimen was connected to the battery , the other surface ( and the electrometer and subsidiary condenser ) being to earth .
When the current had been flowing for a time this surface was disconnected from the earth , and at a later time it was disconnected from the electrometer and subsidiary condenser .
The quantity of electricity which had accumulated in the subsidiary condenser was measured as in the previous experiments .
Then we have where represents the value of the charging current after it has been flowing for a time .
To obtain the electromotive force of polarisation a second battery and a potential divider were used , and the subsidiary condenser was dispensed with .
The apparatus was set up as shown in .
The current was first caused to flow the specimen , and the direction of the movement of the line of light on the scale when was operated was noted .
Both surfaces of the specimen were then connected to the earth until all The Flow of Electricity Dielectrics .
trace of previous ch.arging had disappeared .
The battery I was then connected to one surface of the specimen for a given time .
The sliders , having been clamped together in such a way that K2 and could be operated in succession by one movement of the hand , were pulled rapidly across the frame and the movement of the line of light was noted .
This experiment was repeated for different values of until the line of light remained stationary for an appreciable time after the sliders had been pulled across the frame .
The difference of potential between and was then measured with an accurate voltmeter .
This difference of potential is equal to the electromotive force of polarisation of the dielectric in the given conditions .
The results obtained for a specimen of quartz cut perpendicular to the optical axis , at C. , and for a specimen of Iceland spar cut parallel to a cleavage plane , at C. , are given below .
The Flow of Electricity through Dielectrics .
The area of the silvered surface being 29 sq .
cm .
and the thickness of the specimen cm .
, the specific resistance , , is obtained from the relation:\mdash ; Motion of a Stream of Finite ) past a Body .
The area of the silvered surface being sq .
cm .
and the thickness of the specimen cm .
, The lIotion of a Stream of Finite Depth past Body .
By ROBERT JONES , .
( 1851 Exhibition Scholar of the University of North Wales , ) .
( Communicated by Dr. R. T. Glazebrook , C.B. , F.R.S. Received June 8 , 1915 .
) When a circular cylinder moves uniformly in an ideal fluid ( i.e. frictionless and incompressible ) at rest at infinity , the resultant force acting on it is zero , if no external forces act .
This is , however , only true when the mation is the usual potential motion .
Supposing that in addition to the potential stream produced by the motion of the cylinder a circulation it be considel.ed , velocity of the fluid is increased on the one side , and decreased on the other , and this produces a force acting on the cylinder ) endicuiar to the ffirection of motion .
* Kutta has applied this method of considering the motion of an infinite fluid to determine the thrust on a lamina , and systems of }inae , plane and circular .
The cyclic constant of the circulation he leaves arbitrary , and , 'Hydrodynamics , ' pp. 74 and ( 1906 ) .
Lanchester , nnmics , ' Chap. Kutta , : ' Uber eine mit den Grundlagen des Flugproblems in Beziehung end Zweidimensionale Stromung 'Sitzungsberichte .
Bayerischen Akademie .
Wissenschaften , Phys. Klasse , ' Jahrgang 1910 , 2 Abhandlung .
V0L .
XCII .
|
rspa_1915_0056 | 0950-1207 | The motion of a stream of finite depth past a body. | 107 | 121 | 1,915 | 92 | Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character | Robert Jones, M. A.|Dr. R. T. Glazebrook, C. B., F. R. S. | article | 6.0.4 | http://dx.doi.org/10.1098/rspa.1915.0056 | en | rspa | 1,910 | 1,900 | 1,900 | 4 | 76 | 1,655 | http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1915_0056 | 10.1098/rspa.1915.0056 | null | null | null | Fluid Dynamics | 54.637975 | Formulae | 26.492446 | Fluid Dynamics | [
49.103675842285156,
-33.19506072998047
] | ]\gt ; the length of the lamina , the density of the fluid .
He claims that his results fairly well with experimental results obtaineu ' by Lilienthal .
The same mula has been obtained independently by .
Dr. Tschapligin*for a general case .
He considers an aerofoil with a section of known contour .
Dr. Joukovsky has also investigated the problem , and has obtained interesting contours for the sections of an aerofoil and a strut by representing a circle conformally .
He obtains the force acting perpendicular to the motion of the immersed body in the form being the circulation around the known contour , the velocity , and the density of the fluid .
Blasius applies the methods of the Theory of Functions to hydrodynamical problems related to the above .
The section of the body to be examined is conformally represented as a curve , the motion around which can be determined .
All these problems treat , however , of motion in an infinite fluid .
Prof. L. Prandtl ( of Gottingen ) pointed out that it would be advisable to consider the motion of a stream of finite.breadth flowing past a body , and the author 's thanks are due to him for gesting the lines on which the investigation should be carried out .
The problem resolves itself into two cases , which will in turn be considered .
First the boundaries of the stream are supposed to be free , and secondly the fluid is taken to be flowing in a channel with rigid boundaries .
The method follows somewhat the lines taken by Blasius , the motion is two-dimensional , and is supposed to be symmetrical with respect to the plane of symmetry of the immersed body .
We start with the hodograph of a hypothetical motion and proceed to expressions giving the contour of ths section of the body consistent with this motion .
* Mbscauer Mathematische Sammlung , ' vol. 28 1910 ) .
'Zeitwhrift fur Flugtechnik .
Motorluftschiffahrt , ' Nowember 26 , 1910 .
'Zeitschrift fur Math. .
Physik , ' 1910 and 1911 .
Mr. E. Jones .
The required relation between and is easily seen to be where is a constant the distance of the point in fig. 3 to ( fig. 2 ) from the origin in ) .
lies as before on the real axis , the positions of A and are not known .
Now transform fig. 3 so that the slit OF becomes a circle , radius in the FIG. 3 .
FIG. 4 .
plane ( fig. 4 ) .
If the length of the slit be , the required transformation formula is easily shown to be From the symmetry of the problem , the arcs and are equal , and represent \mdash ; and infinity in the plane , i.e. the regions from which the fluid comes and into which it goes respectively .
Hence we assume a source and a sink to exist at and ( fig. 4 ) respectively , and find a fluid motion in the plane containing the circle DED'F and as closed stream-lines , and to be made up in part by the source and sink .
We first of all suppose a circulation about the origin introduced ; this will not disturb the stream-line EDFD ' of the soqrce and sink .
To obtain the closed curve , we assume a uniPorm stream to flow from \circ ; e round the circle EDFD ' .
These three motions , ) erposed , satisfy the required conditions , and the complex potential of the motion in the plane is where are the -ordinates of , A the strength of the source and 112 Mr. R. Jones .
change by when the integration extends round the contour , and thus not left single-valued .
We rid ourselves of this difficulty by so chopsing that these terms vanish .
From ( 1 ) and ( 2 ) , ( 9 ) where and are the roots of ; hence , on integrating ( 41 we have terms involving Either or corresponds to the point ( fig. outside the contour , and , since , the other musG lie within the circle .
Lt that point be The four points , and , lie within the contour around which we integrate , and consequently each of the first four integrals ( 10 ) is equal to , whereas the other two vanish .
Collecting together the coefficients of these terms , and remembering that has to vanish when taken round the contour , the following equation for is derived:\mdash ; , ( 11 ) where Let us write ( this only fixes our scale ) and integrate ( 4 ) .
Then , . .
( 12 ) The terms in vanish iu virtue of 11 ) .
When by ( 2 ) .
This corresponds to , fig. 3 .
If COF ( fig. 2 ) then 1 ' ( fig. 2 ) is the point , hence by ( 1 ) S. Consider Then and FIO .
5 .
and if the thickness of the stream be , then Hence if be given , the constant A depends on the thickness of the stream .
Again consider .
( 17 ) On substituting , and ( fig. A and this equation gives , as before , S , the direction of the stream at infinity .
Now , if instead of substituting , we substitute the values of and obtained from ( 7 ) or ( 8 ) , we can find the angle between the tangent at the edge of the body and the line joining the extremities of the section .
To simplify the formulae , let us put We have seen that is small and of the same order as ( A and being finite ) , hence is small by the first of the equations ( 8 ) ; we therefore neglect in ( 17 ) .
If be the angle between the tangent at the edge of the body and the chord But from th second of the equations 8 ) , hence also momentum is , hence by to the axis is As a test on the analysis , the alternative analytical method has also been worked out .
around the contour .
Therefore ; and are known in terms of , hence Splitting up by partial fractions , and remembering that and whereas the others vanish , reduces to on making use equation ( 11 ) .
Therefore , since but , therefore We have seen that when , A is infinite and , assuming the circulation to be finite , that A is finite and equal to B. Substituting in we obtain for an infinite fluid , or for finite values of A and .
( ii ) Stream with Straight Rigid Boundaries .
We proceed to treat in a similar way the motion of the fluid in a channel with fixed walls .
Fig. 6 represents the plane , denoting the section of the body and the channel .
hodograph diagram ) is given in fig. 7 .
*Compare Joukovsky , Mr. R. Jones .
This has to vanish round the contour as before , and the : corresponding to ( 11 ) is For purposes of approximation , we will assume that the change of velocityin the neighbourhood of the body is small compared to the velocity infinity , and small compared to , and neglect terms of the second order in is as before taken to be the smaller root of hence is small .
The approximate expression for reduces to ' the origin being changed as in ( 15 ) , and use being made of ( 22 ) .
This equation after equating real and imaginary parts gives [ when , and changes its sign with ] , and , ( 25 ) having the same meaning as in ( 5 ) .
Multiply both sides of equation ( 24 ) by , and consider the value of when ad is then equal to , for when and also .
when is neglected .
We want to find at the edge of the body , i.e. at the point where is supposed to be : igible compared to , i.e. the point This gives us which reduces to in virtue of ( 8 ) .
body is to the top of the channel , the faster the fluid flows above it , as was to be expected .
Let us now consider , where has the same meaning as before , This vanishes when .
along the fixed boundaries .
We shall consider the case of .
Equations ( 8 ) give us , on neglecting ; we neglect , being of order Then taIJ , ( 31 ) and as before decreases as increases .
We now see that , given , and , we have sufficient data to determine a , and , if we make use of our condition ( 22 ) .
Equation ( 29 ) determines , and after substituting in ( 26 ) for is found ; is then obtained from ( 31 ) and finally from ( 30 ) .
As already stated depends on the position of the body in the stream , and knowing and is immediately obtainable .
We have still to consider the thrust on the body .
This is done in the same .
way as before , viz. , by considering the integral taken round the contour .
is , in this case , equal to , which gives on being reduced , ( 32 ) when and ad hence .
( 33 ) When , and ' therefore *Of .
and Joukovsky .
|
rspa_1915_0057 | 0950-1207 | The consumption of carbon in the electric arc. I.- Variation with current and arc-length. II. - Influence upon the luminous radiation from the arc. | 122 | 143 | 1,915 | 92 | Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character | W. Geoffrey Duffield, D. Sc.|Sir Ernest Rutherford, F. R. S. | article | 6.0.4 | http://dx.doi.org/10.1098/rspa.1915.0057 | en | rspa | 1,910 | 1,900 | 1,900 | 17 | 357 | 8,904 | http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1915_0057 | 10.1098/rspa.1915.0057 | null | null | null | Electricity | 39.639138 | Atomic Physics | 18.877534 | Electricity | [
-23.04844093322754,
-14.170084953308105
] | 122 The Consumption of Carbon in the I. with Current and Arc-length .
upon the Luminous Radiation from the Arc. By W. Geoffrey Duffield , D.Sc .
, Professor of Physics , and Dean of the Faculty of Science in University College , Beading . .
( Communicated by Sir Ernest Rutherford , F.R.S. Received July 16 , 1915 .
) CONTENTS .
PAGE I. Variation with Current and Arc-length\#151 ; 1 .
Preliminary , and Method of Experimenting ... ... ... ... ... ... ... ... . .
122 2 .
Experimental Results .
Tables ... ... ... ... ... ... ... ... ... ... ... ... . .
123 3 .
Relation between Loss of Weight and Arc-length ... ... ... ... ... ... ... 124 4 .
Relation between Loss of Weight and Current-strength ... ... ... ... ... 127 i. Long Arcs ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... .
12 ?
ii .
Short Arcs ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... . .
129 5 .
Experiments with Heavy Currents ... ... ... ... ... ... ... ... ... ... ... . .
131 b\ General Conclusions from the Preceding Experiments ... ... ... ... ... . .
132 7 .
Theories of the Electric Arc ... ... ... ... ... ... ... ... ... ... ... ... . .
132 8 .
The Cathode Stream ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... .
133 9 .
The Bearing of the Present Research upon Existing Theories ... ... ... 134 10 .
The Mechanism of the Very Short Arc ... ... ... ... ... ... ... ... ... ... .
137 11 .
Previous Experiments ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... . .
139 II .
Influence upon the Luminous Radiation from the Arc ... ... ... ... ... ... . .
141 I. Variation with Current and Arc-length .
1 .
Preliminary , and Method of Experimenting .
Experiments have been carried out to determine the amount of material lost by the poles of a continuous current carbon arc under different conditions of current and arc-length .
The results indicate that when the arc-length is extremely small , the loss from the cathode of one carbon atom is accompanied by the transfer between the poles of a quantity of electricity equivalent to four electronic charges , a surprisingly simple conclusion when the complex changes of shape of the carbon poles are taken into account .
The experiments were conducted with poles which had been previously burnt to shape by running the arc for some minutes before beginning the weighings .
This prevision is of the utmost importance , and is responsible for the remarkable consistency of the observations .
Method 1.\#151 ; The carbons were held in special clips which could be removed as a whole from an ordinary vertical arc lamp and weighed with the ?
electrodes in position .
They could be replaced in the lamp exactly as before .
i The Consumption of Carbon in the Electric Arc. 123 Method 2.__The knife-edge and scale-pan were removed from one end of the beam of a balance , and a small brass tube fixed vertically to its upper surface to serve as a holder for the lower carbon of the arc .
The current was led to this by a wire which was soldered to the centre of the beam and which dipped into a mercury cup on a level with the central knife-edge .
The beam could be lifted clear of the mercury by the ordinary device for swinging the balance and weighings conducted in the usual way .
This arrangement obviated the necessity for touching the lower pole at all .
The upper pole could be raised vertically by means of a rack and pinion , so that after the arc had been burnt to shape , and the first weighing made , the positive and negative poles could be brought back to their original places and an exact fit obtained .
The current used was derived from a secondary battery ; suitable resistances enabled the current to be kept constant .
An enlarged image of the arc was formed by a lens upon a screen ruled with lines which represented millimetres at the corresponding magnification , and the arc length was maintained constant by watching this screen and adjusting the top electrode .
The first experiments dealt with arcs whose lengths varied from 0*5 to 15 mm. or more , and the current from 1 to 10 amperes .
The carbons employed were initially all of the same diameter ( 1 cm .
) , but , after having been burnt to shape , their diameters in the neighbourhood of the arc gap * were much smaller , the poles having so adjusted themselves that there was a characteristic contour for each value of the current-strength and arc-length .
The carbons were solid , and were freed from gross impurities by washing in acid and water ; for undertaking this work the writer is indebted to Mr. J. W. Dodgson , of the Chemical Laboratory .
The electrode under examination was the lower one , unless the contrary is specifically stated .
The experiments lasted for 5 minutes as a rule , but sometimes longer .
2 .
Experimental Residts .
In Tables I and II details of the experiments upon the anode and cathode are given .
Many of the weighings given in the following Tables were made for me by Mr. Southam , an Honours Student in the Physical Laboratory .
These results are plotted in Diagrams 1 and 2 , which show that consistent results have been obtained , except perhaps in the case of the 1-ampere arc , where the accuracy is less on account of the small quantity of material lost VOL. xcn.\#151 ; A. r Prof. W. G. Duffield .
and the difficulty in maintaining the arc , and where the small error introduced in striking the arc is likely to be appreciable . .
^pfoU.___The diagrams include individual observations ; the Tables , the average values for given arc-lengths .
] Tables I and II.\#151 ; Rate of Consumption per Coulomb .
I. Anode .
II .
Cathode .
Current ( amperes ) ... 2 .
4 .
8 .
10 .
1 .
2 .
4 .
6 .
8 .
10 .
Arc-length .
mm. 0-5 10 -o 10*4 7 T 4*8 4*5 41 1 *0 25 *3 17 *6 12*8 11 *0 20 -2 \#151 ; 9-2 6*5 5*5 5 *4 2*0 26 *6 18 T 1ST 12 *0 27 0 19 *2 10 -7 7*7 61 5*9 3*0 27 *6 19 *4 \#151 ; \#151 ; 35 T \#151 ; 13 -6 \#151 ; \#151 ; \#151 ; 4-0 29 *6 20 -0 13*8 \#151 ; 37 *4 21 *7 14 *5 10 *3 \#151 ; 7 '4 5-0 \#151 ; 21 *3 \#151 ; \#151 ; 37 *7 \#151 ; 15 *5 \#151 ; \#151 ; \#151 ; 6*0 34 *6 \#151 ; 15 *2 \#151 ; 36 *3 23 '9 15*7 11 *4 10 T 8*5 7*0 \#151 ; 21 -4 \#151 ; \#151 ; \#151 ; \#151 ; 15*8 \#151 ; \#151 ; \#151 ; 8*0 34 *5 22 *5 15 *5 \#151 ; 35 T 24 *6 15 -7 12 *0 9-7 8*5 10*0 \#151 ; 22 *2 16*6 \#151 ; \#151 ; 25 T 16 T 12 T \#151 ; 8 9 12*0 \#151 ; 22 *8 15 *9 \#151 ; \#151 ; \#151 ; 16 *0 12*3 \#151 ; \#151 ; 15 *0 \#151 ; 22 *7 16 -0 \#151 ; \#151 ; \#151 ; \#151 ; \#151 ; \#151 ; \#151 ; \#151 ; 10 -1 \#151 ; 17 *0 \#151 ; \#151 ; \#151 ; \#151 ; \#151 ; 25 *8 16*3 \#151 ; \#151 ; \#151 ; 18*0 \#151 ; \#151 ; 16 *4 \#151 ; \#151 ; \#151 ; \#151 ; \#151 ; \#151 ; \#151 ; 20 *0 \#151 ; 22 *9 The above figures , multiplied by 10 5 , express the loss of weight in grammes per coulomb of electricity .
3 .
Relation between the Loss of Weight and the Length of Arc. The loss per coulomb for a given current-density increases with increasing arc-length until a nearly constant value is reached at about 8 mm. This is true both for the anode and cathode , but there is a difference in the initial rates of increase in the two cases , the anode loss per coulomb being at first gradual and then increasing more rapidly as the poles are further separated , whereas the cathode slope is very steep at the outset and shows no point of inflexion .
The general shape of the curves is explained by the increasing oxidation of the hot poles as the arc is lengthened , a limit being reached when increasing the length does not augment the amount of air which has access to them .
As the existence of a crater would suggest , the loss from the anode is greater than the loss from the cathode under similar conditions of arc-length and current^the ratio of anode loss to cathode loss for currents of 2 , 4 , and 8 amperes being 1*36 , 1*40 , and 1*64 respectively when the arcs are long , a slightly increasing ratio .
The Consumption of Carbon the Electric Arc. 2 Amperes ANODE 8 Amperes 100 Amperes Diagram 1 .
ARC LENGTH 20 M MS The ordinates , multiplied by 10"5 , express the loss of weight in grammes per coulomb of electricity .
L 2 Prof. W. G. Duffield .
Loss per Coulomb X 10 grammes ^ o Amp CATHODE 2 Amps .
6 Amps .
8 Amps .
10 Am Diagram 2 .
3-1 x 10 grarpmes ARC LENGTH 20 The Consumption of Carbon in the Electric Arc. 4 .
Relation between Loss and Current-strength .
An important distinction exists between the behaviour of long and short arcs .
( i ) Long Arcs.\#151 ; From Diagrams 1 and 2 we see that the loss of material per coulomb for long arcs decreases with increasing current .
It was expected that with large currents the combustion would be greater on account of the larger amount of heat generated , but this is evidently not the case , probably because with small currents the time taken for the passage of a given CATHODE Long Arc Diagram 3 Short Arc CURRENT IN AMPERES Prof. W. G. Duffield .
quantity of electricity is longer , so that more extraneous combustion occurs .
It means that when the arc is long doubling the time causes more carbon to burn away than doubling the current .
This feature is further illustrated by the upper curve in Diagram 3 , in which the loss per coulomb is plotted Diagram 5 .
Diagram 4 .
Loss OF Weight XIO grammes Loss OF Weight XIO grammes CATHODE 100- 2mms .
Shortest Shortest ANODE Amperes against current-strength .
For long arcs the rate of loss at first decreases rapidly with ^increasing current , but subsequently more slowly until some minimum value is reached for heavy currents .
To examine the rate at which the total loss for each electrode increases The Consumption of Carbon in the Electric Arc. with the current , Diagrams 4 and 5 have been drawn from the data supplied in Tables I and II .
For the anode they show that for currents between 2 and 10 amperes the loss in an arc 10 mm. long is approximately a lineal-function of the current , but that the cathode curve differs in being slightly concave to the axis of current-strength .
Neither curve passes through the origin , indicating that for long arcs the mechanism of the transport of the electric current is only responsible for a fraction of the whole loss , the hulk of which is due to combustion or evaporation .
The behaviour of the 2 mm. arc is similar , but the absolute value of the loss is smaller .
( ii ) Short Arcs.\#151 ; The curves given in Diagram 1 for the anode did not suggest any regularity in the behaviour of very short arcs , but interest was aroused by the shape of the cathode curves ( Diagram 2 ) when the arc-length was small .
In this case all of them appeared to converge towards a point which was not the origin , but rather higher up , representing a loss of about 3 x 10-5 grm. per coulomb for all values of the current-strength .
The coincidence of this number with the value for the electrochemical equivalent of carbon ( 3-109 x 10-5 ) , on the assumption that this element is quadrivalent , appeared too striking to be accidental , so further experiments were carried out ; extremely short arc-lengths were employed , because under these conditions the amount of subsidiary burning is reduced to a small order of magnitude .
Method 'No .
1 ( p. 122 ) was adopted , in which the carbons were held in special clips in an ordinary arc lamp .
The actual length of the arc could not be measured , but it was rarely , if ever , more than one-tenth of a millimetre .
The results of this investigation have been recorded in Table III .
The observations were made by the writer . .
Table III.\#151 ; Very Short Arc-length .
Variation of Loss with Current .
Anode and Cathode .
Current .
Arc- Volts .
Total loss .
Duration of Loss per second .
Loss per coulomb .
length .
Anode .
Cathode .
experi- meant .
Anode.* Cathode .
Anode.* Cathode .
amperes .
2 -0 mm. 0-0 *2 19-32 grm. 0 *198 grm. 0*040 secs .
600 33 *0 x 10"5 6 *7 x 10"5 1 16 *5 x10-5 3 *34 x 10"5 4 0 0-0*2 23 0*284 0*073 540 52 *8 13 *5 13*2 3*38 5*75 0-0 *2 20 0*335 0*120 610 54 *9 19*6 9*5 3*42 8'0 0-0*1 25 0*300 0T05 420 71 *2 24 *9 8*9 3 *12 10 -o 0-0 *2 28 0*552 0*190 600 92 *0 31 *6 9*2 3 *16 * The anode was the upper pole in these experiments .
The anode losses are included in Diagram 1 , the cathode losses in Diagram 3 .
Prof. W. G. Duffield .
Details of the experiments are given in successive columns , and in the final column the loss per coulomb from the cathode is recorded .
It at once became evident from this investigation that each reading , as well as the mean value , 3'28 x 10~5 grm. , was in remarkable agreement with the figure already arrived at from Diagram 2 .
But as the curious forms assumed by the poles when the arc was small made it doubtful whether so regular a rate of loss could be real , the series of observations was repeated .
The second or balance method of conducting the experiments was adopted on this occasion and the observations were carefully carried out by Mr. A. H. Davis , B.Sc. , a Research Student in the Physics Laboratory , and the results are set forth in Table IV .
During this set of readings , after burning the electrodes to shape and starting with a very short arc , the observer watched the voltmeter and ammeter and adjusted the arc-length and resistance to keep their readings constant .
The method was not quite so satisfactory as in the previous series , in which attention was devoted to maintaining as small an arc as possible .
The readings are consequently slightly higher than before , but nevertheless the mean loss per coulomb , 3-47 x 10~5 grm. ( omitting the first observation , where the amount dealt with is very small ) , is in excellent agreement with that previously obtained .
Table IV.\#151 ; Cathode Loss for Very Short Arcs .
Amperes .
Yolts .
Time .
Loss .
Loss per coulomb .
Remarks .
( 1 *0 secs .
grm. grm. 30 300 0*005 1 *67 x 10~ ' ) 1 -o 30 300 0*009 3 *00 x 10~5 2*0 27 300 0*027 4*50 2*0 27 300 0*026 4*33 Carbons touched momentarily .
3*0 22 *5 300 0*024 2*67 3*0 22 *5 300 0*035 3*80 Mushroom growth burnt off , re-formed , and again burnt off .
4*0 20 300 0*044 3*67 4*0 20 300 0*047 3*92 Mushroom growth burnt off once .
5*0 20 300 0*046 3*07 7*0 20 205 0*039 2*72 9*0 20 300 0*092 3*30 Mushroom growth burnt off once .
10 *0 21 330 0*099 3*00 Mushroom growth burnt off once .
* Mean 3 -47 x 10-5 The Consumption of Carbon in the Electric Arc. Notes were made when the mushroom growth dropped off the tip of the lower ( negative ) pole , and it is obvious that part at least of the observed loss is due to this occurrence .
We shall see , in a subsequent paragraph , that the loss of these growths introduces an error which is of the order of , but rather less than , 10 per cent. If this correction be introduced , the above determination approximates still more closely to the theoretical value .
5 .
Experiments with Heamj Currents .
The largest current employed in the above experiments was 10 amperes\#151 ; it seemed desirable to extend the work to higher values in order to see if the same rate of loss held good .
An experiment was therefore undertaken with 100 amperes in the Electrochemical Laboratory of the University of Manchester , through the kindness of Sir Ernest Rutherford , and the writei is indebted to Dr. Pring for interrupting a series of his experiments to allow the use of the heavy current for this work .
The carbons employed were 27 mm. in diameter and about half a metre long , each weighing about 400 grm. A horizontal arc was used , the carbons being first burnt to shape under a pressure across their terminals of 33 volts and a current of 97 amperes ; initially the end of the positive pole was flat and the negative pointed , but after about 15 minutes running with a very short arc the cathode was found to have accumulated a mushroom growth of about the size of an almond , which exactly fitted into a cavity in the anode which had been eaten away .
* The poles were then removed , weighed , and re-inserted in their clamps in the same position as before , the negative growth being fitted into the positive crater , and nearly , but not quite , touching it .
The experiment proper was then begun , the voltmeter and ammeter being read every two minutes .
There was very little tendency for the arc , which was very noisy , to grow longer , but it was kept as constant and as small as possible .
The actual arc was hidden from view , but it was of the order of 0*1 mm. The experiment lasted 15 minutes , and the carbons were then removed , cooled and weighed .
The results of this experiment are shown in Table V and Diagram 3 , the rate of loss , 3*2 x 10"5 grm. per coulomb , agreeing so excellently with both the theoretical value and that previously obtained for smaller currents , that there can be little doubt that within a very close approximation and over a wide range of current , from 2 to 100 amperes , a mass equal to one electrochemical equivalent of carbon , on the supposition that that element is quadrivalent , is liberated from the cathode for each coulomb of electricity which passes between the poles .
' [ A further experiment was carried out with the same apparatus with a Prof. W. G. Duffield .
long arc which increased from 10 to 30 mm. in length during the running of the arc .
Details are given in Table Y below and the readings are plotted on Diagrams 1 and 3 .
] Table Y. Current .
Arc- Volts .
Total loss .
Duration of Loss per second .
Loss per coulomb .
length .
Anode .
Cathode .
experi- meant .
Anode .
Cathode .
Anode .
Cathode .
amperes .
mm. grm. grm. secs .
grm. grm. grm. grm. 100 o-o-i 34 6*980 2-880 900 774 x10"5 320 x 10"5 7 *7 x 10"5 3 -2 x 10~5 100 10-30 52-61 \#151 ; \#151 ; \#151 ; 1316 \#151 ; 13 -2 .
100 10-30 52-61 1020 10 -2 In these experiments the arc was horizontal .
6 .
General Conclusions from the Preceding Experiments .
We may express the results of the preceding investigation by the following general laws:\#151 ; 1 .
The loss of an atom of carbon from the cathode of a very short carbon arc is accompanied by the transfer between the poles of a quantity of electricity equivalent to four electronic charges .
2 .
In long arcs the loss is due to this essential carbon disappearance plus a quantity due to combustion or evaporation .
The first of these is based upon the agreement between the individual results of each set of readings comprised in the first part of this paper , between the mean results of each set , between the values for high and low current densities , between these values and the point to which the curves drawn with decreasing arc-length tend ( Diagram 2 ) and between all these observations and the theoretical value for the electrochemical equivalent of carbon .
In view of the complex structure of the short arc one would hesitate to accept the evidence if it were less overwhelming .
7 .
Theories of the Electric Arc. Before discussing the mechanism whereby the above law can be satisfied in the arc a brief r6sum6 of the existing theories is given :\#151 ; In 1890 Fleming* put forward the view that " the negative carbon is projecting off a torrent of negatively electrified carbon molecules , and these impinging against the positive carbon wear out a crater in it by a sandblast-like action .
Further he says " th$ electromotive force is thus able to * Fleming , 'Roy .
Soc. Proc. , ' vol. 47 , p. 123 ( 1890 ) .
The Consumption of Carbon in the Electric Arc. 133 keep up a projection of negatively charged carbon molecules from the end of the negative carbon , which molecules are loosened from the mass by heat , and then move away from the surface in virtue of the electric charge which they retain .
" Dealing with the potential difference necessary to maintain an arc , * Fleming suggested that a certain fraction of the ^working electromotive force might be employed in detaching carbon molecules from the mass of the poles .
Sir J. J. Thomson* put forward a different view : " The cathode is bombarded by positive ions , which maintains its temperature at such a high value that negative corpuscles come out of the cathode ; these , which carry by far the larger part of the arc discharge , bombard the anode and keep it at incandescence ; they ionise also either directly by collision or indirectly by heating the anode , the gas or vapour of the metal of which the anode is made producing in this way the supply of ions which keep the cathode hot .
It will be seen that the essential feature of the discharge is the hot cathode/ ' DuddelTsf research upon the electromotive forces within the electric arc opened the way for an interpretation by Pollock^ of its mechanism .
According to the latter the forward electromotive force at the surface of the cathode is due to the projection of electrons from that surface , and in a similar way the back electromotive force at the anode is due to the liberation of electrons from that pole .
The falls of potential near the electrodes are due to the distribution of ions within and at the end of the mean free path of the electrons projected from the poles , in which region ions are produced by collision with the molecules of the vapour .
8 .
The Cathode Stream .
The important part played by the high temperature of the cathode can be simply illustrated by the following experiment:\#151 ; Two carbon rods A and B form the positive and negative poles of an arc ; when the arc springs from the end of B to the rounded surface of A , B can be moved rapidly up and down the length of A without extinguishing the arc , whereas if the poles are reversed the arc at once goes out when the positive is moved .
The general effect is much as though the hot spot upon the negative pole acts as a nozzle through which a stream of negative electricity is discharged , the arc * Thomson , 'Conduction of Electricity through Gases , ' p. 613 .
t Duddell , 'Phil .
Trans.,5 A , vol. 203 , p. 305 ( 1904 ) .
+ Pollock , 'Phil .
Mag.,5 vol. 17 , p. 361 ( 1909 ) .
Prof. W. G. Duffield .
developing whenever this stream falls upon another conductor connected to the opposite terminal of the source of current supply .
The experiment may be modified by mounting one pole so that it can be rotated about its long axis , and by forming an arc between its rounded surface and the end of a 'second carbon rod .
When the latter is the cathode , the former can be rapidly rotated without affecting the arc , but not when it is the anode unless the motion is extremely slow , wdien it is possible to wrap the arc completely round the circumference of the cathode , the hot spot upon it remaining fixed and turning with the pole .
9 .
The Bearing of the Present Research upon Existing Theories .
In connection with the theories already discussed we have now to take into account the additional fact provided by this research , namely , that associated with the passage of a definite quantity of electricity through the arc there is a definite consumption of carbon at the cathode .
The most obvious view to take , but one which is not free from objections , is that in the immediate neighbourhood of the cathode the entire current is carried by carbon atoms , each of which as it leaves the cathode takes with it four electrons derived from the source of current supply ( No. 2 in the following summary , p. 136 ) .
The electrons may be subsequently liberated by such means as the incidence of ultra-violet light , or interaction with other ions ; if the latter , it occurs at the end of the mean free path of the carbon atom , where presumably it comes into contact with the other vapour in the arc .
The electrons thus produced play the part assigned to them by Thomson 's theory .
It is , however , difficult to see how we are to escape from the conclusion that some of the molecules of air must penetrate to the surface of the negative pole ( probably conveying positive charges to it ) , and there interact with carbon atoms instead of waiting till they have proceeded some distance from it , and that it is at the pole surface that electrons are ejected by virtue of such collisions and also by virtue of thermionic* and photo-electric agency ( one does not know to what extent the incidence of ultra-violet light from the arc upon the poles is an essential feature of its maintenance ) .
I am inclined to regard the interaction of the gas molecules with the carbon as playing a very important role in the mechanism , because it is recognised that an arc can only with great difficulty be run in an atmosphere which does not readily form a chemical compound with the material of the pole .
Metallic arcs , for instance , burn with difficulty in an atmosphere of hydrogen unless the poles be of magnesium or zinc , or some metal which * Richardson , 'Phil .
Trans.,5 vol. 201 , p. 516 ( 1903 ) , etc. The Consumption of Carbon in the Electric Arc. 135 forms a hydride , and even then the nature of the are is modified , as we can tell by examining its spectrum , which , instead of being confined to metallic lines , is now rich in those of the surrounding gas .
As another instance Arons found it impossible to form an arc between silver poles in an atmosphere of nitrogen , and ascribed this to the absence of chemical combination between the silver and the nitrogen .
Without entering into the question whether thermionic emission requires the presence of a second element , there is considerable experimental evidence that the nature of the second element , if it be present , exerts an important influence upon the amount of ionic ejection , at any rate at atmospheric pressure .
Harker and Kaye , * for instance , dealing with the passage of ions from a hot carbon tube to a cooler brass one longitudinally disposed within it , found that the current flow was affected when hydrogen was substituted for nitrogen between the tubes .
I consequently regard the presence of the gas molecules as an essential feature of the phenomenon of the arc .
It does not appear probable that chemical compounds of a permanent character can be formed within the arc itself on account of its high temperature , but there is reason to believe that there is momentary interaction between the carbon atom at the pole and the visiting gas atoms ( probably , but not necessarily , oxygen ) which may render the electronic content of the former atom unstable ( especially if it possesses a surfeit derived from the current supply ) , and cause it to yield up some of its store .
' In the following I have enumerated categorically the alternative actions which comply with the first of the generalizations given in Section 6 .
Where it is suggested that a chemical compound is formed it does not require that it should be stable ; all that is proposed is that reactions of such a nature should occur as are involved in the formation of that compound ; it is immaterial to the theory , as far as the immediate neighbourhood of the cathode is concerned , whether the product splits up immediately afterwards or not .
The idea common to all is that each carbon atom before being detached from the cathode is furnished with four negative electrons by the current supply , but the process whereby the atom and electrons leave the pole is different in each case ; they may leave together or separately , attached or unattached:\#151 ; 1 .
The ejection of four electrons from each carbon atom under the influence of purely thermionic or photo-electric action , and the subsequent liberation of that atom , uncharged .
* Harker and Kaye , 'Roy .
Soc. Proc. , ' A , vol. 86 , p. 379 ( 1912 ) .
Prof. W. G. Duffield .
This is included in view of the largely accepted view that purely thermal emission occurs , but it is open to the serious objection that an atom , should be less easily detached after having been deprived of its surplus electrons .
2 .
The carbon atom evaporates from the hot pole , being loosened by heat agitation , and carries off the four electrons with it .
The velocity acquired by virtue of its temperature is augmented by the electric forces in the arc .
This has already been discussed .
It agrees with Fleming 's early idea .
The whole of the current from the pole face is borne by atomic masses .
The electrons may be ejected from the carbon atom subsequently , but as has already been stated there is no obvious reason for delaying such action until after it has left the pole .
As far as I am aware , carbon has not been found free with four charges .
J. J. Thomson records the existence of a carbon atom bearing one charge , a positive one , in a positive ray tube .
3 .
As in ( 2 ) the carbon atom evaporates from the hot pole , being loosened by heat agitation .
The surplus electrons are liberated at the same instant .
Photo-electric and thermionic action assist , and may or may not be essential .
The free carbon atom is uncharged and the whole of the current in the immediate vicinity of the poles is carried by electrons .
4 .
The carbon atom is detached from the cathode by interaction with the surrounding gases or vapours .
( a ) All four electrons are liberated at the same instant:\#151 ; Assuming that the interacting gas is oxygen , one oxygen atom , uncharged , unites with and detaches one carbon atom to form uncharged CO. As already stated , this may immediately become uncharged C and 0 .
The point is that the presence of the 0 atom is necessary to loosen the electrons .
The whole of the current is carried by the four electrons thus set free .
( b ) Two of the four electrons are liberated at the same instant :\#166 ; \#151 ; Assuming ' that the interacting gas is oxygen , one oxygen atom arrives with two positive charges , uncharged CO is formed which involves two of the electrons , the remaining two are liberated .
The current is partly carried by oxygen and partly by electrons moving in the opposite direction , the total being equivalent to the transfer of four electronic charges .
( c ) No electrons are liberated:\#151 ; Assuming that oxygen is the interacting gas , two oxygen atoms each with two positive charges arrive at the cathode , uncharged C02 is formed which involves all four electrons .
The Consumption of Carbon in the Electric Arc. 137 The current is wholly carried by the two oxygen atoms .
This is the condition which determines true electrolytic action on the lines of the conduction by liquid electrolytes .
The disappearance of carbon at the cathode is thus analogous to the disappearance of copper from the anode in a Cu H2SO4 Cu electiol^tic cell .
... .
It labours under the disadvantage that electronic projection , which on other grounds seems such a vital feature of the action , is the result of a secondary and not of a primary reaction .
The formation of C02 in the arc is even less favoured by chemists than the formation of CO , but it is to be emphasized that it is the nature of the interaction rather than the stability of the compound which concerns us .
Since however , carbon can be removed by the advent of a single oxygen atom we may agree that 4 ( b ) is more probable than 4 ( c ) which requires the advent of two .
The point at issue really is whether electrons or charged atoms are projected from the poles of an arc as bearers of the current .
My experiments at first sight appear to point to the latter , and to agree with Fleming 's early view , but I have been at pains to point out how electronic emission is also compatible with the facts .
One reason why I am anxious to retain the electronic view is that the back E.M.F. found by Duddell at the carbon surface of the anode seems to require , negative rather than positive emission there .
In a subsequent paper I propose to discuss further experiments bearing upon this point .
10 .
The Mechanism of the Very Short Arc. The mechanism whereby the current is transported across a very short arc-l gap is not as simple as the law stated in Section 6 leads one to expect .
The contours of the poles have been examined by projecting an image of the arc upon a screen of transparent paper and tracing upon it a series of profiles at frequent intervals .
There is no characteristic profile for a short arc of given length and current density , but a characteristic cycle of changes , of which the outstanding feature is the growth of a mushroom form upon the I cathode tip ; while this increases in length a constriction develops behind it , and it eventually falls off , but another growth forms and the cycle is repeated .
Though the development of the growth suggests that the cathode is gaining in weight , on no occasion has this been observed , even during the preliminary burning to shape the cathodic consumption of carbon approximates closely to the rate of loss demanded by the above law .
Though the Prof. W. G. Duffield .
formation of the deposit is more obvious it is less important than the loss of a thin shell of carbon from a surface of considerable extent . .
Fig. 1 , a , b , c , d , shows the changing contours of a very short arc using 6-5 amperes .
In order to trace the top of the negative pole , the positive was momentarily raised .
The arc was fed by lowering the anode , the cathode remaining fixed .
In ( a ) the outlines of both anode and cathode are shown ; we note that the diameters of the crater and of the growth remain constant Fig 1 9 Fig. l.t Carbon 1 " deposited Carbon - ' consumed Fig. 1.9 for a given current density , and that the sides of the anode remain nearly parallel to their original directions .
In ( b ) only the cathode tracings are drawn , the intervals of time between A and B , and B and C , respectively , being 4 and 2 minutes .
The increase in the length of the cathode is well shown , and ' so is the development of the constriction , which grows continually narrower with time .
The material deposited at M during AB is consumed in the interval BC .
The observed The Consumption of Carbon in the Electric Arc. 139 cathode loss is the difference between the amount lost from the constriction and that which is piled up on the tip of the cathode ; ( c ) shows that the former is the larger quantity , so there is always a resultant loss of material .
That the weight of the growth is only a small fraction of the material lost was shown by breaking off three , which were found to weigh 0*004 , 0*002 , and 0*002 grm. respectively .
The largest of these is less than 10 per cent , of the total loss of weight from an arc of the same amperage in the experiments quoted , the others are approximately 5 per cent. When , on account of the narrowness of the constriction , the glowing carbon did not extend appreciably beyond the neck , the loss there was smaller than usual , but it was found that the mushroom itself was consumed .
See fig. 1 ( d ) , in which profile C is the profile C already shown in fig. 1 ( c ) , and D refers to an observation 2 minutes later .
When the necessary quantity of carbon cannot be derived from one part of the arc , it can be requisitioned from another ; in this way the law already quoted is satisfied .
The material of the deposit appears to be derived from the anode , both because the advancing cathode follows so closely the receding crater , and because if the carbon anode be replaced by an iron rod the carbon mushroom no longer develops , but a small quantity of iron is transferred across the arc gap .
It is surprising that the bulk of the consumption of carbon takes place at the constriction , because , though it is all glowing brightly there , the most dazzling part of the cathode , is the tip , and a loss occurring elsewhere would seem to have only a secondary connexion with the process occurring in the arc proper .
It is true , however , that the vapours of the arc embrace the cathode down to , if not below , the constriction ; but , on the other hand , if this plays an essential part , the length of the arc is indeterminate and is not of the order of 1/ 10 mm. but of 2 or 3 mm. The drop in the curves near the origin in Diagram 2 is due not so much to the reduction of the arc gap to its narrowest possible limits , as to the reduction in the amount of extraneous consumption occasioned by the whole of the charged vapour being now in a field of force sufficient to prevent its escape from the arc , and perhaps to the complete protection from oxidation of the tip of the cathode .
11 .
Previous Experiments .
In 1825 Silliman* found that the positive lost weight more rapidly than the negative , and observed " little waste of the points exactly where they are opposed but considerable on the laterally ignited portions of the charcoal .
" * Silliman , 'Silliman 's Journal , ' vol. 10 , p. 123 ( 1825 ) .
VOL. XCII.\#151 ; A. * Prof. W. G. DuffielcL He had previously noted* that if a metal were substituted for the positive carbon , the growth upon the cathode did not develop , and ascribed the deposition to a transfer of material from the anode to the cathode .
Matteucci in the ' Comptes Rendus , ' vol. 30 , p. 201 ( 1850 ) , concludes from experiments , which are not quoted in detail : ( 1 ) The loss is chiefly dependent upon elevation of temperature , other factors being constant .
( 2 ) For carbon and iron the positive pole loses more than the negative , the ratio of the losses varying according to the arc-length from 2 :1 to 5 :1 for carbon , the ratio being smaller for iron .
For zinc , copper , tin , lead , brass , and gold the negative loses more than the positive .
( 3 ) Under diminished pressure the quantity of matter that is lost is less .
( 4 ) The loss depends upon the disposition of the arc with regard to the magnetic meridian .
With regard to these conclusions , ( 1 ) appears to be negatived by Waidner and Burgess'sf experiments , who found that the temperature of the arc only increased by 2'3 per cent , when the current strength was doubled from 15 to 30 amperes , a very much smaller change than that which would have been found in the mass of the poles ; ( 2 ) is chiefly due to the fact that carbon forms a volatile oxide , whereas the products of combustion with zinc , copper , etc. , remain upon the poles , sometimes dissolving in the molten metal j ( 3 ) is in accord with the experiments upon the brightness of arcs under increased pressure , ] ; where the extraneous oxidation increased the intensity of the light .
The explanation of the fact recorded in ( 4 ) is probably that the shape of the outer layers of vapour is influenced by the magnetic field to a small extent , and more or less of the poles embraced by the hot vapours .
W. S. WeedonS has measured the losses from the poles of certain metallic arcs .
Using copper poles he found that , if the current was increased 2'5 times the cathode loss was five times as great , whence he concluded that Faraday 's law did not hold good for the arc .
Using water-cooled electrodes the cathode loss was 1/ 450 of the amount required by Faraday 's law .
A copper arc in hydrogen gave only 1/ 1500 of Faraday 's equivalent , When an iron arc was burnt in hydrogen and the poles water-cooled , the anode lost and the cathode gained .
The metallic arcs suffer from the disability already mentioned in connection with Matteucci 's experiments , No. 2 .
A carbon discharge in hydrogen , 3/ 16-inch arc-length , gave a cathode * * * S * Silliman , 'Silliman 's Journal , ' vol. 6 , p. 342 ( 1823 ) .
( In this paper positive and negative poles should be interchanged .
) t Waidne^and Burgess , Bulletin No. 1 , Bureau of Standards , Washington .
] Duffield , 'Phil .
Trans. , ' vol. 208 , p. Ill ( 1908 ) ; vol. 211 , p. 33 ( 1911 ) .
S W. S. Weedon , 'Trans .
Electrochem .
Soc. , ' vol. 5 , p. 171 ( 1904 ) .
The Consumption of Carbon in the Electric Arc. loss which was about 1/ 40 of the rate of loss for the carbon arc in air for the same current and arc-length , or 1/ 6 of the loss if combustion be excluded .
We may doubt whether this can properly be described as an arc in hydrogen because the discharge was narrowed down to a fine line , which crossed from one pole to the other , and the voltage was abnormally high , 180 volts .
IL Influence of the Consumption of Carbon upon the Luminous Radiation from the Arc. Blondel and Ayrton* have investigated the mean spherical candle-power ( or its equivalent ) of arc lamps , and have arrived at the following conclusions :\#151 ; 1 .
With a constant current the light emitted by the arc increases with increasing arc-length until a maximum is reached ; in some cases there is a slight diminution of the candle-power upon further increasing the arc-length .
2 .
When the length of the arc is kept constant the candle-power increases with the current .
Since these are two of the main facts in the present research if " consumption of carbon " be substituted for " candle-power/ ' the question arises whether the brightness of the arc is not intimately related to the amount of carbon consumed .
A comparison of the curves relating total light and arc-length ( Diagram 6 ) , with those connecting total loss of weight with arc-length ( Diagrams 1 and 2 ) , f suggests that there is a connection , though the low value of the luminosity for short arcs is primarily due to a different cause , namely , the difficulty of getting the light from the arc free from the shadow of the negative pole .
For long arcs the curves are more strictly comparable , and both are characterised by nearly horizontal lines .
If the total loss of weight from both poles is plotted against current ( see Diagrams 4 and 5 ) and compared with curves connecting mean spherical candle-power with current ( Diagram 7 ) , it will be noted that both are approximately linear , but that , whereas the candle-power-current curves point to the origin , the consumption-of-carbon-current curves do not , suggesting that some finite consumption of carbon is necessary before any of its energy can be converted into that of luminous radiation capable of affecting the instruments employed .
It is not improbable that the consumption of carbon should influence the * Blondel and Ayrton .
See ' The Electric Arc/ Mrs. Ayrton .
t Though drawn to represent loss per coulomb these curves represent total loss if the value of the ordinate be suitably altered for each curve .
The shape of the curve is unaffected .
M 2 Prof. W. G. Duffield .
Diagram 6 .
15,00 0 io/ io Siemens 8/ 6 Hard lo/ ioSoft io/ iO Hard Curves connecting Total Light with Length of Arc Current io Amperes Both Carbons Solid .
5000- Length of Arc in Millimetres .
The figures express the diameters of the upper \amp ; lower poles , From Mrs. Ayrton , ' The Electric Arc , ' p. 333 .
Diagram 7 .
5.000 Curves connecting Mean Spherical Candle - Power with Current for Constant Arc-lengths 4,0 00 4mm .
3,000 2,000 Current in Amperes .
5 10 15 Positive cored .
20 25 30 Negative solid .
From Mrs. Ayrton , 4 The Electric Arc , ' p. 366 .
The Consumption of Carbon in the Electric Arc. 143 candle-power , since the consumption of two candles gives twice as much light as one .
The action is exothermic , and the energy thus made available augments the radiant energy produced by electrical agency , to whose amount it bears an appreciable proportion .
To take a specific example :\#151 ; The energy liberated in each second from the anode , which supplies the bulk of the light , by the consumption of the observed amount of carbon ( 120 x 10"5 grm. ) in an arc of 10 amperes ( 52*4 volts ) and 4 mm. in length , upon the assumption that the carbon eventually burns to C02 ( when 97-3 x 103 cals , are produced for each gramme-molecule of C02 ) , is 4*1 x 108 ergs .
The electrical energy supplied per second amounts to 5*25 x 109 ergs , so that the total energy available from all sources is 5*7 x 109 ergs , and of this the energy of combustion is about 7 per cent. If we add to this the energy derived from the cathode consumption , the energy of combustion amounts to 11/ 3 per cent. If this energy is made available at the high temperature of the arc , it adds appreciably to its candle-power .
Increasing the rate of combustion should on this account increase the brightness of the arc .
This explains why soft carbons ( which burn away more rapidly ) have been found to give greater candle-power than hard ones under similar conditions.* The enormous increase in brightness , which the writer found for metallic arcs when burning in compressed air , f is probably due , in part at least , to the same cause ; for a given pressure the brightness was found to be largely dependent upon the freshness of the air supply\#151 ; when the air became contaminated there was a pronounced diminution in the intensity of the emitted light , which could , however , be restored by the admission of fresh air .
Recently it has been announced that increased brightness has been attained by spraying a jet of nitrogen upon carbon poles , which involves an endothermic reaction .
This does not affect our argument , since it is only for the carbon arc in air that it is suggested that the brightness and carbon consumption increase together .
The source of the bulk of the radiant energy is admittedly the current supply .
Mr. A. H. Davis , B.Sc. , and Mr. F. Southam , B.Sc. , whose services have been referred to in the text , assisted efficiently in these experiments , Dr. C. A. Sadler assisted in Section 10 of this paper , and to them and to Mrs. TV .
G- .
Duffield , who undertook the weighings in the early experiments , I express my thanks and appreciation .
To Dr. J. A. Harker , E.R.S. , who read an early draft of this paper , I am grateful for some criticisms of value .
My indebtedness to Sir Ernest Rutherford has been recorded in the text .
* See Diagram 6 .
t Duffield , 'Phil .
Trans. , ' vol. 208 , p. Ill ( 1908 ) ; vol. 211 , p. 33 ( 1911 ) , etc.
|
rspa_1915_0058 | 0950-1207 | On the effect of the form of the transverse section on the frictional resistance to the motion of an elongated body parallel to its length through a fluid. | 144 | 157 | 1,915 | 92 | Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character | Charles H. Lees, D. Sc., F. R. S. | article | 6.0.4 | http://dx.doi.org/10.1098/rspa.1915.0058 | en | rspa | 1,910 | 1,900 | 1,900 | 14 | 165 | 4,330 | http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1915_0058 | 10.1098/rspa.1915.0058 | null | null | null | Fluid Dynamics | 52.759103 | Measurement | 17.50273 | Fluid Dynamics | [
41.28925704956055,
-29.606163024902344
] | ]\gt ; On the Effect of the Form of the Section on the Resistance to the lIotion of an Elongated Body Parallel to its through a Fluid .
By H. LEES , D.Sc .
, ( Received September 28 , 1915 .
) 1 .
The great increase in the lengths of the parallel of recently constructed submarines and airships has raised into prominence the question of the frictional resistance of such elongated bodies moving parallel to their length through fluids , like air and water , whose viscosities cannot be ected .
This resistance increases as the length increases , and becomes comparable with the head and tail resistances , which for short bodies constitute nearly the whole resistance .
, the problem of greatest practical ortance is the determination of the frictional resistance when the motion is rapid enough to produce eddy currents in the fluid , but the difficulties in the way of a theory 01 eddy current motion have prevented a solution being reached .
The simpler problem of the resistance offered by the walls of a circular pipe to the turbulent flow of viscous fluid through the pipe has formed the subject of extensive series of experiments by Saph and Schoder , * of Cornell University , and by Stanton and Pannell at the National Physical Laboratory .
As a result of these observations , it has been shown that the fall of pressure per unit along a smooth pipe of diameter , through which a fluid of density and kinematic viscosity is flowing with mean velocity is equal to , where , and are constants , the values of which are the same over a wide range of fluids and diameters of pipes , viz. , , and 2 .
So far as I know , no observations on the resistance of a pipe with a central solid core concentric with inner wall of the pipe , have been made with a fluid in turbulent motion the annulus .
But in the case of * Saph and Schoder , ' Amer .
Soc. Civil Engrs .
Proc vol. 51 , p. 253 ( 1903 ) .
Stanton and Pannell , ' Phil. Trans , vol. 214 , p. 199 ( 1914 ) .
, 'Boy .
Soc. Proc , vol. 91 , p. 46 ( 1914 ) .
I take this opportunity of correcting several numerical errors in the above paper .
In the six squations at the foot of p. 49 , the three equations at the foot of p. 60 , and the equation at the foot of p. 52 , the quantity should read ; p. 48 , last line , and p. 49 , line 1 , should read ; p. 49 , line 17 , should read ; p. 49 , line 20 , should read ; p. 49 , line 3 from below , should read Frictional Resistance to Motion through a Fluid .
stream-line motion through the PiPe , it can readily be shown that the resistance per unit area is not the same at the inner and outer surfaces .
If the circular pipe is of internal radius , with a concentric core of radius the velocity of flow at a point from the common axis , due to a pressure slope along the pipe of per centimetre , is given by where is the viscosity of the fluid .
The total flow per second through the annular section is , where From these expressions it follows that the resistances per unit area and of the inner and outer walls respectively iven by .
The first term on the right is the mean velocity over the cross-section , the second varies inversely as the radius of the surface considered , while the third varies more slowly with the ratio of the radii of the two surfaces .
Whatever be the ratio of the radii of the two surfaces , the resistance per unit area is greater for the surface of small than for that of large radius , and it seems advisable to test by experiment whether this is also the case when the motion is turbulent instead of stream-line flow .
If and are the forces exerted on the inner and outer surtaces respectively per unit length we have and Hence the ratio of the force exerted on the outer surface to the total force on both is given by In fig. 1 the full line shows how this ratio varies as changes from to 1 .
The dotted line shows how it would vary if the ratio of the total forces were equal to the ratio of the radii ) or the resistances per unit area inversely as the cube roots of the radii .
For values of between and the inverse cube root law is a very close approximation to the facts , while over the from to it is not so seriously in error as to render lt unsuitable for practical purposes .
* Compare Lamb , ' Hydrodynamics , ' 3rd Edit .
, p. 545 .
l.\mdash ; Full line\mdash ; ratio of force on outer surface to total force on both .
Dotted line\mdash ; ratio if resistances of the two surfaces per } area were inversely proportional to the cube roots of the lad of the surfaces .
3 .
In the case of stream-line flow ough a pipe of elliptical section with and for semi-axes major and minor respectively , it has been shown by Greenhill* that the velocity at the point is iven by , where , as before , is the slope of pressure along the pipe per cm .
and is the riscosity of the fluid .
The maximum velocity occurs at the centre and is .
The total delivery per second is , where Greenhilb ' Lond. Math. Soc. Proc vol. 13 , p. 43 ( 1881 ) .
Results for triangular and rectangular sections are also given in this paper .
Lamb , ' Hydrodynamics , ' 3rd Edit .
, p. 646 .
Frictional Resistance to through Fluid .
and the mean velocity , that is half the maximum .
If is the force exerted on 1 cm .
length of the wall of the pipe The resistance per unit area of the wall at is where is measured along the normal at the point whose direction cosines are and Hence where CK is the perpendicular from the centre of the ellipse on to the tangent at Thus the resistance per unit area of the surface of the pipe at any point is inversely as the length of the perpendicular from the centre of the ellipse on the .
tangent at the point .
The resistances per unit area the ends of the axes are as respectively .
The mean resistance per unit area over the whole coIltour of the section is , where and is the complete second elliptic integral .
For , the length of a quadrant of the ellipse , we may in many cases substitute the approximate expression and we then get for the mean resistance This reduces for a circular pipe to , a well-known equation .
It will be noticed that the surfaces of equal velocity are elliptic cylinders similar to and concentric with the inner surface of the pipe , and it is a Dr. C. H. Lees .
matter of importance to ascertain whether this is also the case when the flow becomes turbulent .
4 .
From the remarks in Sections 1 and 2 , it will be gathered that our knowledge of the frictional resistance of an elementary area of a solid along which a fluid is in turbulent motion is very limited , except in the case of flow through circular pipes , and is in the main empirical .
For the frictional resistance of bodies immersed in the fluid stream , we are dependent chiefly ou Froude's* experiments on flat boards towed through water on on boards placed in a current of air .
In both cases , for want of knowledge of the relative effects of flat surfaces , of edges and of corners , the mean frictional resistance onJy could be ascertained , the total frictional resistance found being divided by the total area in contact with the fluid .
These mean frictional resistances have proved sufficiently accurate for practical purposes for many years , but the necessity for further investigation has been felt for some time by naval architects and others .
In view of this demand for further information , it is proposed in the following sections to examine the frictional resistances of a few very ated bodies moving parallel to their long axes , with speeds not high ellough to produce turbulent motion in the fluids through which they move , and to determine the effects of the shape of the section of the bodies and the influence of projecting keels or ridges on that resistance .
In order to keep the head and tail resistances out of the problems , the bodies are taken as infinitely , and are supposed to move parallel to their lengths a concentric tube or pipe whose diameter is supposed to be large .
5 .
Case long elliptic cylinder is in motion parallel .
to its length through the fluid in a wide tube whose inner contour is a confocal ellipse .
To determine the resistance to the motion of the cylinder , the fluid being assumed in stream-line motion .
Take the centre of the ellipses as origin of co-ordinates , and let the axis pass through the foci , each being at a distance from the centre , and le .
The confocal ellipses are converted into lines parallel to the axis in the plane , where by the transformation , where is a constant .
* Froude , ' Brit. Assoc. Rep p. 118 1872 ) , and p. 249 ( 1873 ) .
Zahm , .
Mag vol. 8 , p. 58 ( 1904 ) .
, for example , Sir W. White 's remarks in 'Trans .
Naval Arch vol. 46 , p. 46 1904 ) .
Frictional Resistance to Motion through Fluid .
This gives , on expanding and separating real and unreal parts , .
Hence is the equation to the ellipses of equal velocity , and the equation to the lines of flow of the viscous forces ; these lines are a series of confocal hyperbolas .
The semi-axes major and minor of the ellipses of constant velocity are and respectively , and the sum of the two is .
Hence , is the velocity at the ellipse of semi-axes and and that at the confocal of semi-axes and , so that , we have Since the complete period of is , and the force transmitted per period is , the viscous force transmitted outwards through the whole surface of unit length of each confocal cylinder is Thus the resistance to the motion of an elliptic cylinder in a confocal Dr. C. H. Lees .
elliptic tube is the same as that of a circular cylinder in a circular tube of radii equal respectively to the means of the semi-axes of the The resistance per unit area at the point of the ellipse of senli-axea , is given by , that is , by , where is the of the perpendicular from the centre of the ellipse on to the tangent at Hellae , for the innsr and , for the outer cylinder .
The mean resistance per ullit area .
the inner cylinder is given by where and is the complete second elliptic , and for the outer surface by In each case may for most purposes be replaced by It will be noticed that the mean resistances of inner and outer surfaces are inversely as the areas of those surfaces , which it is evident from other considerations should be the case .
From the expressions for the resistances per unit area and at different parts of the elliptic surfaces it is also evident that the resistances of equal small areas near the ends of the ma.jor and minor axes of either surface are inversely proportional to the lengths of the minor apd major axes respectively of that surface .
If the confocal ellipses become concentric circles owing to vanishing , the total viscous force per unit ]ength is and the expressions for the resistance per lnit area reduce for the inner cylinder to and for the outer cylinder to which are well known .
Frictional Resistance to Motion through Fluid .
If on the other hand the inner ellipse reduces to the straight line of length joining the foci , and the velocity of the plane it represents is , the total resistance of the plane reduces to and the resistance per umit area at the point , to This expression shows how much greater is the resistance per unit area near the edges of the strip than near its centre line .
A comparison of the expressions for the total resistances of a circular rod moving in a wide concentric pipe and of a flat strip movin in a wide confocal pipe , the radius of the wide circular pipe being equal the mean of the axes major and minor of the wide confocal pipe , shows that the total resistance of a strip of width and of contour in contact with the fluid is equal to that of a circular rod of diameter and contour Hence the frictional coefficients deduced for surfaces moving in water by Froude , in air by Zahm , *from experiments on thin boards should , if the relations here established for stream-line flow hold when the flow becomes turbulent , be multiplied by , to give the coefficients for circular cylinders under the same conditions .
If a strip of breadth moves parallel to its length between infinite planes parallel to and at a distance from the strip instead of in a confocal pipe , the resistance to the motion of the strip is the same as that of a strip of width forming part of an infinite plane ostituted for the strip and moving with the same speed .
This result again brings out the exceptional part contributed by the edges of strips to their total resistance .
6 .
Case long rod of reCt ( section is in motion parallel to its length through a viscous liquid contained in a wide pipe of nearly cular section : to determine the resistancs to the motion of the rod .
It has been shown by that if and the transformation , converts the area outside the square in the plaue with sides and into the interior of the circle , p. 148 .
Maxwell , 'Electricity and Magnetism , ' 2nd Edit .
, vol. 1 , p. 278 ; or Thomson , ' Recent Researches , ' p. 218 .
Schwarz , 'Ges .
Werke , vol. 2 , p. 77 ; and Forsyth , 'Theory of Functions of a Complex Variable , ' 2nd Edit .
, p. 639 .
Dr. C. H. Lees .
in the plane , the centre of the circle corresponding to the circle at in the plane ( fig. 4 ) .
In order to convert the area outside the normal rectangular section of the rod in the plane into the interior of the same circle in the plane it is evident we only require to write instead of under the radical .
For the sake of comparison of the results for the case of the rectangular rod with those for a circular rod , it is convenient to invert the circle with respect to its own centre by writing , where for Thus converts the exterior of the rectangle in the plane into the exterior of the circle in the plane , the circles at infinity in the two planes correspondin , to each other , and for all large values of or being equal to .
If we now write ?
, where is the velocity at any point of plane .
On substituting in the original equation we obtain as the equation connecting the position of a point in the plane with the velocity at the point .
circular functions the equation becomes Frictional Resistance to Motion through a Fluid .
On putting this becomes From which we deduce where and are the first and second elliptic integrals respectively .
At A the corner of the rectangle immediately to the right of the origin in the plane we have and where and are the complete elliptic rals .
The resistance of the half side OA of the rectangle is proportional to ?
and since , and the resistance of the side OA is equal to of bhe resistance of the whole rectangle , or of that of a circular cylinder of radius 1 , moving with the same speed .
When exceeds , the value of becomes complex , its real part remaining .
If is the middle point of the second side which starts .
at the corner , then at , and The resistance of the half side is equal to of the resistance of the whole rectangle , or of that of a circular cylinder of radius 1 , moving with the same speed .
7 .
The following Table gives the corresponding values of , and 7/ 0\ldquo ; that is of the half-sides of various rectangular prisms having the same resistance as a circular cylinder of radius unity moving with the same speed .
column giving the ratio of twice the length of the short to the sum of the lengths of long and short sides of the rectangle is given , to facilitate the choice of in calculating the resistance in any given case .
The last colt11m contains the length of the perimeter of the rectangle , which may be compared with the perimeter of the circular cylinder of the same resistance .
In each case the resistance of the short half-side is equal to that part of the perimeter of the cylinder an angle at the centre , and that of the long half-side equal to that of the peritneter the ) ; For many purposes an approximate value of the total resistance of the uS .
prism is all that is required .
The relation may then be used .
If * On writing sn we get gz , where gz is the symmetrical ' elliptic function introduced by Glaisher , ' Quart .
Journ. Math. , ' vol. 20 , p. 350 .
Dr. C. H. Lees .
*These results have been verified experimentally by .
T. W. Blackaby , one of my students , by measuring the conductance of a layer of electrolyte 1 cm .
deep reen a strip , a rectangle , a square and a circle respectively , and an outer circle of circumference six or seven times that of the inner electrode .
is the sum of the lengths of the long , and that of the short sides of the rectangle , the circumference of a circular cylinder having the same resistance when moving with the same speed is given by equivalent erence This relation is accurate to within 2 per cent. 8 .
plane in motion parallel to itself in a viscous fluid has a fin or keel projecting into the fluid at right angles to its surface , its length being in the direction of motion .
To find the effect of the keel on the resistance of the surface , the motion in the fluid being stream-line motion .
The Schwarzian t , ransformation converts the outline of the section of the surface and keel in the plane , where , into the axis of in the plane , where , the middle point of the contour of the keel being taken as origin of co-ordinates in the plane and becoming the origin of co-ordinates in the plane , the outer corners of the keel becoming the points and the inner corners the points in the plane ( fig. 6 ) .
Writing sn the equation becomes where and is the second elliptic If A is tffi outer corner of the projecting keel , OA is given by Frictional l\amp ; sistance to Iotion through a Fluid .
J. 55 where is the complete and is the real quarter-period of The resistance to the motion of the strip of breadth OA is equal to that of a strip of ) readth a of an tite nniform plane moving with the same speed .
For points in ) beyond the inner corner of the keel we have These equations become on expansion At the point , and Thus the resistance to the of the strips OA and AB is equal to that of a strip of breadth of an infinite plane moving with the same speed .
When the point is on the surface at a considerable distance from the keel , is small and we may write or and very nearly .
Hence or , terms in being Thus the resistance of the surface between the middle line of the keel and a parallel on the surface through at a considerable distance from the keel is equal to that of a strip of width of a plane surface moving with the same speed .
The ratio of the half width OA to the depth AB determines and , then gives the other term in } ) VOL. XCIL\mdash ; A. Dr. C. H. Lees .
resistance formula .
It should be noticed that the accuracy of the approximate calculation above will decrease htly as approaches unity .
When becomes small the keel becomes in proportion to its depth , and when is zero it has become an infinitely thin strip projecting a distance from the surface at angles to it .
Putting zero in the general equation for when , it becomes as one would anticipate from the direct transformation .
Fl6.7 Hence if is a point some distance from the projecting strip ( fig. 7 ) Thus the resistance of one side of the projecting strip AB and the portion of the surface between base of the strip and the point has the same resistance as a of width equal to AP of a plane surface moving with the same speed .
9 .
When the keel is not sufficiently thin to allow us to wlite the accurate calculation of the resistance involves the use of tables of elliptic functions .
Since in most practical cases an approximate value expressed in of simple functions will suffice , we proceed to find a simpler expression .
We have found that OA , and AB .
Now is Glashier 's function*and can be expressed in terms of by the series .
Similarly is Glaisher 's .
With the help of these series it may be shown that for small values of the correcting term proportional to .
AB , but for values of and of less than it is not .
A slight generalisation of this form of expression gives the correction to within per cent. , so long as \amp ; es not exceed 2 , and to within 5 per cent. so long as it does not * Glaisher , ' Qnart .
Journ. Math vol. 20 , p. 320 ( 1886 ) .
Frictional Resistance to Motion through Fluid .
exceed 3 .
We shall take as a sufficiently close approximation to the correct value for our present purpose .
Thus the correction which has to be added to ( fig. 6 ) to give the square of the breadth of a strip of a plane surface of equal resistance to OA , AB , and , when moving with the same speed , is , that is the breadth of the strip of a plane surface equal in resistance to the strips OA , AB and BP is for all cases in which OA does not exceed twice AB .
10 .
The cases considered in the previous raphs show that for motions of very ated bodies parallel to their lengths fluids in which motion is produced the movement , the influence of the form and magnitude of the section of the body on the viscous resistance to the motion is considerable .
Values of the resistances per unit area of contact with the fluid and the total resistances are given for the following cases:\mdash ; 1 .
A circular pipe with a concentric core , the fluid moving through the annular space between .
2 .
A of elliptical section through which fluid is moving .
3 .
A long body of elliptical section in motion ) a fluid .
The cases in which the section becomes a circle and a straight line respectively are considered .
4 .
A long body of rectangular section in motion through a fluid .
Square and straight line sections are considered .
5 .
A .
wide surface from which a keel with its length the line of motion projects .
The ratios of to depth of keel cover a rable range .
In all cases the law of resistance may be expressed in a simple form , and it is desirable that measurements of the resistances in the corl.esponding cases in which the motion in the fluid becomes turbulent should be made*in order if possible to carry over these laws to turbulent motion or to proyide any corrections to them which the new circumstances entail .
Nresults .
A. V. Tonnstein , ' VOL. XCU \mdash ; A.
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rspa_1916_0001 | 0950-1207 | Address of the President, Sir William Crookes, O. M., at the anniversary meeting on November 30, 1915. | 158 | 170 | 1,916 | 92 | Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character | Sir W. Crookes | speech | 6.0.4 | http://dx.doi.org/10.1098/rspa.1916.0001 | en | rspa | 1,910 | 1,900 | 1,900 | 4 | 219 | 6,623 | http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1916_0001 | 10.1098/rspa.1916.0001 | null | null | null | Biography | 85.952201 | Reporting | 3.285789 | Biography | [
36.632293701171875,
79.25624084472656
] | Address of the President , Sir William Crookes , O.M. , at the Anniversary Meeting on November 30 , 1915 .
Since our last Anniversary Meeting the Eoyal Society has lost many of its Fellows .
Too long is the list of those who have passed .
If my reference to their work is brief you will understand that is due to the exigencies of time , and not to lack of appreciation .
No words of mine are necessary to perpetuate the memories of men whose names will live among those of the great masters of Science .
In April this year one of our oldest Fellows , William Grylls Adams , Emeritus Professor of Natural Philosophy at King 's College , London , died , after a life of great scientific activity , at the age of 79 .
He was Professor of Natural Philosophy and Astronomy at King 's College , London , from 1865 to 1906 , and was elected a Fellow of the Eoyal Society in 1872 .
His researches covered a wide field , and he was the author of many memoirs in various branches of physics .
In 1875 he delivered the Bakerian Lecture on the forms of equipotential curves and surfaces and lines of flow , and in the same year he published an important paper on the change of resistance produced by magnetisation in iron and steel .
He made an exhaustive investigation of the effect of light in reducing the resistance of selenium , and devised a new form of measuring polariscope .
In later years he made a special study of terrestrial magnetism , and he also published papers on the " Illumination of Lighthouses .
" He was one of the founders of the Physical Society , and was its President from 1878 to 1880 .
He was also President in 1884 of the Institution of Electrical Engineers , and his inaugural Address on the growth of electrical science and the testing of dynamo machines and incandescent lamps was a valuable contribution to our knowledge .
He served on the Council of the Eoyal Society from 1882 to 1884 , and again from 1896 to 1898 .
Dr. E. Assheton , who was one of the most eminent of British zoologists , died on October 24 from , heart failure following influenza .
Dr. Assheton has been described as the first experimental embryologist in England , and his new and original methods enabled him to correct some of the erroneous views of the older school of embryologists .
His premature death , when his intellectual powers were still undiminished , is a heavy blow to science , and it will be felt nowhere more than at Cambridge , where he had recently been appointed Lecturer in Animal Embryology .
Anniversary Address by Sir TV .
Crookes .
159 The death of Henry Charlton Bastian , which occurred on November 17 , removes from our midst a physician of eminence , who will be remembered as the energetic champion of a theory of the spontaneous origin of life .
He was at one time Professor of Pathological Anatomy , and afterwards Professor of the Principles and Practice of Medicine , at University College , London , and was also consulting physician to the National Hospital for the Paralysed and Epileptic .
He was the author of many articles and monographs on paralysis , aphasia and speech defects , and diseases of the nervous system .
In Sir Arthur Herbert Church we have lost one whose position in the world of science was unique .
He was a man of many and diverse gifts and interests , and was an artist of no mean skill and a recognised authority upon precious stones and porcelain .
While Professor of Chemistry at the Poyal Agricultural College , Cirencester , he did valuable work in agricultural chemistry\#151 ; being , for example , the first to describe turacin , an animal pigment containing copper .
He was also interested in mineralogy , and was the discoverer of the native cerium phosphate Churchite .
In 1879 he was appointed Professor of Chemistry at the Eoyal Academy of Arts , and he then turned his attention to researches on paints and pigments , publishing a standard work on the subject , entitled 4 The Chemistry of Paints and Painting/ He conducted an enquiry into the condition of the frescoes in the Houses of Parliament and the stonework of Westminster Abbey , in which his artistic and archaeological knowledge was invaluable .
Sir Arthur Church , who died on May 31 , was elected a Pellow in 1888 .
In May the death occurred of Morgan William Crofton , who , after a brilliant career at Trinity College , Dublin , was for three years Professor of Natural Philosophy at Queen 's College , Galway , and afterwards Professor of Mechanics and Mathematics at the Eoyal Military Academy , Woolwich .
On his resignation in 1884 he was appointed to a Fellowship of the Eoyal University of Ireland .
Dr. Crofton , who was elected a Fellow of the Eoyal Society in 1868 , was the author of papers on Mechanics and Geometry , but is perhaps best known for his work on Probability , upon which subject he contributed an article in the ninth edition of the ' Encyclopaedia Britannica/ David Douglas Cunningham , who died in December , 1914 , rendered great services to science and to the State by his studies of tropical diseases generally , and of cholera in particular .
From 1869 to 1879 he devoted all his energies to the investigation of cholera from a pathological point of view , and in 1879 he was appointed Professor of Physiology at the Medical College at Calcutta , where his gifts and the charm of his manner won him great success as a teacher of Indian students .
Besides his work in pathology , o 2 160 Anniversary Address by Sir W. Crookes .
Cunningham carried out numerous researches in cryptogamic botany , and made exhaustive studies of the diseases of plants and of snake venom , and he also made time to perform the duties of many public offices in India .
He was elected a Fellow of the Eoyal Society in 1899 .
The death of James Geikie , the younger brother of Sir Archibald Geikie , is a great loss to science and to his many friends .
When quite a young man he took an active part in the Geological Survey of Scotland , and published many papers giving the results of his observations .
He afterwards went to Gibraltar with Andrew Eamsay , the Director of the English Geological Survey , to prepare a report on its water supply .
In 1874 he published the first edition of his famous book ' The Great Ice Age/ In 1882 he was appointed Murchison Professor of Geology and Dean of the Faculty of Science at Edinburgh , and thenceforward he devoted himself chiefly to teaching and the preparation of the many valuable educational works which bear his name .
He was one of the founders of the Eoyal Scottish Geographical Society , and was its President for some time .
He was a highly successful and inspiring teacher , and was one of Edinburgh 's most distinguished scientific men .
Sir William Eichard Gowers , who died on May 4 , had won an international reputation in medicine ; His researches dealt chiefly , but by no means exclusively , with neurology .
He studied the diseases of the heart and blood-glandular organs , and was the inventor of an instrument for determining the amount of haemoglobin in blood .
In 1880 he published his work on the 'Diagnosis of Diseases of the Spinal Cord , ' and the following year a book on Epilepsy , founded on his observations made at the National Hospital for the Paralysed and Epileptic , where he held the post of physician .
His chief work was the admirable and widely used 'Manual of Diseases of the Nervous System/ He was elected a Fellow of the Eoyal Society in 1887 and knighted in 1897 .
Dr. Arthur Sheridan Lea , who died in March at the age of 61 , was one of the founders of the Cambridge Physiology School , his research work dealing chiefly with the chemical changes of food during digestion , and the action of rennet and fibrin ferments .
He was a Fellow of Gonville and Caius College , and was appointed University Lecturer in 1884 .
Unfortunately his active career was prematurely cut short by spinal disease , and his later years had been spent in retirement and rest , although he followed with unabated interest the work of his friends and pupils .
Eiciiard Lydekker , who was one of the most prolific writers upon zoology and natural history , died in April of this year .
His first scientific work was connected with the Geological Survey of India , and he made a % Anniversary Address by Sir W. Crookes .
161 very thorough study of the zoology and geology of Kashmir .
Afterwards he devoted himself more to palaeontology , and between 1885 and 1887 he was engaged on the preparation of a catalogue of fossil mammals in the Department of Geology of the British Museum , while some years later he spent some time making a study of the fossil vertebrates in the La Plata Museum .
From 1896 until his death he wTas occupied with the reorganisation of the Mammalian Exhibition Galleries of the Natural History Museum , in which he achieved conspicuous success .
A very rapid worker , he published an enormous number of technical and popular articles , and he also co-operated with Sir William Flower in ' An Introduction to the Study of Mammals , ' and edited the f Eoyal Natural History/ It was with deep regret that we heard that Prof. Eaphael Meldola died suddenly on November 16 , at the age of 66 .
Prof. Meldola was an eminent authority upon the manufacture of coal-tar colours , having worked for many years in the colour works of Messrs. Brooke , Simpson , and Spiller , where he had made important discoveries of new methods and processes .
In 1885 he became Professor of Chemistry at the Finsbury Technical College .
He was a member of the recently appointed Advisory Council for the Organisation and Development of Scientific and Industrial Eesearch , and was an ardent advocate of the necessity of fostering pure research in order to arrest the decline of industry in this country .
He was the author of valuable text-books upon the Chemistry of Photography and the Chemical Synthesis of Vital Products , and also translated and edited Weismann 's ' Studies in the Theory of Descent .
' He was elected President of the Chemical Society from 1905 to 1907 , Fellow of the Eoyal Society in 1886 , and Davy Medallist in 1913 .
We were mueh grieved to learn that the renowned zoologist , Prof. Edward Alfred Minchin , had passed away , and the gap he leaves in the scientific world will long be unfilled .
In spite of the handicap of ill-health in his youth , Minchin was very successful at Oxford , where he was finally elected Fellow of Merton College .
After spending some time in research work at foreign marine zoological stations he returned to Oxford as assistant to Sir Eay Lankester and Demonstrator of Comparative Anatomy , and in 1899 was appointed to the Jodrell Professorship of Zoology at University College , London .
Subsequently , he became the first Professor of Protozoology at the University of London , and Director of Protozoology at the Lister Institute of Preventive Medicine at Chelsea .
In 1911 he was elected a Fellow of the Eoyal Society .
The value of his research in zoology has been fully recognised both in this country and abroad , and in the branches which he made specially his own he had no rival .
The refinement of his methods , his 162 Anniversary Address by Sir W. Crookes .
accuracy and attention to detail , were inimitable , and he put a high ideal of carefulness and thoroughness before his pupils .
He published a valuable text-book , ' An Introduction to the Study of the Protozoa/ which has come to be regarded as the standard work on the subject , and he wrote articles in the scientific journals and the ' Encyclopaedia Britannica/ and was an important contributor to Lankester 's ' Treatise on Zoology/ A man of striking originality and of great gifts , he will be deeply mourned by his many friends .
Dr. Hugo Muller , whose death occurred on May 23 , was elected a Fellow in 1866 .
He had long been resident in this country , and in his early years did valuable scientific work , which he resumed when he retired from his position as partner in the firm of De la Rue and Co. With Dr. Warren De la Rue he devised the chloride of silver-zinc constant battery , and he discovered the value of iodine as a catalyst in chlorination .
Of late years he had worked at the Davy-Faraday Laboratory of the Royal Institution , and published many articles in the ' Journal of the Chemical Society/ The death of Admiral Sir George Strong Hares has robbed the world of a distinguished scientific man who had served his country in more than one capacity .
He did valuable geological work in the Arctic Expedition of 1852-1854 under Captain Kellett , and after a period devoted to the training of cadets , during which he wrote an excellent book on seamanship , he surveyed Torres Strait , part of the coast of Australia , and the Gulf of Suez .
He was a member of the " Challenger " Expedition , but was recalled to take command of a scientific Arctic expedition , which reached 82 ' 27 ' H. The geology and biology of Grant Land and Greenland were thoroughly examined by the party , and Captain Hares himself took the astronomical , meteorological , magnetic , and tidal observations .
In 1878 Sir George Hares surveyed Magellan 's Strait .
He was later appointed Professional Officer in the Harbour Department of the Board of Trade , and subsequently Conservator of the Mersey .
We have lost in Francis Henry Heville a metallurgist whose researches were marked by great precision and acumen .
In 1888 , in conjunction with Mr. C. T. Heycock , he began the investigation of the lowering of the freezing-point of metals by solution in metals , and since that date he had continued his researches on alloys , the most important and complete being those on tin and copper .
His mathematical ability and training ( he took his degree in the Mathematical Tripos in 1871 ) were of great assistance to him in his work*on the alloys , and he brought a cultured mind and a sound judgment to bear upon the problems which he so successfully solved .
Sir Andrew Hoble , whose death occurred on October 22 at the age of 84 , i Anniversary Address by Sir W. Crookes .
possessed an unusual combination of talents , to which his tireless energy enabled him to give full play .
His inventive genius first manifested itself in the design and improvement of naval and military guns , and the firm of Armstrong , Whitworth , and Co. , Limited , owed a great debt to his keen business spirit .
In 1875 , with Prof. Abel , he began his highly important and original work on explosives which has made his name known all over the civilised world .
He served on the Council of the Royal Society four times , and was the recipient of the Royal Medal .
Sir Arthur William RBcker , whose death at the age of 67 occurred on November 1 , was a man of conspicuous organising ability and an excellent teacher and lecturer .
In 1874 he was chosen as the first Professor of Mathematics and Physics at the Yorkshire College , Leeds , and afterwards occupied the Chair of Physics at the Normal School of Science , South Kensington .
In 1901 he was elected Principal of there-organised University of London , and there performed a difficult task with excellent tact and judgment .
He became a Fellow of the Royal Society in 1884 , and was one of the Secretaries from 1896 to 1901 .
He was the recipient of a Royal Medal in 1891 .
His most important scientific work was connected with terrestrial magnetism , and he took a leading part in the Magnetic Survey of the British Isles , preparing a memoir on the subject for the Bakerian Lecture in 1889 .
Dr. William James Sell , University Lecturer and Senior Demonstrator in Chemistry at Cambridge , who died in March , was a man of great ability and untiring perseverance , who played a most useful part in the training of students at Cambridge in experimental science .
He gave many successful courses of lectures in chemistry , and when opportunity offered he showed that he was capable of successful research , one of his most important pieces of work dealing with the chloro-derivatives of pyridine .
Mathematical science has lost one of its most distinguished exponents by the death of Prof. Henry William Lloyd Tanner , to whose educational and administrative talents the University of South Wales and Monmouthshire is deeply indebted .
His views on the mathematical training of students were thoroughly sound , and his services to education were by no means limited to his College or LTniversity .
In addition to his teaching and administrative work at Cardiff he published many important investigations in mathematics , dealing firstly with the solution of partial differential equations and secondly with the theory of numbers .
These latter researches , which were distinguished by great ingenuity and originality , were not by any means completed when failing powers forced him to resign his professorship and cease work .
Lieutenant-General James Francis Tenant , Past-President of the Royal 164 Anniversary Address by Sir W. Crookes .
Astronomical Society , did valuable work in connection with the Great Trigonometrical Survey of India from 1854 to 1869 , and was afterwards responsible for a great number of observations in the total eclipses of 1868 and 1871 and the transit of Venus in 1874 .
He was most assiduous and enterprising iu perfecting methods and collecting data , and the conclusions he drew from his observations were of fundamental importance .
For the last 20 years he had done no active scientific work , but he had followed with the keenest interest the developments of astronomy .
He died on March 6 at the age of 86 . .
Three distinguished representatives of our Foreign Members have died since our last Anniversary Meeting .
The name of Emile Hilaire Amagat is familiar to the physicists of all nations as that of the investigator of the behaviour of gases under pressure , and the brilliant series of researches which he carried through to a successful conclusion showed him to be an experimenter of truly remarkable powers .
He determined the compressibility of a number of fluids , and also investigated the effect of pressure upon the freezing points of liqliids .
During recent years he had been engaged upon the compilation and arrangement of the numerical data obtained in his experimental work dealing with the specific heat of gases , the internal pressure of fluids , and the corresponding states of matter .
Prof. Amagat was elected a Foreign Member of the Eoyal Society in 1897 , and in 1906 he was President of the French Physical Society .
Astronomy has suffered a severe loss by the death of another of our Foreign Members , George Friedrich Julius Arthur Auwers , whose work in connection with the co-ordination of astronomical observations showed him to be a man of extraordinary patience and thoroughness .
His chief work was the re-reduction of Bradley 's observations , to which he devoted some ten years of his life , and the preparation of an exhaustive catalogue of stars for the German Astronomical Society .
He was a member of many German Astronomical Expeditions , including that for the observation of the transit of Venus in 1874 , and he assisted Sir David Gill in observations for the determination of solar parallax at the Cape Observatory in 1889 .
He was the discoverer of the star " Nova Scorpii , " and made many valuable observations of variable stars .
The sudden death of Prof. Paul Ehrlich in August brought to a close a career of great scientific activity and notable achievements .
After graduating in medicine , Ehrlich turned his attention to the affinities of cells for various ^reagents , and some of the methods and staining agents he employed are still in constant use in biological work .
He elaborated a method of standardisation of diphtheria antitoxin , and was the originator i Anniversary Address by Sir W. Crookes .
of the side-chain theory of antibodies .
His name is probably best known in connection with " G06or Salvarsan , as a cure for syphilis .
He was elected a Fellow of the Eoyal Society in 1910 , and he was the Croonian Lecturer and the joint recipient with Metchnikoff of the Nobel Prize .
Finally , it is my sad duty to express the regret of the Eoyal Society at the death of one who , though he had not yet been elected a Fellow , had done work which fully deserved the highest recognition .
If his days had been longer he would undoubtedly have ranked amongst our great physicists .
On August 10 Henry Gwyn Jeffreys Moseley , Second Lieutenant in the Eoyal Engineers , died a soldier 's death at the Dardanelles .
Although only 27 , he had published remarkable work .
His examination of the X-ray spectra of different elements led to the important discovery that the properties of an element are determined by its atomic number\#151 ; which marks a notable advance in our knowledge of the structure of the atom .
He was instantaneously killed in the execution of his duty .
The whole world is the poorer for the tragedy by which he was\#151 ; " Gathered to the Kings of Thought Who waged contention with their time 's decay , And of the past are all that cannot pass away .
" In the Eeport of the Council a brief outline is given of the activities of the Eoyal Society in connection with the scientific problems which confront us in consequence of the war .
Towards the end of last year a War Committee and Sub-Committees were appointed to consider a variety of questions , including the supply of drugs and other chemicals which hitherto have been mostly imported .
It was finally decided that it would be best for the Council as a whole to act as a general War Committee , the original sub-committees being converted into four sectional committees , which have met regularly throughout the year .
A Memorial to the Prime Minister was drawn up , calling attention to the urgent need for closer co-operation between those engaged in scientific research and the directors of the nation 's industries , and was presented by delegates of the Eoyal Society and the Chemical Society .
The President of the Board of Education has since issued a scheme for the Organisation and Development of Scientific and Industrial Eesearch , which has met with approval on all sides , and which indicates that the Government is ready to give the country a strong lead in the way of recognition of the value of scientific training and work .
An important step has been taken in appointing a Committee to prepare a scheme for the establishment of a permanent Board in collaboration with Anniversary Address by Sir W. Crookes .
technical and other scientific societies for the discussion of questions in which joint action appears desirable .
Owing to unavoidable delay in printing , the Royal Society 's Catalogue of Scientific Papers has progressed only slowly , and there appears to be no likelihood of its being completed at the present rate until the middle of 1921 .
The Director of the Catalogue , Dr. McLeod , who has been indefatigable in his labours , has been obliged by ill-health to retire .
It is proposed not to appoint a new Director , but to continue the work under the able management of the Chairman of the Catalogue Committee , Prof. Silvanus Thompson .
Another of the Society 's tasks , the Magnetic Re-Survey of the British Isles , has been continued at a reduced rate and with some interruptions throughout the year just passed .
At present only the Hebrides , Isle of Man , Channel Isles , and six points in England and Wales remain unresurveyed .
The Copley Medal has been conferred upon Prof. Ivan Petrovit-ch Pavlov , one of our most distinguished Foreign Members , whose researches in physiology have led to the acquisition of valuable knowledge .
By a most ingeniously worked out and original method of making fistulse or openings to the exterior , Prof. Pavlov has successfully studied the inter-relation of the functions of the alimentary canal .
His experiments have shown how the presence of food in one cavity controls the secretion of digestive juices into the next , and he has made many discoveries concerning the conditions which influence the secretory process , while his method has facilitated the study of the chemical changes which occur in the food as it passes through the canal .
Moreover , by the method which he calls that of conditioned reflexes , Prof. Pavlov has studied , from a physiological point of view , the influence of the higher brain centres upon the secretion of saliva .
He has also investigated the mechanism of the muscle by which bivalves open and close their shells , and the nervous control of the heart , especially through the sympathetic nerves .
His resourcefulness and skill have enabled him to make important contributions to physiological science , and his work , the true worth of which has , perhaps , not yet been rightly prized , deserves the fullest recognition .
The Royal Medal given annually for physical investigations has been awarded to Sir Joseph Larmor , whose work in mathematics and physics includes a very wide range of subjects\#151 ; geometry , dynamics , optics , electricity , the kinetic theory of gases , the theory of radiation , and dynamical astronomy\#151 ; upon all of which he has published illuminating memoirs .
Possibly hig^chief claim to distinction is the establishment of the theory that radiant energy and intramolecular forces are due to the movements of minute electric charges .
This theory is fully worked out in his treatise f JEther and i Anniversary Address by Sir W. Crookes .
167 Matter.1 For a long time Sir Joseph Larmor acted as Secretary to the Eoyal Society , performing the duties of the office with great success , at the same time continuing with unabated vigour original research .
The offer of the Eoyal Medal is a mark of the Society 's appreciation and admiration of his invaluable services to science .
The other Eoyal Medal , for work in the biological sciences , is this year conferred upon Dr. William Halse Eivers Eivers , whose work in ethnology has contributed largely to the establishment of the subject upon a scientific basis .
He was the first to use the genealogical method in ethnological investigations .
His remarkable originality , combined with sound judgment , have enabled him to produce work which will rank with the best that has been done in ethnology .
All chemists will agree that the award of the Davy Medal to Prof. Paul Sabatier is fully justified .
His lengthy researches on the use of finely divided metals as catalysts are universally known .
The hydrogenation of unsaturated organic compounds , especially by means of nickel , has been thoroughly elucidated by Prof. Sabatier and his co-worker , the Abbe Senderens .
The industrial application of the process to the unsaturated acids of the oleic series has already acquired considerable industrial importance .
It gives me great pleasure to announce the award , so well earned by Prof. Sabatier .
The Hughes Medal is awarded to Prof. Paul Langevin , who has made valuable contributions to electrical science , both on the theoretical and experimental sides .
He has found by experiment the rate of re-combination and the mobility of ions produced by different processes in gases at various pressures , and he has made an exhaustive study of the theoretical aspects of the interdiffusion of gases and the mobility of ions .
We meet to-day in circumstances of unparalleled gravity .
I am sure we are .all deeply conscious of the imperative necessity of modifying the methods of our activities , correcting mistakes , and planning reforms without which we cannot hope to maintain our position among the nations .
England , our England , is passing through a fiery furnace of .
stress and discipline , and we must face without flinching the bitter lessons to be learned .
The nation 's attitude towards science is , I think , largely due to the popular idea that science is a kind of hobby followed by a certain class of people , instead of the materialisation of the desire experienced in various degrees by every thinking person to learn something about innumerable natural phenomena still unsolved ; and , having learned , to control and apply them intelligently for the benefit of the human race .
Many attempts have been made to explain exactly what is meant by science , and to 168 Anniversary Address by Sir W. Crookes .
differentiate true science from its counterfeit ; and it is by no means ' easy to define it so that the vague general idea of the average man can be replaced by clear and precise conception .
Even the most patient investigator , the most acute observer , must constantly feel " Oh , what a dusty answer gets the soul when hot for certainties in this our life .
" If we refer to our Charter , we shall find that the aim of the Royal Society is promoting Natural Knowledge by Experiments , and if we regard science as synonymous with natural philosophy we may describe it as knowledge relating to natural objects and phenomena connected therewith based upon experiments .
Life has been defined as the act of correspondence with our environment , and science may equally tersely be defined as the use of intelligence in effecting that correspondence .
I believe that the " hobby " attitude is due to our national character , and can only be rectified slowly , step by step .
We cannot suddenly become a truly scientific nation , either now during the war , or immediately on its conclusion .
We shall have to make many fundamental alterations in our ideas and almost to change our natures before such a change can be effected. .
First among our defects must surely be placed mental inertia , our reluctance to do our thinking for ourselves and the slowness of our intellectual apprehension .
This condition is fundamentally different from docility of mind , and its results are more disastrous because it tends to inhibit action on the part of those who should be leaders .
Associated with it of course is our inherent stolid conservatism , which makes us too readily satisfied to continue in the ways of our forefathers\#151 ; ways which , though good enough once upon a time , are now obsolete and undesirable .
We are sometimes prone to underestimate our opponents ' abilities and powers , and usually we have a hearty contempt for outside criticisms of our methods .
Our mental inertia makes us slow to put our latent organising power into action .
The problem before us is twofold .
We have , firstly , to find out how best to organise all our present forces and employ the material at our disposal to win victory .
Many suggestions have recently been made as to the best way to mobilise science and invention , so that , for example , schemes that show some likelihood of having military or naval value can be put at once to the test .
At the beginning of the war the Royal Society appointed Committees for this purpose .
Their scope could be extended usefully .
They include men of naval and military experience , whose practical skill and knowledge supplement the theories of men of science .
The second part of the problem is closely interwoven ^with the first , and its importance to the nation is hardly inferior .
If we neglect to alter our ways , if we continue to disregard the value of scientific work and are content with ignorance of scientific methods on the Anniversary Address by Sir Crookes .
169 -part of the authorities , we shall assuredly suffer total defeat in the industrial war which must of necessity follow upon the conflict of arms now raging .
This is a matter in which men of science have a great responsibility to the nation .
We must not cease to bring to the notice of the public the facts of which we are too fully aware .
The attitude of the Government and the public towards science has been mistaken .
For this formidable error we suffer and , I fear , must long continue to suffer .
The remedy involves many sacrifices and heavy expenditure , probably at first without apparent return .
It is to the New Generation now being educated that we must look for betterment of our position ; and it is for youth we must now make plans .
We must make all education more scientific .
It is admitted we have much to learn from our adversaries ; we must bring scientific methods to the front .
As a well-known writer has said of our young generation , We must not let their schooling interfere with their education .
" I am , however , glad to note that already there are signs on the part of some of our larger companies and more intelligent manufacturers of a disposition to remedy shortcomings .
The numerous " Polytechnics " that spring up in every manufacturing town ( some wonderfully well equipped and organised ) are turning out men with at least an insight into the scientific principles that underlie their particular spheres of work , and such men find their services readily accepted .
There are also within my knowledge many instances where -manufacturers encourage their lads to attend these institutions , giving them the necessary time and opportunity .
But so far this is the isolated action of a few individuals , and needs both encouragement and organisation .
Should not science be represented on the Privy Council ?
It is astonishing that in so august a body science is almost ignored .
Ought we not to have in the Cabinet a Minister of Science with a board of advisers similar to that of Agriculture , with the proviso that the Minister of Science should hold his \#166 ; office primarily by virtue of his scientific capacity ?
Power of organisation and general business ability should be regarded as essential secondary qualifications .
The newly appointed Science Councils and Committees might be incorporated under the Ministry of Science\#151 ; then , and then only , pure research would begin to take its place as an invaluable profession , with .
a status of its own at least on a level with that of other learned professions .
The leaders of its rank and file would be doing work of fully as much value to the nation as the work of the officers of our naval and military forces .
Then , I feel convinced , the next generation would see the disappearance of listless co-operation between manufacturer and scientific worker , and we should hear less of the inferiority of British science as compared with that of our opponents .
Given equal opportunities , our men would speedily give 170 Prof. J. Joly .
On a Method of Estimating proof of fertility of ideas , of organising powers , and of resource and initiative .
Eesearch could be so thoroughly well organised that Suitable workers would be jointly engaged with those problems for the speedy elucidation of which there is the greatest need , and the results of their investigations would be at the disposal of all British manufacturers .
It rests with us to keep these ideas before the mind of the public , now that at last it is ripe to consider them .
" Be wise to-day ; it is madness to defer .
" And now I must pass on to my latest task\#151 ; perhaps the most fateful of all the tasks I have ever undertaken .
I bid a sincere regretful farewell to my official colleagues of the Boyal Society , whose unfailing and courteous help in my discharge of the duties of the presidential office I gratefully acknowledge .
I deeply appreciate the honour conferred on me during the last two years , and if I may utilise " an intelligent appreciation of events before they occur " I heartily congratulate the Society on its election of my successor .
We all know , and the world knows , the lofty place held by Sir Joseph J. Thomson in the august realms of science\#151 ; and we all must feel that our Society could not have selected a more suitable and distinguished President .
On a Method of Estimating Distances at Sea in Fog or Thick Weather .
By J. Joly , Sc. D. , F.E.S. ( Eeceived October 20 , 1915 .
) The problem of estimating distances at sea in fog or thick weather is obviously one of much importance to navigation .
Notwithstanding the more perfect means of communication between ship and shore , or between ship and ship , which recent scientific advances have secured , and which are at the command of the more important ships and lighthouse stations at the present time , I can find no reference to the fact that these improved means of communication suffice to solve the problem referred to under a great variety of circumstances .
In the present paper I shall confine myself to the determination of distance between ship and shore .
In a subsequent paper I hope^to discuss the application of the methods involved to finding the distance between ship and ship , and thereby lessening risk of collision .
The method I have to propose is based generally on the differing velocities
|
rspa_1916_0002 | 0950-1207 | On a method of estimating distances at sea in fog or thick weather. | 170 | 175 | 1,916 | 92 | Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character | J. Joly, Sc. D., F. R. S. | article | 6.0.4 | http://dx.doi.org/10.1098/rspa.1916.0002 | en | rspa | 1,910 | 1,900 | 1,900 | 4 | 113 | 2,687 | http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1916_0002 | 10.1098/rspa.1916.0002 | null | null | null | Fluid Dynamics | 25.309405 | Biography | 19.014895 | Fluid Dynamics | [
34.5562858581543,
-5.134700775146484
] | 170 Prof. J. Joly .
On a Method of Estimating proof of fertility of ideas , of organising powers , and of resource and initiative .
Research could be so thoroughly well organised that Suitable workers would be jointly engaged with those problems for the speedy elucidation of which there is the greatest need , and the results of their investigations would be at the disposal of all British manufacturers .
It rests with us to keep these ideas before the mind of the public , now that at last it is ripe to consider them .
" Be wise to-day ; it is madness to defer .
" And now I must pass on to my latest task\#151 ; perhaps the most fateful of all the tasks I have ever undertaken .
I bid a sincere regretful farewell to my official colleagues of the Royal Society , whose unfailing and courteous help in my discharge of the duties of the presidential office I gratefully acknowledge .
I deeply appreciate the honour conferred on me during the last two years , and if I may utilise " an intelligent appreciation of events before they occur " I heartily congratulate the Society on its election of my successor .
We all know , and the world knows , the lofty place held by Sir Joseph J. Thomson in the august realms of science\#151 ; and we all must feel that our Society could not have selected a more suitable and distinguished President .
On a Method of Estimating Distances at Sea in Fog or Thich Weather .
By J. Joly , Sc. D. , F.R.S. ( Received October 20 , 1915 .
) The problem of estimating distances at sea in fog or thick weather is obviously one of much importance to navigation .
Notwithstanding the more perfect means of communication between ship and shore , or between ship and ship , which recent scientific advances have secured , and which are at the command of the more important ships and lighthouse stations at the present time , I can find no reference to the fact that these improved means of communication suffice to solve the problem referred to under a great variety of circumstances .
In the present paper I shall confine myself to the determination of distance between ship and shore .
In a subsequent paper I hope^to discuss the application of the methods involved to finding the distance between ship and ship , and thereby lessening risk of collision .
The method I have to propose is based generally on the differing velocities Distances at Sea in Fog or Thick Weather .
171 of signals in different media : ( 1 ) luminous or " wireless " signals ( electromagnetic disturbances ) may be regarded as instantaneously propagated over the distances concerned ; ( 2 ) submarine sounds\#151 ; bell-strokes under water\#151 ; travel in the water at the rate of about 1400 metres , or 4700 feet .per second ; ( 3 ) aerial sounds move at the rate of about 330 metres , or 1100 feet per second .
Explosive signals travel somewhat faster in water and air .
Now , if simultaneously emitted signals are sent out in two differing media , the gain of the faster upon the slower travelling disturbance will be proportional to the distance travelled .
Hence a ship picking up such simultaneously emitted signals can at once estimate her distance from the signal station from which they originated .
For instance , if a submarine bell be struck simultaneously with another bell which is above the surface of the sea , the relative displacement in time of the two signals will have amounted to 4'3 seconds at a distance of 1 nautical- mile .
At 5 miles it will be 21*5 seconds .
The navigator , listening to the submarine sounds in the telephone , and provided with a seconds watch , easily estimates the interval separating these from the aerial sounds to i second .
But this time lag corresponds to a distance of about 700 feet , or 117 fathoms .
Closer readings of time are possible with many sound signals .
Hence it is evident that the method proposed will give results enabling distances to be measured with an accuracy more than adequate to the objects in view .
A simplification in the nature of the observations required on board the ship , which possesses many advantages , may be secured by regulation of the signals .
Thus we may arrange for the submarine signals to be sent out at intervals , which are definitely timed .
There might be one bell-stroke every 2 seconds ( as sometimes adopted at present ) , or even one bell-stroke per second .
These signals are sent out in groups .
There might be 30 successive strokes , followed by an interval of silence of half a minute .
Simultaneously with the first stroke of each group the air signal is made .
This convention is known to the mariner , and , when the first stroke of each group of bell-strokes is heard on the ship , he has only to count up the strokes till he hears the sound signal transmitted through the air in order to determine his distance from the signal station .
Thus , if the bell-strokes are timed one per second , the air signal reaches a ship 1 mile away a very little after the fifth stroke of the bell .
If the bell-strokes are timed every 2 seconds , the air signal coincides nearly with the third stroke of the bell , coming about ^ second later .
On this system the use of time-measurers on board ship is not required .
The signals themselves tell the mariner his Prof. J. Joly .
On a Method of Estimating distance from the shore .
The degree of accuracy secured is ample for the safety of his ship .
It will be evident that the grouping of the submarine signals on the lines suggested above may be distinctive for the station , and in thick weather may render its identification certain .
Wireless telegraphy is so generally at the disposal of ships at the present day that signals transmitted by its aid might well be used to supplement the submarine and air signals .
There would be , then , signals simultaneously sent out in the three media .
The special value of this would be that , in the event of particular atmospheric conditions interfering with the propagation of sound in the air , the approaching vessel can always judge her distance by the lag of the submarine signal on the setherial .
The sensitiveness here is about 1*2 seconds to the nautical mile .
A knowledge of her distance from the signal station of less than % mile would be in most cases easily obtained .
Again , in this case , vessels which had no auditory apparatus for submarine signals might determine distance by wireless and by air sounds .
This combination secures the maximum sensitiveness , i.e. about 5*5 seconds to the nautical mile .
A ship at 5 miles from the signal station receives the aerial sound 27*5 seconds after the wireless signal .
Where wireless was already installed at the signal station , the increased cost of sending out periodic signals with it would be insignificant contrasted with the advantages gained .
It is , of course , open to choice whether the wireless signal should go out with every sound signal or only coincide with it periodically .
If the mariner can infer the direction in which he receives the sounds , whether in air or in water , and if he determines his distance from the signal station , he , of course , is able to define his position completely .
Even if he cannot infer the direction from which the sounds reach him , but if he can lay down his own course upon the chart , his position is determined as one of two possible points by his distance from the signal station .
If the sounds from two coastal signal stations are audible to him his position is defined even if he is , to start with , ignorant of his course upon the chart .
Eor in the two distances he possesses the radii of two circles which are centred at the signal stations .
Their intersection on the chart gives him his position .
Finally there is the possible case ( especially if submarine signals are not available ) of his knowing neither the direction of the sounds nor his line of advance on the chart and hearing one signal station only .
In this case his position is still determinable on the result of successive estimates of distance and^t knowledge of his own compass course .
Thus in fig. 1 the ship which is at the position 0 , and which is heading N.N.E. , hears the signals from the coast and determines her distance as d0 i Distances at Sea in Foy or Thick Weather .
from the signal station .
Setting out on paper the course direction N.N.E. and taking any point on this line as the position O , the mariner strikes a circle to the radius d0 .
In five minutes , say , he picks up another signal and obtains the distance dx .
He knows the new position of his ship , for he can estimate his own speed .
This gives him the point marked 1 .
From this point a circle is struck to the radius dx .
This circle intersects the first circle on two points , P and S. These , in general , lie the one to port the other to starboard .
If dx is greater than d0 the two points lie aft ; the ship^is going away from the station .
If dx is less than d0 the conditions are reversed and she is nearing the station .
The mariner knows that the signal station lies on one or other of the points P and S. He may decide between them by altering ' his course towards one of the points till he picks up a third signal .
He is now at 2 and obtains the distance d2.The circle to radius d2 decides the question .
In general the position is determined according as is greater or : less than dx .
Having got the bearing of the signal station and its distance , i his own position is fully known .
There are two special cases when he can determine the bearing of the station without altering his course ; when his fehip is heading directly towards or away from the station .
For in these cases the increase or diminution of the distance as given by any two signals will conform to the ship 's run in the interval .
VOL. xcn.\#151 ; a. 174 Prof. J. Joly .
On a Method of Estimating We have assumed above that the timing of the signals is not effected closer than to \ second .
As already stated this corresponds to an accuracy of 700 feet in the determination of distance .
For all practical purposes this would suffice and , indeed , might be said to be needlessly precise .
It is , however , worth pointing out that , even by unpractised observers , closer results would probably be obtained .
For the error in effecting the readings is always of the same sign .
What error there is must arise from operating the stop-watch after the exact moment of passage of the sound wave .
Here the personal equation of the observer and any mechanical lag in the instrument are responsible for the delay .
But both observations\#151 ; that of starting and of stopping the seconds hand of the watch\#151 ; are affected in the same manner by this source of error .
It is the difference between the two readings we take for our calculation .
The error , therefore , tends to be reduced or actually eliminated .
In the case of practised observers it would probably be very nearly eliminated .
In high winds an error arises from the convection of the sound disturbance with the medium .
This is not , under any ordinary conditions , important .
It can in any case be allowed for .
A wind blowing at the velocity of 40 knots , or say 60 feet per second , introduces an error which may be positive or negative in sign and may attain to about 5 per cent. This would be , in most cases , negligible .
The variation of the velocity of sound with the temperature of the air is also capable of correction , but is so small as scarcely to call for consideration .
Between 0 ' C. and 15 ' 0 .
the velocity has been found to vary from about 330 metres per second to 340 metres per second .
If neglected this introduces an error of but 3 per cent. The velocity of sound in air or in water is greater than normal if the sound is explosive in origin .
The special rates for explosions in air and in sea water have been recorded and if desired may , of course , be used .
For accurate timing of sound signals the nature of the sound must be abrupt , either upon starting or stopping , or of brief duration .
Ordinary gunfire signals are readable to a fraction of a second even at a distance of five or six miles .
The effect of distance is to blur the definition , but it is to be remembered that at considerable distances this matters little .
One second error in our readings introduces an error of one quarter mile .
In five miles this would , obviously , matter little .
If the methods herein advocated were brought into use , a very little training introduced into the courses for Master 's and Mate 's certificates would render all the operations required easy and certain .
The amount of skill required is of the smallest .
Tables reducing time-intervals to distance , for ordinary and for explosive sounds in water and air , with simple statement of corrections , Distances at Sea in Fog or Thick Weather .
and even time-measurers reading directly to distances , might be used to further simplify what is already a simple operation .
It is surely needless to labour the question of the importance of this addition to the usefulness of lighthouse stations round our coasts .
The nature of the alterations required at any station or lightship will , of course , depend upon the existing equipment .
The electrically operated submarine bell and any explosive air signal operable by electric firing\#151 ; for instance the acetylene gun\#151 ; are especially adapted to the emission of synchronised signals .
Signals electrically operated may be rendered periodic by a simple clockwork mechanism to distribute and regulate the contacts .
Wireless signals naturally fall into the same category .
In other cases mechanical or pneumatic connection could generally be introduced without serious outlay .
The nature of the problem is , of course , determined by the particular nature of the machines , which have to be regulated to unison , and is not a general one .
But all outlay of money and labour must be considered in relation to the advantages gained .
Navigation in fog and thick weather would gain both in speed and safety if the mariner , as his ship advances , knows his distance from the coast .
This is more especially the case where important landfalls are made , but it applies with almost equal force to every important harbour and every dangerous coastal feature of our shores .
|
rspa_1916_0003 | 0950-1207 | On a method of avoiding collision at sea. | 176 | 183 | 1,916 | 92 | Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character | J. Joly, Sc. D., F. R. S. | article | 6.0.4 | http://dx.doi.org/10.1098/rspa.1916.0003 | en | rspa | 1,910 | 1,900 | 1,900 | 4 | 123 | 3,252 | http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1916_0003 | 10.1098/rspa.1916.0003 | null | null | null | Fluid Dynamics | 29.410053 | Measurement | 24.003435 | Fluid Dynamics | [
34.3353271484375,
-6.255556583404541
] | 176 On a Method of Avoiding Collision at Sea .
By J. Joly , Sc. D. , F.R.S. ( Received October 22 , 1915 .
) I have in the foregoing paper already described a method of finding distances at sea in fog or thick weather .
It is desirable to briefly recapitulate here the principle involved .
Signals travelling at differing rates are simultaneously sent out from the lighthouse or signal station .
Thus there might be a submarine sound along with an aerial ; or , again , a wireless signal along with an aerial sound ; or , finally , the combination might be the sound in water and the wireless signal .
Such simultaneously emitted signals become relatively displaced as they are propagated outwards .
After travelling a distance of one nautical mile a sound in air will lag behind a sound in water by a time interval amounting to about 4*3 seconds .
And an aerial sound will lag behind a wireless or a luminous signal as much as 5*5 seconds in the mile .
Hence as the lag continues to increase at these rates per mile , the observation of the interval separating the reception of the signals on the ship will enable the navigator to determine his distance from the signal station .
It is obvious that similar methods will enable the mariner to tell the distance of another vessel .
An error so great as one half second corresponds with an error of only 90 fathoms in the case of the most sensitive combination\#151 ; that is wireless signal and aerial sound .
The application of this method to the end of avoiding collision at sea involves the means of emitting crisp , and sufficiently loud , sounds in air , which can be timed to coincide in moment of emission with wireless signals , or , in certain cases , with luminous signals .
Long-distance wireless signals are not required .
A more perfect installation would include the power of emitting and receiving submarine signals .
There can be no serious difficulties in the way of imparting to the signals the quality of simultaneity .
Where electric control can be used directly or indirectly the problem involves little more than the provision of suitable clockwork for regulating contacts .
Again the degree of skill or intelligence called for in timing the receipt of the signals is not so great as to limit the use of the method to the more highly educated seaman .
A very little practice , which can be obtained at any time , will give all the requisite skill in using the stop-watch .
With ordinary care to read the successive signals in the same manner , the error in estimating the interval between them will probably On a Method of Avoiding Collision at Sea .
be small .
This I have already discussed in my former paper .
There are , I believe , neither mechanical nor personal difficulties in the way of good determinations of distance between ship and ship .
Nor would the necessary additions to the Board of Trade Rules be considerable , as will presently appear .
The means by which the determination of distance may serve to reduce or eliminate the risk of collision I shall now explain .
I am fully alive to the fact that to expect of the mariner the solution of complex analytical or geometrical problems , under the conditions of anxiety obtaining on a vessel being navigated in thick fog , would be futile .
The following solution of the problem of foretelling whether or no there is risk of collision with another vessel , and if there is such risk indicating the precise time at which the danger is imminent , even under circumstances when the direction of sound in the air cannot be inferred , is so simple that I would hope it may be of use .
The diagrammatic nature and repetitional character of the steps required protect it from risk of oversight or mistake .
When two ships provided with the means of determining distance , as described above , become aware of one another 's presence in fog\#151 ; either by the reception of periodically sent out wireless signals or by the usual regulation sound signals\#151 ; the following procedure would be adopted .
* Each ship sends out : ( 1 ) a code signal by wireless giving her course ; ( 2 ) a signal giving her speed ; ( 3 ) the wireless signal always emitted simultaneously with the aerial sound signal .
* These three signals are made in close succession .
They are repeated at intervals : ( 1 ) and ( 2 ) perhaps every 10 or 15 minutes , or when course or speed are altered : ( 3 ) at intervals of , say , two minutes .
In this way each ship knows the course and speed of the other ship and on the result of two successive observations of distance the navigator is able to determine the rate of approach or recession of the other vessel .
These data are dealt with at the moment by a simple geometrical construction now to be described .
The decision as to whether there will be collision or not turns upon the fact that if the rate of mutual approach of the ships is the maximum for the given conditions of course and speed there will be collision .
If they are approaching one another at a rate less than the maximum rate there will not be collision .
The truth of this statement is evident when it is considered that the point of collision ( if there is one ) is a common point on the line of advance of both vessels : and the speed of each ship is being directed to bring her straight to that point .
Hence their mutual distance must be diminishing at the maximum rate for the assigned courses and speeds at every instant .
If the 178 Prof. J. Joly .
ships are not directed towards a common point a certain component of their velocity is always acting to separate them , or , in other words to lessen their rate of approach .
Considered when the ships are approaching end on ( suppose one is going north and the other is going south ) the statement is obviously true ; for only when they are advancing in the same line is the rate of approach a maximum , and then only can they collide .
Similarly it is obvious for one ship overtaking another on a common course .
The general statement perhaps needs more consideration .
It will presently be more fully set forth .
In fig. 1 let one ship be going north .
This ship we will call A. Her speed is such that she occupies at successive intervals of two minutes the positions N 0 , 1 , 2 , 3 , etc. These are , therefore , her positions when receiving the successive signals from another ship we will call B. When A*is at the point O she receives the first signal from B , to the effect that B is holding , say , a south-east course at a speed of n knots per hour .
The distance signal shows that B is at a distance of d0 knots .
On a Method of Avoiding Collision at Sea .
179 The navigator on A strikes a circle with the point 0 as centre and with the radius do taken to the same scale as he used in setting out the points 1 , 2 , 3 , etc. As no reliance is supposed to be placed on the fancied direction of sounds from B , nothing more is known on A beyond the fact that B is somewhere upon the circle having the radius d0 .
and marked d0 upon the diagram .
Laying off from the point 0 , a line bearing south-east , the navigating officer on A lays off from 0 along this line , and still to the common scale , a few points giving the displacement of B on her course every two minutes .
With these points successively as centres , he strikes the circles I , II , III , etc. , to the common radius d0 .
He knows that B will be transferred from one of these circles to the next in the course of successive intervals of two minutes .
This is true , no matter where she is placed on the first described circle .
He now awaits the second signal from B. giving her new distance .
The new distance is di knots .
If di is greater than d0 ) the vessel B is evidently receding from A , and must occupy some place on the south-east half of the circle I. To prove this it is only necessary to take the distance di in the compass and with the new position of A as centre , that is to say , point 1 on the course of A , to cut the circle I. The two points of intersection will lie on the south-east half of circle I. One or other of these points of intersection must be the position of B. Hence , when di is found to be greater than d0 , the observations need not be carried further .
If di is less than d0 , B is approaching A. In this case a circle struck with di as radius ( always to the common scale ) , and the new position of A as centre ( i.e. point 1 ) , in general intersects circle I in two points , These points are in the north-west half of circle I , and in one or other of them B must be located at the instant .
For these points are the only points common to circle d0 and circle I , and we know she is on both circles . .
The arc dh in place of intersecting circle I , might touch it only , i.e. be tangent to it .
In this case w'e get but one point on circle I. This unique point is the position of the ship B. If the arc di intersects circle I there is no risk of collision .
If it touches it only there will be collision .
In stating the result in this definite manner , we assume quite accurate conditions and measurements .
Some error there must be , however , and , from the practical point of view , it is only correct to affirm that , if the circle to the radius di clearly cuts the circle I at two points so that the result is beyond the limits of error , there is no risk of collision , while , if it touches it , or within the limits of error might touch it , there is risk of collision .
Prof. J. Joly .
In the case where there is intersection , and a line bearing south-east is drawn through each point of intersection , the ship B is advancing along one or other of these lines , marked X and Y on the diagram ( fig. 1 ) .
The mariner cannot distinguish which of these lines she is on , either from this or from succeeding observations .
He can only do so by altering his course and testing the results as to distance .
But this is of no importance .
In general , if he knows he is clear of the other ship , it is all he cares about .
Considering the result that there are two possible lines of advance for B when di gives us two points on circle I , we recognise that there cannot be two lines of advance leading B into collision with A , that is to say , leading to one particular point on the line of advance of A. For the two lines holding the same course are parallel , and hence cannot meet at a point .
This is proof of the theorem that if the arc struck from 1 to to the radius dx meets circle I on two points there cannot be collision .
While it is true that if collision is not going to occur , there are two possible lines of advance for B , it is also true that if collision is going to occur there is but one line upon which B can be advancing .
This unique line of advance is determined when the arc d\ is tangent to circle I ( fig. 2 ) .
For we have only now to draw a line bearing south-east ( the given course of B ) through the point of contact of arc and circle .
Where this line cuts the successive circles II , III , etc. , the ship B will find herself in the succeeding intervals of three minutes .
If we follow the advance of B upon the diagram in this way , and compare the successive positions of ship A , we will find that both vessels meet at a common point of advance .
In order to fix with more precision the position of this line of collision , join the points 1 and 1 ' , and produce to intersect circle I. This gives the point of tangency when the arc d\ touches the circle .
It is well to check the position of the collision line by also joining 2 and 2 ' , and 3 and 3 ' , and intersecting the circles II and III with the lines so found .
Before proceeding further we may revert to our original statement that the line of collision may be defined as that of the maximum rate of approximation of A and B. Our construction is based upon that fact .
For when d\ gives a tangent arc it is evidently the least distance which conforms to the condition that the second position of B is on circle I. Hence the value of d\ is the least possible , and it follows that the rate of approach of B to A has been the greatest consistent with the conditions of course and speed .
Similarly we see that if d\ intersects circle 1 a greater value of di than the minimum is involved and* therefore the rate of approach of B to A is not the greatest ; that is , it is not so great as when there is a line leading to collision .
Having ascertained that there is risk of collision with B , the navigator can , On a Method of A voiding Collision at Sea .
181 if circumstances permit , continue to observe the approach of B upon the diagram and thus confirm the first inference .
If the successive arcs d2 , d2 , continue to indicate risk of collision , according to the rules of the road the vessel B keeps out of the way of A. On the question of the usefulness of this method we have two considerations before us : the reliability and definiteness of its indications and the degree of facility with which it can be put in execution .
N Begarding the first point , the method proposed claims to tell the mariner ( 1 ) whether there is risk of collision or not , and ( 2 ) the probable moment of danger if collision is threatened .
These claims are undoubtedly justified , although certainty in the prediction of collision is unattainable , for the simple reason that perfectly accurate estimates of speeds , courses and distances are unattainable .
But risk of collision is foretold .
In fig* .
3 possible effects of error are shown .
We here assume that large errors of Prof. J. Joly .
distance , of the same sign , have affected the observations throughout .
Tangent arcs have become intersecting arcs .
The distinction between this and the case of fig. 1 is obvious .
For error of observation is not cumulative .
Each determination of distance is an independent observation .
Hence the successive arcs , d\ , d2 , etc. , are separated by similar radial elevations above the arcs they intersect .
Such a feature at once warns the mariner that the intersection is not real .
Under conditions of safety each observation shows an increasing departure from the conditions of danger , the separation of the arcs getting more and more pronounced .
The diagram , in fact , faithfully interprets the external facts , for , of course , lag in the approach of the ships behind that of maximum rate of approach constantly adds up , the evidence for safety becoming more apparent in successive observations .
Hence the method tells the mariner whether there is risk of collision or not .
On a Method of Avoiding Collision at Sea .
183 It also tells him the moment of danger .
This is obvious .
For the given courses and speeds the point of collision is fixed .
Of course , currents and tidal drift might affect the ships differently .
Or , again , speeds or courses might vary .
It can only be answered that some latitude must be allowed for these things .
It may be noted that error introduced into position of the circles I , II , III , etc. , due to these causes may be checked at intervals , if time permits , by treating any of the distance determinations as originating a succession of circles of position .
If the ship B was a long way off when the first signal was received precision would be gained by this procedure .
It is , , of course , quite simple .
We start a n6w diagram , say , with dh and with the nearest coinciding statement of B as to her course and speed .
The construction already described is then repeated .
On the second point , the facility with which the observations are carried out , it must be remembered that all the arithmetical work of determining the distances to be scaled off on the diagram can be eliminated by the use of tables .
Quite brief tables would suffice .
If B signals that her speed is 12 knots the navigator on A reads at once from his tables what this amounts to in three minutes , or whatever other interval exists between the signals .
His scale is , say , 1 knot to the inch .
The tabulated number is taken up off a scale of inches divided to tenths .
In laying off bearings time is saved by using paper divided to compass points around a central point .
He lays the course of his own ship through this point .
The bearing of the other ship being given , he at once plots it .
The rest consists in describing a few circles and joining a few points .
The practical seaman must judge for himself how far this procedure is repaid by the security gained .
|
rspa_1916_0004 | 0950-1207 | On the theory of the capillary tube. | 184 | 195 | 1,916 | 92 | Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character | Lord Rayleigh, O. M., F. R. S. | article | 6.0.4 | http://dx.doi.org/10.1098/rspa.1916.0004 | en | rspa | 1,910 | 1,900 | 1,900 | 13 | 169 | 3,240 | http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1916_0004 | 10.1098/rspa.1916.0004 | null | null | null | Tables | 42.427751 | Fluid Dynamics | 29.169362 | Tables | [
38.15889358520508,
-27.794225692749023
] | ]\gt ; On the Theory of the Tube .
By , O.M. , F.B.S. Received October 26 , 1915 ) .
A recent paper by Richards and Coombs*discusses in some detail the determination of surface tension by the rise of the liquid in capillary tubes , and reflects mildly upon the inadequate assistance afforded by mathematics .
It is true that no complete analytical solution of the problem can be obtained , even when the tube is accurately cylindrical .
We may have recourse to graphical constructions , or to numerical calculations by the method of who took an example from this very problem .
But for experimental purposes all that is really needed is a sufficiently approximate treatment of the two extreme cases of a narrow and of a wide tube .
The former question was successfully attacked by Poissorl , whose final formula [ ( 18 ) below ] would meet all ordinary requirements .
Unfortunately doubts have been thrown upon the correctness of Poisson 's results , especially by Mathieu , who rejects them ether in the only case of much importance , i.e. when the liquid wets the walls of the tube\mdash ; a matter which will be further considered later on .
Mathieualso reproaches Poissou 's investigation as implying two different values of , of which the second is really only an improvement upon the first , from a further approximation .
It must ) admitted , however , that the problem is a delicate one , and that Poisson 's explanation at a -ical point leaves to be desired .
In the inyestigation which follows I hope to have succeeded iu the approximation a stage beyond that reached by Poisson .
In the theory of narrow tubes the lower level from which the of the meniscus is reckoned is the free plane level .
In experiment , the lower level is usually that of the liquid in a wide tube connected below with the narrow one , and the question arises how wide this tube needs to be in order that the inner part of the iscus may be nearly enough plane .
Careful experiments by Richards and Coombs led to the conclusion that in the case of water the diameter of the wide tube should exceed : mm. , and that probably 38 mm. suffices .
Such smaller diameters as are often employed 20 mm. ) very appreciable error .
Here , again , we should naturally look to mathematics to supply the desired information .
The case of a straight 'Journ .
Amer .
Chem. Soc No. 7 , July , 1915 .
' Math. Ann vol. 46 , p. 175 ( 1895 ) .
'Theorie de la Capillarite , ' Paris , 1883 , pp. 46-49 .
On Theory of the wall , making the problem two-dimensional , is easy , that of the circular wall is much more complicated .
Some drawings ( from theory ) given by Kelvin , indicate clearly that diameters of 1.8 cm .
and cm .
are quite inadequate .
I have attempted below an analytical solution , based upon the assumption that the necessaly diameter is large , as it will be , if the prescribed error at the axis is small enough .
Although this assumption is scarcely justified in practice , the calculation indicates that a diameter of cm .
may not be too As Richards and Coombs remark , the observed curvature of the lower of the meniscus may be used as a test .
Theory shows that there should be no sensible departure from htness over a of about 1 The For the surface of liquid standing in a vertical tube of circular section , we have , ( 1 ) in which is the vertical co-ordinate measured ) from the free plane level , is the horizontal co-ordinate measured from the axis , is the the at any point makes with the horizontal , and where is the surface-tension , the acceleration of gravity , and the density of the fluid .
The equation expresses the equilibrium of the cylinder of liquid of radius .
At the wall , where assunles a given value , and ( 1 ) becomes .
( 2 ) If the radius ( r ) of the tube is small the total curvature is nearly constant , that is , the surface is nearly spherical .
We take , ( 3 ) where is the of the centre and the radins of the sphere , while represents the correction required for a closer approximation .
If we omit ?
/ altogether , ( 2 ) gives .
( 4 ) * Compare 'Phil .
Mag vol. 34 , p. 309 , Appendix , 1892 ; ScieDtific Papers , ' vol. 4 , p. 13 .
The reference is given below .
It may be remarked that is sometimes taken to denote the double of the above quantity .
Lord Rayleigh .
Also , if be the height at the lowest point of the meniscus , the quantity directly measured in experiment , .
( 5 ) In this approximation , and thus in terms of .
( 6 ) When the ] of contact ( i ) is zero , , and , ( 7 ) the well known formula .
When we include , it becomes a question whether we should retain the value of , i.e. , sppropriate when the surface is supposed to be exactly spherical .
It appears , however , to be desirable , if not necessary , to leave the precise value of open .
the value of from ( 3 ) in ( 1 ) , we get , with neglect of .
( 8 ) For the purposes of the next approxinlation we may omit and the integra ] , which is to be divided by .
Thus , ( 9 ) and on integration .
( 10 ) We suppose with Poisson and Mathieu that so that , ( 12 ) corresponding to ( 13 ) To determine we have the boundary condition , ( 14 ) which gives in ternls of and .
Explicitly .
( 15 ) These latter equations are given by Mathieu .
On the Theory of the Tube .
We have now to find the value of to the corresponding approximation .
the observed of the meniscus ; ( 16 ) In the important case where , the liquid wetting the walls of the simply , and .
( 18 ) This is the formula given long since by Poisson , only difference being that his is the double of the quantity here so denoted .
It is remarkable that Mathieu rejects the above equations as applicable to the case , on the ground ) then in ( 13 ) becomes infinite when .
But , with which comes into comparison , is infinite at the same time ; and , in fact , both and in equation ( 8 ) when .
It is this circumstance which really determines the choice of in ( 11 ) .
We may now proceed to a yet closer oximation , introducing approximate values of the terms previously olected aether .
From ( 13 ) and from ( 12 ) ' Nouvelle Theory de l'Action Capillaire , ' 1831 , p. 112 .
Lord Rayleigh .
Thus constant .
We have now to choose , or rather , and it may appear at first sighb as though we might take it almost at pleasure .
But this is not the case , at any if we wish our results to be applicable when .
For this purpose it is necessary that be a small quantit ) , and only a articular choice of will make it so .
For when terms vanishing when We must therefore take lltaking .
( 21 ) It should be noticed bhat so determined does not become infinite when and : For we have Also with the general value of ( 22 ) As before On the Theory of the Capillary Tube .
and .
( 23 ) The integral in ( 23 ) can be expressed .
We find .
( 24 ) The expression for in terms of is complicated , and so is the relation between and demanded by the boundary condition ( 25 ) But in the particular case of greatest interest much simplification ensues .
It follows easily from ( 25 ) that When we introduce this condition into ( 24 ) , we get , ( 26 ) and accordingly .
( 27 ) Hence by successive approximations .
( 28 ) If the ratio of to is at all such as should be employed in experiment , this formula will yield , viz. , , with abundant accuracy .
Our equations give for the whole height of the meniscus in the case .
( 29 ) Another method of calculating the correction for a small tube , originating apparently with Hagen and Desains , is to assume an elliptical form of surface in place of the circular , the minor axis of the ellipse being vertical .
In any VOL. XCII.\mdash ; A. Lord Rayleigh .
case this should allow of a closer approximation , and drawings made for by Prof. Perry suggest that the representation is really a good one .
If the semi-axis minor of the ellipse be , the curvature at the end of this axis is , and in our previous notation .
Also , being equal to and .
This yields a quadratic in ; hence approximately .
It will be seen that this differs but little numerically from ( 28 ) , which , however , professes to be the accurate result so far as the termin inclusive .
The Wide Tube .
The equation of the second order for the surface of the liquid , assumed to be of revolution about the axis of , is well known and may be derived from ( 1 ) by differentiation .
It is ( 32 ) If be small , ( 32 ) becomes approximately In the interior part of the surface under consideration may be neglected , and the approximate solution is .
, denoting , as usual , the Bessel 's , or rather Fourier 's , function of zero order , and being the elevation at the axis above the free absolutely plane level .
For the present purpose is to be so small as to be igible in experiment , and the question is how large must be .
When is small enough , may be large while still remains small .
Eventually increases so that the formula fails .
But when is large enough this occurs , we may if necessary carry on with the twodimensional solution properly adjusted to as will be further explained 'Proc .
Roy .
Inst 1886 ; 'Popular Lectures and Addresses , ' I , p. On the Theory of the Capillary Tube .
IQ the meantime it will be convenient to give some numerical examples in .
In the usual notation the values of , up to , are tabulatsd .
* In the case of water cm .
If we take , and have , so that is still fairly small .
Here for water cm .
and cm .
A diameter of cm .
is thus quite unless an error exceeding cm .
be admissible .
suppose , and take .
Then , again small .
For water cm .
, and cm .
This last value of is about given by Richards and Coombs as the maximum admissible of reading , and we may conclude that a diameter of cm .
is quite to take advantage of this degree of refinement .
We may go further in this example without too great a loss of accuracy .
Retaining , let us make .
I find , about , that the extreme value of is , still moderately small .
Here cm .
, which is thus shown to be inadequate in the case of water .
But apart from the question of the necessary diameter of tube , information for experimental purposes can be derived in another manner .
The value of ( on the axis ) is ; and when ) .
when .
For the best work should be on the limit of what can be and then and could just be distinguished .
The observer may be satisfied if no difference of level can be seen over the range in the case of water this range is cm .
, or say 1 cm .
It has already been remarked that when is small enough may become great within the limits of application of ( 35 ) .
To shorten our expressions we will take temporarily as the unit of length .
Then when is very great , Thus if be the angle thoe tangent to the curve makes with the horizontal , ; ( 37 ) equation which may be employed when is so small that a large is nsistent with a small In order to follow the curve further , up to , we may employ two-dimensional solution , the assumption being that the region of Bril .
Assoc. Rep. for 1889 ' ; or Gray and Mathews ' ' Bessel 's Functions , ' Table VL Lord Rayleigh .
moderate occupies a range of small in comparison with its actual value , i.e. a value not much less than , the radius of the tube .
On accoUnt of the magnitude of we have only the one curvature to deal with .
For this curvature so that since when is exceedingly small .
Accordingly .
( 39 ) Also ) , and .
( 40 ) The constant is determined by the consideration that at the wall thus , ( 41 ) since is small .
The value of is supposed to be the same here as in ( 37 ) , so that , ( 42 ) whence on elimination of and restoration of .
( 43 ) With sufficient approximation , when is small enough , we may here substitute for , and thus .
( 44 ) This formula should give the relation between and when is small enough , but it is onJy roughly applicable to the case of greatest interest , where , corresponding to the accuracy of reading found by Richards and Coombs .
In this case For this value of we should have .
It is true that according to ( 44 ) will be somewhat greater , but on the other hand the proper value of ( replaced by r ) is less than .
We may fairly take making cm .
cm .
This calculation indicates that a diameter greater even than those conOn the Theory of the Tube .
templated by Richards and Coombs may be necessary to reduce to negligibility , but it must be admitted that it is too rough to pire great oonfidence in the close accuracy of the final number .
Probably it would be feasible to continue the approximation , employing an approximate value for the second curvature in place of neglecting it altogether .
But although the integration can be effected , the work is rather long .
[ Added November 17.\mdash ; Since this paper was communicated , I have been surprised to find that the problem of the last paragraphs was treated long ago by Laplace in the 'Mecanique a similar method , and with a result equivalent to that ( 44 ) arrived at above for the relation between the radius of a wide tube and the small elevation at the axis .
Laplace uses the definite integral expression for , and obtains the approximate form appropriate to large arguments .
In view of Laplace 's result , I have been tempted to carry the approximation further , as gested already .
In the previous notation , the differential equation of the surface may be written In the first approximation , where the second curvature on the left is omitted , we get being the elevation at the axis , where .
For the present purpose is to be regarded as exceedingly small , so that we may take at this stage , as in ( 39 ) , S .
( 46 ) We now introduce an approximate value for the second curvature in ( 45 ) , writing , where is the radius of the tube , and making , according .
( 47 ) On integration C-cos , ( 48 ) on substitution in the small term of the approximate value of .
When is very small , so that , and , ( 49 ) is the second approximation to * Supplement au Livre , pp. 60-64 , 1805 .
Lord Rayleigh .
From We are now in a position to find by the relation the constant of integration being determined by the correspondence of .
Thus , ( 52 ) giving when is small , ( 53 ) where .
( 55 ) The other equation , derived from the flat part of the surface , is in which is regarded as large ; or .
( 57 ) In equations and are to be identified .
On elimination of , ( 58 ) in which we may put , ( 59 ) in which , since is nearly equal to may usually be neglected .
Also , in view of the smallness of and , it is scarcely necessary to retain the denominator , so that we may write .
( 60 ) On the Theory of the Tube .
The effect of the second approximation is the introduction of the second term on the right of ( 60 ) .
To take an example , let us suppose as before that , so that .
By successive approximation we find from ( 60 ) , ( 61 ) so that if cm .
( as for water ) , cm .
( 62 ) The correction to Laplace 's formula is here unimportant .
The above is the diameter of tube required to render ible according to the standard adopted .
It may sometimes be convenient to invert the calculation , and deduce the value of from the diameter of the tube ( not much less than 4 cm .
) and an approximate value of .
For this purpose we may use ( 60 ) , or preferably ( 69 ) , taking for instance .
The calculated value of would then be used as a correction .
The accompanying small Table may be useful for this purpose .
We have supposed throughout that the liquid surface is symmetrical about the axis , as happens when the section of the containing tube is circular .
It may be worth remarking that without any restriction to symmetry the differential equation of the nearly flat parts of a large surface may be taken to be , ( 63 ) so that may be expressed by the series ( 64 ) denoting the usual polar co-ordinates in the horizontal plane .
]
|
rspa_1916_0005 | 0950-1207 | Skin friction of the wind on the Earth's surface. | 196 | 199 | 1,916 | 92 | Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character | G. I. Taylor, M. A.|Sir Napier Shaw, F. R. S. | article | 6.0.4 | http://dx.doi.org/10.1098/rspa.1916.0005 | en | rspa | 1,910 | 1,900 | 1,900 | 1 | 16 | 515 | http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1916_0005 | 10.1098/rspa.1916.0005 | null | null | null | Tables | 38.452659 | Fluid Dynamics | 35.693349 | Tables | [
41.475154876708984,
-30.69936752319336
] | ]\gt ; small surface when subjected to the action of the very high wind which correspond with the same value of In reducing the tract of land to a similar small flat plate , the trees and houses would be reduced to a mere roughness on the plate .
It is to expected therefore that , if the skin friction on unit area of the surface be expressed in the form , ( 1 ) being the wind velocity near the surface and the ensity of air , the constant be the same as the constant which would be found in the laboratory by experimenting with a small , slightly roughened plate , if a sufficiently high value of could be obtained .
It should be noticed , however , that the velocity which should be compared with Q. is the velocity close to the solid surface and not the general velocity of the air in the case of a flat plate , or the mean velocity over a cross section in the case of flow in a pipe .
In the case of a fluid flowing through a pipe , it has been shown by that for high values of the velocity , V , of the fluid near the wall is about of the velocity in the middle , and that the mean velocity , , is about of the velocity in the middle , so that .
It was found that the skin friction for the highest values of fv which Stanton able to obtain could be expressed by the formula , which equivalent to .
The constant of equation ( 1 ) must therefore be compared with The object of this paper is to show that it is possible to use observations Auid , linear dimension of the system , V the velocity of tho esearches of the National Physical Labor$tory , ' vol. 9 The value of wi be calculated for each of groups separately .
( a ) Winds .
Substituting these values equation ( 2 ) , it will be found that JfoderoXe Winds .
, Q. Henoe Strong Winds .
: Hence Condusions .
( 1 ) The coefficient does not appear to increase or decrease with wind velocity , a three-fold increase in velocity corresponding increase in skin friction .
It appears therefore that the skin friction on the earth 's surface is proportional to the square of the wind velocity .
2 ) The actual values of the skin friction coefficient are of the o1der of magnitude , but probably somewhat smaller than thom found in the laboratory , being to as against the found for friction in a pipe .
It appears therefore that approximately the skin friction applies to small flat plates and pipes and to the friction of tin atmosphere on the ground .
The ratio of the values of for the two is of the order .
It certainly seems therefore that the " " scale effed ' skin friction over this immense range of values of is not large .
|
rspa_1916_0006 | 0950-1207 | Memorandum on the Kew heliograph. | 199 | 203 | 1,916 | 92 | Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character | Dr. C. Chree, F. R. S. | article | 6.0.4 | http://dx.doi.org/10.1098/rspa.1916.0006 | en | rspa | 1,910 | 1,900 | 1,900 | 5 | 89 | 2,582 | http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1916_0006 | 10.1098/rspa.1916.0006 | null | null | null | Biography | 43.280475 | Astronomy | 26.427392 | Biography | [
36.08606719970703,
4.4897942543029785
] | 199 Memorandum on the Kew Heliograph .
( 3 ) It is evident that if we had assumed originally that the skin friction of the air blowing over the earth 's surface obeys the same law that it does in the case of the small scale models which are tested in the laboratory , the analysis given above might be used , in conjunction with the results given in the author 's previous paper , to furnish an explanation of why it is that the wind near the ground is , on the average , about 0*7 of the gradient wind in the case of light winds , or about 0*6 of the gradient wind for strong winds .
Memorandum on the Kew Heliograph .
By Dr. C. Chree , F.R.S. , Superintendent of the Kew Observatory .
( Presented to the Gassiot Committee , May 26 , 1915 .
) The Report of the Kew Committee , presented to the Council of the British Association June 27 , 1855 , describes the construction of the apparatus as follows:\#151 ; " The apparatus suggested by Sir John Herschel for photographing the spots on the sun 's disc is progressing under the superintendence of Mr. Warren De la Rue .
The Solar Photographic Telescope is promised by the maker complete in three months . . . .
The diameter of the object glass is 3*4 inches , and its focal length 50 inches ; the image of the sun will be 0*465 inch , but the proposed eyepiece will , with a magnifying power of 25*8 . . .
, increase the image to 12 inches . . . .
The object glass is undercorrected in such a manner as to produce the best practical coincidence of the chemical and visual foci .
... It was originally intended to place the telescope in an observatory 12 feet in diameter , provided with a revolving roof .
... It has , however , been found possible to somewhat alter the construction of the tube , so as to reduce its length sufficiently to allow of the telescope being placed under the dome of the Kew Observatory/ which is only 10 feet in diameter .
" The Report of the Kew Committee for 1856-57 contains the following statement:\#151 ; " On May 20 , 1854 , Benj .
Oliveira , Esq. , F.R.S. , placed the sum of \#163 ; 50 at the disposal of the Council of the Royal Society , to be appropriated during that year in any manner the Council might consider most in harmony with the interests of science .
Mr. Oliveira further stated that he might probably in future years offer a similar sum if the mode of its disposal appeared to Dr. C. Chree .
him eligible , and an application having at the same time been made by the Kew Committee for the sum of \#163 ; 150 , in order to erect a photographic apparatus for registering the position of the spots in the sun 's disc , as suggested by Sir John Herschel , the Council of the Royal Society devoted to this purpose the donation of Mr. Oliveira , and proposes , should it be continued , to apply it for the next two years in replacement of the sum of \#163 ; 100 , which the Council in the meantime advanced from the donation fund of the Royal Society , in order that the undertaking might not be delayed .
This arrangement was approved by Mr. Oliveira , and the apparatus has , under the direction of Warren De la Rue , Esq. , F.R.S. , been completed by Mr. Ross at the cost of about \#163 ; 180 .
" The Report finishes with a description of the telescope and clock .
The Kew Committee Report for the year 1858-59 also refers to the photoheliograph .
It says : " . . .
Since the last meeting of the Association , the unfortunate death of Mr. Welsh has retarded the experiments with the photoheliograph , but from time to time they have been gone on with , at first by Mr. Chambers . . .
and latterly by Mr. Beckley . . .
, and , in order that they might be prosecuted more continuously , the Committee have fitted up a photographic room in close contiguity to the instrument .
" This refers presumably to the wooden structure on the roof , which continued to be known as the " Sun Room " until its demolition in 1913 .
The Report goes on to state that the best photographic definition was obtained when the sensitised plate was from 1/ 10 to 1/ 8 inch beyond the visual focus in the case of a 4-inch picture , and that in this position beautiful pictures of the sun 4 inches in diameter were obtained , which bore magnifying with a low-power lens .
In this way considerable detail was shown on the sun 's surface , while the spots were well defined .
The Report proceeds : " Mr. De la Rue , by combining two pictures obtained by the photoheliograph at an interval of three days , has produced a stereoscopic image of our luminary , which presents to the mind the idea of sphericity .
Under Mr. De la Rue 's direction , Mr. Beckley is making special experiments , having for their object the determination of the kind of sensitive surface best suited for obtaining perfect pictures . . . .
Now that the photographic apparatus has been brought to a workable state , Mr. De la Rue and Mr. Carrington , joint Secretaries of the Astronomical Society , propose to devote their attention to the best means of registering and reducing the results obtained by the instrument , provided the funds which may be necessary are placed at their disposal .
" The Kew Committee Report for 1859-60 says :\#151 ; " The photoheliograph has been an occasional source of occupation to the Mechanical Assistant ; but Memorandum on the Kew Heliograph .
before daily records of the sun 's disc can be obtained , it is absolutely requisite that an assistant should be appointed to aid Mr. Beckley . . . .
Unfortunately , the funds at the disposal of the committee are quite inadequate for this purpose ; and unless a special grant be obtained , the photoheliograph will remain very little used .
At present Mr. Beckley is preparing the instrument , under Mr. De la Rue 's direction , for its intended trip to Spain , for the purpose of photographing the eclipse which takes place on J uly 18 .
The expenses of these preparations , and of the assistants who will accompany Mr. de la Rue , will be defrayed out of the grant of the Royal Society for that object .
" The expedition proved a very successful one .
The results obtained were discussed by Mr. De la Rue in the Bakerian Lecture for 1862 " On the Total Solar Eclipse of July 18,1860 , observed at Rivabellosa , near Miranda de Ebro , in Spain."* The Kew Committee Report for 1861-2 mentions that amongst the exhibits sent from the observatory to the great exhibition in 1861 were some sun pictures taken by the photoheliograph .
A medal was awarded for these to Mr. Beckley .
The same report says the photoheliograph was intended to be used for observing a transit of Mercury and a partial eclipse of the sun , but on both occasions the weather was bad .
It refers to good sun pictures obtained at Kew by Mr. Beckley in November and December .
It adds " The photoheliograph was sent from Kew at the beginning of January to Mr. De la Rue 's observatory , and Mr. Beckley attended at Cranford to assist in erecting and adjusting it to focus . . . .
Altogether up to the September 12 , . . .
177 photographs have been taken on 124 days . . . .
During the month of August , Dr. Sabler , Director of the observatory of Wilna in Russia , resided at Cranford , and received instruction in astronomical photography .
A photoheliograph is being constructed for him under Mr. De la Rue 's superintendence by Mr. Dallmeyer , and a micrometer by the Messrs. Simms .
This heliograph will embody all the . . .
improvements suggested by the experiments with the Kew instrument . . . .
The experience obtained during the past year has been such as to lead Mr. De la Rue to recommend that photographic records should be continued for a series of years at some public observatory .
The Committee . . .
have come to the conclusion that the heliograph might be worked at an annual expense of \#163 ; 200 . . . .
" The Kew Committee Report for 1862\#151 ; 63 mentions that the photoheliograph was brought back from Cranford to Kew in February , 1863 , and again erected in the dome , and that since May 1 it had been continuously worked by a * ' Phil. Trans. , ' vol. 152 , pp. 333-416 .
Dr. C. Chree .
qualified assistant under Mr. Beckley 's supervision .
Apparently a grant of \#163 ; 150 had been made by the British Association in 1861 for sun pictures , and an earlier grant of \#163 ; 90 had come from the same source for a photographic assistant .
Early in 1863 a grant had also been obtained from the Royal Society .
The report for 1863-64 mentions the employment of Mr. Loewy , " formerly assistant in the Flagstaff Observatory , Melbourne , " in reducing the negatives obtained with the photoheliograph .
Use was made of a micrometer designed by Mr. De la Rue , and that gentleman , it is mentioned , was " having an arrangement made , by means of which the proportion of the sun 's disc obscured by spots may be conveniently measured .
" The Report for 1864-65 mentions the acquisition of valuable material intended for comparison with the records from the photoheliograph .
This consisted of Mr. Carrington 's original drawings , " in which the size and appearance of the spots are delineated with great fidelity , " and also the long series of original drawings made by Hofrath Sehwabe .
The ultimate destination of the latter was apparently the Royal Astronomical Society .
" In order to realise this generous bequest of Hofrath Schwabe , Mr. Loewy . . .
went to Dessau , taking with him a selection of duplicate negatives and prints of the sun , which he presented , in the name of the ( British ) Association , to that gentleman .
" The Report for 1865-66 contains the copy of a letter from Mr. De la Rue referring to enquiries made by Father Secchi about the Solar work at Kew : " The pictures taken by means of the Kew heliograph are all measured by means of my micrometer ; the positions of the spots are then reduced to distances in terms ( fractional parts ) of the sun 's radius , and the angles of position corrected for any error in the position of the wires .
Pictures of the Pagoda* are taken from time to time , and the measurements of the various galleries of the Pagoda serve to determine the optical distortion of the sun 's image , and the corrections to be applied to the sun pictures .
The heliocentric latitudes and longitudes of the spots are then calculated .
The areas of the spots and the penumbra are also measured , and the areas corrected for perspective are tabulated in terms ( fractional parts ) of the area of the sun 's disc .
The areas of the spots , etc. , on all of Carrington 's original pictures have recently been measured .
" The same Report mentions the publication , at the expense of Mr. De la Rue , of a memoir , " Researches on Solar Physics by Warren de la Rue , B. Stewart , and B. Loewy .
First Series : On the Nature of Sunspots , " dealing with the earlier results obtained with the photoheliograph .
Abstracts of this and of * In the Royal Gardens .
Memorandum on the Kew Heliograph .
a " second series " appear in the Royal Society 's ' Proceedings , ' vol. 14 , 1865 .
Subsequently two long papers* by the same three authors contained full particulars of the positions and areas of the sunspots observed with the photoheliograph from 1862 to 1866 .
A list including the above and several other papers relating to the Kew photoheliograph , written by Mr. De la Rue , either alone or in conjunction with Messrs. Stewart and Loewy , will be found in the " History of the Kew Observatory , " by Dr. R. H. S'cott.f The photoheliograph seems to have continued in regular use until March , 1872 , completing 10 full years of observation .
The Report of the Kew Committee for the year ending October 31 , 1873 , mentions that the photoheliograph had been lent to the Astronomer Royal for taking sun pictures at Greenwich .
The instrument seems to have remained at Greenwich until January 5 , 1876 , when it was returned to Kew .
Subsequent to this date the instrument seems only to have been used for visual observations .
The work of measuring sun pictures went on at Kew Observatory for many years , Mr. De la Rue making an annual grant of \#163 ; 100 a year for the purpose from 1874 to 1880 .
According to Dr. R. H. Scott 's " History " Mr. De la Rue 's total disbursements in connection with the photoheliograph exceeded \#163 ; 2000 .
In the Kew Report for 1882 we read : " The measurements and reductions of sunspot positions as determined by means of the Kew pliotoheliograph , from 1864 to 1872 , having been completed for Mr. De la Rue , he has deposited the manuscript with the Council of the Royal Society .
" The instrument was used for many years for the purpose of taking drawings of sunspots after the manner of Schwabe .
Eventually the question of the utility of the results so obtained was raised by the Superintendent in 1897 .
The Kew Committee applied for advice on the subject to several eminent astronomers , but the opinions expressed were somewhat diverse .
A request was then addressed for a formal opinion to the Solar Physics , Committee , and in accordance with the reply received the use of the photoheliograph ceased at the end of 1897 .
Not much had been done for many years previously to keep the instrument , in repair , and except for an occasional cleaning of external parts nothing has been done since .
* ' Phil. Trans. , ' vol. 159 , pp. 1-110 ( 1869 ) , and vol. 160 , pp. 389-496 ( 1870 ) .
+ ' Roy .
Soc. Proe .
, ' vol. 39 , pp. 37-86 .
VOL. XCII.\#151 ; A. K
|
rspa_1916_0007 | 0950-1207 | An application of the theory of probabilities to the study of a priori pathometry.\#x2014;Part I. | 204 | 230 | 1,916 | 92 | Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character | Lieut.-Colonel Sir Ronald Ross, K. C. B., F. R. S., R. A. M. C. T. F. | article | 6.0.4 | http://dx.doi.org/10.1098/rspa.1916.0007 | en | rspa | 1,910 | 1,900 | 1,900 | 1 | 10 | 325 | http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1916_0007 | 10.1098/rspa.1916.0007 | null | null | null | Biology 1 | 49.446463 | Formulae | 18.24768 | Biology | [
-26.283859252929688,
3.219900369644165
] | ]\gt ; II .
The problem before us is as follows .
Suppose that we have a populatiol of living things numbering individuals , of whom a number are affect : by something ( such as a disease ) , and the remainder A are not so affect suppose that a proportion of the non-affected become affected in element of time , and that , conversely , a proportion of the affeotSd become unaffected , that is , revert in every element of time to the non-affected group ; and , lastly , suppose that both the groups , the affected and the non- affected , are subject also to possibly different birth-rates , death-rates , and immigration and emigration rates in an element of time ; then what will b6 the number of affected individuals , of new cases , and of the total ) living at any time ?
For the solution of this and the subsidiary problems I have ventured to suggest the name " " Theory of Happenings It covers many cases which occur not only in pathometry but in the analysis of questions oonuected with statistics , demography , public health , the theory of evolution , and even commerce , politics , and statesmanship .
The name ( pathos , happening ) was previously suggested by myself in antithesis nosos , a disease ) for the quantitative study of parasitic in ffl individual .
III .
( i ) Let , rndt , denote respectively the nativjty , mortality , gration , and emigration rates of the non-affected part of the population in the .
element of time ; and Ndt , , Idt , denote the similar rates the affected part .
Then , as argued in my previous writings and as will easily seen , the problem before us may be put in the form of the followirS .
} : : system of differential equations:\mdash ;
|
rspa_1916_0009 | 0950-1207 | The consumption of carbon in the electric arc. No. III.\#x2014;The anode loss. | 247 | 252 | 1,916 | 92 | Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character | W. G. Duffield, D. Sc.|Mary D. Waller, B. Sc.|Sir E. Rutherford, F. R. S. | article | 6.0.4 | http://dx.doi.org/10.1098/rspa.1916.0009 | en | rspa | 1,910 | 1,900 | 1,900 | 11 | 95 | 2,742 | http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1916_0009 | 10.1098/rspa.1916.0009 | null | null | null | Electricity | 33.663351 | Biochemistry | 20.310509 | Electricity | [
-19.354795455932617,
-59.9873046875
] | 247 The Consumption of Carbon the Electric Arc. containing small amounts of free fatty acid , is much smaller than that of the undecomposed soap .
( 3 ) The " surface activity " of free alkali in a soap solution is less than that of the same concentration of alkali in water .
( 4 ) The addition of alkali to a soap solution increases the " surface activity " of the soap .
( 5 ) This effect is much too large to be explained by the suppression of hydrolysis .
( 6 ) It is suggested that the effect is partly due to an increase in the colloidal nature of the " semi-colloidal " soap solution* The Consumption of Carbon in the Electric Arc. No. III.\#151 ; The Anode Loss .
By W. G. Duffield , D.Sc .
, and Mary D. Waller , B.Sc. ( Communicated by Sir E. Rutherford , F.R.S. Received November 8 , 1915 .
) 1 .
In a previous communication to the Royal Societyf experiments conducted in the Physical Laboratory of University College , Reading , have been described , from which it appears that the rate of consumption of carbon from the cathode of a very short arc is such that the departure of one atom is accompanied by the transference between the poles of four electronic charges .
The loss of weight of the anode is larger than this , on account of subsidiary combustion or evaporation occasioned by the high temperature of the crater .
An experiment has been described in the paper referred to which demonstrates the supreme importance of a hot cathode ; the arc could be maintained with a hot cathode alone , but not with a hot anode alone .
It was suspected in consequence of this that the anode consumption of carbon was unimportant , and the experiment was repeated in the following manner for the purpose of testing this .
* It may be pointed out that many of the facts relating to the effect of electrolytes on the adsorption of dyestuffs may be explained by the effects produced on the colloidal state of the dye , and on the potential difference between the fibre and the solution .
See Harrison , " The Electrical Theory of Dyeing , " 'Journal of the Society of Dyers and Colourists , ' December , 1911 .
t Duffield , ' Roy Soc. Proc. , ' p. 122 , supra .
Prof. W. G. Duffield and Miss M. D. Waller .
2 .
The carbon anode , 20 cm .
long and 1*8 cm .
diameter , was mounted in a lathe so that it could be rotated about its axis , the bed of the lathe being earthed .
The cathode carbon , 1 cm .
diameter , was fixed at the same level in the saddle of the lathe , and could be moved along the lathe bed parallel to the anode , and also perpendicular to it for the purpose of adjusting the arc-length .
This carbon was insulated from the lathe and connected through suitable resistances , ammeter , and voltmeter to the negative terminal of the 200-volt mains , the positive terminal of which was earthed .
When an arc was started between the curved surface of the anode and the pointed end of the cathode the anode could be rotated at a high speed and the cathode moved rapidly backwards and forwards without extinguishing the arc , whereas when the polarity was reversed it at once blew out .
This provided a means for obtaining an arc in which the anode remained comparatively cool because the crater did not have time to develop .
The carbons were removable PLAN ELEVATION ^ ^ .
Carbon - ve ( ) C % w - \gt ; x r Chuck of Lathe and were weighed before and after each experiment , during which the current and arc-length were maintained as constant as possible .
For observing the latter a lens was placed above the anode , and it projected an image of the arc upon a horizontal card supported higher up .
As the carbon was not quite cylindrical there was a variation in the arc-length during the rotation , apart from the irregular lengthening due to the air currents produced by the rotation .
The carbons employed were solid and were not specially purified , because purification had not been found appreciably to affect the results in the previous experiments .
They were , however , soaked in acid for some days , and washed with distilled water to free them from impurities .
The chief difficulty lay in the fact that moisture was driven from the carbons during the running of the arc , and on cooling moisture was absorbed from the Atmosphere , causing the carbons to increase in weight with time\#151 ; about 17 mgrm .
in 13 hours for the heavy anode ; the cathode gain was not The Consumption of Carbon in the Electric Arc. 249 appreciable .
This is chiefly a mechanical effect due to the deposit of water in the interstices of the carbon from the moist air of the laboratory .
To obviate the difficulty of weighing , the carbon anode was always put into a brass cylinder immediately after each experiment , weighed in it and only removed when everything else was ready for the next experiment .
The weighings were made not less than 25 minutes after the conclusion of the experiment , when the carbon was quite cold .
3 .
Table I gives the loss of weight occasioned by running arcs of different current strength for the times stated in the fourth column .
The consumption of carbon per coulomb appears in columns 7 and 8 , followed by columns representing the corresponding losses when the carbons were fixed ( loc. cit. ) .
The discrepancy in the cathode readings in the two cases , which is only marked in the 6-ampere arc , is chiefly due to the indeterminate arc-length in the present experiments , and to the arc being horizontal instead of vertical .
The important thing to notice is that , whereas the anode loss is the greater in the fixed carbon arc , it is the less in the arc with rotating anode , also that in the most reliable experiments the ratios of anode loss with fixed poles to the anode loss with rotating anode are 17*6 to 0*25 , 13*5 to 0*13 , 12*8 to 0*33 , and 10*8 to 0*36 respectively .
The lowest value for the loss from either pole in a normal arc occurred at the cathode when the arcs were indefinitely small , when 3T x 10"5 grm. were consumed for the passage of each coulomb of electricity ( this is the value of the electrochemical equivalent of carbon if the element is quadrivalent ) .
The above experiments demonstrate that the loss from the rotating anode is very much less even than this , and it is significant that , with increasing mastery of the technique of the experiment on the part of the observer ( Miss Waller ) , the loss becomes smaller , the concluding observations involving total losses from the anode of only 3 , 2 , 8 , and 13 mgrm .
respectively .
It would no doubt be possible to arrange that the heating of the anode should be still further reduced , but no good purpose would be served by achieving this ; from the trend of the results the conclusion is irresistible that the anode loss of carbon is unimportant in the mechanism of the *arc , and that the main function of the anode is to receive the carriers of the current produced by the essential process occurring at the surface of the cathode .
The usual rate of rotation of the anode was about 750 per minute ; at this speed there is a considerable wind , which disturbs the arc and makes it longer than the shortest distance between the carbons .
As the flame of the arc is sensible to this current of air , it is obvious that , in the space between the poles , some , at least , of the carriers are of atomic dimensions , though it Prof. W. G. Duffield and Miss M. D. Waller .
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f The Consumption of Carbon the Electric Arc. 251 is not established in what proportion they are produced by ionisation or by direct ejection from the cathode .
As the arc-length decreases there is a smaller deflection with rotation , and , using extremely small arcs , the deflection is scarcely appreciable , probably because the bulk of the current is then carried by electrons moving with high velocities .
In the normal type of arc the formation of the crater is accidental , and is not vital to the are , though it is its most prominent and obvious feature .
Two factors are responsible for the formation of the crater upon the anode , and not upon the cathode .
One is the fact that electronic emission must occur at the anode as well as at the cathode once it is hot , and , as this constitutes a current against the main current in the arc-gap , an excess of ions in the opposite direction is required ; these fall on to the pole and heat it .
The other consideration is that negative electrons fall in great quantities upon the anode , but never upon the cathode , which consequently can only be bombarded by ions of atomic dimensions .
Since electrons probably suffer less reduction in velocity in passing through the vapours of the arc than the gaseous atoms , their impacts occur with accelerated , and not with constant , velocity , and the heat developed is correspondingly greater .
4 .
In the following Table II the differences in potential between the poles are compared for arcs with rotating and fixed anodes .
The former are the smaller , in spite of the fact that the effective arc-length with rotating anodes is probably even longer than is stated , for reasons already given ; this should involve an increased , and not a diminished , potential difference .
Table II .
Current .
Potential difference .
Fixed poles .
Rotating anode .
amperes .
Arc-length , 0 *5 mm. Arc-length , 0 *75 mm. 4 43 35 6 40 33 8 40 32 -5 Arc-length , 2 *0 mm. Arc-length , 2 2 mm. 8 48 40 This is accounted for by the reduction of electronic emission from the anode , which is comparatively cool when rotating .
In the normal arc this emission is equivalent , as Pollock has suggested from Duddell 's experiments , to a back E.M.F. When the anode is cool it is not necessary to supply a VOL. xcn.\#151 ; a. u Prof. J. Joly .
forward E.M.F. to overcome it .
The reduction in the electronic emission involves the potential difference between the poles in another way , because it diminishes the ionisation , and therefore increases the resistance of the vapour of the arc .
For this reason the back E.M.F. at the anode is not quite the same as the difference between columns 2 and 3 , namely , 7*5 volts .
A Collision Predictor .
By J. Joly , Sc. D. , F.R.S. ( Received November 22 , 1915 .
) In a recent paper in these Proceedings* I described a method by means of which the mariner is enabled to foretell risk of collision at sea , assuming that he knows the course and speed of each of the vessels concerned and that he is at intervals able to ascertain the distance separating them .
For an account of the principles involved I must refer to my former paper .
A simple geometrical construction enabling them to be applied is therein given .
This construction informs the navigator whether there is risk of collision or not , and also enables him to ascertain the instant at which the danger is greatest .
However simple in character , it is probable that , to the average seaman , the operations involved in a geometrical construction would appear less practical than a mechanical or instrumental mode of interpreting the observations .
It will be an additional attraction to an instrumental method if time be saved by its use .
For the time available for the solution of the problem involved may be short .
This might well be the case if the earlier signals for any reason escaped notice .
Accordingly I have endeavoured to reduce the work of interpreting the observations to the simplest form .
Of various types of apparatus for the interpretation of the geometrical principles involved , that which I now describe is , I believe , the easiest both to work and to construct .
The instrument consists ( see fig. 1 ) of the half disc , d , which is graduated to compass divisions ( and to degrees if desired ) ; the points being named both for easterly and westerly bearings .
Rotating stiffly around the centre of the circle , on a joint which admits of being clamped , two graduated limbs , a and 6 , are fixed .
These limbs are mutually inclinable on a friction joint similar to that used on an ordinary folding rule .
The limb b carries a sliding piece , * P. 176 , supra .
|
rspa_1916_0010 | 0950-1207 | A collision predictor. | 252 | 260 | 1,916 | 92 | Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character | J. Joly, Sc. D., F. R. S. | article | 6.0.4 | http://dx.doi.org/10.1098/rspa.1916.0010 | en | rspa | 1,910 | 1,900 | 1,900 | 8 | 152 | 3,704 | http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1916_0010 | 10.1098/rspa.1916.0010 | null | null | null | Measurement | 45.494703 | Fluid Dynamics | 14.773233 | Measurement | [
33.93037033081055,
-6.613061904907227
] | 252 Prof. J. Joly .
forward E.M.F. to overcome it .
The reduction in the electronic emission involves the potential difference between the poles in another way , because it diminishes the ionisation , and therefore increases the resistance of the vapour of the arc .
For this reason the back E.M.F. at the anode is not quite the same as the difference between columns 2 and 3 , namely , 7*5 volts .
A Collision Predictor .
By J. Joly , Sc. D. , F.R.S. ( Received November 22 , 1915 .
) In a recent paper in these Proceedings* I described a method by means of which the mariner is enabled to foretell risk of collision at sea , assuming that he knows the course and speed of each of the vessels concerned and that he is at intervals able to ascertain the distance separating them .
For an account of the principles involved I must refer to my former paper .
A simple geometrical construction enabling them to be applied is therein given .
This construction informs the navigator whether there is risk of collision or not , and also enables him to ascertain the instant at which the danger is greatest .
However simple in character , it is probable that , to the average seaman , the operations involved in a geometrical construction would appear less practical than a mechanical or instrumental mode of interpreting the observations .
It will be an additional attraction to an instrumental method if time be saved by its use .
For the time available for the solution of the problem involved may be short .
This might well be the case if the earlier signals for any reason escaped notice .
Accordingly I have endeavoured to reduce the work of interpreting the observations to the simplest form .
Of various types of apparatus for the interpretation of the geometrical principles involved , that which I now describe is , I believe , the easiest both to work and to construct .
The instrument consists ( see fig. 1 ) of the half disc , d , which is graduated to compass divisions ( and to degrees if desired ) ; the points being named both for easterly and westerly bearings .
Rotating stiffly around the centre of the circle , on a joint which admits of being clamped , two graduated limbs , a and 6 , are fixed .
These limbs are mutually inclinable on a friction joint similar to that used on an ordinary folding rule .
The limb b carries a sliding piece , * P. 176 , supra .
A Collision Predictor .
e , which supports the arm c.This arm rotates round a centre located upon that edge of b which passes through the centre of rotation of 'and It is Fig. 1 .
also on one edge of the sliding piece .
It can be securely clamped in any position .
All three bars are graduated to any convenient scale of subdivisions .
Millimetres would be suitable .
These are given to natural scale u 2 Prof. J. Joly .
in the figure , but it would , in general , be advisable to construct the instrument to larger dimensions than those shown .
* The Collision Predictor is used in the following manner .
When the first signals are received by a ship ( which we will call A ) from another ship ( which we will call B ) the navigator on A places the limbs a and b to the courses of the two vessels and clamps them in those positions : the limb b being set to the course of the vessel B and the limb a to the course of A. Thus , in the figure , B is holding a course N.E.fE .
and A is holding a course due south .
The navigator next slips the slider e along the limb b till it reads on the scale of \amp ; a number of millimetres representing the displacement of B in the interval between the signals .
We will assume that this interval is two minutes .
He also sets the arm c to read , on the limb a , a number of millimetres along the limb representing the displacement of his own ship A. during the same interval , and to the same scale .
This is most easily done by reading on the scales one scale division ( i.e. one millimetre ) per knot per hour .
Thus , if B is doing 11 knots the slider is advanced to 11 on the limb 6 , and if A is doing 16J knots the arm c is brought to intersect the limb a at 16 J scale divisions on a. Taking one millimetre to represent one knot this is the same as multiplying the distances done in two minutes by 30/ The distance separating the vessels as given by the first signal is now laid off\#151 ; still to the same scale\#151 ; along the arm c. Suppose it was 4 knots .
The navigator lets 120 ( = 4 x 30 ) upon c represent this distance .
A sliding marker on the arm c may be provided , if desired , to mark the number representing the first distance .
These operations are in preparation for the second signal .
When the second signal arrives , giving him the new value of the distance separating the vessels , the navigator considers how many divisions on c it represents according to the scale already chosen .
Thus if the new distance is 3-2 knots this corresponds to 96 ( = 3*2 x 30 ) divisions of the scale c. And now the first crucial reading is obtained .
For if the intercept on c by the limb a is 24 divisions ( or very nearly this ) collision is threatened .
If it is a different number there is no danger .
It will be noticed that 24 + 96 = 120 ; which is the reading on the scale c representing the original distance .
In order to confirm this observation the navigator now sets forward the slider e in readiness for a third signal .
He need not interfere with the arm c , for this moves along with e , keeping parallel to its first position .
It will , therefore , automatically take up the right position on a corresponding to the shift of *e .
In the figure I suppose the slider e brought into the position for * * In the figure double these readings are shown because the Collision Predictor is .supposed to be set for the third signal , as will presently appear .
A Collision Predictor .
the third signal .
It reads 22 , i.e. it has been advanced another 11 mm. The reading on a is also twice the first reading .
The navigator notices that this movement makes the intercept on the scale c closely 50 divisions .
Ifr then , the first reading is to be confirmed the ensuing distance signal will correspond to 70 divisions ( or nearly this ) on the scale ; for 70 + 50 = 120 , .
which is the reading for the original distance .
When it comes at the end of two minutes the distance is found to be 2*3 knots .
Now 2*3 x 30 = 69 .
Hence the first indication of threatened collision is confirmed .
This observation may be further confirmed by the fourth signal according as time permits .
The approach of the two vessels to one another may in this way be kept under observation .
But it is well , so soon as danger is certainly indicated , to ascertain the moment when the danger is greatest and collision may actually occur if precautions are not taken .
The moment of collision is ascertained as follows .
When the distance separating the ships is reduced to nothing is the moment of collision .
Now the distance is 0 when the intercept by a on the arm c is 120 divisions .
But at the rate of shifting the slider e , three more shifts will bring the division 120 ( on c ) a little past the edge of a. But three shifts represent six minutes since the receipt of the third signal , assuming two minutes as the interval between the signals .
Collision may thus be regarded as imminent at a time 5 J minutes from the receipt of the third signal .
It will be seen that the navigator has , here , ascertained the moment of threatened collision by moving the slider along the limb b till the division on c representing the original distance reaches the edge of a , and reckoning two minutes for every 11 divisions by which the slider is displaced on the limb b. It will be gathered from what has now been stated that the operations involved\#151 ; arithmetical and mechanical\#151 ; are of the simplest kind .
Under the circumstances which may often attend the use of the instrument , it is important that they should be of a character which are not likely to be confused , and which can be rapidly performed .
A very little practice will suffice to place the navigator in complete command of the operations involved .
These amount , essentially , to observing whether the distances determined by the successive signals are equal to the balance of the original distance left upon the scale of c after the intercept between the limbs a and b is deducted .
Between each signal the mariner has , therefore , only to shift forward the slider by the assigned amount\#151 ; conveniently , a number of millimetres equal to the knots per hour done by the ship B. He then reads the balance of distance left upon the scale of c , i.e. , between its point of contact with a and the scale number representing the original distance .
That is to say , he makes one shift of e and takes one reading on c. Prof. J. Joly .
He is then ready fori the next signal .
These operations are easily effected in less than half a minute of time .
He has ample time to consider his position , or , it may be , to attend to another vessel .
But for the latter contingency a duplicate Collision Predictor should be at hand .
The theory of this instrument is simple enough .
In fig. 2 , from the point 0 we lay off the course of B as a line OBi bearing N.E.fE .
and the course of the ship A as a line bearing due south .
With 0 as centre and the first Fig. 2 .
A Collision Predictor .
distance d0 as radius , the circle d0 is described .
If we assume A to be at 0 , B is situated somewhere upon this circle .
Keeping the radius d0 , we now go to the points 1 ' , 2 ' , 3 ' , etc. , which are spaced to represent the displacement of B on her course every two minutes ( or whatever other interval separates the signals ) , and describe the circles I , II , III , etc. We know that B , in succeeding intervals of two minutes , is transferred from one of these circles to the next .
Along the course of A from 0 , we lay off the points 1 , 2 , 3 , etc. , spaced to represent the displacement of A along her course every two minutes .
In these representations of distance we preserve the same scale throughout .
Now , when A has got to 1 , the second signal is received , giving the distance separating the ships as d\ .
If , therefore , we describe a circle about 1 with di as radius , we know that B at this instant is situated on this circle .
But she is also upon circle I struck from 1 ' .
We know , then , that she is located at either of the two points of intersection of the circles , but we cannot tell which .
Now , this is the case for safety from collision , as explained in my former paper ( loc. cit. ) .
But in the particular case when collision is threatened , the two circles touch at a point of tangency ( as in fig. 2 ) .
At this point B must be placed .
Similarly , if we repeat this construction , going to the point 2 with the distance d2 , we get a point of tangency on the circle II .
We may do this for each new position of A and B. The line joining these points of tangency must be the path of B approaching A. It necessarily keeps a N.E.fE .
course , and is therefore parallel with the line through 0 representing the course of B. We might , evidently , have found the line of advance of B from a single point of tangency by drawing through this point a line having the N.E.fE .
direction .
The tangent points are lettered ph p2 ) etc. , in the figure .
This construction , I may recall , is based upon the fact that if collision is to occur , the rate of approach of B to A must be the greatest possible for the courses and speeds of the two ships. .
The distances lph 2p2 ) etc. , are evidently the least distances connecting the points of position 1 , 2 , etc. , with the arcs of position I , II , etc. , and it follows the rate of approach of B to A is greatest along the line prpb .
Now , the tangency of two circular arcs involves the point of contact being upon the line connecting the centres of the circles .
Hence , when collision is threatened , the lines Ipi , 2p2 ) etc. , which are equal to d\ , d2 ) etc. , must be in direction with the lines l'l , 2'2 , etc. , and as the line pip5 is necessarily parallel with the line OB ' ( both being directed in the course of B ) , and the lines l'p\ } 2'p2 ) etc , are mutually parallel owing to the similarity of the Prof. J. Joly .
triangles l'Ol , 2'02 , etc. , the distances l'pi , 2'p2 , etc. , are equal to one another and to the original distance d0 .
From this simple geometry the use of the Collision Predictor is evidently justified .
For the distance of B from A at any instant , as read along the arm c , is , in fact , the distance marked d\ , d2 , etc. , in the figure , and the amount of the intercept of the limb a on the arm c is the length l'l , 2'2 , etc. The fact that when their summation equals the value of d$ collision is threatened amounts to the same statement as that there is tangency of the successive circles of position , and hence greatest rate of mutual approach of the vessels .
The confidence we place in the use of this instrument must depend on the sensitiveness with which it interprets the observations .
With sharply engraved divisions and suitable dimensions , the Collision Predictor will be found to read as closely as the errors incidental to the observations render desirable .
That is to say , in the case of a threatened collision , a small departure from the rate of maximum approach is unmistakably revealed .
Fig. 3 will serve to contrast the nature of the readings obtained in the case of threatened collision and of safety .
The vessels A and B are directed on the courses shown .
That is , B is heading N.W. and A is heading W.N.W.* B is going the faster , so that she is overtaking A. Now , for collision , we have the condition shown by the full-drawn arcs giving the tangent points p2 , etc. , of the unique line marked B , for the path of the ship B. Collision will occur when this line meets the line A. For conditions of safety the arcs with broken lines are drawn .
These give two possible paths for B , each marked ft. Now the arc d0 is , of course , common to both conditions .
But if it is to be safety the values of d\y d2 ) etc. will be greater than the corresponding values in the case of collision .
Thus di = 1^ , the radius of the first dotted arc , is greater than lp\ , the radius of the first tangent arc , by the bit pvrri .
Similarly 2p2 ( collision ) is exceeded by p2ir2i when there is safety .
And , again , 3p2 is exceeded by p2ir2 .
And these excesses are evidently sufficient to reveal the different conditions of safety and danger .
Thus the mariner obtains assurance of safety or intimation of danger at an early stage in his observations .
The limits of observational errors must always be borne in mind , but the errors will not accumulate .
They will involve a certain latitude in each determination of distance .
We may assume this latitude or uncertainty to be approximately known in amount .
But each observation is independent of * These bearings are set over eastward as they would lie upon the Collision Predictor .
A Collision Predictor . .
259 its predecessor as a determination of distance .
Hence when we see an increasing value for the excess pir in successive readings on the arm c , we are justified in concluding that the condition of maximum rate of approach is really departed from and there is no danger of collision .
In fig. 3 , jpiiri might pe__we may suppose\#151 ; an excess based on error .
But we see that p*ir2 is considerably greater than piirx .
The value p3tt3 is still greater and altogether beyond the limits of error in reading the distance from the signals .
W.NW Fig. 3 .
The Collision Predictor tells the navigator whether collision is threatened or not , and it also tells him when it is threatened .
It does not give him the two alternative paths of the other ship when she passes wide of his own vessel .
This , however , is information which the sailor does not , generally , require .
When A and B are holding the same or a directly opposite course , the Collision Predictor cannot be profitably applied .
But the question of collision or safety is in these cases , as before , solved by simple addition or subtraction of figures .
If the courses are opposite and if collision is threatened the Sir N. Lockyer and Mr. JEL E. Goodson .
vessels must be in line and the rate of approach the maximum .
Hence if A does m knots between the signals and B does n knots the rule holds that d^ = di+ { m + n ) =rf2 + 2(m-fn)3 etc. Again , if one vessel is overtaking the other , both being on the same course , the rate of approach is a maximum if collision is threatened and \lt ; 70 = d\+ ( tn\#151 ; n ) = d2 + 2(m \#151 ; n ) , etc. , when A is overtaking B. If this arithmetical relation is not found to hold for the successive determinations of distance , and if the amount of departure from equality increases with each observation , there is safety .
The vessels are not proceeding in the same line .
On the Oxy-hydrogen Flame Spectrum of Iron .
By Sir Norman Lockyer , K.C.B. , Hon. D.Sc .
, LL. D. , F.R.S. , and H. E. Goodson , A.RC .
Sc. ( Received December 6 , 1915 .
) A few lines in the visual region of the oxy-hydrogen flame spectrum of iron were recorded in 1887 by Sir Norman Lockyer.* * * S This list was supplemented in 1893f by a map showing all the then known flame lines of iron in the photographic region .
In the following year Hartley^ published his researches on " Elame Spectra at High Temperature , " including a list of lines in the spectrum obtained by heating compounds of iron in the oxy-hydrogen flame .
This list extends from \ 5927*7 to A 30211 .
Flame spectra of iron have been studied in great detail by de Watteville , working alone or in collaboration with Hemsalech .
In particular they have publishedS an extensive list of wave-lengths and intensities of lines observed in the oxy-hydrogen flame fed by a current of oxygen previously passed through a globe in which an electric spark was being maintained between iron poles .
It may also be mentioned that reproductions of photographs of the iron flame spectra have been published in the atlases of Hagenbach and Konen ( 1905 ) and Eder and Yalenta ( 1911 ) .
Some preliminary results obtained from a spectrum of iron burning in the * \#163 ; Eoy .
Soc. Proc. , ' vol. 43 , p. 120 ( 1887 ) . .
t ' Phil. Trans. , ' A , vol. 184 , pp. 675-726 , Plate 28 ( 1893 ) .
X ' Phil. Trans. , ' A , vol. 185 , pp. 199-202 ( 1894 ) .
S 6 Comptes Rendus , ' vol. 146 , p. 964 ( 1908 ) .
|
rspa_1916_0011 | 0950-1207 | On the oxy-hydrogen flame spectrum of iron. | 260 | 265 | 1,916 | 92 | Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character | Sir Norman Lockyer, K. C. B., Hon. D. Sc., LL. D., F. R. S.|H. E. Goodson, A. R. C. Sc. | article | 6.0.4 | http://dx.doi.org/10.1098/rspa.1916.0011 | en | rspa | 1,910 | 1,900 | 1,900 | 4 | 118 | 2,900 | http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1916_0011 | 10.1098/rspa.1916.0011 | null | null | null | Atomic Physics | 81.272215 | Fluid Dynamics | 7.918865 | Atomic Physics | [
15.150588035583496,
-43.3499755859375
] | 260 .
Sir N. Lockyer and Mr. JEL E. Goodson .
vessels must be in line and the rate of approach the maximum .
Hence if A does m knots between the signals and B does n knots the rule holds that d^ = di+ { m + n ) = rf2 + 2(m-fw ) , etc. Again , if one vessel is overtaking the other , both being on the same course , the rate of approach is a maximum if collision is threatened and \lt ; 70 = d\+ ( tn\#151 ; n ) = d2 + 2(m \#151 ; n ) , etc. , when A is overtaking B. If this arithmetical relation is not found to hold for the successive determinations of distance , and if the amount of departure from equality increases with each observation , there is safety .
The vessels are not proceeding in the same line .
On the Oxy-hydrogen Flame Spectrum of Iron .
By Sir Norman Lockyer , K.C.B. , Hon. D.Sc .
, LL. D. , F.R.S. , and H. E. Goodson , A.RC .
Sc. ( Received December 6 , 1915 .
) A few lines in the visual region of the oxy-hydrogen flame spectrum of iron were recorded in 1887 by Sir Norman Lockyer.* This list was supplemented in 1893f by a map showing all the then known flame lines of iron in the photographic region .
In the following year Hartley^ published his researches on " Elame Spectra at High Temperature , " including a list of lines in the spectrum obtained by heating compounds of iron in the oxy-hydrogen flame .
This list extends from \ 5927*7 to A 30211 .
Flame spectra of iron have been studied in great detail by de Watteville , working alone or in collaboration with Hemsalech .
In particular they have publishedS an extensive list of wave-lengths and intensities of lines observed in the oxy-hydrogen flame fed by a current of oxygen previously passed through a globe in which an electric spark was being maintained between iron poles .
It may also be mentioned that reproductions of photographs of the iron flame spectra have been published in the atlases of Hagenbach and Konen ( 1905 ) and Eder and Yalenta ( 1911 ) .
Some preliminary results obtained from a spectrum of iron burning in the * * * S * \#163 ; Eoy .
Soc. Proc. , ' vol. 43 , p. 120 ( 1887 ) . .
t ' Phil. Trans. , ' A , vol. 184 , pp. 675-726 , Plate 28 ( 1893 ) .
X ' Phil. Trans. , ' A , vol. 185 , pp. 199-202 ( 1894 ) .
S 6 Comptes Rendus , ' vol. 146 , p. 964 ( 1908 ) .
On the Oxy-hydrogen Flame Spectrum of Iron .
261 oxy-hydrogen flame were communicated to the Royal Society by Sir Norman Lockyer* in 1911 .
The present paper contains an account of further work on the same spectrum carried out on glass negatives taken from a copy , also on glass , of a spectrogram secured with the 3-inch Cooke prism spectrograph of the Solar Physics Observatory , then at South Kensington .
In this spectrum 64 lines of iron have been identified between W 3856*52 and 5615'88 ; 15 of these lines have not hitherto been recorded in the iron flame spectrum .
Identification of the lines was effected by measuring approximately portions of the spectrum in turn under the microscope of a star plate measuring machine .
The measures were reduced by the Cornu-Hartmann interpolation formula and the means compared with the list of arc lines of iron given in the first part of Eder and Yalenta'sf atlas and also with the lines in the list given by King4 Eder and Valenta 's wave-lengths have been adopted where corresponding lines appeared in their list .
In those cases where they give no line Rowland 's solar wave-lengths have been taken .
In a few cases it was impossible to discriminate between the components of pairs of lines in Eder and Yalenta 's list , and the measured wave-length was consequently retained .
The flame spectrum was next compared with similar copies of an iron arc spectrum .
Two well-marked groups of lines were at once distinguished , the one consisting of lines stronger , i.e. relatively more conspicuous , in the flame than in the arc , including a number of lines which did not appear to be represented in the arc spectrum employed , and the other containing lines weaker , i.e. relatively less conspicuous , in the flame than in the arc .
The remaining lines , nearly equal in both spectra , but which were all described as doubtfully weakened in the flame , formed an intermediate group .
All the lines have been placed in one or other of these categories , designated respectively:\#151 ; Group A. Lines stronger in flame than arc .
" B. " weaker " " " C. " nearly equal in both sources .
The results of this comparison are given in Table I , which follows .
A small number of lines in this list are recorded absent from the 'Comparison spectrum ( arc ) and a still smaller number\#151 ; two only\#151 ; do not appear in the list of lines given by Eder and Valenta for the arc spectrum of iron .
All , however , are recorded by KayserS among the arc lines of iron , * * * S * 'Roy .
Soc. Proc.,5 A , vol. 86 , pp. 78-80 ( 1911 ) .
t 'Atlas Typischer Spektren , ' Vienna , 1911 .
+ ' -Astrophys .
Journ.,5 vol. 37 , p. 252 et seq. ( 1913 ) .
S ' Handbuch der Spectroscopie,5 vol. 6 , p. 901 ( 1912 ) .
Sir N. Lockyer and Mr. H. E. Goodson .
Table I.\#151 ; Behaviour of Iron Lines in Flame and Arc. Flame lines of iron .
Hill Observatory .
Behaviour in flame spectrum compared with that in arc .
Group .
Flame lines of iron .
Hill Observatory .
Behaviour in flame spectrum compared with that in arc .
Group .
AA .
Int. AA .
Int. 3856 52 3-4 Much strengthened ... A 4325 -94 5-6 ?
Weakened C 3860 *05 4-5 )j \gt ; } ... A 4376 -10 4-5 Strengthened A 3865 *67 0-1 Much weakened .
... B 4383 -72 5-6 ?
Weakened c 3872 -70 0-1 B 4404 -93 2-3 Weakened B 3878 -17 0-1 Yery much weakened* B 4415-30 2 Much weakened B 3878 -72 4-5 Strengthened A 4427 -49 3-4 Much strengthened ... A 3886 *43 5-6 a A 4435 -321 0-1 No line in this position A 3887-19 0-1 W eakened B in S.K. arc 3895 -80 4 Strengthened A 4461 -84 2-3 Much strengthened ... A 3899 -85 5 A 4482 -39 1-2 Strengthened A 3903 -10 0-1 ) ) Much weakened B 4489 '93 0-1 Much strengthened ... A 3906 *62 2 Strengthened A 4957 -79 0-1 Yery much weakened B 3920 *40 4 } } A 4094 -32 0-1 Not visible in S.K. arc A 3923 *06 5 ) ) A 5012 -25 1 yy yy A 3928 -07 5 A 5041 -26 0-1 yy yy A 3930 -49 5 ) } A 5051 -83 0-1 yy yy A 3969 -41 1-2 Much weakened B 5110-57 2 A 4005 *42 1-2 B 5166 -45 1-2 Strengthened A 4045 -98 7 ?
Weakened C 5167 -68 0-1 Yery much weakened B 4063 -76 5-6 C 5169 -07 1-2 Strengthened A 4071 -90 4-5 Slightly weakened B 5171 -78 0-1 Not visible in S.K. arc A 4132 *25 1 Much weakened B 5204 -77 0-1 \gt ; \gt ; if A 4143 *8 2 Weakened B 5227 -2 1 ?
Weakened C 4202 -20 1-2 B 5269 -72 4-5 Strengthened A 4206 *862 0-1 Much strengthened ... A 5328 -24 3 ft A 4216 -33 2-3 Greatly strengthened ... A 5371 73 2 ft A 4250 -95 2 Weakened B 5397 -34 1-2 A 4260 -66 0-1 Very much weakened B 5405 -99 1-2 tt Slightly strengthened A 4271 *93 4-5 ?
W eakened C 5429 -91 1-2 Strengthened A 4291 *63 0-1 Doubtfully present in A 5434 -74 0-1 tf A S.K. arc .
5447 -13 1-2 A 4294 *29 0-1 Weakened B 5455 -83 1 A 4308 *09 5-6 ?
Weakened C 5615 -88 1 Yery much weakened B * In the arc X 3878 *17 is slightly stronger than A 3878 '72 , but in the flame X 3878 *72 is much the stronger , X 3878 *17 having very nearly vanished .
Thus this pair affords a very good example of intensity inversion .
and all appear also as solar lines in Howland 's preliminary Tables of solar wave-lengths .
A detailed comparison has been made with the results recently published by King* in an important memoir on the variation with temperature of the electric furnace spectrum of iron .
It has been found that the lines recorded in the flame include all the stronger lines observed by King in the low-temperature furnace .
All lines of iron of an intensity in that source superior Fo 6 ( maximum 25 ) have been recorded in the flame spectrum , and * ' Astrophys .
Journ. , ' vol. 37 , p. 239 ( 1913 ) .
On the Oxy-hydrogen Flame Spectrum of Iron .
263 whilst the great majority of the lines of less strength have not been included , yet a few weaker lines have been recorded as very faintly represented .
Twelve lines , including seven of King 's Class Ia and four of Class Ib , stronger in the low-temperature furnace than the above have not been recorded in the flame ; seven of these , however , fall between XK 4994 and 5507 , where the iron flame spectrum is much obscured by continuous spectrum and bands .
These differences indicate that the oxy-hydrogen flame spectrum of iron obtained by burning the metal represents a temperature level somewhat above the low-temperature furnace conditions employed by King .
The lines of Group A form part , with only one exception , of King 's Classes Ia and Ib\#151 ; the typical low-temperature classes .
The lines of Groups B and C , on the other hand , are principally included in King 's Class II , a few being placed in Classes III and IV .
The flame lines having the greatest strength are nearly all of King 's Class II , and have been placed in Group C. The lines of King 's Class Ia , seven of which are herein recorded in the flame , are all very weak arc lines , their arc intensities ranging from 2 to 4 ( maximum 60 , King ) .
They are all weak in the flame . .
The flame spectrum has also been compared with the list of solar iron lines and their behaviour in sunspot spectra given by Adams , * in his valuable paper on the core and flame spectra of the iron arc .
The lines herein described as Group A flame lines of iron , which appear in the list given by Adams , are nearly all about twice as strong in the flame of the electric arc as in its core , and none are less than one and a half times as strong .
Thus , of course , the lines of Group A are strengthened in sunspot spectra .
The lines of Groups B and C , on the other hand , are either unchanged or reduced in intensity .
The stellar behaviour of the flame lines has been investigated by comparison with the observations of Miss Mauryf on the intensities of the so-called " solar lines " in a number of typical stellar spectra .
Although it is recognised that the level of initial appearance in stellar spectra cannot be precisely stated , yet the occurrence of lines probably involving the iron flame lines of Group A seems limited by the Sirian stars , and they are quite definitely established at the level of Procyon .
Lines of Groups B and 0 , however , seem to range as high as / 3 Persei ( Alg .
) , and are well established in a Canis Majoris .
Homogeneous data are available for nine lines of Group A between * ' Astrophys .
Journ. , ' vol. 30 , p. 98 ( 1909 ) .
+ ' Harv .
Coll. Obs. Ann. , ' vol. 28 , Part I ( 1897 ) .
264 On the Oxy-hydrogen Flame Spectrum of Iron .
W 4206#9 and 44894 in regard to six stellar spectra representing five* successive levels of the Kensington classification and six groups in the classification of Miss Maury .
The behaviour shown by these nine lines is uniform .
Although only two of them have been recorded in the Sirian stage , all are possibly represented in a Canis Minoris ( Proc. ) and the succeeding lower stages , and in all cases except one where the quoted intensities refer to a pair of lines in a Canis Majoris which are separated at lower levels , an increase of intensity is shown in passing from the higher level to that of a Orionis .
In nearly every case the increase is uniformly progressive .
The stellar behaviour of the Group A lines referred to above is shown in the accompanying diagram ( fig. 1 ) .
The stellar intensities are represented proportionately by the width of the lines on the several horizons .
Behaviour of Croup A Flame Lines of Iron in Stars MaRKABIAN , ocPegasi .
Is Sirian , o^Canis Majoris \#171 ; Geminorum Pr0CY0NIAN , c\lt ; Canis Minoris ot .
AuRICAE Arcturian , Boons AnTARIAN \#171 ; Orionis Wave-lengths , CD Op N K s ' s S S \ s * J S V S S s s \ JJ 1 f8 ro CM O \#171 ; o I 3 I o* 5\gt ; to ** The Shaded Portions Indicate that the Stellar Line Includesan Adjacent Line .
Fig. 1 .
In the region on the less refrangible side of X4489*9 data are only available for three stellar stages , and , except in two cases , the intensities of the-lines show an increase in passing from the hotter to the cooler stellar level The Theory of the Helmholtz Resonator .
265 With regard to the two outstanding lines Keeler* has recorded that they are both stronger in a Orionis than in the solar spectrum .
The stellar behaviour of the iron flame lines of Group A is thus exactly in accord with their behaviour in the sunspot spectra as compared with the Fraunhoferic , and also just what would be expected from their laboratory behaviour .
The Theory of the Helmholtz Resonator .
By Lord Rayleigh , O.M. , F.R.S. ( Received December 15 , 1915 .
) The ideal form of Helmholtz resonator is a cavernous space , almost enclosed by a thin , immovable wall , in which there is a small perforation establishing a communication between the interior and exterior gas .
An approximate theory , based upon the supposition that the perforation is small , and consequently that the wave-length of the aerial vibration is great , is due to Helmholtz , !
who arrived at definite results for perforations whose outline is circular or elliptic .
A simplified , and in some respects generalised , treatment was given in my paper on " Resonance .
" : } : In the extreme case of a wave-length sufficiently great , the kinetic energy of the vibration is that of the gas near the mouth as it moves in and out , much as an incompressible fluid might do , and the potential energy is that of the almost uniform compressions and rarefactions of the gas in the interior .
The latter is a question merely of the volume S of the cavity and of the quantity of gas which has passed , but the calculation of the kinetic energy presents difficulties which have been only partially overcome .
In the case of simple apertures in the thin wall ( regarded as plane ) , only circular and elliptic forms admit of complete treatment .
The mathematical problem is the same as that of finding the electrostatic capacity of a thin conducting plate having the form of the aperture , and supposed to be situated in the open .
The project of a stricter treatment of the problem , in the case of a * Quoted " Spectra of Stars of Secchi 's Fourth Type , " 'Pub .
Yerkes Obs.,5 vol. 2 , p. 371 ( 1903 ) .
t ' Crelle Jl .
Math. , ' vol. 57 ( 1860 ) .
+ ' Phil. Trans.,5 vol. 161 , p. 77 ( 1870 ) ; ' Scientific Papers,5 vol. 1 , p. 33 .
Also ' Theory of Sound,5 ch .
xvi .
|
rspa_1916_0012 | 0950-1207 | The theory of the Helmholtz resonator. | 265 | 275 | 1,916 | 92 | Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character | Lord Rayleigh, O. M., F. R. S. | article | 6.0.4 | http://dx.doi.org/10.1098/rspa.1916.0012 | en | rspa | 1,910 | 1,900 | 1,900 | 2 | 4 | 120 | http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1916_0012 | 10.1098/rspa.1916.0012 | null | null | null | Fluid Dynamics | 52.522695 | Tables | 44.347284 | Fluid Dynamics | [
46.48576354980469,
-42.78697204589844
] | ]\gt ; ( 20 ) ( 21 ) ( 22 ) ( 23 ) ( 24 ) ( 25 ) ( 26 ) showing that is of the ( order , so that this equation gives ffie between and to a sufficient approximation .
iHelmha , corresponds to the neglect of the second and third terms on the left of : making where denotes the linear radius of the circular aperture .
If we introduoo , denoting the capacity of the sphere , tfle known pproxinl S The third term on the left of represenffi deoay of due to the propagation of energy away from the resonator .
omitting for the moment , we have as the corrected value of
|
rspa_1916_0013 | 0950-1207 | The reduction of metallic oxides with hydrogen at high pressures. | 276 | 285 | 1,916 | 92 | Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character | Edgar Newbery, M. Sc.|John Norman Pring, D. Sc.|Prof. Sir E. Rutherford, F. R. S. | article | 6.0.4 | http://dx.doi.org/10.1098/rspa.1916.0013 | en | rspa | 1,910 | 1,900 | 1,900 | 1 | 42 | 925 | http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1916_0013 | 10.1098/rspa.1916.0013 | null | null | null | Chemistry 2 | 40.034178 | Thermodynamics | 37.890198 | Chemistry | [
-13.272726058959961,
-51.247310638427734
] | ]\gt ; hydrogen is determined at eviven temperature by the concentration of hydrogen and that of the water yapour produced by the reduction .
Thus , if the equation:\mdash ; denotes the concentration of the hydrogen and that of the water vapour .
we have the relation:\mdash ; where is a constant at any given temperature .
If can be arranged to be greater than , the reaction expressed in the above equation proceeds from left to right .
This state of affairs may be realised:\mdash ; ( a ) By increasing the pressure of the hydrogen present .
( b ) By diminishing the pressure of the water vapour formed during the reaction .
If the reaction is endothermic , by raising the temperature , when the value of is diminished according to va n't Hoffs equation , whence ln const .
Here represents the heat absorbed by the progress of the reaction at the temperature in question .
If therefore is positive , or the reaction is endothermic , is diminished ith the rise in temperature and the change shown in the above equation proceeds from left to right .
The work described in the present paper was undertaken with the object of seeing how far these theoretical considerations can be applied practically , and also of preparing pure metals or lower oxides of metals free from impurities which are unavoidably present in such substances when prepared by other means . .
' to remove 150,000 litres of gas from 1 .
of , a process requiring least four months ' continuous working , further experiment on these line abandoned .
Part 2.\mdash ; Reaction between Refractory and Eydrogen at High Temperatures and Pressures .
Experiments on the following oxides were carried out with the apparatus shown in fig. 1:\mdash ; sample of Merck 's specially pure chromium oxide was heated to redness in a quartz crucible , cooled in a desiccator , and about .
2 .
placed in the experimental crucible of magnesia or alumina .
air was displaced from the furnace by passing in hydrogen to about 30 atmospheres pressure and after a time allowing it to escape .
The hydrogen pressure was then raised to 100 atmospheres and a current of 17 amperes , at 40 volts , passed through the tungsten wire , all cases was about 50 cm .
in length .
The walls of the furnace were cooled by a current of cold water passing round them .
After five hours ' heating , it was allowed to cool and the furnace opened .
The greater part of the had been reduced to the which was well crystallised in needle-shaped crystals .
At the of the crucible , small quantity of metallic chromium was found mixed with the monoxide .
The temperature attained was very high , over 2000o C. near the bottom of the crucible .
The crucible itself was partially fused and shrunk considerably where the temperature had been greatest , while the magnesia packing was : volatilised near the tungsten wire and condensed again in small transparent crystals forming a hollow crust round the lower part of the orucible .
hydrochloric or sulphuric acid .
Its chemical and physical properties be identical with those of metallic vanadium , and only a estimation of the vanadium present was capable of proving that the substance really was the monoxide .
This crystalline form of the monoxide does not appear to have been prepared before .
A further experiment with proved conditions gave a mass of monoxide with clean well-formed crystals in the hottest part of the crucible , but further reduction could not be produced .
Uranium Oxide.\mdash ; A sample of pure was heated to ness , cooled , and placed in a magnesia crucible as before .
Several attempts were made to reduce this , but even with long contin heating to a temperature of over C. with 150 atmospheres hydrogen pressure , the reduction could not be carried further than the dioxide .
This was in the form of a blaok semi-crystalline substance , insoluble in acids , with the exception of strong nitric acid , in which it dissolved with evolution of brown fumes .
When heated in the air on ] atinum foil , it glowed , swelled up , and fell to a black powder .
No evidence of the presence of metal could be obtained .
Some magnesium uranate appears to be formed at the same time .
Thoria , Zirconia , and Yttria.\mdash ; Samples of each of these were treated in the same way as the uranium oxide , but no evidence of reduction could be obtained : Titanic Acid.\mdash ; Pure titanic acid was heated in a magnesia crucible with a pressure of 130 atmospheres of hydrogen .
Some of the substance was absorbed by the magnesia of the crucible , yielding a bluish-white magnesium titanate round the upper part of the crucible .
The remainder was converted into a rod of well cryetallised black monoxide , , which was completely coated with the gold-coloured mono-nitrids , evidently formed from $h small quantity of nitrogen which is always present in commercial " " pure hydrogen .
Cerium \mdash ; This oxide , , was obtained by igniting the nitrate .
When treated as before , with 130 atmospheres hydrogen it was completely converted into the pale yellow-green uioxidd : FIG. 1 .
Soc. Proc. , , vol. 92 , Plate 1 .
FIG. 4 .
|
rspa_1916_0014 | 0950-1207 | Discontinuous fluid motion past a curved boundary. | 285 | 304 | 1,916 | 92 | Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character | H. Levy, M. A., B. Sc.|Prof. A. E. H. Love, F. R. S. | article | 6.0.4 | http://dx.doi.org/10.1098/rspa.1916.0014 | en | rspa | 1,910 | 1,900 | 1,900 | 18 | 222 | 7,647 | http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1916_0014 | 10.1098/rspa.1916.0014 | null | null | null | Formulae | 43.56461 | Fluid Dynamics | 36.357584 | Mathematics | [
44.357906341552734,
-31.91473960876465
] | Discontinuous Fluid Motion Past a Curved Boundary .
285 The following oxides were reduced to lower oxides:\#151 ; V205 to VO .
Ti02 to TiO .
Nb2Os to NbO .
Ce02 to Ce203 .
U308 to U02 .
' The following oxides were unchanged:\#151 ; .
A1203 , MgO , Zr02 , Y203 , Th02 .
The metals obtained , chromium and manganese , are probably purer than those prepared by any of the methods used hitherto.* This supposition is supported by the sharp nature of their melting points , a feature which has not been observed with samples prepared by other methods .
Part of the incidental expenses of this investigation has been met by a grant kindly made by the Chemical Society .
Discontinuous Fluid Motion Past a Curved Boundary .
By H. Levy , M.A. , B.Sc. , Carnegie Research Fellow , late 1851 Exhibitioner of University of Edinburgh .
( Communicated by Prof. A. E. H. Love , F.R.S. Received November 2 , 1915 .
) Although many writers have devoted their attention to the problem of the motion of a fluid past a curved boundary , no method so simple , yet so effective , as that developed for the case of a plane barrier by Kirchhoff and others , and since elaborated by Mitchell , f Love , f Bryan and Jones , f etc. , has been discovered for the more general case .
Within the past few years a group of mathematicians in Italy and in France , in particular Levi-Civita , Cisotti , and Villat , * and J. Gr .
Leathern in this country , have published notable advances on this subject .
In aeronautics alone recent developments have shown the practical necessity for an effective discussion of the case where the plane is cambered .
In this paper I propose to show how two-dimensional problems of the motion of a curved surface through a fluid , or the efflux of fluid through an orifice in a vessel of any shape , may be solved , how to find the form of the free stream-line , and how the components of resistance may be calculated * The purest samples examined by Burgess and Waltenberg contained 97-98 per cent , manganese and 98-99 per cent , chromium , and melted at 1255 ' and 1520 ' respectively .
t See Bibliography .
28.6 Mr. H. Levy .
from the solution obtained .
It will be assumed that the fluid is of vanishingly small viscosity , that the motion is two-dimensional and steady , and that the surface in its motion gives rise to a free stream-line , along which the pressure , and therefore the velocity , is constant , extraneous forces such as gravity being neglected .
Problems in which the surfaces are planes have been solved by a series of conformal transformations , and a similar process will be adopted here .
The following functions and notation will be employed:\#151 ; z = x + iy , where x and y are the co-ordinates of any point in the plane of the problem ; w = cf ) -f- iyfr , where ( f\gt ; = const , and yfr = const , correspond to the equipotential and stream lines respectively , \#163 ; 1 = log ( dz/ dw ) = log q~l ( cos 0 + i sin 6 ) = log q~l + i0 , where q is the velocity , and 6 gives the direction of motion at any point .
Along the free stream-lines and surface ( see fig. 1 ) , EACODBE , it is evident the following facts are known :\#151 ; ( 1 ) Along AE and BE , q = constant = V. ( 2 ) AE and BE are ultimately parallel with the direction of the velocity at infinity I , supposed here to be horizontal .
( 3 ) The form of the surface BDCA is given , i.e. , the value of 6 at every point is known .
( 4 ) The stream-line divides at O , and therefore q \#151 ; 0 .
Z-PLANE Fig. I. Discontinuous Fluid Motion Past a Curved Boundary .
287 All our knowledge of the problem is comprised in these four headings , and .
knowing these , the problem must be determinate .
Consider what the figures in the w- and fi-planes become , corresponding to our problem .
IOAE and IOBE are really the same stream-line , say ^ = +0 and yfr = \#151 ; 0 , and we will for the moment suppose that at O \lt ; f\gt ; = 0 .
The w-plane then assumes the form given in fig. 2 .
Suppose w expressed in terms of another variable t , , such that along EAO and EBO t ranges from 0 to + co and 0 to \#151 ; oo respectively .
To obtaiii E A ) Q----------------E B ur- Plane O A ===)HE----------------- O B u V-Plane Fig.2 .
this expression we have to transform the region of the problem in the w-plane to the upper half of a new \#163 ; -plane , and this will be facilitated by making use in the first place of an intermediate ^_1-plane .
By means of the Schwarzian transformation , we obtain at once = *2/ D + E , and , since vr1 \#151 ; 0 when t = 0 , w = D/ t2 .
D will be at once determinate if we know another pair of corresponding values of t and w. If on the other hand the problem is that of the flow of liquid through an orifice or between two surfaces , each infinite in one direction only , the figure in the w-plane will consist of two lines parallel to the real axis , and the corresponding transformation is evidently w = D | y = D log t + E. Mr. H. Levy .
Since all the circumstances of the problem will be known , or at least easily derivable , once we have discovered the relation between z and w , and therefore between z and t , it is obvious from ( 1 ) that the question will , in the same sense , be solved if we express 12 in terms of t , for then | dw en = j* ^ en dt .
Success or failure therefore depends on the possibility of determining the transformation to change the region in the 12-plane into the upper half of the \#163 ; -plane .
\#163 ; l-plane\#151 ; 12 = log ( f1 + id. Lines parallel to the real axis correspond to boundaries along which 6 is constant , that is to say , to straight lines in the 2-plane , while lines parallel to the imaginary axis are such that the velocity is constant .
AE and BE ( fig. 1 ) , therefore , representing stream-lines of constant velocity , will correspond to portions of lines parallel to the 6 axis .
Along BO and AO , both 9 and \lt ; / vary , and the corresponding boundary in this plane will be curved , while to 0 , the point at which the velocity is zero , will correspond the point at infinity .
Eig .
3 shows the representation in the 12-plane .
In order that the problem may be one of the type we desire , the impact of a fluid against a finite continuous surface , 12 must be such that ( fig. 3 ) :\#151 ; ( 1 ) A finite portion AB must be straight , otherwise there would be no free surface , and the problem would be that of the impact of fluid against an infinite surface .
( 2 ) CO and DO must ultimately be horizontal and at a distance nr apart if the gradient of the surface is continuous at O. If , on the other hand , n- Plane F i g .
3 .
\#187 ; Discontinuous Fluid Motion Past a Curved Boundary .
289 there is an angle 7 at this point on the surface , then CO and DO must ultimately be a distance 7 apart .
If the surface AB in the 2-plane is concave to the impinging fluid , A and P\gt ; are farther from the real axis in the O-plane than the asymptotes of CO and DO , while if OA is concave and OB convex to the fluid , A is farther off and B nearer to the real axis than CO and DO respectively .
If CO and DO in the O-plane are straight lines , AC and BD being the only curves in the figure , the problem is that of the impact of fluid against a plane surface with the ends rounded off .
The problem to transform such an area as that above described to the upper half of the +plane , as I shall presently show , yields to an artifice about to be developed .
O = F(\#163 ; ) , the formula of transformation to the \#163 ; -plane , may also be regarded as the equation to the curve traced out by the extremity of the vector O when the freedom variable t ranges over all real values between the two infinities .
The point O being thus the extremity of a vector , the point 0 + D ' will be obtained from 12 and 12 ' by adding them according to the vector law for the same value of t. Should 12 and 12 ' both trace out lines parallel to the real or the imaginary axis , 12 + 12 ' will likewise trace out a line parallel to the same axis , for the real parts or the imaginary parts , as the case may be , of 12 , 12 ' , and therefore of 12 + 12 ' , will be constant .
If O = F ( t ) and O ' = G ( t ) then represent two curves in the 12-plane , transforming the areas bounded by these curves to the upper half of the \#163 ; -plane , then 12 !
= F ( 0 + G(0 will represent the curve obtained by adding vectorially the points 12 and 12 ' obtained from the same value of t , and this new function will transform this new curve to the upper half of the \#163 ; -plane .
It should now be obvious that if 12 and 12 ' both have the essentials of the boundary OCABDO as set out on p. 288 , the resulting curve 12i = 12 +12 ' will have these same character- , istics ; and generally if 121 } 02 , ... , On each represents such a formula of transformation , 12 = A1D1 +A2Q2+ ... ... + An12w will also represent such a formula when A3 , Aa , ... , An are all real constants .
It is especially to be remarked that all the functions O involved must include in the curve they each represent in the 12-plane a part of a finite straight portion parallel to the imaginary axis for the same range of values of t. It is not necessary that these functions be limited to a finite number , provided always the constants Ai , A2 , ... , are so selected as to keep part of the curve 0 = 5 AnOn in the finite region of the plane .
Mr. H. Levy .
For the sake of clarity we shall illustrate with the case of two functions Hi and Xl2 representing two regions in the H-plane , rectangles with corners at t = \#177 ; 1 , at A and B , and t \#151 ; at F and G respectively ( fig. 4 ) , where a \gt ; 1 , and suppose F ' and G ' correspond to t = a and t \#151 ; \#151 ; a on the rectangle OABO .
Combining these rectangles vectorially for the range \#151 ; 1 , the resultant curve will have a straight-line boundary parallel to AB .
From t = +1 to t = + a the boundary will be rounded off , and from t \#151 ; a to t = + co , and t = \#151 ; a to t =\#166 ; \#151 ; -go , the boundary simply consists of two straight lines parallel to the real axis .
The lower diagram ( fig. 4 ) gives the resultant curve , a rectangle with the t=*a t \#151 ; \gt ; +oo t = -a t - oo Fig.4 corners rounded off .
By referring to fig. 3 it will be at once seen that this is the type of curve we are seeking .
To this we may now add , by the same method , another rectangle and obtain another curve of the required type , and we may repeat the process as often as we please , always provided in so doing the horizontal parallels and the vertical do not move off to an infinite distance .
It is moreover evident that the values of t at which the curve at the rounded corner begins and ends are the greatest and the least values of t " at corresponding corners of the series of superposed rectangles .
It is quite unnecessary , although it has been done in the illustration for the sake of Discontinuous Fluid Motion Past a Curved Boundary .
291 simplicity , to place the two rectangles symmetrically above the real axis , but any position in the plane would be sufficient so long as their infinite sides are parallel to that axis .
If the values of t are symmetrically distributed round each of the rectangles , the resulting boundary in the fl-plane will be a symmetrical figure , and will therefore represent a symmetrical surface , while if t*he rectangles have a common value of t for one of the angles the surface will be a plane with a curved end .
Should one of the rectangles include for the straight vertical portion , say , an infinite range for t , the resulting curve in the fl-plane will have a horizontal asymptote and therefore represents a surface no portion of which is straight .
Analytically these considerations are expressible in the following manner .
By means of the Schwarzian transformation applied to the case of the rectangle under discussion with corners at t = a and t = \#151 ; a respectively it is at once seen that fli = A | ( ft \#151 ; a ?
} = : ^ cosh-1 ( t/ a)-\- A\ .
The exact specification of the rectangle in the fl-plane would determine A and A ' uniquely , A evidently as a real quantity and A ' complex , but as it is intended to sum up a number of such A 's , and as we are only concerned with the exact specification of the final curve obtained , it would be pointless for us to attempt to insert these values .
It is sufficient to note that A and A ' are real and complex respectively .
Summing n such rectangles vectorially , A = 2 flw = 2 { An cosh-1 ( t/ dri ) + A'n } i .i = 2 Anlog{\#163 ; + v/ ( \#163 ; 2\#151 ; an2 ) } + logp \#151 ; where p and a are real constants and where we will suppose \lt ; * !
\gt ; a2\gt ; an\gt ; 0 , which in reality involves no restriction .
Consider what A becomes for various ranges of t. ( 1 ) +oo \gt ; *\gt ; \amp ; ! .
Here log g~l + iO = 2 Anlog{\#163 ; + s/ ( t2\#151 ; an2 ) } + logp \#151 ; ia , and 6 = \#151 ; a , q~l = p II { \#163 ; + y/ ( t2\#151 ; an2)}x\ This therefore corresponds to a straight part of the surface , and the bend , if any , will begin at t = a\ .
The stream we have supposed divides at t \#151 ; * oo , VOL. XCII.\#151 ; A , Z 292 Mr. H. Levy .
at which point q must be zero , and this therefore gives , as a first condition on the A 's 2 An \gt ; 0 .
At t = n e = -a , q-1 = pax^ n { ^1 \#151 ; \/ ( ct\2 \#151 ; an2)}^ ' .
( 2 ) aiyt^a2 .
log q- ' + iO = Ailog { t + i v/ Oi2 \#151 ; 12 ) } + % An log { \#163 ; + \/ ( f \#151 ; 0 } -flogp \#151 ; m , = Ai log CL\ + 2 An log + \/ ( ^2 \#151 ; ^n2 ) } + log p 2 + ^[Ai tan"1 { \/ ( ai2""^2)/ 0""a]\gt ; so that 6 = Ai tan-1 y/ or t = ax cos { ( 0+ \#171 ; )/ Ai } .
Also q~ 1 = / x* !
Ai A Hence in this region the boundary is a curve which , from t = a\ to \#163 ; = \lt ; x2 , turns through an angle Ai tan"V^i2 \#151 ; a22)/ \#171 ; 2 , and by choosing the sign of Ai properly we can arrange to have the surface concave or convex to the stream just as we desire .
( n ) an-1 \gt ; \gt ; t \gt ; \gt ; an .
n log q- ' + id = 2 A.-1log{f + iv/ ( ^\#187 ; -i-\lt ; *)}+A\#187 ; log { * + , / ( 72-a"2 ) } -blog p\#151 ; m. = 2 Awe _ i log an -1 + An log { t + v/ ( t2~ a\#187 ; 2 ) } + log p 2 + i[2 An-i tan"1 { y/ ( aa\#187 ; -i \#151 ; so that ( 9 = \#151 ; *+ 2 An_i tan"1 ( an-i2 \#151 ; t2)/ t}f and 2-1 = paiAla2A2-..a"-iA'- ' { \#163 ; +v7(\lt ; 2 \#151 ; a\#187 ; 2)}A"(w+1 ) 0= \#151 ; a + 2 A"tan_1 { v/ ( a\#187 ; 2\#151 ; 0/ 0 , q~1 = f\gt ; a\A'a2X'2. .
.anA'Hence along this range for t the velocity is constant ( = Y , say ) and this represents the free stream-line .
Hence p-1 = Ya^a2K\gt ; ... an^ Discontinuous Fluid Motion Past a Curved Boundary .
293 If the fluid at an infinite distance along this stream-line flows horizontally , 0 = 0 when 0 .
Hence 2 A"7r/ 2 = a , n or 2 A " = 2a/ 7r , and since 2 A " \gt ; 0 , a. must be positive .
The surface being obviously one with an axis of symmetry , it is unnecessary to consider ranges of negative values of t except at the branch point \#151 ; oo .
( \#151 ; 1 ) \#151 ; \#171 ; i co .
log 2-i + id = 2 A " log { -t + v/ ( *2-0 ) + 2 A " log ( -1 ) + log taking the proper branch .
Hence 0 = \#151 ; \#171 ; + tt 2 A " = \#171 ; , S~1 = P n { -* + v/ ( *2-\#171 ; \#187 ; 2)}A'At f \#151 ; -f oo , 0 = \#151 ; a , and at t\#151 ; * \#151 ; oo , 0 = + a , and therefore the problem is that of the impact of a fluid against a surface , or the efflux of a fluid through an orifice of a surface along its axis of symmetry ( fig. 5 ) .
OXi is straight and along it 0 = \#151 ; \#171 ; .
X"_iXn is curved and given by d= ~a + 2 A"_ !
tan-1 { v/ ( aa\#187 ; -i\#151 ; \lt ; 2)/ 0This expression involves ( \#187 ; -l ) of the constants A , and since the only restriction on them is n 2An = 2a/ 7T ( a \gt ; 0 ) , these in-1 ) coefficients may obviously be chosen to make all or any of the portions X1X2 ) X2X3 , ... , X"_ !
X " concave or convex .
There are in fact altogether ( 2n-2 ) constants to be determined , viz.:\#151 ; D , Ab A2 , ... A " , a1 ; a2 , ... and the ( 2w-2 ) conditions to fix them viz.gradients at 0 , X , , X2 , ... .
X " , and lengths OXi , XiX2\gt ; X"_iX " , along with the condition 2 A = 2a.fir , and thus we are in a position to solve the problem of the impact of a fluid against a body in a direction along its axis of symmetry , the surface behm made up of a series of portions specified in a manner about to be described ' Mr. H. Levy .
t = -CL n-i t - + co Fig. 5 .
The distance X"_iX " is evidently obtained as follows .
Suppose w = D/ t2 , then Xn- !
X " Jo , dt Jo , d\lt ; f ) dt Jo , q -2DpaiA\gt ; a2A* ... a"-iA"-\gt ; j " ' jA v7 }A " 2D Ya ; 8D " Y a ; 5_r AM J n * ( ir " 2Ji '\#171 ; n\#151 ; ] J\#177 ; f { t + W-On*)}** a"_]fcin+ J [ ( a\#187 ; -i/ aw)2-l ] dv vA"+1 ( v2\#151 ; l)/ ( v2+ l)3 , Discontinuous Fluid Motion Past a Curved Boundary .
295 and in the same way the other distances are easily calculated .
The inclination to the horizontal at Xi is 0\ = \#151 ; X2 is 02 = \#151 ; \#171 ; + Aitan-1 W i.ai2~a22)/ a2 , X3 is 03 = \#151 ; \#171 ; + Aitan-1 { v/ ( \#171 ; i2\#151 ; a32)/ a3 } + tan-1 \#151 ; a32)/ Xn is 0n = \#151 ; \#171 ; + Ai tan 1 { \lt ; / ( ai2\#151 ; an2)/ an } + A2tan 1 { \/ ( a22\#151 ; an2)/ an } + ... +AB_X tan-1 { v/ ( a"_i2\#151 ; It is evidently almost impossible to determine otherwise than approximately the values of the constants involved in these equations , but , the last ( n)being linear in A , ... , An-i , and in an especially convenient form , these quantities may be quite simply expressed in terms of ah ... , an , which greatly facilitates their choice .
To the extent that these equations are practically only soluble approximately , the solution we have found for our problem is not really complete but more adaptable for constructing cases , which may , however , be made to approximate closely to the type of problem requiring solution .
Any number of cases may , of course , be quite simply constructed by giving values to Ax , ... , A " , au ... , a " , and from the above equations obtaining 0h ... , 0n and a. In a short time one becomes quite expert at choosing values for the quantities Ax , etc. , to make the surface take a desired shape .
Example.\#151 ; The problem is that of the escape of a liquid through a hole in a plane bent into the form ABC , A'B'C ' ( fig. 6 ) .
The corresponding curve in the H-plane is evidently obtained by the t \#187 ; *a t - a t * + oo A t-1 B f\gt ; b B A i t\#187 ; o D D t\#171 ; o F i G .
6 .
Mr. H. Levy .
round them .
Xi = log q~l + id , =A log { t + y/ ( t2\#151 ; a2 ) } +B log + v/ \amp ; 2 ) } + log i* .
Let the stream-lines ABCD and A'B'C'D ' correspond to y]r \#151 ; c and \#166 ; tfr = \#151 ; c respectively , where 2 c is the final breadth of the issuing stream at infinity , and suppose CC ' lies on the equipotential = 0 .
As we have seen , for a problem of this type w = ci , t = b , and w = \#151 ; ci , t= \#151 ; b , are corresponding values of w and t. Suppose BC turns through an angle r/ 6 , so that at 0,9= \#151 ; $.71- .
a^ty\gt ; b. 0 = Atan 1 { \/ ( \#171 ; 2\#151 ; t*)/ t } + x = Atan 1 { \/ \#151 ; tt , \#171 ; being equal to \#151 ; v , since this is the value of at \#151 ; +00 .
Hence at t = b , where q = V and 0 = \#151 ; $7r , Hence p = l/ YaAbB and \#151 ; -|7r = A tan 1 { -x/ C\#174 ; 2Cl = ilog{* + v/ ( *2-4 ) } + |log{* + .v/ ( \lt ; 2-l)}-logV-ilog2-Mr .
Hence , for the curve BC , 6 = \tan-1 { ^(4\#151 ; t2)/ t}\#151 ; ttor q = Y/ { t-^/ ( t2-l)}* , w = \#151 ; ( 2c/ 7r)log\#163 ; + ci , w \#151 ; M log + N , w = \#151 ; ( 2c/ 7r)log(\#163 ; /5 ) + ci The condition on A and B becomes A + B = 1 .
q_1 = aK { t+*y { t2\#151 ; -1 1/ Y = aHBp .
or Atan 1 { \/ } = \#163 ; 7r .
Hence , if we choose a = 2 , b = 1 , that Atan J^/ 3 = ^-7r , A = | and B = \#163 ; .
8 = = Discontinuous Fluid Motion Past a Curved Boundary .
297 which therefore determines the intrinsic equation to the curve and the length of the curved portion .
Free Stream-line.\#151 ; 6 = Jtan"1{v/ ( 4-t2)/ t } + b tan-1 { v/ ( l \#151 ; t2)/ t}\#151 ; ir , V = q = d\lt ; f)/ dsy giving \lt ; /\gt ; = Vs , s being measured from c , or ( f ) = \#151 ; ( 2c/ 7r)log\#163 ; along yjr = c , so that t = which expresses 6 in terms of \#163 ; , and \#163 ; in terms of s , giving the intrinsic equation .
There is an obvious extension to the whole of this discussion .
When considering the vectorial addition of the rectangles there was no limitation on the number so added provided the figure ultimately obtained was situated on the finite part of the plane .
In the limit , therefore , if we suppose an infinite number of rectangles superposed , the values of t at whose corners range from t = a\ to t = a2j the A 's may be considered as functions of a , and the final value of II will be given by r\lt ; h ft = A ( a ) cosh l(t/ a)da + B , J \lt ; 12 where A ( a ) is an arbitrary function of a , except in so far as it must be n chosen to satisfy the condition equivalent to %An = 2 a/ 7r , viz. , , ra2 )a , J A ( a ) da = 2a/ 7r , or ft = 2a .
j A(a)da ^ .
J A ( a ) cosh-1 + where A ( a ) is real but otherwise now quite arbitrary .
This will evidently represent , for any A , a surface curved from t = a\ to t \#151 ; a2 impinged upon by a fluid in the direction of its axis of symmetry , the angle on the surface at the point at which the fluid divides being 2 a. If one of the limits , a\ say , is infinite there is no straight portion in the surface at all .
Example.\#151 ; A ( a ) = 1 jd2 .
\ : da . .
t Tr. .T -\#171 ; cosh 1 - -f- K \#166 ; + iL a* a cosh'11 - ( t2-l)/ t + i/ t + K + iL : l0g\#163 ; _1 + 10 .
Mr. H. Levy .
+ t1 .
q = e^^-^ 1 ) } , e = i/ ^+l .
Suppose at t-~ + co , = = 0 , 1 , 2 = V. Then L = ^7r , K = log(l/ V ) .
XI = cosh_1i(\#151 ; \#151 ; ~ + l'g ^ + * ( j + i77- ) q = YeV(^-i)/ 7{\lt ; + v/ ( ^_ i)| 6 = 1/ t + ^ir .
Suppose t = +1 lies on the equipotential ( f\gt ; = c and the stream-line yp ' \#151 ; 0 .
Then w = D/ t2 = = \lt ; f\gt ; , along the surface , and therefore a = f # = f e~ V(\#171 ; 2-D/ \#171 ; J # J V \ f3/ and 6 = 1/ \#163 ; + ^7t gives the intrinsic equation to the surface .
The free stream-line answers to the range 1 \gt ; \gt ; 0 .
Now log \lt ; r1 + id = log { t + v ( i .
-t2 ) } + log 1+i [ 1+1 ] , so that q = V and 6 \#151 ; tan-1 { x/ ( l ( 1 \#151 ; t2)/ t-{- l/ t + ^rrr .
Also $ = Vs + c = cjt2 .
Hence the intrinsic equation to the free stream-line is 0 = tan-1 ( Ys/ c)\#151 ; v/ ( Ys/ c)-f ^(lq-Vs/ c ) + |7r .
When 5 = 0 , # = -*- tt 4-1 = 147*3 ' approx. 5 \#151 ; CO 6 \#151 ; * TT .
Again so that z !
dz og^ ' v ; /+y ( ff_ i ) } ( C0B r+* si4 ) Hence the Cartesian equations to the curve are 2c f+0 ' c-V(\#171 ; 2-i)/ t .
1 * " + V j t 1 ) } sin 1 * 2 c r+Q0 g-vo2- !
)/ * i y = ~ V J t t2 [ t + ^/ { t2\#151 ; 1 ) ) cos7 Discontinuous Fluid Motion Past a Curved Boundary .
299 and the chord and camber of the surface are at once given by evaluating these integrals for t = 1 .
Fig. 7 gives a diagrammatic representation of the whole problem .
All the surfaces so far included in our discussion are symmetrical and t\#171 ; + oo F i g .
7 .
placed with their axis of symmetry along the direction of motion of the fluid , but we may by a similar method discuss other forms , and we proceed to the case where the surface is composed of two planes meeting at an angle , at which the fluid divides , one of the planes rounding off at the free end ( fig. 8 ) .
The boundary in the fl-plane is obviously a rectangle with one T =\#187 ; -oo \ t \#171 ; 4-00 f Fig.8 .
corner rounded off , to be derived , as we have already seen , by superposing a number of rectangles with a common value for t at one corner , and a common finite range for t along part of the side parallel to the imaginary axis .
For the moment we shall confine ourselves to the case of two such component rectangles having corners at i = a and t = \amp ; , t = a and t = c , respectively , Mr. H. Levy .
where c\gt ; b\gt ; a , the infinite ends corresponding as before to \#151 ; + oo , so that in the resulting surface the curved end will correspond to a range of values from t = cto t \#151 ; b s/ { { t\#151 ; b ( t\#151 ; a ) } + B x/ -a ) } A cosh-1 \#151 ; ( / i + b)g cogj1 i 2\#163 ; \#151 ; ( a + c ) congj .
b\#151 ; a c\#151 ; a = A log \t\#151 ; \(a , + V ) + \/ { ( \#163 ; \#151 ; a ) } ] + B log [ t \#151 ; J ( a + c ) + y/ { ( t \#151 ; a ) } ] + log fa , where A , / 3 , p , and a are constants .
Consider the following ranges for t. ( 1 ) +co\gt ; \#163 ; \gt ; c. Here q~x = p\t\#151 ; \(a + b ) + V { ( t\#151 ; b)(t + a)}\#165 ; L\t \#151 ; ^{c + a ) + s/ { ( \#163 ; \#151 ; c)(\#163 ; \#151 ; \#171 ; )}]B and 0 = \#151 ; a. Hence , if we suppose the point at which the fluid divides corresponds to t = + oo , then q = 0 for this value of t , and a first condition on A and B is A + P\gt ; \gt ; 0 .
( 2 ) c \gt ; t\gt ; b. Here q~ ' = p[t\#151 ; ^(a + b ) +{(t\#151 ; b)(t\#151 ; a)}]p { J(c\#151 ; a)}B , and 0 = \#151 ; a + B tan-1 v " { ( c~0(\lt ; -\#171 ; ) } _ t-7\gt ; ( c + Ct ) ( 3 ) b^\gt ; t^\gt ; a , corresponding to the free stream-line .
Here q~l = p{\#163 ; ( 6-a)}A { \#163 ; ( c-A)}B , and 0= \#151 ; a +A tan-1 { ( \amp ; ~0 ( *-\#171 ; )}+ B ten-i^(c-Q(*-a)}. .
t\#151 ; ^{b + a ) t\#151 ; %(c + a ) ( 4 ) a \gt ; t \gt ; \#151 ; oo .
Here log ?
1 + i0 = Alog[\#151 ; t-\-\(b + \amp ; ) + v/ { ( \amp ; \#151 ; t)(a\#151 ; \#163 ; ) } ] + Blog[ \#151 ; t + %(c + a ) + ^/ { ( c\#151 ; t)(a\#151 ; t ) } ] + log p \#151 ; it* .
+ A log ( \#151 ; 1 ) + B log ( \#151 ; 1 ) .
Hence 2-i = p[-^ + |(6 + a ) + v/ { ( \amp ; -0(^-0}]A[-^ + K^ + ^ ) + v/ { ( ^-0(\#171 ; ~0}]B and 0 \#151 ; \#151 ; a + ( A -f B ) it .
Suppose ^\gt ; nce more that , when t \#151 ; oo , ?
\#151 ; \gt ; 0 , 0 = ft. A + B = ( / 3 + a)/ 7r 0 .
( Fig. 8 .
) Discontinuous Fluid Motion Past a Curved Boundary .
301 For some value of t between a and 0 = 0 , and this will correspond to the point at infinity on the free stream-line .
If the skin velocity along the free surface is V , then l/ V = p{H\amp ; -\#171 ; )}AU(*-\#171 ; )}B\gt ; giving the expression for p. At t = b , g=V , and g = -\#171 ; + B ton '\#166 ; v ' .
and , as before , we may calculate the values of the lengths of the various plane and curved portions in terms of the constants .
By suitable adjustments of these constants we may arrange to have the plane and curved parts of desired lengths and the angle at what we please .
One of the most important cases practically is where / 3 = tt \#151 ; x , so that A + B = 1 , and the problem is that of the impact against a plane surface with one bend .
And , generally , by superposing n such rectangles with a common corner t = a , the other corners corresponding to bh b2 , ... , bn , we obtain fl = SB i .J y/ { { t\#151 ; a)(t\#151 ; bn ) } 2 B " cosh-1 \#151 ; + g ) + const , j Oft CL and , by suitably choosing the constants involved , we may , just as in the symmetrical case , make the surface fit as closely as we please to that of a given one of the type here under discussion .
If a and f3 have the same meaning as in the previous cases If , now , we suppose the number of superposed rectangles to become infinite , and t = \amp ; i , t == b2 , to be the values of t corresponding to the largest and smallest values of t at the corners , rt = fV)co\#187 ; h-\gt ; " * with the condition that P*B(\amp ; )d\amp ; = ( \#171 ; + / S)/ ir .
Jft , If one of the limits become infinite there will correspond a boundary made up of one plane portion meeting a curved portion at an angle \#171 ; + yQ , so that n ( a + / 3)/ 7r .
f B ( 5 ) cosh-1 ^ ^ db _________________Jfe , ____________________(o \#151 ; a ) rao B ( b ) J 6 , Mr. H. Levy .
where B is now quite arbitrary , and to every such function B there will correspond a surface of the type considered .
The method adopted in the discussion of these two special types of boundary will now have made obvious the course to be adopted when the boundary does not necessarily conform to one of these types , but is composed of a plane portion as large or as small as we please , with curved ends of continuously varying curvature .
The method of superposition of rectangles will enable us to build up the expressions required , provided always the sides parallel to the imaginary axis of all the rectangles have a range of t in common .
If t = a\ , t = bi , correspond to the corners of one of the rectangles , and t = + oo to the point at infinity , then ll = AlJ Ai cosha/ { { t \#151 ; ai ) ( t \#151 ; bi ) } Hence , superposing mn of these rectangles , 21\#151 ; ( ax \#151 ; \amp ; i ) a\\#151 ; b\ f const .
X A my n n \#151 ; 1 cosh 1 2 t \#151 ; ( dn + bjn ) ctn bm \#166 ; f const .
, where an \gt ; \gt ; ?
/ 3i ; \gt ; bn , t for each of che rectangles thus having the common range t \gt ; / 3i , and we may proceed , as we have already done in the previous cases , to determine the constants , so that the surface may coincide with the required one .
It would serve no purpose to go through the calculation in the general case , which is similar to those already discussed , and no new features are developed which have not already been brought out .
The same condition , S An \#151 ; m \#151 ; 1 f3 -j- \amp ; IT 7 applies in this case as in the others , the same meaning being attached to ( ol and / 3 .
In particular if both m and n become infinite , that is to say if we superpose an infinite number of such rectangles , H = J J da db A ( a , b ) cosh-1 ^ a^'b^9 r\#171 ; i rPi where A ( a , b ) da db = ( \lt ; x + / 3)/ tt , J oli * bj and the limits a\ and b\ may become infinite , in which case there will be no plafte portion at all .
And generally if the point at infinity in the fl-plane corresponds to a i Discontinuous Fluid Motion Past a Curved Boundary .
303 finite instead of an infinite value of tie as has so far been supposed , the corresponding value for Hi takes the form Hi = A cosh"1 \#151 ; , t + c giving H == 2 Art v cosh-1 , and a corresponding integral expression .
One further important point remains to be considered .
Will the method here outlined of superposing rectangles enable us to build up any surface , or will only certain classes of such surfaces be formed no matter how many and in what manner such rectangles are combined ?
It has already been shown that the constants involved in the expressions obtained by properly choosing the number of terms are just of sufficient number to enable us to construct as the surface one having given inclinations at a given number of points of given distances apart measured along the surface .
It is obvious that by taking these points of sufficient number and sufficiently close together we can theoretically make the surface we have constructed differ by as little as we please at any point from an arbitrary surface , and it will always be possible , by the method here developed , to find the required expression for fl. But this is equivalent to saying that by the superposition of , if necessary , an infinite number of rectangles our formula gives the solution for any arbitrary surface .
Calculation of the Resistance .
The method above described expresses H and w in terms of t , or for certain ranges of that variable 0 = 0(t ) , q = q(t ) , = If p and q are the pressure and velocity on the upstream side of the surface , and p0 and Y the corresponding expressions for the dead-water region , then P-2\gt ; o = y(V2-q2 ) .
The horizontal component of the thrust is then T* = | ( p\#151 ; po)ds sin 6 = %j ( V2\#151 ; sin 6 .
q~Y d(f\gt ; , and the vertical component Tie = | ( p\#151 ; Po)dscos 0 = ip | ( V2\#151 ; g^cos 6 .
g-1 d\lt ; j\gt ; , and every term under both integral signs is expressible in terms of t. 304 Discontinuous Fluid Motion Past a Curved Boundary .
BIBLIOGRAPHY .
( 1 ) Mitchell , 44 On the Theory of Free Stream-Lines , '5 'Phil .
Trans.,5 A , vol. 181 ( 1890 ) .
( 2 ) Love , " On the Theory of Discontinuous Fluid Motion in Two Dimensions,55 4 Camb .
Phil. Soc. Proc. , ' vol. 7 ( 1891 ) .
( 3 ) Hopkinson , 44 Discontinuous Motion involving Sources and Sinks , " 4 Lond. Math. Soc. Proc.,5 1898 .
( 4 ) Levi-Civita , T. , 44 Sulla resistenza dei mezzi fluidi , " 4 Recondiconti della R. Accademia dei Lincei , ' Ser. Y , vol. 10 , p. 7 ( 1910 ) .
( 5 ) Villat , H. , 44 Sir le mouvement discontinu d'un fluide dans un canal renfermant un obstacle,5 ' 'Comptes Rendus,5 vol. 152 ( 1911 ) .
( 6 ) Villat , H. , " Sir la resistance des fluides,55 4 Annals de l'Ecole Normale , ' III S6rie , vol. 28 ( 1911 ) .
( 7 ) Page , " Some Two-dimensional Problems in Electrostatics and Hydrodynamics , " 4 Lond. Math. Soc. Proc. , ' vol. 11 ( 1911 ) .
( 8 ) Cisotti , U. , 44 Su alcune recenti ricerche di idrodinamica,55 4 Estratto dagli Atti della Societa Italiana per il Progresso dell Scienze , V. Riunione , Genova , 1912.5 ( 9 ) Y. Karman and Riibach , 44 tiber den Mechanismus des Flussigkeits und Luftwiderstandes , " 4 Phys. Zeit.,5 vol. 13 ( 1912 ) .
{ 10 ) Bryan and Jones , " Discontinuous Fluid Motion past a Bent Plane,55 4 Roy .
Soc. Proc.,5 1915 .
( 11 ) Levy , H. , 44 On the Resistance to the Motion of a Body in a Fluid,5 ' 'Roy .
Soc. Edinburgh Proc.,5 1915 .
( 12 ) Leathern , J. G. , " Applications of Conformal Representation to Hydrodynamics , " 4 Phil. Trans.,5 A , 1915 .
|
rspa_1916_0015 | 0950-1207 | On the single-line spectra of magnesium and other metals and their ionising potentials. | 305 | 312 | 1,916 | 92 | Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character | J. C. McLennan, F. R. S. | article | 6.0.4 | http://dx.doi.org/10.1098/rspa.1916.0015 | en | rspa | 1,910 | 1,900 | 1,900 | 2 | 129 | 3,888 | http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1916_0015 | 10.1098/rspa.1916.0015 | null | null | null | Atomic Physics | 92.226557 | Fluid Dynamics | 4.118884 | Atomic Physics | [
5.9604811668396,
-49.90963363647461
] | 305 On the Single-Line Spectra of Magnesium and other Metals and their Ionising Potentials .
By J. C. McLennan , F.R.S. ( Received November 13 , 1915 .
) [ Plate 2 .
] 1 .
Introduction .
It has been shown by Frank and Hertz* that when heated mercury vapour is traversed by electrons possessing kinetic energy slightly above that acquired in a fall of potential of 4*9 volts the vapour is stimulated to the emission of the single spectral line A = 2536*72 A.U. It has also been shown by McLennan and Hendersonf that a spectrum consisting of this single line only can be obtained from mercury vapour when it is bombarded by electrons possessing energy corresponding to any fall of potential within a range beginning at about 5 volts and extending up to slightly over 10 volts .
The investigation has also been extended by McLennan and Henderson to include a study of the radiation emitted by zinc and cadmium vapours when traversed by electrons .
With these vapours they have found that single-line spectra can be obtained when the electrons traversing these vapours possess kinetic energy lying within a limited and clearly defined range , which has not been fully investigated as yet but which corresponds roughly to potential differences lying between 4 volts and 13*6 volts .
With zinc vapour the single-line spectrum consists of light of wave-length X = 3075*99 A.U. , and with cadmium vapour of light of wave-length X = 3260*17 A.U. It should be pointed out here that the lines X = 2536*72 A.U. , X = 3075*99 A.U. , and X = 3260 17 A.U. are respectively the first members of Paschen'sJ combination series v = 2 , p2\#151 ; m , S , for the elements mercury , zinc and cadmium .
2 .
The Single-Line Spectrum of Magnesium : Since the publication of the results described above , the radiation from magnesium vapour traversed by electrons has been investigated by the writer and it has been found with this element , too , that a single-line spectrum can be obtained if the electrons bombarding the vapour possess energy lying within a certain range , whose limits also have not as yet been definitely * 4 Verh .
d. Deutscli .
Phys. Ges .
, ' vol. 11 , p. 512 ( 1914 ) .
+ 4 Koy .
Soc. Proc. , ' A , vol. 91 , p. 485 ( 1915 ) .
I Paschen , 4 Ann. der Phys. , ' vol. 35 , p. 860 ( 1911 ) .
* 306 Prof. J. C. McLennan .
On the Single-Line Spectra of determined but which covers a portion at least of the ranges mentioned above for mercury , zinc , and cadmium .
In carrying out these experiments the apparatus used and the procedure followed was precisely the same as that described in the paper by McLennan and Henderson .
With magnesium the single-line spectrum consists of light of wave-length X = 2852*22 A.U. The ordinary spark spectrum of magnesium in air is shown in the upper row in Plate 2 , fig. 1 , and the single-line spectrum of the vapour of the metal in the second row of the same figure .
The latter was obtained with a three-hour exposure , and the electrons which stimulated the vapour to the emission of this radiation acquired their kinetic energy with an arcing potential of 8*2 volts applied between the Wehnelt cathode and the positive terminal .
3 .
The Absorption Spectra of Magnesium and other Metallic Vapours .
In a paper recently published by McLennan and Edwards* it has been shown that in the absorption spectrum of mercury there is an absorption band at X = 2536*72 A.U. and one at X = 1849*6 A.U. With this vapour it has been found that there is also a complex band obtainable at X = 2338 A.U. when high vapour densities are used .
With zinc and cadmium vapours it has been shown by the same writers that the absorption spectra consist of but two absorption bands .
With zinc vapour these are at X = 3075*99 A.U. and at X = 2139*3 A.U. , and with cadmium vapour they are at X = 3260*17 A.U. and at X = 2288*79 A.U. As pointed out above , the lines X = 2536*72 A.U. , X = 3075*99 A.U. and X = 3260*17 A.U. are the first members of Paschen 's combination series for the three elements represented by v = 2 , p2 \#151 ; S , and they are therefore the lines of this series corresponding to the value m == 1*5 .
Again , it will be seen by referring to Paschen'sf paper that the lines X = 1849*6 A.U. , X = 2139*13 A.U. and X = 2288*79 A.U. are the first members of the series v = 1*5 , S \#151 ; m , P , predicted by Paschen and later identified by WolffJ for the three elements mercury , zinc , and cadmium .
It does not appear from communications which have come to the notice of the writer that a series of lines corresponding to v = 1'5 , S\#151 ; m , P , has as yet been identified in the spectrum of magnesium , but if we assume that the line X = 2852*22 A.U. is the first line in the combination series w= 2 , p2\#151 ; m , S , for this element sufficient information is given in a paper by DunzS to cal * * * S * McLennan and Edwards , 'Proc .
Roy .
Soc. of Canada , ' 1915 ; 4 Phil. Mag. , ' November , 1915 .
t Paschen , loc. cit. f Wolff , 4Ann .
der Phys. , ' vol. 42 , p. 525 ( 1913 ) .
S Dunz , 6 Bearbeitung unserer Kenntnisse von den Serien , ' Inaug .
Diss .
, Tubingen , 1911 .
Magnesium and other Metals and their Ionising Potentials .
307 culate the first and the last member of the series v = 1*5 , S \#151 ; m , P , for this metal .
In the paper by Dunz referred to the frequency of = 2 , p % , in the magnesium spectrum is given as 39793-21 .
If we take the frequency of the line X = 2852'22 A.U. to be 35050-45 it follows that the frequency v = 1*5 , S , is equal to 74843b6 .
This will then be the frequency of the last line of the series spectrum of magnesium given by 1 '5 , S\#151 ; to , P. Again , in the paper by Dunz the frequency v = 2 , P , is given as 26612-7 and from this it follows that the frequency of the first line in the series v = 1-5 , S \#151 ; to , P , i.e. v= 1'5 , S\#151 ; 2 , P , is 48230-96 .
This it will be seen is the frequency of the line X = 2073-36 A.U. If then the vapour of magnesium behaves as regards absorption in a manner analogous to the vapours of mercury , zinc , and cadmium , the absorption spectrum of magnesium vapour should contain absorption bands at X = 2852'22 A.U. and at X = 2073-36 A.U. On looking up the literature on the subject it was found that Wood and Guthrie , * and Ederand Yalenta.f had already shown that there is an absorption band in this spectrum at X = 2852-22 A.U. , but as no one seemed.to have found any band at X = 2073-36 A.U. some experiments were made to see if it really existed .
The experiments confirmed its existence and a reproduction of one of the photographs taken is shown in fig. 2 .
The upper portion of this figure was taken with the light from the spark between magnesium terminals in air and the lower one with the same light after it had traversed an evacuated clear fused quartz tube containing heated non-luminous magnesium vapour .
As the reproduction shows , absorption occurred at X = 2852-22 A.U. and at X = 2073-36 A.U. as well .
In addition a narrow absorption band appears at X = 2536-72 A.U. This band also appeared in the experiments of McLennan and Edwards referred to above in the absorption spectrum of zinc and cadmium vapours , and it was no doubt due to a trace of mercury vapour which may have come from mercury originally present as an impurity in the metals or from mercury which got into the absorption tubes containing the vapour when these tubes were exhausted by the Gaede mercury pump .
'From this result it will be seen that the absorption spectrum of magnesium vapour is exactly analogous to the absorption spectrum of mercury , zinc , and cadmium .
The analogy , moreover , between the absorption spectrum of magnesium and that of mercury is more perfect than would appear from the above considerations , for the absorption band at X = 2536*72 A.U. in the absorption spectrum of mercury vapour comes out with small vapour densities as two narrow absorption bands whose wave-lengths have been given by * Wood and Guthrie , ' Astrophys .
Journ. , ' vol. 29 , No. 1 , p. 211 ( 1909 ) .
t Eder and Valenta , 'Atlas Typischer Spectren , ' Table XXVII .
VOL. XCII.\#151 ; A. 9 .
308 Prof. J. C. McLennan .
On the Single-Line Spectra of E. W. Wood* as X = 2536 A.U. , and X = 2539 A.U. The absorption band at X = 2852*22 A.U. in the absorption spectrum of magnesium vapour has also been found to consist of two narrow sharply defined bands very close together .
These are shown in the reproduction in fig. 3 , which was obtained by greatly enlarging the band shown in fig. 2 , at X = 2852*22 A.U. The bands at X = 3075*99 A.U. , and X = 3260*17 A.U. , in the absorption spectra of zinc and cadmium vapours have not as yet been resolved into analogous doublets .
* 4 .
The Ionising Potentials of Different Elements .
In the paper by McLennan and Henderson mentioned above attention was drawn to a paper by Frank and Hertzf which described experiments leading to the conclusion that the minimum energy required to ionise an atom of mercury was that acquired by an electron in passing through a fall of potential of 4*9 volts .
Attention was also drawn in this paper to a second communication by Frank and Hertz , J in which it was shown that in the quantum relation Ve = hv , where V = 6*6 x 10-27 erg sec. , 4*9 volts is the potential fall which corresponds to the frequency of the line X = 2536*72 A.U. From this it follows that for mercury atoms at least a knowledge of the wave-length of the single-line spectrum of this element is sufficient to enable one to calculate the ionising potential .
If the relation just pointed out be applicable generally to all the elements it follows that if the vapour of an element can be shown to be capable of exhibiting a single-line spectrum the frequency of this single spectral line may be used to deduce the minimum amount of energy required to ionise the atoms of that element .
From the considerations already presented in this paper it will be seen that the wavelengths of the single spectral lines in the single-line spectra of the elements have the frequencies given by v = 2 , p2 \#151 ; 1*5 , S , and as these frequencies are now known for mercury , zinc , cadmium , and magnesium , it follows that if Frank and Hertz have put the correct interpretation upon their experiments \#151 ; and it may be added here that their experiments have apparently been confirmed quite recently by NewmanS\#151 ; then the ionising potentials for the atoms of all these elements can be calculated by the relation Ve = hv .
The results of this calculation are given in Table I. In the paper by McLennan and Henderson it was pointed out that in order to obtain the single-line spectra with mercury , zinc and cadmium vapours , it was necessary that the electrons bombarding these vapours should not * E. W. Wood , 'Astrophys .
Journ. , ' vol. 26 , No. 1 , p. 41 .
* t Frank and Hertz , ' Verh .
d. Deutsch .
Phys. Ges .
, ' vol. 10 , pp. 457-467 .
X Frank and Hertz , ' Verh .
d. Deutsch .
Phys. Ges .
, ' vol. 11 , p. 512 .
S Newman , ' Phil. Mag. , ' vol. 28 , pp. 753-756 ( November , 1914 ) .
Magnesium and othev Metals and them Ionising Potentials .
30 9 Table I. Element .
Wave-length with frequency v = 2 , p*\#151 ; 1 *5 , S. Ionising potential calculated on bases of conclusions of Frank and Hertz .
A.U. volts .
Mercury 2536 72 4*9 Zinc 3075 -99 3-96 Cadmium 3260 -17 3*74 Magnesium 2852 -22 4*28 possess kinetic energy greater than that acquired in passing through falls of potential of 12-5 , 11-8 , and 15'3 volts respectively for the three vapours .
If the electrons possessed kinetic energy greater than that given by these voltages visible arcs were struck and the many-lined spectra were obtained for the three elements .
In the paper mentioned it was also stated that as these voltages gave with the relation Y approximately the wave-lengths of the limiting lines in the series v = 1*5 , S\#151 ; ra , P , for the three elements , the results might be interpreted as indicating possibly a second type of ionisation which the atoms of these elements might be capable of undergoing .
If this interpretation should turn out to be correct it would follow , since the frequencies of the limiting lines in the series v \#151 ; 1'5 , S\#151 ; m , P , are given by v= 1-5 , S , that the ionising potentials of the second type are given by Y = h(T5 , S)/ e. Applying this relation to the results already obtained and given above , the ionising potentials of the second type have been calculated for mercury , zinc , cadmium , and magnesium , and are given below in Table II .
Table II .
Element .
Wave-lengths corresponding to frequency v = 1 *5 , S. Ionising potentials calculated from V - h ( 15 , 8)/ e. A.U. volts .
Mercury 1188 *0 10 *27 Zinc 1320 *0 9*24 Cadmium 1378 *7 8*85 Magnesium 1336 -1 9*13 5 .
Ionising Potentials and Bohr 's Theory of the Origin of Radiation .
In the theory which has been brought forward by Bohr , * the atom of an element is supposed to consist of a positive Rutherford nucleus surrounded * Bohr , 'Phil .
Mag. , ' vol. 26 , pp. 1 , 476 , 857 ( 1913 ) ; vol. 27 , p. 506 ( 1914 ) ; and vol. 30 , p. 394 ( 1915 ) .
310 Prof. J. C. McLennan .
On the Single-Line Spectra of by one or more rings of electrons , revolving in stationary or non-radiating orbits about the nucleus .
In the neutral or most stable state the electrons are revolving in the orbits of smallest possible area .
The diagram in fig. 4 may be taken to illustrate this point .
A neutral atom may be supposed , for example , to consist of a positive nucleus E surrounded by two rings of revolving electrons A and B. If \D \ / _____ / / / , o"'"a \c \ !
/ 0 " Pb \ \ / ' / C* P ' ' 'Qa I \#187 ; \#166 ; $ \ ' , , H ^ f i* i !
\ ' ^ '-o-c !
\#163 ; ' \ \ 0 ,0 / / \ \ \amp ; / / V Fig. 4 .
\ through some agency such as an electronic bombardment , one or more of the electrons in the ring B be made to revolve in the orbit C , then , according to the theory of Bohr , these electrons would not radiate while revolving in the orbit 0 , but they would send out a radiation of a single determinate wave-length in passing back from the orbit C to the stable orbit B. Extending the theory still further , if the disturbing agency caused one or more of the electrons in the orbit B to revolve in the orbit D , then , as the electrons might drop back either directly to the orbit B or to the orbit C first and then to the orbit B , it would appear that an atom subjected to such a disturbance would be capable in returning to the neutral state of emitting a radiation consisting of two , and possibly three , definite and determinate wave-lengths .
It would then seem from Bohr 's theory that atoms of a vapour bombarded by electrons should be capable of emitting either a singleline spectrum , a two- or three-line spectrum , a three- or six-line spectrum , etc. , according to the violence of the shock to which it was subjected .
Again , according to the theory of Bohr , ionisation of an atom could only be said to have taken place when the disturbing agency caused one or more electrons to be projected out from the electronic system beyond the outermost stationary or non-radiating orbit of the atom .
This theory would Magnesium and other Metals and their Ionising Potentials .
311 therefore predicate but one type of ionisation for atoms .
By applying the theory to the matters discussed in the present communication , it would appear that atoms in the state to emit a single-line spectrum could not be said to be ionised .
It would follow , then , that if Bohr 's theory of the origin of radiation be correct , the interpretation placed by Frank and Hertz on the results of their direct investigation of the ionising potentials for mercury atoms cannot be the correct one .
On the other hand , in the experiments of Henderson and myself , in which the single-line spectra were obtained with mercury , zinc , cadmium , and magnesium vapours when they were bombarded by electrons , the fields in which these bombarding electrons acquired their energy covered a range of from about 5 volts to slightly over 10 volts .
It is probable that , under these conditions , the great majority of the bombarding electrons would acquire just sufficient energy to stimulate the atoms of the vapours traversed to the emission of a radiation of but a single wave-length .
The second absorption bands , however , in the absorption spectra of mercury , zinc , cadmium , and magnesium vapours , it will be recalled , come at A = 1849-6 A.U. , A = 2139-3 A.U. , A = 2288 79 A.U. , and A = 2073-36 l.TJ .
respectively , and it will be seen , therefore , that if the quantum relation Ye = hv be applicable , the potential falls corresponding to these wave-lengths are well within the range extending from 5 to 10 volts .
One would have expected , therefore , that with arcing potentials of 10 volts , one should have found traces , at least , of the lines X = 1849-6 A.U. , X = 2139*3 A.U. , X = 2288*79 A.U. , and X = 2073*36 A.U. , accompanying the lines X = 2536*72 A.U. , X = 3075-99 A.U. , X = 3260*17 A.U. , and X = 2852*22 A.U. , in the spectra emitted by the three vapours .
No indication of these lines , however , was found in any of the experiments of Henderson and myself , even with exposures of five hours ' duration , and with vapours covering a wide range of densities .
It should be remembered , however , that even if some of the atoms of the vapours traversed were stimulated to the emission of the shorter wave-lengths mentioned , the radiation of these wave-lengths might have been absorbed in passing through the outer layers of the vapour in the arcing tube .
The experiments of Henderson and myself cannot , therefore , be taken as being opposed to the correctness of Bohr 's theory .
If , however , this theory be correct , then it does follow that Frank and Hertz have incorrectly interpreted their results .
Moreover , if it should turn out that they , and also Newman , have placed the wrong interpretation on the results of their investigations , then the ionising potentials for mercury , zinc , cadmium , and magnesium would not be those given in Table I , but they would in all probability be those given in Table II , and we would therefore arrive at the conclusion that there is but one type of ionisation for atoms .
312 Single-Line Spectra of Magnesium and other Metals .
6 .
Summary of Results .
1 .
It has been shown that magnesium vapour traversed by electrons can be stimulated to the emission of a single-line spectrum consisting of the wavelength X = 2852*22 A.U. 2 .
It has been shown that the absorption spectrum of non-luminous magnesium vapour contains an absorption band at X = 2852*22 A.U. , and one at X = 2073*36 A.U. 3 .
As the lines X = 2852*22 A.U. , and X \#151 ; 2073*36 A.U. , are respectively the first members of the series v = 2S , and v = 1*5 , S \#151 ; m , P , respectively , the absorption spectrum of magnesium vapour has been shown to be analogous to the absorption spectra of the vapour of mercury , zinc , and cadmium .
4 .
The ionising potentials have been deduced for atoms of magnesium , in addition to those for the atoms of mercury , zinc , and cadmium .
5 .
Considerations have also been presented which show that if Bohr 's theory affords an explanation of the origin of single-line spectra , then Frank and Hertz and also Newman must have placed a wrong interpretation on the results of their direct investigation of the ionising potentials for mercury atoms .
In conclusion the writer wishes to acknowledge his indebtedness to his assistant , Mr. P. Blackman , for his help in connection with the photographic work of the present investigation .
McLennan .
Roy .
Soc. Proc. , A , 92 , Plate 2 .
Fro .
2 .
Fig. 3 .
|
rspa_1916_0016 | 0950-1207 | A portable variometer for magnetic surveying. | 313 | 321 | 1,916 | 92 | Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character | George W. Walker, A. R. C. Sc., M. A., F. R. S. | article | 6.0.4 | http://dx.doi.org/10.1098/rspa.1916.0016 | en | rspa | 1,910 | 1,900 | 1,900 | 5 | 96 | 2,518 | http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1916_0016 | 10.1098/rspa.1916.0016 | null | null | null | Tables | 27.803646 | Meteorology | 27.474046 | Tables | [
44.912986755371094,
-3.129467248916626
] | ]\gt ; A Portable Variometer veying .
GEORGE W. , A.R.C.Sc .
, M.A. , , formerly Fellow of Trin ity College , Cambridge .
( Received November 25 , 1915 .
) The method of measuring the horizontal component of the earth 's magnetic force in absolute units devised by C. F. Gauss ( ' Collected Works ' ) will probably always be regarded as one of the most important contributions to the science of terrestrial magnetism .
By its introduction magnetic forces were for the first time expressed in terms of the fundamental physical units .
The principles of Gauss ' method have continued in general use 1836 up to the present time ; but it seems likely that before long it will be superseded by simpler electrical methods .
Gauss ' method consists essentially of a vibration experiment and a deflection experiment .
The former requires a considerable amount of practice before good results can be obtained , and is always somewhat difficult to perform .
The whole operation required to give the magnetic force cannot be completed in much under an hour ; so that if the earth 's field is changing rapidly only an average value is obtained , and this is not simply related to the ordinary average value of the force during the time .
Moreover , a number of instrumental constants have to be obtained by special experiments before absolute measures can be assigned , and it is by no means certain that those constants can be used for any very extended period .
Unless the greatest care of the magnets is taken , the constants are liable to secular change .
If one requires an accuracy of 1 in 300 the matter is uot very serious ; but modern work in some cases requires , or at least claims , an accuracy to 1 ( gauss ) , and with the values of force as at Greenwich at present this means an accuracy of 1 in 18500 .
Such an accuracy involves a number of minute corrections to the simple fundamental theory and experiments , so that the whole method has become very cumbersome , and it is certain that absolute accuracy to 1 is not attainable by magnetometers of which the New unifilar pattern may be regarded as typical .
Even relative accuracy in , different experiments to this extent does not seem possible .
It is difficult to get detailed data from observatories as to this .
But my own experience is that even under favourable conditions the average error is not likely to be less than and for a single observation it may amount to 20 or even more .
.3 I 4 Mr. G. W. Walker .
If this is so for a fixed observatory , where special precautions can be taken , it seems clear that , in the field work of a survey , where the conditions are not controllable and vary from place to place , we should expect greater errors to arise .
Personally I should doubt if the relative average error in determinations by a Kew unifilar could be put at less than 15 , while a single observation ight be 30 or even 40 wrong .
It may be remarked that this still means an accuracy of 1 in 500 , and there are not many laboratory experiments as good as In a magnetic survey it is essential to get the differences in the values of the magnetic elements at different places so that when the absolute values have been obtained at one place ( base station ) for the epoch selected , the whole state of the surveyed is known .
Thus , as regards horizontal force , it would appear more scientific to eplace the method of taking absolute observations at each by a method which gives the differencs between two places in a simple way .
I was invited by the Royal Society in 1913 to undertake a magnetic re-survey of the British , and while it seemed desirable that the work should be done by the orthodox method hitherto in use , it was apparent that a good opportunity was available for testing a simpler meChod of measuring the horizontal force .
At a fixed place variations of magnetic force are determined as follows : A magnet is suspended by a vertical wire or fibre so that the axis of the magnet is horizontal , and the wire is twisted by means of a torsion-head until the ynetic axis of the magnet is nearly at right angles to the magnetic meridian at the time .
The position of the magnet so obtained gives a zero from which changes of force may be reckoned .
If the horizontal force changes , the magnet its direction in azimuth , and so we measure changes of force on a scale that can be evaluated by direct experiment .
Small changes of declination do not affect the results , nor need the setting be correct to more than .
What does the accuracy is instrumental change produced by change of temperature , of zero due to secular change in the moment of the magnet or of the torsion of the suspension .
Thus we require to know the temperature A Portable riometer for gnetic Sveying .
315 , coefficient , and from time to time the base value of the zero must be determined by an absolute observation .
In symbols the theory is as follows:\mdash ; Let ON be the magnetic meridian , and AB the axis of the magnet , an angle with ON .
Let angle of twist of the torsion head measuredclockwise from ON .
moment of the magnet .
horizontal component of earth 's magnetic force .
torsional constant .
In equilibrium Let the zero values be , and let change to .
Since does not change we get Thus if we Thus the variations of are proportional to the changes of H. We also see that if differs a little from S the result will not be appreciably affected unless is very small compared with .
Further , a small change in the direction of , i.e. a small change in declination , does not ) roduce an appreciable change in It was argued that such a variometer could be set up at one place , where the apparatus was adjusted in definite relation to the magnetic meridian there , and then traIlsferred to another place and set in the same relative position to the magnetic meridian at the second place ; then , if the setting of the torsion head has not been changed , the apparent change of would give the difference of magnetic force between the two places .
Moreover , small errors of relative setting amounting to a few minutes of arc would not measurably affect the result .
These views were put before Dr. Schuster , who encouraged me to them in practice , and a grant for the apparatus was made by the Government Grant Committee of the Royal Society .
The Kew unifilar Elliott 66 , which was used in the survey , suffices to give the maguetic meridian , and is provided with an azimuth circle reading to The new variometer was therefore designed to fit ' and geometrically on the Kew instrument so that the same relative positi ) Mr. G. W. Walker of variometer , unifilar and magnetic meridian was always obtained .
My past experience of variometers having indicated the small magnets with quartz suspensions , I arranged for the } system to be a cylindrical magnet 2 cm .
long and 1 mm. in diameter , suspended by a quartz fibre about 8 cm .
long .
A torsion-head provided for initial adjustment and was then screwed in position .
A screw arrangement was provided for clamping the suspended part while carrying the instrument from place to place , and was only released when the was to be made .
consultation with Mr. Horace Darwin I decided to use an autocollimation method to determine the changes of position of the suspended magnet .
The moving system carried an optically plane mirror with its surface vertical and at right angles to the magnet .
This mirror was viewed by a horizontal telescope which fitted geometrically in a rigid frame attached to the casing .
A right-angled prism was inserted so that one of the small faces crossed by a vertical quartz fibre lay in the focal plane of the object glass .
Thus an image of the fibre was returned from the plane mirror to the focal plane of the object glass .
A glass scale divided horizontally in 100 divisions was placed in the focal plane and then viewed by a Ramsden eyepiece .
Thus the position of the image of ) fibre on the scale was read .
A section of the apparatus is shown in Plate 3 .
The question of scale value and range had to be considered .
I expected that the region surveyed in 1915 would have a range rather less than , so that a scale value of to per division was aimed at .
Each small division being read to tenths , the smallest difference that could be estimated would b or A suitable quartz fibre was obtained by trial and proved to have a diameter of 65 .
The scale value and temperature coefficient were determined and a preliminary trial of the instrument was made at 15 stations in and Wales in April , 1915 .
When compared with the absolute observations the differences varied more than I had expected , and on my return to I found that small differences of level made very appreciable changes in the reading .
This could not be explained by any mechanical or optical defect and could only be accounted for by local spurious magnetisaGion close to the magnet .
This proved to be the case , and , on removing a small copper damping sheath which came very close to the magnet , a comparatively change of level could be made without altering the reading .
A new damping sheath was fitted , and although it was not entirely free from spurious magnetisation I verified such error of as one make from day to day did not produce a change of more than one-tenth division , and I accepted the result .
A Portable riometer .
for Magnetic Surveying .
The reorganised instrument was again standardised .
I had perforce to do this by means of collimator magnet 66 , using corrections for magnetic val.iations supplied from Greenwich .
The results cannot be very far wrong , but doubtless a standardisation by electrical methods with the aid of neighbouring variometers is what is really wanted .
If is the absolute value where the reading is and the temperature Centigrade , then the value of when the reading is and the temperature is iveu by , where per C. per scale division were the values obtained b.y the experiments made ab Cambridge .
The instrument was tried at six more points in Licestershire in June .
The agreement with the absolute observations was better than before , but the results suggested a secular change of zero .
I was not able to resume the survey work until August , when I proceeded to Ireland .
The instrument had rested during the interval and had not been readjusted .
It has lJow been successfully carried all over Ireland and back to Cambridge without injury .
Comparative observations with it and the Kew unifilar are now available at 48 different points in Ireland and from August to October .
Before discussing the results I may describe the method of using the apparatus in the field .
The unifilar is set up and the circle reading of the magnetic meridian obtained in the usual way .
The variometer then mounted on the base of the unifilar and the circle turned to from the netic meridian .
The level is carefully adjusted and then the clamping screw is released .
In about two minutes the needle is practically steady , and the reading of tlre scale and of the temperature may be made and the time noted .
I find the interval between making the declination readings , mounting the variometer and getting its reading is usually rather less than 10 minutes .
Further the reading is at a definite instant of time .
In my work I then proceeded to determine in the ordinary way by the unifilar .
The interval between these two determinations being considerable , may have changed .
I have had to assume that the variation supplied by Greenwich is applicable ovel the region surveyed .
Of course this is not correct , but no other course is open at present , and one can only hope that it gives the most substantial part of the variation .
I found it convenient to take scale reading 50 and temperature C. as my base , and a Table readily supplies the value in magnetic units of 1 of A Portable for gnetic Surveying .
The greatest difference that occurs in the series is 52 at Killarney , and I little hesitation in ascribing this largely to the unifilar .
The temconditions were the worst I experienced in the whole of my survey .
At Killarney the temperature changed C. during the vibration experiviz .
, C. , while the temperature during the deflection experiwas C. The variometer is specially arranged with non-conducting material , to rapid changes of temperature .
I consider that the investigation supports the view that the portable will normally give the force within 5 ut the error may rise to 13 , while the unifilar in the field will normally give the force within , but the error may rise to about 40 There can be no question of the enormous simplification of the field work such a portable variometer produces , and the principle should be valuable for detailed survey of small local disturbances .
Clearly , single observations by the unifilar are not good for the base val and secular change of zero of the variometer ; what is really wanted is access at suitable intervals during a rvey to operly equipped observatory where magnetic values at any time can be with an accuracy of 1 or 2 I find that high winds are rather apt to keep the needle oscillating , but , if the tripod stand is very firmly bedded in stiff soil , this trouble is very serious .
Another point may be noted .
By the use of a small source held near the reflecting prism , readings can be obtained at night as as during the day .
The apparatus was made by the Scientific Instrument by aid of a financial grant from the Government Grant Comof the Royal Society .
VOL. xcn.\mdash ; A.
|
rspa_1916_0017 | 0950-1207 | On the structure of broadened spectrum lines. | 322 | 328 | 1,916 | 92 | Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character | Thomas R. Merton, B. Sc. (Oxon.)|A. Fowler, F. R. S. | article | 6.0.4 | http://dx.doi.org/10.1098/rspa.1916.0017 | en | rspa | 1,910 | 1,900 | 1,900 | 4 | 116 | 3,437 | http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1916_0017 | 10.1098/rspa.1916.0017 | null | null | null | Atomic Physics | 59.696402 | Fluid Dynamics | 10.763874 | Atomic Physics | [
15.36764907836914,
-51.448055267333984
] | On the Structure of Broadened Spectrum Lines .
Thomas E. Merton , B.Sc. ( Oxon .
) , Lecturer in Spectroscopy , University of London , King 's College .
( Communicated by A. Fowler , F.E.S. Eeceived December 7 , 1915 .
) [ Plate 4 .
] In a recent paper , Lord Eayleigh* has discussed the causes which determine the widths of spectrum lines , and which he summarises as follows:\#151 ; ( i ) The translatory motion of the radiating particles in the line of sight , operating in accordance with Doppler 's principle .
( ii ) A possible effect of the rotation of the particles .
( iii ) Disturbance depending on collision with other particles either of the same or of another kind .
( iv ) Gradual dying down of the luminous vibrations as energy is radiated away .
( v ) Complications arising from the multiplicity of sources in the line of sight .
Of these ( ii ) does not in fact occur , and ( v ) , which is not an independent cause of broadening but merely aggravates other causes , need not be considered in the present communication .
It is shown that in vacuum tubes at low pressures , excited by uncondensed discharges , ( i ) is the important effect , and in fact completely accounts for the widths of the lines .
Under these conditions , the limiting order at which interference can be seen is given by the equation N = K^M/ T ) , where N is the limiting order of interference , M the mass of the luminous particle in terms of the mass of the hydrogen atom , T the absolute temperature , and K a constant , the exact value of which depends on an estimate of the smallest value of the " visibility " for which interference fringes can be recognised , the visibility V being defined by the equation Y = ( h \#151 ; U ) / ( I1 + I2 ) , where Ii is the intensity of light at the maxima and I2 at the minima .
Thus Lord Eayleigh gives K = 1*427 x 106 , this value being based on experiments made with fringes , produced by means of double refraction , which could be perfectly controlled .
Buisson and Fabry f adopt the value K = 1*22 x 106 , based on a higher estimate for the limiting value of Y. The equation N = TLffM/ T ) has been experimentally verified by Buisson and Fa]jry ( loc. cit. ) for vacuum tubes at low pressures when excited by * 4 Phil. Mag.,5 vol. 29 , p. 274 ( 1915 ) .
t e Journ. de Physique , ' vol. 2 , p. 442 ( 1912 ) .
On the Structure of Broadened Spectrum Lines .
323 uncondensed discharges , and they have also shown that the temperature of the luminous gas is that of the tube or not much higher , as originally assumed by Michelson .
The widening of spectrum lines which occurs at higher pressures cannot be said to rest on a secure theoretical basis .
It has been assumed that this widening is due to collisions of the luminous particle with other atoms , on the supposition that the length of the wave train is limited by the interval between the collisions , though , as Lord Kayleigh points out , this treatment is far from complete , since it assumes that an entirely fresh start is made at each collision and " there must surely be encounters of a milder kind where the free vibrations are influenced , but yet not in such a degree that the vibrations after the encounter have no relations to the previous ones .
" An important case of broadening is that which occurs when condensed discharges are used .
Widening of this type is very marked in the Balmer series of hydrogen , and to a somewhat smaller extent in the ordinary helium spectrum , and is especially prominent in the case of lines of the " spark " type , such as the " 4686 " line of helium .
The magnitude of the widening in vacuum tubes depends to a great extent upon the pressure of the gas in the tube and is not conspicuous at very low pressures .
It is well known , however , that in hydrogen tubes at high pressures , excited by heavy condensed discharges , the lines widen until they become scarcely recognisable .
I have investigated the effect of condensed discharges on helium and hydrogen at pressures of about a millimetre by means of a Fabry and Perot interferometer .
The apj\gt ; aratus and method have been described in a previous paper.* The numerical results of this investigation are not considered to be of quantitative interest , for reasons to be given later , but the main results which are in agreement with those of other investigators , may be stated .
( i ) Whilst with uncondensed discharges the limiting order of interference N is constant for different lines belonging to the same element , this is no longer the case when condensed discharges are employed .
( ii ) For a given series the value of 1ST becomes less as the series number of the line increases , that is to say the more refrangible lines undergo the greatest broadening . .
( iii ) Different series are affected to a different degree .
( iv ) The magnitude of the broadening decreases as the pressure decreases .
We may draw certain conclusions as to the possible origin of the broadening .
In the first place , it is evidently not due to a rise of temperature at each impulse of the condensed discharge .
From the equation ^ = KX/ ( M/ T ) , we see that a rise of temperature would lower the value * ' Boy .
Soc. Proc. , ' A , vol. 91 , p. 421 ( 1915 ) .
324 Mr. T. E. Merton .
of N , but that the value of N should remain constant for all the lines , which in fact does not occur .
Bohr* has suggested that the breadth of the spark line of helium at \ = 4686 A.U. may be due to the charge carried by the luminous particles , in virtue of which they must be expected to acquire high velocities in the electric field of the discharge tube .
Such an effect must be expected to occur in all cases in which the luminous particles are electrically charged .
With vacuum tubes excited by uncondensed discharges , it certainly does not occur , or is negligibly small , since Buisson and Fabry ( cit. ) have shown that the temperature of the luminous gas calculated from the limiting order of interference gives a value little different from that of the walls of the tube , and the effect suggested by Bohr would simply be equivalent to an increase in the value of T in the equation .
In any case the effect should consist of a uniform lowering of the value of N throughout the spectrum , which is not in accordance with observation .
Thus , while some broadening of the lines is to be expected if the luminous particles carry an electric charge , it does not appear to be important or to offer in any way a satisfactory explanation of the experimental results .
One may , indeed , question whether , under the conditions ordinarily obtaining in vacuum tubes , any considerable proportion of the luminous particles do carry an electric charge .
It is difficult otherwise to explain the failure of numerous investigators to detect any Doppler effect in an end-on vacuum tube when the direction of the current is reversed .
It would thus appear doubtful whether the broadening-produced by condensed discharges can be due to the movement of the luminous particle as a whole , but rather that it must be referred to processes more intimately connected with the problem of radiation .
Sfarkf has suggested that the broadening is intimately connected with the electrical resolution of spectrum lines , being in fact due to the influence of the electrical field of neighbouring particles on the luminous atom .
Stark points out that the electrical resolution of lines of a series increases with the term-number , and that the broadening increases in a similar manner ; also that lines in the spectra of helium and lithium , which show an asymmetrical broadening , are also asymmetrically resolved by the electric field .
Though little is known of the potential gradients which occur when a vacuum tube is excited by condensed discharges , it seems improbable that the potential fall in the capillary of the tube would be great enough to give rise to any considerable broadening .
I have made the following experiment , which would appear to show that * * 4 Phil. Mag. , ' vol. 30 , p. 401 ( 1915 ) .
t ' Elektrische Spektralanalyse Chemischer Atom , ' 1914 .
i On the Structure of Broadened Spectrum Lines .
325 no appreciable broadening is due to the field of the tube .
It is evident that with a condensed discharge the separation of the outer components D , due to the electric field of the discharge tube , will oscillate between D = 0 and D =/ ( V ) , where V is the maximum value to which the potential gradient rises , the result being a broadening of the lines .
Now Stark has shown that the hydrogen line Ha examined in a direction perpendicular to the electric field is resolved into three components , the outer components being polarised at right angles to the centre component , which is coincident in wave-length with the unresolved line .
If , therefore , the outer components are cut out by means of a Nicol prism , the line should appear to become narrower .
A vacuum tube containing hydrogen was excited by an uncondensed discharge , and the line Ha was examined with a Fabry and Perot interferometer , the plates of which were set at a distance such that the fringes were distinctly visible .
On exciting the tube with a feebly condensed discharge all trace of interference vanished .
By reducing the distance between the plates the fringes could be made visible again .
A Nicol prism was interposed and slowly rotated whilst the observations were being made , but under no conditions could any change in the width of the line be detected .
It would , therefore , appear that the effect due to the field of the discharge tube is negligible , but rather that the broadening is due to the electric field of neighbouring particles , as assumed by Stark .
In accordance with this is the fact that the mean distance between the particles will be diminished by an increase of pressure , also an increase in the number of charged particles will result from the considerable current density which obtains when condensed discharges are employed , both these circumstances giving rise to a broadening of the spectrum lines .
We may now consider the distribution of intensity to be expected , on the above view , when the hydrogen lines are broadened .
It is evident that the effects due to electric fields perpendicular to and along the line of sight will be superposed .
In the former case ( the transverse effect ) , there are components polarised parallel to the field ( p components ) and other components polarised perpendicular to the field ( s components ) .
In the latter case ( the longitudinal effect ) , the components are unpolarised and agree in position and relative intensity with the s components of the transverse effect .
Fig. 1 shows the electrical resolution of the three lines Ha , Hp , and Hy , the relative intensities being denoted by the diameters of the circles .
It may probably be assumed without serious error that the total intensity of light emitted in the longitudinal effect is equal to twice the total intensity of the s components of the transverse effect .
To obtain the resultant of all the superposed effects , it is therefore necessary to combine Mr. T. II .
Merton .
the jo and scomponents of the transverse effect , increasing the intensities of the s components threefold to provide for the longitudinal effect .
Now if the mean value of the electric field is Y , there will he a maximum in the H a H / . .
\#187 ; \#151 ; --- ?
f ?
\#187 ; \#151 ; *\#151 ; \#187 ; -\#166 ; . .
.\#151 ; . .
.----- Fig. 1 .
P s p s p s intensity distribution curve corresponding to the electrical resolution of each component by an electric field V , these points being the maxima of curves relating the displacements corresponding to a certain electric field to the number of particles subject to a field of that magnitude .
The undisplaced central components of Ha and Hy will remain as narrow lines , whilst the displaced components will be spread out , the lines thus having a strong central core with nebulous wings depending on the mean intensity of the field , the winged effect being much more pronounced in Hy than Ha , since the electrical resolution of the latter is much smaller .
The case of Hp is different .
The central undisplaced component of this line is feeble in comparison with the displaced components , and there should , in consequence , be a minimum of intensity in the centre of the broadened line .
An attempt has been made to study the distribution of light in the three lines considered , whereby these views may be put to an experimental test .
It is at once evident that observations with the interferometer are of no value for this purpose .
The interpretation of the limiting difference of path at which interference phenomena can be seen depends on a previous knowledge of the intensity distribution , and the use of the interferometer is therefore restricted to cases in which the intensity distribution can be predicted .
The structure of spectrum lines photographed under a high dispersion has recently been investigated by King and Koch , * whose method consists in a measurement of the degree of blackening of the photographic plate at different points on\#187 ; the broadened line , this being accomplished by means of an * 'Astrophys .
Journ. , ' vol. 41 , p. 214 ( 1914 ) .
I On the Structure of Broadened Spectrum Lines .
327 ingenious automatic device for recording continuously the density of the plate at different wave-lengths .
Methods of this type have yielded valuable information of the asymmetry of lines under different conditions , but they would appear to be vitiated by the eccentricities of the photographic plate , the most important of which is that the degree of blackening is not proportional to the intensity of the light .
It is thus difficult to attach any quantitative meaning to the curves obtained in this way .
In the present investigation a method has been adopted , by means of which it is believed that an accurate quantitative measurement of the intensity distribution in spectrum lines can be made , and the qualitative structure of broadened lines can at once be seen .
The method consists of an application of the neutral-tinted wedge method which is used for recording the sensibility curves of photographic plates .
A neutral-tinted wedge of density graded from 0#2 to 4*2 was mounted vertically on the slit of a spectrograph and the slit was illuminated with light from the source to be studied , care being taken , before the wedge was put into position , that the required length of the slit was evenly illuminated .
Under these conditions the spectrum appears to consist of lines , bright at the points corresponding to the thin end of the wedge , and gradually fading off with increased density .
It is evident that , from the apparent lengths of two lines , their relative intensities can be calculated , provided that they are so close together that errors due to the variation of the sensibility of the plate to different wave-lengths do not arise .
A broadened line gives a wedgeshaped image on the plate , the apex corresponding to the maximum of intensity in the line , and , from the shape of these wedges , the intensity at different distances from the maximum can be calculated .
It will be seen that the method consists in picking out points of equal density at different wave-lengths and determining the thicknesses of the wedge to which they correspond .
Points of equal density must indicate equal illumination , since they are exposed for the same time and subjected to the same treatment .
The method is thus unaffected by the eccentricities of the photographic plate , and it is only necessary to assume that there is one particular density that can be recognised at different points .
For the investigation of the hydrogen lines , which were produced by the passage of condensed sparks through hydrogen at atmospheric pressure , the dispersion of a single-prism spectrograph was sufficient , and the neutral wedge was mounted in front of the slit as described above .
A number of plates were taken , and the results were also confirmed by visual observations .
In Plate 4 is shown an enlargement of a photograph obtained in this way .
It is doubtful whether the detailed structure can be seen , but , in On the Structure of Broadened Spectrum Lines .
all the original negatives , certain outstanding features were evident .
Ha consisted of strong maximum , falling off rather rapidly , and apparently regularly.* In Hp the intensity falls off* much less rapidly , and there is a distinct minimum at the centre of the line , which appears to be a hazy doublet .
H7 has a bright central line with very wide nebulous wings .
This appearance of Hy has been previously noted by Rossi , f and Prof. Fowler has informed me that the appearance of Hp .
with a minimum at the centre , is familiar to him .
The essential point would appear to be the different behaviour of the three lines produced under identical conditions .
It may be regarded as extremely improbable that the minimum in is due to reversal , for in this case one would expect , a priori , that the effect would be more strongly marked in either or Hr The observed effects appear to be in close agreement ( at least qualitatively ) with the intensity distribution deduced from Stark 's observations of the electrical resolution of the lines , and the results would appear to support strongly Stark 's view that the broadening of spectrum lines at high pressures and under conditions of powerful excitation is due to the resolution of the lines by the electric field of neighbouring atoms .
In this paper the exact shape of the curves obtained has not been discussed .
Quantitative measurements , with improved experimental arrangements , are now in progress , and it is hoped that material will be obtained for a theoretical investigation of the distribution curves , but , in view of the time which these investigations will occupy owing to pressure of other work , it was thought that the results given above might be of sufficient interest for separate publication .
* It will be observed that the image of Ha shows some solarisation .
This is easily distinguished from true doubling or reversal by the fact that it is most conspicuous at the base of the wedge and does not extend to the apex , whereas true doubling or reversal appears at the apex and becomes less conspicuous towards the base , t ' Astrophys .
Journ./ vol. 41 , p. 232 ( 1914 ) .
r Merton .
Roy .
Soc. Proc. A , PI .
|
rspa_1916_0018 | 0950-1207 | A diagram to facilitate the study of external ballistics. | 329 | 337 | 1,916 | 92 | Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character | W. E. Dalby, F. R. S. | article | 6.0.4 | http://dx.doi.org/10.1098/rspa.1916.0018 | en | rspa | 1,910 | 1,900 | 1,900 | 1 | 30 | 572 | http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1916_0018 | 10.1098/rspa.1916.0018 | null | null | null | Tables | 47.640217 | Fluid Dynamics | 28.929144 | Tables | [
43.41545104980469,
-23.25666618347168
] | ]\gt ; -VELOCITY CURVE however , represents the area of a curve whose ordinates are .
This curve is plotted below the velocity axis in fig. 1 and is marked 2 .
Points on it are quickly found by the aid of the slide-rule .
The magnitude of corresponding toa particular velocity is scaled off Curve 1 and the quotient is calculated , and arbitrarily any convenient soale , this quotient is plotted vertieaUy downwards against the velocity .
The black area markedA represents thevalua of the between the ] and .
Seleoting The distance represented by the area depends upon the time scale and the velocity scale which have already been chosen .
Thus 1 inch represents feet second ; 1 inoh represents 2 second\amp ; Therefore 1 square inch tk area represents feet .
Distance is set out to the arbitrarily \amp ; n soale lin\amp ; feet .
ider now the change of direotion in the trajectory caused by the action of gravity .
..bt Os fig. be the velocity of the projeotile at a point in the Before this can be integrated must be known as a function of the time .
But as a function of the time is given by curve No. 3 .
Therefore take a series of values of the time and plot the auxiliary curve .
No. 5 by measuring off the velocity corresponding to a given time , and then by means of a slide-rule calculating the value .
Then integrate curve No. 5 with respect to the time .
Thus the area represents the direction in the time OT .
This area plotted to any convenient scale gives the point and other points found in the same way determine the curve No. 6 .
The change of direction represented by the area depends upon the time scale and the scale on which the values of are plotted .
In the figure the original scales were : 1 inch horizontally units , 1 inch downwards represents 2 .
Therefore 1 square inch of the area represents on the original drawing a change of direction of radian or degrees .
And the scale on which change of direction is plotted is approximately 1 inch degrees or radian .
The change of direction is integrated in relation to the diagram time .
The change of direction given by the ordinates to Curve 6 measured horizontally from the time axis is , therefore , the diagram change .
The actual change of direction is found by multiplying this diagram change by the ballistic coefficient of the projectile .
Curve No. 7 shows the linear kinetic nergy in foot-tons stored in the projectile per pound weight of the projectile .
The striking energy corre- sponding to any terminal velocity can be obtained from this curve .
The actual striking energy in foot-tons is the energy found from the curve multiplied by the weight of the projectile in pounds .
The group of curves shown fig. 4 constitute the ballistic diagram .
Let be any given muzzle velocity , and let be the final velocity .
Through V and draw vertical lines to cut the time-velocity ourve No. 3 , and these points draw horizontal lines to cut the time-distance curve in X and ; finally draw vertical lines through X and to cut the distance axis in and .
Then is the distance travelled by the
|
rspa_1916_0019 | 0950-1207 | Surface friction: Experiments with steam and water in pipes. | 337 | 353 | 1,916 | 92 | Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character | Cecil H. Lander, M. Sc., A. M. I. C. E.|Prof. J. E. Petavel, F. R. S. | experiment | 6.0.4 | http://dx.doi.org/10.1098/rspa.1916.0019 | en | rspa | 1,910 | 1,900 | 1,900 | 5 | 151 | 4,518 | http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1916_0019 | 10.1098/rspa.1916.0019 | null | null | null | Tables | 31.246889 | Thermodynamics | 30.797886 | Tables | [
41.89922332763672,
-30.424095153808594
] | ]\gt ; Surface Friction .
337 It will be understood from this problem that many similar problems in . .
unnery can be solved by the aid of this diagram with an accuracy probably pear enough for most practical purposes .
An accurately drawn ballistic diagram accompanies this paper and is nproduced in the folded plate , reduced to slightly less than half size .
It may be used in the way exemplified by for the solution of problems of gunnery relating to fire .
The scales to which the of $bis is drawn Velocity , 1 inch feet per second .
Distance , 1 inch feet .
Time , 1 inch second .
Energy , 1 inch foot-tons .
Auxiliary curves:\mdash ; , 1 inch unit .
, 1 inch unit .
Surface iction : Experiments with and Water in Pipes .
By CECIL H. , M.Sc .
, A.M.I.C.E. ( Communicated by Prof. J. E. Petavel , F.R.S. Received December 3 , 1915 .
) During the past hundred years much work , both theoretical and experimental , has been carried out with a view to determiuing the character of the laws the resistance to tangential motion between solid surfaces and liquids or gases .
A general relation between the dimensions of the surface , the velocity , the density of the flllid , and its viscosity had [ been surmised as a consequence of the laws of motion by Stokes , and Osborne Reynolds , but it was left to Lord Rayleigh* to show , from the principle of dynamical similarity , that the phenomena involved could be expressed definitely by a simple mathematical formula .
The laws governin the friction between solid surfaces and water have formed the subject of experimental ations by Froude , Osborne I Reynolds , Darcy , etc. , whilst the parallel case of the resistance to motion between solid surfaces and perfect gases has occupied the attention of Zahm , Brix , Stockalper , and others .
Practically all these investigators ( devoted their energies to experimental determinations of the friction in the mediunl which they employed , and it was not until the subject was taken * Phil. Mag p. 321 ( 1899 ) .
'Advisory Committee for Aeronautics Report , ' 1909-10 , p. 38 .
VOL. XCII .
338 Mr. C. H. Lander .
Surface : by Stanton and Pannell* that any attempt was made to investigate , under certain conditions , of the motion of fluids which widely mollgst the1nselves in their properties of densities and The same ators also took up the question of the limits of of the formulae currently accepted at the time and used in calculations of surface friction .
Experimental upon the filiction between steam and metal or other has been out arry and Carpenter , former on long pipes in the Lambrecht Mine at Anzin , the latter in the laboratories of the Sibley College .
Barry 's results have been reduced to an approximate formula by Ledoux .
These investigations extended only over a relatively small range of vclocity , and the accuracy of the results obtained was insufficient to establish any systematic departure from the velocity squared law ; the investigators therefore contented themselves with finding values of the constant suitable use at the particular mean velocity of their experiments , assulning that object of the present research was in the first place to obtain accurate for the resistance to flow in pipes conveying steam and other vapours with a to checking the accuracy with which Osborne Reynolds ' dimensional law of flow could be made to represent the friction of these fluids .
The work was afterwards extended to ranges over which this law did not accurately apply , and the results have been used to extend the work of Stanton and to the important case of friction between steam and metal surfaces .
Bxpressions for The expression cferred to above as given ) Lord Bayleigb and connecting the linear dimensions of the ) with the , the velocity and the 1-inematical viscosity of the fluid may ) written , where is a function of the one variable , resistance per unit area , densit of fluid , velocity , diameter of the pipe , kinematical viscosity of the fluid .
Trans , vol. 214 , p. 199 ( 1914 ) .
des Mines , ' Ser. 2 , 1892 .
Ledoux on " " Loss of Pressure in Pipes Proc. Inst. Mech. Eng. of ' 1893 .
Experiments with Steam and Water in Pipes .
Previous to the establishment of the above expression Reynolds had ihown from the theory of dimensions that , assuming the frictional resistance flow to vary as the power of the mean velocity , the relation between Ae resistance , the viscosity , the density , and the velocity would be erxpressed by assumption made by Reynolds is equivalent to taking the function of in Rayleigh 's formula to be the power or that In the reduction of his experimental work on the flow of water in pipes Reynolds* found that over the range of velocities used the expression held with considerable accuracy in any one pipe , but that varied in some manner with the roughness of the surface , and also increased with the pipe diameter .
Above the critical velocity varied from for a smooth pipe inch diameter up to for Darcy 's rough pipes of 20 inches diameter .
Stanton and Pannell found that a considerable deviation from the simple exponential law became apparent when the velocity in the pipe varied to 3000 cm .
per second , but that for small ranges Reynolds ' formula fitted in with the experimental results to a fair of Limits of Present Experimental In the research the moving fluid was in most cases either dry saturated or slightly wet steam , and the experimental range extended habitually to 4000 cm .
per second , although in a few experiments a velocity of 6000 cm .
per second was obtained .
It was found undesirable to extend the work to speeds above this , since extremely speeds , such as can be obtained easily with steam , are associated with superheating down the pipe , making the reduction of the results obtained too complicated and unreliable .
The maximum value of , however , amounts to about C.G.S. units , since by at a pressure the value of the kinematical viscosity may be considerably rednced below that of air at atmospheric pressure and a increase in effected .
the low values of corresponding to the experimental pipes used , water was adopted as the moving fluid , and thus the curve extended backVards to values of this function corresponding to the point where the Oharacter of the curve changes , and below which the resistance varies directly as the velocity .
In all pipes values of the resistance corresponding to low velocities of 'Phil .
Traus 1883 , p. 935 .
.340 steam decreases , until eventually relial ) results become impossible to the serious eflects of condensation .
Condensation is also of importance when the experimental pipe is long since the effect of heat loss causes the steam to become wetter as it down the pipe , the specific volume and the density are altered , and the velocity is slightly from point to point .
The difficulty , however , measurmg the extremely small pressure differences which obtain in lengths of caused the author to adopt pipes varying in length from about 30 to 80 feet , and correcting for the effects of condensation and change in velocity in the manner hereafter described .
For the final plotting of the results , the experimental values were reduced to those obtaining over the first unit length of the pipe , thus making a comparison possible with other investigators ' results for air and water .
nental Apparatus .
apparatus consisted of three mild steel steam pipes of commercial quality , the joints made by screwed overlapping the ends of the two pipes , which were butted one against the other , leaving a uniform bore across the joint .
Each pipe was connected by means of a short leadingin with a large separator supplied with steam by a 300-H.P .
Babcock and Willcox boiler .
The large capacity of the boiler rendered it easy to maintain steady pressure conditions the trials , which frequently occupied upwards of one hour .
The measurements of pressure drop were made at points in the tube a definite distance apart .
At these points , A and ( fig. 1 ) , a number of small holes were drilled round the pipe , the inside being carefully smoothed down .
It follows from the work of Bramwell and on Pitot tubes , that by this method the static pressure at any point may be accurately determined .
The difference in pressure the two ends of the measured length was obtained for the bulk of the experiments by a -tube containing lmercury , ( fig. 1 ) , the two legs of the being connected by couplings Fi and and tubes and I to the of holes at the two " " take-off\ldquo ; points A and B. For the smaller pressure differences the -tube gauge was inverted ( fig. 2 ) , water being used to measure the difference in head , an 'Advisory Committee for Aeronautios , ' 1912-13 , p. 33 .
BramwelI and Fage on .
A DeteIsnination on the Whirling Table of the Pressure Velocity Constant for a Pitot ( Velocity Head and Static Press ) Tube ; and on the Absolute Measurements of Velocity in Aeronautical Work bke-off castings and and the pressure tubes and I. The level of the water in these chambers could be read on the gauge glasses and M. A scale for the -tube was marked off , being calculated in pounds per square inch , corresponding to mercury }ater , and scales for the glasses in pounds , to the water heads , the two latter bein reduced to the same zero by careful levelling .
will be seen , then , that the pressure difference at the two ends of the experimental pipe was equal to the reading in pounds of the mercury added to the difference in pounds between the two readings of the water glasses .
Both collectors were carefully lagged to reduce the condensation to a minimum .
The amount of water densed was collected from the gauges by the cocks , and measured by weighing in a known quantity of water .
In the upper of the two collectors the condensed water was due entirely to the heat loss from the tor itself , and may be taken as a measure of the steam flow the pressure holes , C. The amomlt was small , and such that the dynamic head corresponding to its velocity did not in any case exceed per cent. of the least pressure differenc observed .
The pressure , as measured , could therefore be considered static .
In the lower of the two collectors the water collected was due both to a proportion of the water condensed in the experimental main and to that condensed in the collector .
It is clear that the former will make no difference to the measurements of the static pressure , and the latter will only affect the readings to the same extent as that in the high-pressure collector .
The total amount of water collected in the low-pressure collector was added to that discharged in the hot well , since all results have been reduced to the initial velocity in the pipe , and this water in the of steam has already passed the high-pressure take-off point .
It is obvious that proper precautions must be taken to ensure that water and mercury arc continuous in the pressure-measnring devices , and not intercepted by spaces .
After passing the second of the two take-off points , the steam was led into a separator , and thence passed through a plug valve to the condenser .
The plug valve was arranged to act as a throttling calorimeter , a pressure and a thermometer pocket being inserted in the pipe on the low-pressure side .
Condensed water was pumped out of the condellser by an air pump , and collected in a calibrated tank .
The separator was fitted with a gauge glass and a scale calibrated to read in pounds collected in the separator .
The whole of the piping was well clothed with slag wool wrapped with canvas , the thickness of the covering averaging inches throughoub . .
number of experiments were also carried out on the bare pipe .
Mr. C. H. Lander .
Surface Friction : The condition of thoe inlet steam was adjusted by means of a throttle valve on the inlet pipe , situated at a distance of about 6 feet from the high-pressure measuring point , the method being to obtain a few rees of superheat at a thermometer pocket and Bourdon feet from the high-pressure measuring point .
Dry steam at the entry of the experimental length was thus ensured .
Any instability of flow due to the thermometer would die down in the 20 or more diameters before it reached the take-off holes , and in any case its effects would be negligible in view of the long experimental pipes used .
Finally Bourdon pressure were connected directly to the takeoff muffs in order to obtain readings at high velocities .
Results .
The observations taken con.sisted of the initial temperature and pressure of the steam , the pressure difference between the take-off points , the dryness on the second separator and the weight of steam that condensed in the lower of the two take-off muff chambers ( see Columns 1 , 3 , 7 , and 8 of Table ) .
Tests were also made on the heat loss from the main by allowing an extremely small flow through the pipe , collecting at the same time the condensed water .
The method of inferring the velocity from the volume passing and the diameter of conduit necessitates a very accurate determination of the latter since the value of depends on the fifth power of the diameter .
For this purpose a measured length of the pipe was filled with water , emptied and the quantity accurately weighed , the diameter being inferred from the volume .
The mean result obtained from six determinations was taken as the correct value .
This method appeared to the author to be the most suitable one , since by leaving a wet surface ou the interior of the pipe it approximated more accurately to the actual diameter and state of the surface wheu steam was flowing .
Condensation continually takes place and a onary film of water is of necessity adhering to the fhness of the interior surface .
of Experimental Values .
In order to detelmine the form of the law governing the frictional losses in any one pipe at ven initial steam pressure Reynolds ' form of 's law was adopted , since the range of velocity was small and well within the limits of accuracy of the exponential law .
then that .
let weight of steam condensed per second per linear foot of pipe , this being the intrinsic amount of water present due to the loss through the pipe covering partly neutralised by drying effects of friction , weight of dry steam entering pipe per second , .
weight of dry steam flowing past a given point distant along pipe ; then The relation between the volume of unit weight of dry steam and its absolute pressure has for this purpose been taken as that iven by constant , since the change in specific volume down the pipe is small .
Density of dry vapour Volume of weight of dry vapour But the actual substance past any section of the pipe is a mixture of steam and a small proportion of fine drops of water .
The density of the mixture , and therefore .
The velocity of the fluid .
Inserting these values of and in the dimensional formula , we ' which may be written Assuming the viscosity to be sensibly constant down the pipe*and integrating between lengths and , pressures and , we get In order to plot the results the formula was put in the form , ( 1 ) for any given value of the diameter and the pressure .
values of * The justification for his assumption may be inferred from an inspection of the final plot , fig. 3 .
At low pressures in small pipes , i.e. where this error would have its greatest effect , the value of works out at about .
At pressures of kgrm .
per sq .
cm .
reatest observed dence oressure wkgrm.sq.corresponding theoretical change oiscosity .
Since tev iscosityappearsinthe formula with the index or , or say 0.5 per cent. , the maximum relative of error will be If now represents the pressure at a point distant unit from we get , ( 2 ) but oyel unit length at the entry to the experimental length approx. Dividing ( 1 ) by ( 2 ) we are thus led to the equation since small ; from which the drop in pressure over unit length at the entrance to the pipe can calculated .
The principal values of the resistance per unit surface and the velocities , with values of and , are given in Tables I , II , III , and .
Details of the rednction of typical experimental values will be found in Table In reductions , values for the viscosities* at the various steam temperatures have been obtained by linear extrapolation of the results given by Puluj , Kundt and , and Meyer and Schumann for temperatures and 10 respectively , this method being justified since i.nspection of the esultant curve ( fig. 3 ) shows it to be comparatively insensitive to slight inaccuracies in the values of the viscosity , thus an error in the estimation of the viscosity as great as 10 per cent. would only cause a horizontal shifC of the point involved by , an amount which in view of the comparatively slow change of ordinate with abscissa is negligible and commensurate with the accuracy of other parts of the ation .
In the bulk of the expsrinlents bhe pressure head corresponding to the increase in velocity did not exceed per cent. In the cases , however , where pressure drops were experienced a correction was applied to allow for the proportion of the pressure drop necessary to accelerate the steam from the initial to the final velocity .
values of the viscosities for saturated steam at temperatures above C. are not accuratoly known .
From experiments carl.ied out below that temperattlre it appears , however , to follow a law and being approximately and respectively .
Mr. C. H. Lander .
Surface : Comparison of tlRsults with those of other nenters on Water and In fig. the values of all the experimental results have been plotted with as ordinates and as abscissae .
The mean results as calculated from the formulae Ledoux for their steam velocity are also plotted on the diagram .
The boundary curves for Stanton and Pannell 's results upon a drawn brass pipe are shown , together with their interpretation of ' experiments upon lead pipes .
A curve has also been drawn illustrating Stanton's* experiments on artificially roughened pipes , in which by cutting screw threads in alternate directions on the inside of the pipe he succeeded in obtaining two pipes in the resistance varied directly as the velocity squared .
The resistance for these pipes as given by Stanton is expressed by the formula where is the velocity at the axis .
From the curve in Stanton 's paper giving the radial distribution of velocity in these pipes the value of the mean velocity has been determined , the horizontal line in fig. 3 the resistance in the screwed pipes reduced to terms of the mean velocity .
It will be noted that the author 's points for steam lie with fair accuracy upon a smooth curve slightly higher than Stanton and Pannell 's boundary curves for low values of becoming proportionately higher for large values .
This characteristic is quite in conformity with the curves for rough and smooth brass pipes , the rough pipe offering proportionately much more istance than the smooth pipe at the high values of It has been shown by Lees that the results of Stanton and Pannell 's experiments can be represented with considerable accuracy by an expression of form the constants for air and water in smooth brass pipes being , and .
With a modification of the constants the same expression represents the mean of the present experiments , the line in fig. 3 having been plotted using the values : From the general trend of their curves for high values of Stanton and Pannell predicted a limit beyond which the resistance would be constant and hence independent of .
This is equivalent to the resistance varying as the square of the velocity .
In the steam curves , owing probably to the ' Roy .
Soc. Proc , vol. 85 , p. 'Roy .
Soc. , vol. 91 , p. 46 .
352 Surface Friction .
pipes being htly rougher , this limit would appear to be reached earlier and the ultimate value of to be considerably above that corresponding to the smooth pipes used by Stanton and Pannell .
The characteristics of the various curves appear to denote that the limiting value of beyond which the resistance varies as the velocity squared becomes less with the roughness of the pipe surface , until , for a very rough surface , the resistance val.ies as the velocity squared for values only exceeding by small amounts that corresponding to the critical velocity .
The hness of the steam pipe surface appears to be about the same as that of Darcy 's pipes , the bulk of which were bitumen covered .
points out that if the law of similarity is to apply it must extend even to the proportionality of the projections and hollows which constitute the rou,.lmess of two given surfaces .
Since in the present experiments three different diameters of pipe were used , the surfaces of which were probably of the same of roughness , it appears that , as was observed by Stanton and Pannell , in this the effect of any want of proportionality of roughness is small .
The close reement between the results obtained by steam and water in the same mains will also be noted .
Conclusions .
Further direct evidence has been produced to demonstrate the truth of the dimensional law , which is now shown experimentally to extend to the case of saturated vapoul .
S. The fact that for the first time a range of pressures extending from about 11- ) inches of vacuum to .
per square inch above atmosphere has been used for the gas experiments is also not without interest .
It is hoped that the work will prove of value to those who require data as to the resistance in steam and other mains , and who up to the had to content themselves with a velocity squared law constants for few values of the velocity .
Again , .the further demonstration of law of dynamical similarity appears to open up a wide field for testing purposes .
The metLod of inferring th resistance of bodies of val.ious shapes to the flow of air from experiments made on models in water has been in use for some time .
The present work , by demonstrating the truth of the law as applied to the flow of steam and water in pipes , opens up the possibility of inferring the resistance of complicated steam passages , such as are met with in tnrbines , by tests on models the law of similarity .
It is hoped in the future to extend the work on lines .
Converging Sequences in of In conclusion the author desires to express his sincere thanks to Prof. E. Petavel and the authorities of the Uniyersity of Manchester for the valuable granted for the carrying out of the work , and also to express his gratitude to the Council of the Royal Society for grant to defray the cost of the special apparatus needed .
on xistence of Sequences Succession.s By Prof. W. H. , Sc.l ) .
, Received Angust 1 .
The object of the note is I ; prove , in large important , a succession of functions can be shown to contain sub-sets of functions which converge .
The interest attaching to the question is well known , and is sufficientl illustrated by the use I have nladc of these considerations , for example , in my paper on the conditions that a metrical series should have a certain form , as well as elsewhel.e .
theorem on the subject is , as is there pointed out , due to 2 .
Theorem th tinuovs on the , there is countable set of everywhere , such that the of th , function at any ) not to set is the limit of the of th ' function at set in neighbourhood of the point that up to th In fact , since the limits of approach are the same on the left and on the , except at a countable set of points , it follows that , except a countable set of points , the fnnction is both lowel semi-conl , inuous and upper semi-continuous ; in other words , that it is , ) at the points of such a set .
Add to this set , should it not be everywhere , any countable everywhere dense set , and we get such a set as contemplated in the enunciation .
For a point not belonging to it the value is the unique limit of values in the eighbourhood equally , whether we confine our attention to points on the countable set or not .
A revision of one part of the proofs , due to .
Grace Chish eiveot on October 25 , 1915 , and has been porated in the paper .
Published in these oceedings , vol. 88 .
The theorunl in .
to Theorem 4 of para .
of the present communication is there utilised , but its proof is in part based ou an roneous theorem , qnoted from the ' Proc. Loudou Math. Soc. ' VOL. XCII.\mdash ; A. 2
|
rspa_1916_0020 | 0950-1207 | Note on the existence of converging sequences in certain oscillating successions of functions. | 353 | 356 | 1,916 | 92 | Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character | Prof. W. H. Young, Sc. D., F. R. S. | article | 6.0.4 | http://dx.doi.org/10.1098/rspa.1916.0020 | en | rspa | 1,910 | 1,900 | 1,900 | 1 | 62 | 1,935 | http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1916_0020 | 10.1098/rspa.1916.0020 | null | null | null | Formulae | 80.516377 | Tables | 11.032638 | Mathematics | [
72.35893249511719,
-48.51569747924805
] | Converging Sequences in Oscillating 3j3 In conclusion the author desires to express his sincere thanks to Prof. J E. Petavel and the authorities of the University of Manchester for the valuable facilities granted for the carrying out of the work , and also to express his gratitude to the Council of the Royal Society for a monetary grant to defray the cost of the special apparatus needed .
Note on the Existence of Converging Sequences Certain Oscillating Successions of By Prof. W. H. Young , Sc.l ) .
, F.R.S. ( Received August 16 , 1915.* ) 1 .
The object of the following note , is to prove that , in a large class of important cases , a succession of functions can be shown to contain sub-sets of functions which converge .
The interest attaching to the question is well known , and is sufficiently illustrated by the use I have made of these considerations , for example , in my paperf on the conditions that a trigonometrical series should have a certain form , as well as elsewhere .
The first theorem on the subject is , as is there pointed out , due to Arzela .
2 .
Theorem 1.\#151 ; Given a function which is upper semi-continuous on the left and lower semi-continuous on the right , there is a countable set of points dense everywhere , such that the value of the function at any point not belonging to the set is the unique limit of the values of the function at points of the set in a neighbourhood of the point when that neighbourhood shrinks up to the point .
In fact , since the limits of approach are the same on the left and on the right , except at a countable set of points , it follows that , except at a countable set of points , the function is both lower semi-continuous and upper semi-continuous ; in other words , that it is continuous , except at the points of such a set .
Add to this set , should it not be everywhere dense , any countable everywhere dense set , and we get such a set S as that contemplated in the enunciation .
For a point not belonging to it the value is the unique limit of values in the neighbourhood equally , whether we confine our attention to points on the countable set S or not .
* A revision of one part of the proofs , due to Mrs. Grace Chisholm Young , was received on October 25 , 1915 , and has been incorporated in the paper .
t Published in these ' Proceedings,5 vol. 88 .
The theorem contained in Cor. to Theorem 4 of para .
5 of the present communication is there utilised , but its proof is in part based on an erroneous theorem , quoted from the ' Proc. London Math. Soc. ' VOL. XCII.\#151 ; A. 2 1 ) 354 Prof. W. H. Young .
Existence of Converging 3 .
Theorem 2.\#151 ; At a point at v:hich all the lower functions of an oscillating succession are lower semi-continuous on the right , all the upper functions are also lower semi-continuous on the right .
For proof see my paper on homogeneous oscillation in 4 Lond. Math. Soc. Proc. ' 4 .
Theorem 3.\#151 ; -If all the lower functions of a succession of functions are upper semi-continuous on the left and lower semi-continuous on the right , then in any sub-succession of the functions a sequence of the functions can be found , having a unique limiting function , which is upper semi-continuous on the left and lower semi-continuous on the right .
Take any countable set of points dense everywhere , Pi , P2 , ... , Pw , ... .
Select any one of the limits at Pi ; suppose , for instance , it is the lower limit ; we then choose out a sub-succession of the functions , having , for the value of x corresponding to Pi , this selected limit as unique limit .
Omitting , now , the first function , / ij2 ( x ) , of this sub-succession , let us , in like manner , choose out a sub-succession of the remaining succession , having at P2 a unique limit , which we select to be the value at P2 of the lower function of the first sub-succession .
We then repeat this process , that is , we omit the first function , f2 , \ ( x ) , of this new succession , and determine a sub-succession of the remaining succession , having at P3 a unique limit , which we select to be the value at P3 of the lower function of the second sub-succession .
Proceeding thus , ad infinitum , we take the succession / l , l ( \#171 ; )\#187 ; A1 ( \#187 ; ).\#166 ; .
, f(\#171 ; )-. .
, ( 1 ) formed by the successive omitted first members .
As a sub-succession of the first sub-succession , this has a unique limit at Pi .
As all but the first member belong to the second sub-succession , it has a unique limit at P2 , and so on for the remaining points P3 , ... , Pw , ... .
But these points are dense everywhere , so that if x is any point not belonging to this countable set , and such that at x the upper and lower functions of the succession ( 1 ) are continuous , these functions will agree at x , for the value of either of them is then the unique limit of their common values at points of the countable set , when we approach x along this set .
But , as pointed out in the proof of Theorem 1 , a function which is of the type specified for the lower function is continuous except at a countable set of points .
Also , by Theorem 2 , the upper function is of the same type , and therefore also continuous , except at a countable set of points .
Hence , except at a countable set of points , our sub-succession ( 1 ) has a unique limit at each point x. Sequences in Certain Oscillating Successions 355 Let the exceptional points be Qi , Q2 , ... .
We can now form a sub-succession of ( 1 ) , having a unique limiting function .
We only have to perform anew the process already described , substituting the sub-succession ( 1 ) for the original succession , and the points Qi , Q2 , ... , for Pi , P2 , \#151 ; Thus , we form first a sub-succession of ( 1 ) , having at Qi a unique limit ; we omit the first member , of this subsuccession , and form from the remaining members a second succession , having at Q2 a unique limit , and so on .
The sub-succession ( 2 ) formed by the omitted first members has then a unique limiting function .
For , as a sub-succession of ( 1 ) , it has at each point x which is not one of the points Q)t a unique limit ; and , as a sub-succession of the first subsuccession of ( 1 ) , it has at Qi a unique limit ; as a sub-succession of the next sub-succession it has at Q2 a unique limit , and so on .
Thus , at every point , the sub-succession ( 2 ) has a unique limit , so that ( 2 ) is such a sequence of the original functions as was sought ; for the limiting function of this sub-succession , being one of the lower functions of the original succession , is upper semi-continuous on the left and lower semi-continuous on the right .
This proves the theorem .
Cor. The theorem is still true if infinite values he and the functions are unbounded , the word sequence then being defined in the extended sense , in which proper divergence may take the place of convergence .
o. Theorem 4 .\#151 ; Ifall the lower functions of a succession of integrals are upper semi-integrals , there is in any sub-succession a sequence of integrals converging to an upper semi-integral .
lor an upper semi-integral is lower semi-continuous on the right , and upper semi-continuous on the left .
Cor .\#151 ; If a succession of integrals of function which are bounded below in their ensemble oscillates boundedly , there is in every sub-succession a sequence of the integrals converging to an upper semi-integral .
For since the succession is bounded below , and the succession of integrals is bounded , the former is semi-integrable below and therefore all the lower functions of the succession of integrals are upper semi-integrals .
6 .
It may be remarked that the above theorems and corollaries give rise to other similar theorems if we interchange the words upper and lower , above and below throughout .
It is also worthy of notice that in the Cor. of the last article the restriction that the succession of integrals oscillates boundedly is not a necessary one .
n fact by adding a suitable constant A to the functions in the successions to 356 Converging Sequences in Oscillating Successions of Functions .
' ' . .
be integrated , we can secure that they are all positive at the cost only of adding Ax to their integrals .
The integrals are now all monotone increasing , and the same is* therefore necessarily true of the upper and lower functions of the succession formed by them .
Hence these lower ( as also the upper ) functions of the succession of integrals are lower semi-continuous on the right and upper semi-continuous on the left .
This holds good if from these we subtract the continuous function Ax .
Hence Cor. 2 of Theorem 3 is applicable .
7 .
In other words , if by a sequence we mean a succession of functions which everywhere either converges , or diverges properly , we can enunciate the ?
following theorem .
Theorem 5.\#151 ; If a succession of summable functions is bounded in one sense , " then the integrals of the functions form a succession such that in every subsuccession there is a sequence converging to a semi-integral , which is upper if the original succession be bounded below , and lower if it be bounded above .
8 .
Yet another form can be given to our results in a very particular case .
We may consider any succession of functions of bounded variation with the single restriction that the total variations of these functions are bounded in their ensemble .
By expressing each function as the difference of its positive and negative variations to a constant pres , we may then replace the succession by two bounded successions of monotone increasing functions of which it is the difference .
We thus easily see that the following is true : Theorem 6.\#151 ; If a succession of functions of bounded variation has its variations bounded in their ensemble then there is in any sub-succession of the succession a sequence of the functions converging to an unique limiting function , which is ' % of course itself a function of bounded variation .
|
rspa_1916_0021 | 0950-1207 | The microscopic structure of semipermeable membranes and the part played by surface forces in osmosis. | 357 | 372 | 1,916 | 92 | Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character | Frank Tinker, M. Sc.|Sir Oliver Lodge, F. R. S. | article | 6.0.4 | http://dx.doi.org/10.1098/rspa.1916.0021 | en | rspa | 1,910 | 1,900 | 1,900 | 11 | 269 | 7,521 | http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1916_0021 | 10.1098/rspa.1916.0021 | null | null | null | Biochemistry | 40.499368 | Biology 3 | 15.722947 | Biochemistry | [
-19.80449867248535,
-29.18985939025879
] | 357 The Microscopic Structure of Semip Membranes and the Part Played by Surface Forces Osmosis .
By Frank Tinker , M.Sc .
( Communicated by Sir Oliver Lodge , F.R.S. Received October 13 , 1915 .
) [ Plate 6 .
] In the following investigation an attempt has been made to arrive at some of the fundamental facts associated with the mechanism of osmosis .
Hitherto very few experimental observations have been made in this connection .
Raoulfc , Flusin , Kahlenburg , * and a few others have shown , however , that certain membranes such as parchment , gelatin , and rubber absorb the liquids to which they are permeable , and are impermeable to liquids which they do not absorb ; Bigelow and Bartellf have shown that , under certain conditions , the rate of flow of water through membranes such as copper ferrocyaniae obeys Poiseuille 's law for the rate of flow through capillary tubes ; whilst Beutner , Donnan , J and others have proved that certain precipitation membranes can act as electrodes , reversible with respect to various ions .
The further questions which are dealt with in the present communication are experimental ones : such as what is the size of the colloidal particles of which a semipermeable membrane is composed , and how is the membrane built up from those particles ; to what extent does a membrane show the properties of the gelatinous precipitates or gels as ordinarily prepared by bulk precipitation , and how does its structure differ from these ; how is the structure of the membrane altered by variations in the method of its formation , the nature of the solutions bathing it , and the treatment to which it is subjected ; and what is the size of its pores , the extent to which they are under the control of surface forces , and therefore of adsorption phenomena also .
* Raoult , ' Comptes Rendus , ' vol. 121 , p. 187 ( 1895 ) ; Flusin , ' Comptes Rendus , ' vol. 131 , p. 1110 ( 1901 ) ; Kahlenburg , ' Journ. Phys. Chem. , ' vol. 10 , p. 141 ( 1906 ) .
t Bigelow , 'Journ .
Amer .
Chem. Soc. , ' vol. 29 , p. 1675 ( 1907 ) ; Bartell , 'Journ .
Phys. Chem. , ' vol. 15 , p. 659 ( 1911 ) .
I Beutner , 'Journ .
Phys. Chem. , ' vol. 17 , p. 344 ( 1913 ) ; Donnan and Allmand , 1 Trans. Chem. Soc. , ' vol. 105 ( 2 ) , p. 1941 ( 1914 ) .
VOL. XCII.\#151 ; A. ' Mr. F. Tinker .
The Microscopic Structure 1 .
Microscopic Examination of Precipitation Membranes : Apparatus , Structure of Membrane , and Size of Grain .
In an investigation covering the foregoing ground it was thought desirable to limit the initial enquiry to the precipitation membranes first studied by M. Traube .
These membranes comprise the various silicates , tannates , and ferrocyanides of copper , iron , lead , etc. , and also tannate of glue , barium sulphate and silver chloride .
They show varying degrees of permeability to salts in solution .
Copper ferrocyanide is not permeable to either of the solutions from which it is formed , nor to barium chloride , calcium chloride , ammonium sulphate , barium nitrate , sugar , etc. , but it is permeable to potassium chloride .
Tannate of glue is permeable to most of the above substances , bub not to potassium ferrocyanide .
The metallic silicate and tannate membranes show an intermediate degree of semipermeability , in each case being practically impermeable to the salt solutions from which they are formed .
Barium sulphate , when used for clogging the pores of a tannate of glue membrane , renders the latter impermeable to ammonium sulphate and barium nitrate , in addition to potassium ferrocyanide ; whilst if silver chloride is precipitated in the pores of a copper ferrocyanide membrane , the latter will no longer allow potassium chloride to pass through it.* Fortunately , these membranes can be very easily prepared in thin transparent films suitable for microscopic examination .
In a preliminary set of experiments this was done by forming the semipermeable film in between two drops of the mutually precipitating liquids , e.g. , copper sulphate and potassium ferrocyanide , the one drop being placed on the microscope slide , and the other on the cover-glass .
On bringing the two drops together by gently lowering the cover-glass on to the slide , the film precipitated at the surface of contact of the drops was found to be quite thin and transparent , and quite stable enough to prevent further mixing and precipitation of the two solutions .
The films so prepared were first examined by the ordinary microscopic methods in which transmitted light is employed .
Several of them , notably the various silicates , showed a distinctly granular structure , very similar to a layer of sand particles placed side by side , the average size of the grain being different with different membranes .
The films of the ferrocyanides of copper and iron , however , seemed to be perfectly transparent and continuous .
" No structure could be detected with certainty , the particles forming the film * These facts are taken from M. Traube 's paper on these membranes ( ' Archiv fiir Anat .
Physiol , und Wissenschaft .
Medizin , ' pp. 87-165 ( 1867 ) ) .
of Semipermeable Membranes .
being apparently so small that the simple methods employed were not good enough to render them visible .
But the fact that the structure of some of the films had been resolved , rendered it likely that all might be resolved by improving the microscopic technique .
Two great improvements were made in the apparatus , in the lenses , and in the illuminating system respectively .
Through the generosity of Sir Oliver Lodge , Messrs. Carl Zeiss supplied me with a specially selected oil-immersion fluorite objective of great resolving and penetrating power .
Through the same agency I was also enabled to obtain a Zsigmondy-Seidentopf ultramicroscope* so that I might utilise its illuminating system , and attach it to the ordinary microscope .
In this illuminating system , which is the most perfect yet devised , the source of light is an intensely illuminated narrow slit which can be reduced to either point or line dimensions , thereby enabling the lenses in the optical system to exert their maximum resolving power .
In setting up this new and improved apparatus for the examination of the semipermeable films the ultramicroscopic outfit was made the basis .
To adapt it for the purpose in hand , the special microscope and separate Abb4 condenser supplied for the ultramicroscopic examination of colloids were removed from the optical bench , and an ordinary Zeiss microscope mounted instead .
A sketch of the complete apparatus so put together is given in Diagram 1 .
The beam of light from a powerful arc A is focussed by means of a lens B on to a graduated and adjustable slit C , which can be shortened and narrowed down to any desired extent .
The faint beam of light proceeding from the slit is then condensed twice ; first by means of the lens D , and subsequently by means of the Abbe condenser of the microscope E ; from which it passes on to and through the semipermeable film mounted on the microscope stage .
It was found advisable to reduce the length and width of the slit to as great an extent as possible , short of destroying the transmitted beam altogether .
The best results were obtained with a slit 1 mm. long and three-hundredths of a millimetre wide .
* A complete description of this instrument is given in the Zeiss catalogues , Micros .
227 and 228 .
Mr. F. Tinker .
The Microscopic Structure Much better films were obtained by using a Thoma 's hsemocytometer ( Diagram 2 ) instead of the simple microscopic slide and cover-glass used in COVER CLASS F/ LM Diagram 2 .
the preliminary experiments .
So prepared , the films were quite uniform and free from creases , and also quite stable when mounted vertically with the microscope , as in Diagram 1 .
Their thickness was about one-thousandth part of a millimetre ( 1 jj .
, ) .
Incidentally , it might be mentioned also that the solutions used for precipitating the films were usually decinormal .
More satisfactory films were obtained when the acetates of the metals were employed instead of the salts of the mineral acids .
The method of conducting the microscopic examination of the films prepared in the above way was as follows : The film was examined first by means of a No. 7 dry objective and a No. 5 eyepiece , in order to find a good portion free from furrows , and then more thoroughly by the selected Zeiss oil-objective already mentioned .
If the film was good enough , it was subsequently photographed by substituting a projection eyepiece for the No. 5 lens , and bringing the camera into position as shown in Diagram 1 .
Specimen photographs of the films are shown in Plate 6 , figs. 1 to 6 .
These photographs were usually taken about 15 minutes after the film had started to form .
An inspection of them shows that precipitation membranes are not as continuous and homogeneous in structure as commonly supposed .
They consist of collections of very small particles of precipitate , which are just large enough to be within the limit of microscopic vision ( 0T / jl ) .
These particles are of slightly different sizes , and are apparently aggregated together as closely as possible .
They approach the spherical in shape , but where they touch they seem to show a tendency to be flattened , and to cling together , just as if they were attracted to one another .
Moreover , the precipitate particles in the various films do not vary greatly in degree of fineness from film to film .
The average size of the particles in any one film is in all cases between 0T and 1*0 / jl .
The order of size , the colour of .
the film , and the approximate diameter of the particles , are given in the subjoined Table .
It will be seen from the Table that copper ferrocyanide and Prussian blue are the finest grained membranes , whilst tannate of peptone\#151 ; comparable to Traube'* tannate of glue\#151 ; is the coarsest .
The particles composing the former range from 0T to 0'4 ^ in diameter , whilst those in the latter lie of Semipermeable Membranes .
361 TaMe I.__Showing Order of Size of Particles in Precipitation Membranes .
Membrane .
Colour .
Size of particles .
Prussian blue Blue 0 T to 0 *4 fx .
Copper ferrocyanide Ferric si lien , the Chocolate red Yellowish white 0 T to 0 *4 fx .
Lead ferrocyanide White Copper silicate Greenish blue 0 2 to 0 *5 fx .
Tannate of iron Black Tannate of copper Dark brown Lead silicate White 0*6 to 0 *8 p. Lead tannate Dirtv w'hite White Peptone tannate 0*5 to 1-0/ u. Barium sulphate White 1 Coagulate into large particles , J 3 or 4 fx in diameter .
Silver chloride White 1 between 0*5 and 1-0 / x. Generally speaking , the iron membranes are slightly finer-grained than the copper , and copper membranes finer-grained than lead .
In the same way , the ferrocyanide membranes are not as coarse-grained as the silicates , and the silicates not as coarse as the tannates .
Although all the particles in the precipitation membranes are apparently visible by the microscopic method already outlined , it seemed advisable to ascertain whether there are any free unaggregated particles of ultramicroscopic dimensions ( i.e. less than 0T / x ) in such membranes .
In order to test this point , freshly precipitated copper ferrocyanide was shaken vigorously with excess of water for a few hours in a butter-churn driven by a small motor .
A microscopic examination of the emulsified mixture showed that the copper ferrocyanide in it was very difficult to break up .
Free particles of the same size as those in the membrane were present , however , and showed a vigorous Brownian movement .
In order to determine whether any uljramicroscopic particles had also been washed out of the aggregated precipitate , the emulsion was centrifuged until all particles visible by the microscopic method outlined above had been brought down .
When the centrifuged liquid was clear when examined by the microscope\#151 ; therefore containing no particles greater than 0T fi\#151 ; it was examined for the colour of copper ferrocyanide in the 18-incli cell of a Lovibond tintometer .
The tinge of colour , though slight , was too small to be measured .
It would hence appear that the small visible particles , of which precipitation membranes are made* , are totally fine suspensoid in character rather than colloid .
It would seem as if there are no free or unflocculated colloidal particles amongst their number at all .
But it must be remembered that the above experiment was performed in presence of traces of potassium sulphate , which would keep such ultramicroscopic copper ferrocyanide Mr. F. Tinker .
The Microscopic Structure particles precipitated .
But the fact that the membrane particles may themselves be flocculated ultramicroscopic particles ( see later ) .in no way detracts from the above observations as to membrane structure , for potassium sulphate is also present when the copper ferrocyanide membrane is formed from copper sulphate and potassium ferrocyanide .
The average size of the precipitate particles in semipermeable films is accordingly about the same as that of the metallic suspensions formed by the coagulation of colloidal metals , of the smallest dust particles in freshly distilled water , of the particles in gum gamboge and pigments in general , * and also the same as that of the particles of oil in kerosene emulsions and freshly shaken suspensions of water in kerosene.f In all probability this size is such as would be imposed by the combined action of the electrical charge on the particles and the tension at the boundary surface between the particles and the enveloping medium .
2 .
The Colloidal Properties of Precipitation Membranes : Relation to Sols andOrdinary Gels .
It is well known that the common precipitation membranes are colloidal in nature .
They are gels which are formed from colloidal solutions or sols by the segregation of the ultramicroscopic particles suspended in the latter .
But inasmuch as they are really very thin films of gel , and are formed by surface precipitation rather than bulk precipitation , it is to be expected that they will have properties peculiar to themselves , in addition to the properties of gels in general .
We will , therefore , consider the relation of the membrane to the sol on the one hand and the gel as ordinarily prepared on the other ; confining attention mainly to copper ferrocyanide .
Copper ferrocyanide sol was first described by Graham , J who showed that it is best prepared by dissolving the washed gelatinous precipitate dn just sufficient neutral ammonium oxalate solution , the latter being subsequently dialysed away .
In this way a saturated sol containing 3 or 4 per cent , of copper ferrocyanide can be obtained .
In size , the ultramicroscopic particles in the sol are not far below the microscopic limit of visibility .
The largest of them can be seen quite readily by means of the paraboloid condenser and dark ground illumination on the ordinary microscope .
When examined by the Zsigmondy-Seidentopf ultramicroscope , their size would appear to range from about 50 to 90 / x/ x. None * These facts are taken from Zsigmondy 's book on 'Colloids and the Ultramicroscope ' ( Alexander 's Trans. , pp. 132-136 ) .
t Lewis , ' Zeit .
Colloid .
Chemie , ' vol. 4 , p. 211 ( 1909 ) .
f ' Chemical and Physical Besearches , ' pp. 583 et seq. of Semipermeable Membranes .
of the copper ferrocyanide is in true solution\#151 ; as distinguished from colloidal solution\#151 ; since the characteristic ferrocyanide colour is removed completely by shaking the solution with a little Seitz absorbent asbestos .
This substance , which is much used in technical practice for clearing the haziness from wines , has little or no effect on the concentration of true solutions or even solutions of emulsion colloids .
It would appear therefore that the whole of the ultramicroscopic particles in copper ferrocyanide sol are in the submicron range .
It is also negative in character , * being precipitated by hydrion and the multivalent cations with the greatest ease .
The general properties of copper ferrocyanide gel are too well known to merit description .
To examine its structure microscopically , a thin film of it can be prepared in the way usually adopted for examining the structure of gels.f The structure seems to be that of a somewhat irregular network having a mesh of the order 05 to 1*0 / x. In this respect it seems to be similar to most of the other ordinary gels such as gelatin , silicic acid , etc. , which have been examined with great thoroughness by Biitschli , Hardy , van Bemmelen , von Weimarn , Quincke , Zsigmondy , Pauli and others .
The difficulties attendant on the preparation of gels , and the ease with which their real structure is altered in the handling of them have , however , caused their structure to be a subject of much dispute .
But there seems to be general agreement now that most of them consist of a lattice work system in which a semi-solid phase encloses a more liquid phase .
If we now consider the membrane , it will be seen that the small particles revealed by the refined microscopic examination are too large to be the individual ultramicroscopic particles which are suspended in the sol .
Each precipitate particle in the semipermeable film is rather an aggregate formed by the flocculation of the latter ; so that the membrane as a whole can be regarded as formed by the flocculation of sol particles into small precipitate particles just microscopically visible , whilst these small precipitate particles themselves aggregate together to form the continuous film .
The whole of this flocculation process by which the membrane is formed can be followed quite readily by the microscopic method already outlined .
The first stage in the production of a semipermeable film is the formation of a layer of ultramicroscopic particles at the boundary surface separating the two mutually precipitating liquids .
This is evidenced in the case of a copper ferrocyanide film by the appearance of a brick red tinge at the boundary surface some two or three minutes before any particles in the film * Duclaux , ' Comptes Rendus , ' vol. 143 , pp. 296 , 344 ( 1906 ) .
t An object glass is placed at the bottom of a shallow vessel containing the saturated sol , and a very thin layer of gel allowed to separate out on it .
364 Mr. F. Tinker .
The Microscopic Structure are microscopically visible .
After the first few minutes , precipitate particles produced by the flocculation of these colloidal particles begin to appear\#151 ; the process being fairly rapid at first , but going on at a gradually diminishing rate for some hours .
The gradual change which takes place in the appearance of the film with the lapse of time is shown in the two photographs of the same portion of a copper ferrocyanide film taken half-an-hour and eight hours respectively after formation ( figs. 1 and 2 , Plate 6 ) .
The flocculating effect shown in these photographs is a very marked and unmistakeable one .
But it is shown more strongly still by crystalloidal precipitates such as barium sulphate .
An inspection of fig. 6 ( Plate 6 ) indicates that after several hours the whole of a barium sulphate film has broken up completely and aggregated into large particles 2 or 3 microns in diameter .
But , as is now generally recognised , the difference between colloids and crystalloids in this respect is merely one of degree .
Furthermore , the rate at which the flocculation process takes place depends on the concentration of the precipitating solutions and their nature .
In the case of copper ferrocyanide the microscopically visible precipitate particles appear much sooner when strong precipitating solutions are used , and in presence of traces of acids or potassium sulphate .
They do not appear so readily when the acetate of copper is employed instead of the salts of the mineral acids ; neither do the particles grow to quite the same size .
The membrane is disintegrated by ammonium oxalate solution or on washing too thoroughly with water .
For it to remain stable traces of copper sulphate or potassium sulphate must be present in the solution bathing it .
Precipitation membranes accordingly show most of the properties of the corresponding gelatinous precipitates or gels which are produced when the mutually precipitating liquids are mixed in bulk .
Both the membrane and the gel proper are formed by the flocculation of colloidal particles of ultramicroscopic dimensions , and the behaviour of the aggregates so formed is the same in each case .
But although therefore we are justified in defining a precipitation membrane as a very thin layer of gel , it will be seen that the physical structure of the membrane is not the same as that of the gel produced by bulk precipitation .
There is a fundamental difference in the method of formation of the two , which seems to cause a fundamental difference in texture and geometrical form .
During the formation of the membrane , the interaction of the two liquids and the flocculation of the colloidal particles are limited to a plane ; whilst when the ordinary gel is produced by precipitation in bulk , these colloidal particles come together from all directions in the three dimensions of space .
This difference would seem to cause the texture of the membrane to be much finer than that of the gel proper .
Whereas the of Semipermeable Membranes .
ordinary gel has the structure of a somewhat open lattice-work , the precipitation membrane has the more irregular structure of a layer of sand grains laid close together side by side ; the nearest approach to the lattice-work structure being the tendency of the small particles to cling together and flatten at the point of contact .
It is probable that the lattice work structure is incompatible with the property of perfect semipermeability ; for if it were formed even temporarily the mutually precipitating liquids would leak into the mesh-work and precipitate one another still further , thus blocking up the cavities .
But in spite of these differences in physical structure between semipermeable films and gels proper , it is quite clear that there are the same binding forces operating in membranes as give rigidity to ordinary gels .
Copper ferrocyanide and Prussian blue films are possessed of great tensile strength\#151 ; a fact which accounts to a large extent for their success as membranes .
The silicate films are not so strong as the ferrocyanide films , and break up much more readily ; the tannate films fall to pieces more readily still ; whilst a barium sulphate film breaks up almost immediately after formation .
But it is important in this connection to remember that the stability of any given membrane film is determined almost wholly by the nature of the liquid surrounding it .
If , for example , the barium sulphate film is precipitated from solutions of sulphuric acid and barium acetate in alcohol diluted with a little water , the gelatinous film produced at the boundary surface remains quite stable and elastic , just as does the corresponding gel produced from similar solutions by bulk precipitation.* For the precipitation membrane to be stable , the substance of which it is composed must have a negligible true solubility in the surrounding medium .
The particles of the membrane will then undergo no change , since crystallisation is inhibited by the fact that molecules cannot be transferred from one particle to another by intermediate solution .
If on the other hand the substance of the membrane has a slight solubility in the medium , molecules can be transferred , and the large particles can grow at the expense of the smaller onesr the whole film meanwhile crystallising and breaking up .
Though these effects are known to occur in the case of colloids considered in extenso , it does not seem to have been generally recognised that they can take place in the case of membranes .
But there is no doubt that the nature of the liquid bathing the membrane can cause fundamental and irreversible changes in its colloidal character to take place , and also exercise a great influence on its capacity for showing osmotic properties.j- * Kato , 4 Journ. Chem. Soc. , ' A , vol. 11 , p. 850 ( 1910 ) .
+ In this connection we await wTith great interest the results of H. N. Morse , who announces that such changes in structure take place when a copper ferrocyanide Mr. F. Tinker .
The Microscopic Structure 3 .
Size of Pores in Membranes .
From what has been said above about the structure of semipermeable films it will be seen that there are two classes of pores perforating a precipitation membrane : ( 1 ) the larger pores consisting of the interspaces between the microscopically visible precipitate particles , ( 2 ) the smaller pores penetrating !
these visible particles and formed between the ultramicroscopic particles composing them .
There is , however , no sharp dividing line between these two classes , since the largest individual submicroscopic particles have a size ( 90/ / , / / , for copper ferrocyanide ) approaching that of the smallest precipitate particles ( 100/ / , / / , for copper ferrocyanide ) .
If we assume the precipitate particles and the submicroscopic particles from which they are formed to be approximately spherical , we can form an estimate of the diameter of both classes of capillaries .
To do this , consider three particles A , B and C ( Diagram 3 ) , which are of equal size and touching Diagram 3 .
one another .
The triangular interstice PQE formed between them is typical of all the pores in the membrane , whatever size they may be .
The centre 0 of the interstice is the point of greatest distance from the surfaces of the particles ; hence the perpendicular distance OP can be regarded as the radius of the interstice or pore , since it would be equal to the radius of a spherical membrane Is bathed by various aqueous salt solutions .
They also take place with zinc ferrocyanide and manganese ferrocyanide even in water ( ' Report on Osmotic Pressure of Aqueous Solutions/ Chaps .
IY and XI , Carnegie Institute of Washington , 1914 ) .
of Semipermeable Membranes .
particle which would just be able to go through the pore without being blocked mechanically .
Now it can be shown by simple geometry that the radius OP is approximately equal to 0'08 times the diameter of the particles A , B , and C , so that the pore diameter would be twice this , or about 016 times the size of the particles enclosing the interspace .
If , therefore , we know the size of the particles of a precipitation membrane , we can easily calculate the diameter of its pores .
We will apply the above result to find the approximate maximum , minimum , and average pore diameters in a copper ferrocyanide membrane .
The largest pores are formed in between the largest precipitate particles , and their maximum diameter is 0*16 x 0 4/ x , which is equal to 0*06 / x or 60/ x/ x. The smallest possible pores are enclosed by the smallest submicroscopic particles , their minimum diameter being 016 x 50 / x/ x or 8 / x/ x. In the same way the average diameter of the capillaries in between the submicroscopic particles is about 10 / x/ x , whilst that between the precipitate particles is about 48 / x/ x. The average for the membrane as a whole is much nearer the former .average , since the number of capillaries between the submicroscopic particles is much greater than the number between the precipitate particles .
Its value is probably between 15 and 20 / x/ x. If now we consider a series of precipitation membranes , it is evident that their average pore size increases as the average size of their component particles increases .
The order of the membranes with respect to pore diameter is therefore the same as that given for the size of the particles in Table I. Prussian blue and copper ferrocyanide have the smallest pores , whilst peptone tannate has the largest .
In the latter case the largest pores have a diameter approaching 160 / x/ x. If we proceed still further and compare the list of membranes placed in order of increasing size of particles and pore diameter with Traube 's list of their capacity for showing osmotic effects ( loc. cit. ) it will be seen that there is also a close relationship between the pore diameter of a membrane and its capacity for acting as a semipermeable film .
Copper ferrocyanide and Prussian blue have the smallest pores , and are also the most efficient of membranes .
The silicates and tannates have larger pores than the ferrocyanides , and are not such efficient differential septa ; whilst peptone tannate , with the largest pores of all , is the least efficient membrane of all .
This conclusion is in harmony with Bartell 's observations on the relation between pore diameter and the capacity for showing osmotic effects.* Using an indirect method of measuring the pore diameter based on Jurin 's Law , this investigator found that as the * k Journ. Phys. Chem. , ' vol. 16 , p. 318 ( 1912 ) .
368 Mr. F. Tinker .
The Microscopic Structure # # \#187 ; pore diameter of porcelain or porcelain clogged with various precipitates decreases , the osmotic effect simultaneously increases .
With copper ferrocyanide osmotic effects become noticeable at a pore diameter of about 900 / x/ x\#151 ; a figure which Bartell further showed is more or less the same for all membranes .
The osmotic effect increases very rapidly as the pore diameter gets less , and has become quite appreciable at 180 / x/ x , which was the least average diameter Bartell worked with .
It is quite understandable , therefore , that when the average pore diameter of a membrane has been reduced to 15 or 20 / x/ x\#151 ; which is the value for a well formed copper ferrocyanide film\#151 ; the membrane will have become almost truly semipermeable .
Hence pore size is one of the most important factors determining the osmotic properties of a precipitation membrane .
Although such a result would follow if the osmotic properties of a membrane were due to a selective mechanical blocking of the solute molecules , a moment 's consideration of the following approximate calculation will show that this cannot be the case , since the calculation indicates that the smallest pores in membranes have a diameter many times that of the average crystalloidal molecule .
Perrin and others have proved conclusively that there are very nearly 7 x 1023 molecules in the gramme-molecule\#151 ; a result which would give the diameter of the unassociated water molecule , for instance , as about 0*05 / x/ x. Since the smallest pore diameter in a copper ferrocyanide membrane is about 8 / x/ x , it follows that from 100 to 200 water molecules could be placed in a chain from one side of such a pore to the other , and that several thousands could be travelling across the cross section of the pore at the same time .
A selective mechanical blocking of even large hydrated crystallised molecules is hence out of the question , and this hypothesis for accounting for osmotic effects\#151 ; already largely rejected\#151 ; is no longer tenable .
Nevertheless , such a hypothesis might account for the blocking action exerted by the membrane on colloids , and on the suspension colloids more especially .
4 .
Range of Surf ace Forces inside Membrane Capillaries and Adsorption Effects .
Consider again the typical membrane interstice or pore formed between the three particles A , B , and C ( Diagram 4 ) .
Part at least of this interstice is always under the influence of the surface forces , whatever size the three particles may be ' ; and if the particles are sufficiently small , the whole of the interspace is within the surface force range .
Suppose first that the particles are large , and that the distance OP from the centre of the interspace to the surface of the particles is greater than the radius of molecular attraction PX .
There is then a central canal of Semipermeable Membranes .
( marked by the dotted line DEI ' in Diagram 4 ) , passing down the middle of the interspace , over which the surface forces have no control .
If the size Diagram 4 .
of the interstice or pore is reduced , the size of this central canal is diminished also ; and it is diminished very rapidly as compared with the rate of diminution of the pore itself , since the range of molecular attraction PX remains unchanged whatever size the pore may be .
When the distance OP from the middle of the interspace to the surfaces has become equal to the range PX of the surface forces , this central canal disappears , and the whole pore is under the control of the surface forces .
Many investigators have made determinations of the range of surface forces .
The most important for our present purpose are those based on surface condensation effects .
Such determinations are those of Parks , * who measured the thickness of the water film condensed on glass wool , and found it to be 13*4 x 10"6 cm .
or 130/ qa ; and of W. C. McLewis , f who determined the range of the adsorption-concentration effects at an oil-water interface and found it to be about 140 ( ip .
Other investigators , such as Quincke , Eeinold and Pucker , Plateau , Johannot , Vincent , etc. , working by different methods , have given values ranging from 100/ qa to 10/ qa .
The most likely interpretation of these different values is that the surface forces are very * 'Phil .
Mag. ' ( 6 ) , vol. 5 , pp. 517-523 ( 1903 ) .
t 'Phil .
Mag. ' ( 6 ) , vol. 17 , p. 428 ( 1909 ) . .
370 Mr. F. Tinker .
The Microscopic Structure strong up to a range of 10/ xya , and they become increasingly weaker from this point up to a range of 140/ zya , whilst beyond the latter point they are negligible . .
* We can now apply these results to determine the extent to which the pores of precipitation membranes are under the control of the surface forces .
In order to find out first which membranes have a central canal which is definitely out of range , we must take the upper limit of the above determinations ( 140fjbfju ) .
This figure would give a pore diameter of 280/ jl/ jl as the limit above which the central canal has a definite existence .
None of the precipitation membranes studied have pores so large as this , but it is noteworthy that the pores in gelatin , parchment , and porcelain capable of showing osmotic effects have values just above it ( 0*2 to lya).* On the other hand , if we wish to ascertain in which membranes the central canal has definitely vanished on account of the smallness of the pores , we must take the lower limit of the range of molecular attraction .
Taking this as 10/ Jbjjby the corresponding pore diameter for a completely and strongly controlled capillary is 20/ xya .
The bulk of the pores in copper ferrocyanide and Prussian blue membranes are at or below this limit , although some are possibly larger .
But the silicate and tannate membranes have pores with diameters just larger than this value , and the central spaces in their pores , if controlled by the surface forces at all , are controlled only very weakly .
The relation between the extent to which the capillaries of a membrane are controlled by the surface forces and the osmotic properties of the membrane is , however , an apparent and noteworthy one .
Copper ferrocyanide and Prussian blue\#151 ; the most perfect of membranes\#151 ; have their pores completely under control ; the tannate and silicate membranes , which are not so efficient , have a central space within their capillaries throughout which the surface forces are comparatively weak ; whilst membranes such as gelatin and parchment , which are permeable to all crystalloids , have pores which possess central canals outside the surface force range .
How , then , is this close relationship between the degree to which the capillaries are " controlled " and the osmotic properties accounted for ?
It is well known that any liquid in immediate contact with a surface is bound or adsorbed to the surface , the thickness of the adsorbed film being coincident with the surface force range .
All the liquid which gets into the pores of a precipitation membrane such as copper ferrocyanide is therefore adsorbed liquid .
Moreover , since adsorption is selective in nature , either the solvent or the solute is preferentially attracted to the surface and into the pores of the membrane .
Since it is evident also that those substances which can get * Of .
the work of Bartell already mentioned .
of Semipermeable Membranes .
into the pores of the membrane can also get through , it follows that a membrane such as copper ferrocyanide is relatively impermeable to solutes which it adsorbs negatively , but permeable to solutes which it adsorbs positively .
With the membrane bathed by cane sugar , for instance , the water would seem to be adsorbed into the capillaries rather than the sugar , and the water , being thus taken up into the pores , is able to get through , whilst the sugar , being unable to approach the surfaces of the particles , is not .
We must , however , qualify this generalisation according to the size of the pores .
If the membrane is one which has very fine capillaries , in which the central canal out of the surface force range has long vanished , the adsorption effects within the pores will be very strong .
In fact , they will be the same as the adsorption effects in the layers of surface film in immediate contact with a surface , which are not of necessity the same as those in the surface film as a whole or in its outer layers .
It is perhaps necessary to emphasise this point , since the modern measurements of adsorption effects with charcoal and other solids and liquids have referred to the complete surface film , and not to that portion in immediate contact with the surface .
If , on the other hand , we consider those membranes whose pores are large enough to possess a central canal out of range , it will be seen that the adsorption effects are not of such great importance , since free , unadsorbed solution of unchanged concentration can travel unhindered through the central canal .
But , though such membranes are permeable and leaky , they can show slight osmotic effects , since part of the liquid in their capillaries is adsorbed liquid .
Since the proportion of adsorbed liquid is increased by reducing the capillary diameter , osmotic effect is also increased in the same way ; but a perfect selective action is not attained until the pore size has diminished to such an extent that the central canal of unadsorbed liquid has vanished completely .
But I advance the above view of the cause of osmotic effects only tentatively .
To prove it more rigorously it will be necessary to show ( 1 ) that moisture is taken up by precipitation membranes from solutions bathing them , and ( 2 ) that such moisture is adsorbed on to the surfaces of the colloidal particles composing the membrane rather than absorbed into their substance by either hydration or solution proper.* Summary .
1 .
The common precipitation semipermeable membranes are composed of small precipitate particles , ranging from OT ^ to 1*0 these particles * Work now in progress tends to confirm these conclusions .
372 The Microscopic Structure of Semipermeable Membranes .
being packed closely together .
Each of these precipitate particles is , however , not simple in structure , but is itself an aggregate formed by the flocculation of submicroscopic colloidal particles .
The particles composing the membrane are smallest in the case of copper ferrocyanide and Prussian blue .
2 .
Precipitation membranes show most of the properties of gels , as ordinarily prepared , both in their method of formation and in the changes they undergo in various solutions .
Like ordinary gels , they are possessed of great tensile strength , which varies in membranes of different kinds .
Their stability in the colloidal condition also varies greatly .
But , although they show the physical properties of gels , they have not the same mechanical structure , the membrane being much more closely knit together than the gel proper .
3 .
The pores in a copper ferrocyanide membrane range from 8 to 60 yaya in diameter , the average diameter being from 15 to 20 ya/ a. The pore size is too great for the membrane to act osmotically by exerting a selective mechanical blocking action .
4 .
The order of a series of membranes in pore size is the same as that of their efficiency as semipermeable membranes .
Copper ferrocyanide and Prussian blue are the most efficient membranes , and they have also the smallest pores .
5 .
There is a very close connection between the osmotic properties of a membrane and the extent to which the membrane capillaries are under the control of surface forces .
Osmotic effects are probably the result of selective adsorption phenomena occurring at the surface of the membrane and in the capillaries , the membrane being relatively impermeable to solutes which are negatively adsorbed , but permeable to solutes which are positively adsorbed .
In conclusion , I desire to express my thanks to Sir Oliver Lodge , whose generous provision of instruments and materials has rendered the above work possible ; to Prof. A. J. Brown and Mr. T. H. Pope , B.Sc. , for much kindly advice and help ; and to Mr. Edward Robinson , Jr. , of Sir Oliver Lodge 's laboratory , for valuable assistance in taking the photographs .
i mer. Roy .
Soc. Proc. A , vol. 92 , PI .
6 .
Fig. 1 .
COPPER FERROCYANIDE x 550 , after 30 minutes .
Fig 3 .
PRUSSIAN BLUE x 550 , after 15 minutes .
Fig. 2 .
COPPER FERROCYANIDE x 550 , same film as Fig. 1 after 8 hours .
Fig. 4 .
COPPER SILICATE x 550 after 15 minutes Fig. 6 .
BARIUM SULPHATE x 550 .
|
rspa_1916_0022 | 0950-1207 | On speed effect and recovery in slow-speed alternating strees tests. | 373 | 376 | 1,916 | 92 | Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character | W. Mason, D. Sc.|Prof. B. Hopkinson, F. R. S. | abstract | 6.0.4 | http://dx.doi.org/10.1098/rspa.1916.0022 | en | rspa | 1,910 | 1,900 | 1,900 | 5 | 39 | 1,384 | http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1916_0022 | 10.1098/rspa.1916.0022 | null | null | null | Measurement | 44.452607 | Biochemistry | 20.575882 | Measurement | [
47.029483795166016,
-62.6748046875
] | 373 On Speed Effect and Recovery in Slow-Speed Alternating Stress Tests .
By W. Mason , D.Sc .
( Communicated by Prof. B. Hopkinson , F.R.S. Received December 14 , 1915 .
) ( From the Engineering Laboratory , University of Liverpool .
) ( Abstract .
) In a series of repeated torsion tests of steel the writer noticed that when the steel had become fatigued the angular strain became considerably greater when the frequency of the cycles of stress was decreased , and vice versA although the maximum and minimum stresses of the cycle were unchanged The frequencies used were between 2 and 200 cycles per minute .
This effect was absent when the cyclic strains were purely elastic , while it became increasingly apparent as non-elastic strain developed .
Discussion of Results .
The results may be stated thus:\#151 ; If a piece of the steel used in the experiments has undergone a considerable number of cycles of torsional stress at 2 cycles per minute , then if the speed is changed to 200 per minute , the cyclic non-elastic strain immediately decreases about 50 per cent. ; if the piece has endured a large number of cycles at 200 per minute , then on changing to 2 per minute the cyclic non-elastic strain is increased by 50 to 75 per cent. The reduction of range of non-elastic strain found for the above change of speed appears to be the counterpart , for slow speeds , of the comparatively small range of extra-elastic strain discovered by Prof. B. Hopkinson* for very high frequencies .
After a change of speed from 200 to 2 cycles per minute , or vice versed , the condition of the steel is not a stable one .
After the former change there is a shrinkage in the extra-elastic strain , and after the latter change the strain increases at a more rapid rate than normally would be the case .
The shrinkage may be regarded as recovery\#151 ; though not necessarily as recovery of elasticity\#151 ; because , if the speed is put back to 200 per minute after an intermediate run at 2 per minute , the new range of the strain is found to be equal , approximately , to the original range at 200 less the shrinkage during the intermediate run .
The development * The range of extra-elastic strain for Hopkinson 's very high speed tests appears to have been about 1/ 15 of the range of the elastic strain ( \#163 ; Roy .
Soc. Proc./ A , vol. 86 ( 1912 ) ) .
VOL. XCII.\#151 ; A. 2 F 374 Dr. W. Mason .
On Speed Effect and Recovery in of cyclic strain appears to be definitely set back by the " recovery , " though it is by no means certain that the progress of fatigue , whatever that may be , has received a corresponding check .
The rate of variation of this recovery , as illustrated by the diagram , is rather significant .
The rate is very big just after the change from 200 to 2 per minute , and subsequently diminishes quickly .
It is not easy to believe that recovery of elasticity can take place rapidly at a time when the cyclic strain has been largely augmented and the repetitions of the stress are continued .
And it is still less easy to reconcile with the supposition that such contractions of range of strain are to be regarded as recovery of elasticity the fact that a period of rest , interpolated between two runs at 200 per minute , results in less contraction of range of strain than a change of speed to 2 per minute , a subsequent run at this speed of the same length of time as the period of rest , and a change back to 200 per minute .
It seems more reasonable to suppose that the shrinkage of range of strain is due mainly , if not wholly , to hardening or loss of mobility in the material .
Considering the form of the stress-strain curve as found by Dr. L. Bairstow* for a cycle of stress ( tension and compression ) , there are curved lines corresponding to imposition of stress , and , what is rather remarkable , straight lines inclined at a gradient equal to the modulus of elasticity for relief of stress .
There would seem to be some change in the nature of the resistance to stress between imposition and relief of stress in a cycle , such as would result from hardening ; otherwise the lines for relief of stress would not be straight lines whose inclination is determined by Young 's modulus .
Under this view , the main factors concerned in the alteration of non-elastic strain , both in a cycle and in a series of cycles of stress , would be variation in mobility in the steel and speed of cycle .
It seems to the author that an explanation of the phenomenon of strain during alternating stress may be obtained on the basis of Prof. G. T. Beilby'sf hypothesis of formation of mobile material during slipping on crystalline gliding planes , and of the tendency to rapid hardening of such mobile material .
If it be assumed also that when crystalline slipping has once begun the rate of formation of mobile material depends largely on the rate of such slipping , and that loss of mobility ( or hardening ) requires a time not too small in comparison with the intervals of time afforded in a cycle for hardening , then an explanation of the foregoing experimental facts may be obtained** Thus , suppose a test proceeding at 200 cycles per minute , that * 'Phil .
Trans.,5 A , vol. 210 .
t 'Institute of Metals Journ.,5 vol. 6 ( 1911 ) .
Slon'-Speed Alternating Stress Tests .
* I S * / TOJOO-ZO pUCOJ U9LU/ C 9(/ s 9 \#163 ; 10-^6* SJ/ UJ/ / 9S91/ J Utl/ J/ M pi jjDjS ' / C/ goqojd j/ oojj 7'V Js\gt ; d S9/ oXb \#163 ; // p99Gfr JO T S/ JJZXJaddo JOJJ/ LU jo 9/ cog C/ O S9-/ J9LL/ /JC/ 9Q __ ' C/ /C-/ /g JO odl/ D^J / cyoj 2 f 2 s ts c ?
\gt ; 1$ $ e : I CO V. o 2*b 5 a* f. If S* 10 M til lS o\gt ; ^ v 5 0 b c : \lt ; ; n x2 fc\gt ; S I* !
tl s* I \#171 ; I 376 Speed Effect in Slow-Speed Alternating Stress Tests .
a considerable range of extra-elastic strain has appeared , and that the assumed opposing processes of production of mobility and of hardening are approximately balanced .
Let the speed be changed to 2 per minute ; there is now 100 times the interval for crystalline sliding to operate , and the range of strain is much increased , but the rate of production of mobile material will be less because the average rate of slipping is only something like one-sixtieth to one-eightieth of the previous rate , while the intervals afforded per cycle for hardening are 100 times as great .
The increased range of strain will thus tend to decrease until an approximate balance between production of mobile material and the hardening thereof is attained in a cycle .
Suppose now that the speed is increased to 200 .
The range of stress immediately becomes less , because of the diminished time for slipping ; the rate of slipping , and therefore the production of mobile material , becomes more , while the time for hardening per cycle is less , the resultant being an increase of range of strain until again an approximate balance per cycle is approached .
The cost of the machine and apparatus used in the experiments has been defrayed by grants from the Eoyal Society , the Institution of Mechanical Engineers , and the University of Liverpool .
The author is indebted also to Prof. W. H. Watkinson for facilities for carrying on the work in the engineering laboratories of the University of Liverpool .
|
rspa_1916_0023 | 0950-1207 | On Prof. Joly's method of avoiding collision at sea. | 377 | 381 | 1,916 | 92 | Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character | H. C. Plummer|Prof. J. Joly, F. R. S. | article | 6.0.4 | http://dx.doi.org/10.1098/rspa.1916.0023 | en | rspa | 1,910 | 1,900 | 1,900 | 3 | 91 | 2,060 | http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1916_0023 | 10.1098/rspa.1916.0023 | null | null | null | Tables | 26.660294 | Fluid Dynamics | 22.849492 | Tables | [
34.09297180175781,
-6.459843158721924
] | 377 On Prof. Jolys Method of Avoiding Collision at Sea .
By H. C. Plummer .
( Communicated by Prof. J. Joly , F.R.S. Received February 10 , 1916 .
) The ingenious method proposed by Prof. Joly* for avoiding collision at sea is so simple , both in principle and in practice , so far as can be judged without actual experience , that it may seem superfluous to attempt to introduce still greater simplicity .
But this quality is so important in expedients of the kind that an attempt may find excuse .
Since the problem of collision is essentially a question of relative position , it is naturally reduced to the lowest terms of simplicity by employing the relative speed of the approaching ship B. By the familiar artifice of superposing the reversed speed of ship A on both ships , A is brought theoretically to rest without altering the conditions of the problem .
It is therefore necessary that the relative speed should be known .
The method presupposes that the speed and course of the approaching ship B is communicated beforehand to A by wireless .
By a combination of three scales similar to Prof. Joly 's collision predictor , f a seaman on the ship A is in a position to find this speed very simply without any numerical calculation .
He lays the scale a ( fig. 1 ) in a direction representing his own course , and the scale b in the direction representing the course of the approaching a X * P. 176 , supra .
t P. 252 , supra .
Mr. H. C. Plummer .
On Prof. Jolys ship B. The corresponding speeds being OX , OY , a scale c being brought into the position XY measures the relative speed and direction of approach of the ship B. So long as the course of A is unaltered , the point X is fixed , and for any passing ship it is only necessary to rotate b and c in a suitable manner .
If millimetre scales be used , knots may be represented by centimetres , and ample accuracy will be obtained without excessively long scales .
The most convenient form of this simple apparatus is a matter of detail .
The relative speed and course of every passing ship should be recorded .
When the relative speed of the approaching ship B is known , the conditions are considerably simplified .
When the actual courses are used , the locus of B is a series of circles of which the centres advance with A at the time when the successive signals are received .
With the relative speed , A is brought to rest and the locus of B at the successive signals is a series of concentric circles .
The principle involved is now obvious .
The rate of approach to the centre from an outer to an inner circle is a maximum along a radius .
If ( fig. 2 ) the relative course is radial , the change of distance indicated by two signals , at an interval of 2 min. , is equal to the displacement produced by the relative speed in 2 min. If there is perfect accuracy a collision will then ensue .
If the distance indicated by the signals is less , the approaching ship will pass on the one side or the other .
The distance is calculable , but there is nothing to decide between the two courses c\ and c-2 .
The distance indicated by the signals cannot be greater than that which is covered in 2 min. at the relative speed , unless a mistake has been made .
It remains to consider the simplest and most rapid way in which the comparison is to be effected between the actual displacements shown by the signals and the displacements which correspond to the relative speed maintained during successive intervals between the signals .
Prof. Joly has described one method .
Two others may be suggested .
In the first ( fig. 3 ) a proportional scale is used .
The top line is divided to show knots , corresponding to the relative speed .
A vertical line under 30 knots is divided to show miles on a convenient scale .
These divisions are joined to the zero of the horizontal scale by straight lines which correspond to the intervals of time , 2 min. , 4 min. , . . .
Thus , if a vertical scale S , divided in the same scale of miles , be placed at any point of the top line , say at 15 knots , the position of the zero at the bottom of the scale will indicate the time necessary for a given displacement at 15 knots .
Hence it is only necessary to place the scales at the position on the knot line corresponding to the relative speed .
When the first signal gives the distance of the approaching ship , the scale S is moved vertically to this distance and clamped .
Then the position of the bottom of this scale gives at once the Method of Avoiding Collision at Sea .
time at which the collision is to be expected , if it occurs at all .
When the second signal is received the distance is compared directly with the reading of S on the 2 min. line .
If it agrees within the limit of error , danger is indicated .
The distance shown by the third signal is compared with the reading of S on the 4 min. line , and so on .
If several signals can thus be compared with a scale always in view , the advantage will be gained of being able to discriminate to some extent between accidental errors and the cumulative deviations in the readings which indicate a real margin of safety .
For simplicity of explanation the scale S has been taken to be divided so as to show nautical miles .
But the signals give directly a lag in seconds , from which the distance in miles is deduced by dividing by an appropriate factor , 4*3 for aerial and submarine sounds , 5*5 for aerial and simultaneous wireless signals .
This division , though it would naturally be done by a Table , can be avoided altogether .
The scale S can be divided so as to read directly the number of seconds in the time lag instead of the corresponding distance in miles .
No calculation is then involved .
The same object could be secured in another way , if it were desired to retain miles , and there is 380 On Prof. Jolys Method of Avoiding Collision at Sea .
an obvious advantage in this .
Prof. Joly proposes to use a stop-watch to measure the lag .
It would be easy to provide a dial which would indicate miles directly , either on one system of signals , or if necessary on both .
The other method avoids the use of the proportional scale and the scale S. This comes very near Prof. Joly 's own method .
Advantage has already been taken of his Collision Predictor .
It has been supposed that the three scales ay b , and c ( fig. 1 ) are divided so as to show knots .
Instead , let c be divided so as to show the number of seconds in the signal lag which corresponds to the displacement produced by the relative speed maintained for 2 min. , the interval between successive signals .
As a simple numerical process is now intended , an example will serve the purpose of explanation best .
Let the reading on scale c of the Collision Predictor be 3*6 sec. , which corresponds to a relative speed of about 20 knots .
Let the first signal noted show a lag of 18'4 sec. Then the following numbers may be written down :\#151 ; c. Signal .
c. 0 .
0 1 o sec. min. sec. sec. 3*6 0 18 4 18 *4 \#151 ; 2 14 -8 14 *9 + 0*1 4 11 *2 11 *5 + 0*3 6 7*6 8*2 + 0*6 8 4-0 5*4 + 1*4 10 0*4 4*0 As soon as the number 18*4 has been received , the column headed C can be written down at once by subtracting 3'6 in succession .
This shows that a collision will take place , if at all , after the lapse of 10 min. The lag given by each signal is recorded under 0 as received .
The column 0 \#151 ; C records the difference .
Here the second signal gives a distinct warning .
This becomes less insistent with the third signal , but a margin of error must be allowed .
The fourth signal is fairly reassuring , but the fifth signal is .
decisive .
In this example the ships pass within a mile of each other .
The process is the numerical counterpart of the scales used in the first method .
In order that the principle involved may be used effectively , it is clear that the ship which under the rules for avoiding collision at sea is not responsible shall hold its course unchanged regardless of consequences .
Geometrically , the principle may be expressed in the obvious form that the shortest distance between two concentric circles is along a radius .
To this simple fact is due the unique solution of the collision problem from measures of mutual distance .
It is also evident that this use of a minimum The Ignition of Gases hy Impulsive Electrical Discharge .
381 property does entail a corresponding disadvantage .
It implies a lack of sensitiveness , which is geometrically obvious , in the method when the relative course lies fairly near the critical course .
Whether this would give rise to false alarms which might tend to discredit the method , is a question which must be decided by practical experience .
The Ignition of Gases hy Impulsive Electrical Discharge .
By Prof. W. M. Thoenton , D.Sc .
, D.Eng .
, Armstrong College , Newcastle-upon-Tyne .
( Communicated by the Hon. Sir Charles Parsons , F.R.S. Received November 15 , 1915 .
) 1 .
Sparking Distance .
Disruptive electrical discharge through a gas depends upon the number and nature of the molecules between the sparking points.* On the theory log */ p *-/ 3 of ionisation by collision , the sparking distance S where is the number of pairs of ions generated by a negative ion in moving through a centimetre of the gas , / 3 the number generated by a positive ion.f In a mixture of gases , a and f3 both vary with the degree of mixture .
The addition of air to pure helium , for example , lowers / 3 more than a , and increases S. The electric strength of solid and liquid insulators has been shown to have at first the law S = av + bv2 up to values of S measured in centimetres ; following this , a final stage v = A + BS is generally found .
In gases , the measurements of de la Eve and Muller have shown that the first law holds for airJ up to 11,000 volts ; many subsequent measurements can be represented by the second , especially when the gas pressure is reduced to a few millimetres of mercury .
There appear to be no values on record of the change of the electric strength of gases when the pressure is impulsive .
A few of these are given in fig. 1 ; both stages are well marked .
When the mixture is inflammable , the passage of a spark may cause * W. de la Rue and H. W. Muller , 4 Phil. Trans. , ' vol. 171 , p. 102 ( 1880 ) .
t J. S. Townsend , 'Electricity in Gases , ' p. 322 .
J C. P. Steinmetz , " On the Disruptive Strength of Dielectrics , " 'Trans .
Amer .
I.E.E. , ' vol. 10 , p. 64 ( 1893 ) .
|
rspa_1916_0024 | 0950-1207 | The ignition of gases by impulsive electrical discharge. | 381 | 401 | 1,916 | 92 | Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character | Prof. W. M. Thornton, D. Sc., D. Eng.|The Hon. Sir Charles Parsons, F. R. S. | article | 6.0.4 | http://dx.doi.org/10.1098/rspa.1916.0024 | en | rspa | 1,910 | 1,900 | 1,900 | 12 | 330 | 7,178 | http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1916_0024 | 10.1098/rspa.1916.0024 | null | null | null | Thermodynamics | 43.809514 | Electricity | 27.323105 | Thermodynamics | [
3.9011802673339844,
-52.668487548828125
] | The Ignition of Gases hy Impulsive Electrical Discharge .
381 property does entail a corresponding disadvantage .
It implies a lack of sensitiveness , which is geometrically obvious , in the method when the relative course lies fairly near the critical course .
Whether this would give rise to false alarms which might tend to discredit the method , is a question which must be decided by practical experience .
The Ignition of Gases hy Impulsive Electrical Discharge .
By Prof. W. M. Thoenton , D.Sc .
, D.Eng .
, Armstrong College , Newcastle-upon-Tyne .
( Communicated by the Hon. Sir Charles Parsons , F.R.S. Received November 15 , 1915 .
) 1 .
Sparking Distance .
Disruptive electrical discharge through a gas depends upon the number and nature of the molecules between the sparking points.* On the theory log */ p of ionisation by collision , the sparking distance S where is the number of pairs of ions generated by a negative ion in moving through a centimetre of the gas , / 3 the number generated by a positive ion.f In a mixture of gases , a and f3 both vary with the degree of mixture .
The addition of air to pure helium , for example , lowers / 3 more than a , and increases S. The electric strength of solid and liquid insulators has been shown to have at first the law S = av + bv2 up to values of S measured in centimetres ; following this , a final stage v = A + BS is generally found .
In gases , the measurements of de la Eve and Muller have shown that the first law holds for airJ up to 11,000 volts ; many subsequent measurements can be represented by the second , especially when the gas pressure is reduced to a few millimetres of mercury .
There appear to be no values on record of the change of the electric strength of gases when the pressure is impulsive .
A few of these are given in fig. 1 ; both stages are well marked .
When the mixture is inflammable , the passage of a spark may cause * W. de la Rue and H. W. Muller , 4 Phil. Trans. , ' vol. 171 , p. 102 ( 1880 ) .
t J. S. Townsend , 'Electricity in Gases , ' p. 322 .
J C. P. Steinmetz , " On the Disruptive Strength of Dielectrics , " 'Trans .
Amer .
I.E.E. , ' vol. 10 , p. 64 ( 1893 ) .
Prof. W. M. Thornton .
ignition , but in many gases it is possible to have brilliant sparks which do not cause ignition of the most inflammable mixtures.* PRIMARY AMPERES Fi ; yl C V V .
l 5 1 o 1 5 r lo 2 .5 .
30 SPARK LENGTH .
MILLIMETRES .
2 .
Ignition by Impulsive Discharge .
The curves of fig. 2 show that the relation between igniting spark length and voltage V is very different from that of fig. 1 .
The shorter the spark the AMPERES .
SPARKGAP MILLIMETRES * " The Electrical Ignition of Gaseous Mixtures , " 'Roy .
Soc. Proc. , ' A , vol. 90 , p. 272 : ( 1914 ) .
The Ignition of Gases hy Impulsive Electrical Discharge .
383 more difficult ignition becomes , except in those mixtures which are ignited by the first spark that passes .
Carbon monoxide has a regular series of steps which are of exceptional interest .
Their envelope has the simple law ( i\#151 ; a ) S = b , a constant .
The sectional area of the spark is proportional to the current passing , approximately .
Since a is small , the volumes of the least igniting sparks are the same whatever the spark length .
Tn other words , the number of electrons required for the ignition of this gas is the same always .
It will be shown later that Y is proportional to i , the primary current broken .
Writing IS = c , and substituting for S its value in either of the equations of S 1 , V is seen to be constant for all spark-lengths or of the form given by van der Waal 's equation , a horizontal line dividing the unstable part of the curve equally .
This is the shape of the experimental curve , a hyperbola on which are superposed steps having V constant .
The principal steps apparently originate from and coincide with the end of the transition stages in the pure combustible gas and in air in fig. 1 of the spark or glow .
When the voltage between the sparking points is maintained , the spark passes at a lower voltage than when it is impulsive .
Recent experiments on oils have shown that twice the steady sparking voltage is necessary in the latter case.* Under steady pressure there is always an interval of time between its application and the passage of a disruptive spark .
With impulsive pressures , such as are produced in high-tension magneto-ignition of internal combustion engines , the electric field and rate of initial ionisation must of necessity be greater in order that a spark may pass before the impulse has died down .
3 .
Impulsive Brush Discharge and True Spark .
Impulsive sparks , observed by focussing a lens magnifying five diameters upon the gap , differ in appearance from those obtained by maintained voltage .
As the sparking voltage is raised by increasing the primary current there appears first a bright momentary glow or brush discharge at each pole .
Observed by the eye alone without magnification these appear to be ill-defined sparks , but at a critical voltage the discharge becomes suddenly a true spark , more brilliant and of uniform cross-section throughout its length , which the glows were not .
Ignition is not confined to the true spark , but may occur with an intense brush glow , the formation of the glow appearing to depend upon whether the poles are thoroughly cleaned .
After several explosions , even of hydrogen and air , or after standing for many minutes in * W. Peek , Jun. , " The Law of 'Corona ' and Spark-over in Oil , " 'General Electric Review , ' New York , vol. 18 , No. 8 , p. 826 ( August , 1915 ) .
Prof. W. M. Thornton .
contact with carbon monoxide , for example , before the spark is made , the latter becomes more difficult to produce .
The ratio of the brush to the true sparking voltage is shown in fig. 1 for hydrogen , and is about 0'6 in several cases .
4 .
Secondary Voltage Proportional to Primary Current .
The voltage induced in the secondary circuit of a transformer or induction coil when a steady current in the primary circuit is broken is perhaps the most easily controlled impulsive pressure .
In every such case the secondary voltage e2 = dN2/ dt , the rate of change of the flux N2 through the secondary coils .
From the theory of transformers , N2 = 47rhTiT2/ E , R being the reluctance of the magnetic circuit , i\ the primary^ current , Ti , T2 the primary and secondary turns .
In a transformer with an open magnetic circuit , such as an induction coil , R does not vary with the primary current , the magnetisation of the iron is on the straight part of the BH curve .
When the primary current is steady and suddenly broken , e2 varies as di\jdt .
For the same mechanical rate of break , di\/ dt is directly proportional to i ] .
In this case the secondary volts are proportional to the primary current .
It is therefore necessary to use a switch with a constant spring release in order to obtain consistent results .
In the following work the ordinates of the curves are the primary currents which , when broken , cause a secondary spark that just ignites the mixture .
These single impulsive discharges have been called " jump-sparks , " * to distinguish them from " extra-current " sparks made at the point of breaking a circuit .
5 .
Condenser Discharge and Stepped Ignition .
The discharge of a condenser by bringing together quickly wires attached to its terminals is impulsive , for ionisation does not begin until the gap is extremely small , and the discharge is complete in a millionth of a second , before the gap is closed .
Ignition by condenser discharge has definite critical stages , which occur as the percentage of oxygen is diminished . !
The difficulty of choice between an oxygen atom and several possible partners of combustible gas becomes suddenly acute , in steps which form a regular progression , each rise corresponding to the want of an oxygen atom .
There may be more than one combustible molecule in the critical group causing the step .
These steps have been considered , from the point of view of combustion , by Prof. Bone , J who believes that they cannot be accounted for by the usual * " The Reaction between Gas and Pole in the Electrical Ignition of Gaseous Mixtures , " loc. cit. , p. Xfc4 .
t " The* Ignition of Gases by Condenser Discharge Sparks , " 'Roy .
Soc. Proc. , ' A , vol. 91 , p. 17 ( 1914 ) .
X Presidential Address to Section B , British Association , Manchester ( 1915 ) .
The Ignition of Gases by Impulsive Electrical Discharge .
385 chemical laws .
The evidence for them , based on many observations , is complete , and they must be regarded as pre-chemical atomic combination , caused by direct electrification , made visible by the extreme rapidity of this electrical discharge .
Steps of a similar kind have been obtained in the ignition by impulsive discharge of gases below atmospheric pressure .
They appear in a rising series as the pressure is lowered .
When they are not found the product of the voltage and gas pressure is approximately constant .
Steps have also been found by varying the length of the spark-gap , as shown in fig. 2 , from a different cause .
6 .
The Products of Combustion are Ionised .
The role of ionisation in explosion is still in debate .
There is strong probability that it dominates electrical ignition ; during self-ignition and the passage of flame there is evidence that it exists .
I have found that the products of gaseous explosion , especially of carbon monoxide , carry a strong positive charge , with the exception of the combination of hydrogen and oxygen , where there is little or none .
7 .
Percentage of Gas Varied .
When the spark-gap length is kept constant and the percentage of combustible gas in the mixtures is varied , curves connecting igniting impulsive voltage and percentage of gas are obtained , which are of interest when compared with those found with other kinds of ignition .
The purpose of the present paper is to give examples of these and to show by another method the existence of stepped ignition in certain gases , of which cyanogen is the best representative .
In a recent paper by Bone* and others a remarkable proof was given that the affinity of oxygen for methane is many times greater than for hydrogen .
In the present work a mixture of hydrogen and methane in equal volumes , with air just sufficient to burn both completely , requires electrical ignition as if of methane alone .
The hydrogen influences the magnitude but not the type of reaction .
8 .
Experimental Method and Gases used .
The essential apparatus for the production of impulsive discharge , the technique of which is simple , is a powerful induction coil of the usual X-ray type .
The vibrating contact of the primary circuit is locked together and the current made or broken by a separate quick-break switch , which may have a condenser across the break .
The method is to set the sparking points * W. A. Bone , " Gaseous Combustion at High Pressures , " 'Phil .
Trans.,5 A , vol. 215 , pp. 275-318 ( 1915 ) .
Prof. W. M. Thornton .
to a convenient distance apart , 0*5 mm. for hydrogen , 2 mm. for methane , and , starting withi a small current , to break the circuit and observe .whether a spark passes in the explosive mixture .
It is always possible to find a limit to the spark which will fire an inflammable mixture , and the work consists in adjusting the current until a secondary spark is obtained which just causes ignition .
The conditions of ignition are surprisingly sensitive and certain , but the magnitude of the current and , to some extent , the differences observed , depend upon the kind of coil and switch used .
The results are therefore only comparative , and their interest lies in the types of gaseous combustion which are found , rather than in the absolute values of the electrical quantities .
The igniting sparks were made between the flat end of a platinum rod , 2*5 mm. diameter , and a platinum wire , 0*8 mm. diameter .
When smaller wires are used the gap varies , and when they overlap , as in explosion pipettes , the result is .
much less certain .
It is of the first importance that the rods to the sparking points should be led through rubber stoppers , the inside surface of which should be smeared with some non-hygroscopic substance to prevent condensation .
If not , the vessel must be kept thoroughly dry by exhaustion after each explosion , with a Geryk pump , for example .
Working in darkness , a discharge around the inner surface of the glass can be seen when these precautions are not taken , which increases the measured igniting current .
The poles were removed after every few explosions , thoroughly wiped with a fresh filter paper , and set by gauge to the same distance apart .
The gases were examined in four groups : ( 1 ) paraffins\#151 ; hydrogen , methane , propane , and pentane ; ( 2 ) olefines\#151 ; ethylene , and acetylene ; ( 3 ) carbon monoxide and cyanogen ; ( 4 ) coal gas and a mixture of hydrogen and methane .
The methane and propane were condensed and fractionated , and for them I am indebted to Dr. R. Y. Wheeler .
The others were carefully prepared and purified , but without liquefaction .
9 .
Hydrogen .
The results with hydrogen are given in fig. 3 .
The limits of inflammability , with a gap of 0*5 mm. , were 9 and 61*5 per cent. The curve has a mean straight line base , inclined upwards as the percentage of hydrogen is raised , in the manner of ignition of hydrogen by alternating current break-sparks , * or of the^paraffins by continuous current breaks .
In the present case , however , there are to be observed points of selective difficulty of ignition * " The Electrical Ignition of Gaseous Mixtures , " loc. cit. , p. 284 , fig. 6 .
The Ignition of Gases by Impulsive Electrical Discharge .
387 which are persistent .
There is a cusp at 17*5 per cent. , others at 29*5 per cent , and at 42 per cent. , a rapid rise at 55 per cent. , and the limit towards 62 per cent. These may be compared with the following:\#151 ; H2 + 02 = 17*1 per cent. PERCENT ofhydrogen in air in air , H2 + 0 = 29*2 per cent. , 2H2+0 = 45*2 per cent. , 3H2 + 0 = 55*2 per cent. , and 4H2 + 0 = 62*2 per cent. The steps in condenser ignition* were at 29*5 , 45 , 55 , and 70 per cent. , the upper limit with that type of ignition , which is at 6H2 + 0 = 70 per cent. It is impossible , in the agreement of the new points with the condenser curve , to resist the conclusion that when singular points or critical conditions of ignition arise they are in both cases of impulsive discharge associated with the number of atoms in contact , irrespective of whether known compounds are formed .
Sir J. J. Thomson has shown that transient groups in every possible combination of the gases present are formed by discharge in high vacua , f An inclined line passing through the origin was shown to be characteristic of ignition by break-sparks , J and was there attributed to the * " Ignition by Condenser Discharge Sparks,55 loc. cit. , p. 21 .
+ ' Rays of Positive Electricity and their Application to Chemical Analysis,5 figs. 35 et seq. X " The Electrical Ignition of Gaseous Mixtures,55 fig. 2 .
Prof. W. M. Thornton .
effort required to ionise the combustible gas .
It is now found with a spark the essential feature of which is ionisation .
10 .
Methane .
With this kind of ignition methane appears to be sensitive to slight changes on the surface of the poles .
With the pure gas sent by Dr. Wheeler the limits were 6 and 12'5 per cent. , as shown in fig. 4 .
If the poles were AMPE .
RES 7 6 I o II IZ 13 14PER CENT OF METHANE IN AIR not cleaned after every few explosions , steps appeared in the curve even with this gas , which disappeared again when the poles were cleaned .
The fact that steps are found at all indicates that from a chemically clean surface of platinum ionisation is more difficult to start than after it has been in contact with products of combustion , for the stepped type is associated with great rapidity of action .
The steps with condenser discharge were at 11 , 13 , and \#171 ; \#166 ; 14 per cent.* In the present case they were at 6 , 7 , 7'5 , 9'75 , 11 , and 12 per * " Ignition by Condenser Discharge Sparks , " loc. cit. , fig. 2 .
The Ignition of Gases hy Impulsive Electrical Discharge .
389 cent. If there were any rigorous relation between steps and percentage , it might be expected to be found in both kinds .
There is one common point at 11 per cent. The relative slowness of ignition of methane , and the fact that the steps can be prevented with this kind of ignition , render it necessary to use only condenser discharge in the examination of the formation of atomic groups of methane and oxygen , or to work withi reduced pressures .
The base of fig. 4 is horizontal ; ignition is thus independent of the percentage of combustible gas or of the heat of combustion of unit volume of the mixture .
The disruptive voltage Y = aS4-\amp ; is constant for a given spark length S , and as the percentage of methane in air is varied can be shown to remain nearly constant .
A separate determination ( fig. 1 ) of the relation of Y and S in terms of the primary current gave the following , S being in millimetres and i in amperes .
i = 0*12 S +0*25 , for methane , i = 0*074 S + 0*4 , for air .
With a spark gap of 4 mm. i = 0*49 in pure methane , 0*548 in air alone , and 0*495 in 10-per-cent , methane in air .
The change of disruptive voltage with percentage of gas is therefore small .
Since the heat of combustion of unit volume of the mixture varies greatly between the limits of inflammability , the conclusion is that the electrical ignition of methane is a process unaffected by thermal reactions in the gas , , that it is in fact electrical and not chemical .
The view that would seem to* satisfy the conditions is that during the active ionisation preceding the spark there is recombination depending chiefly upon the sign of the charges carried .
It is in this stage that the stepped ignition originates , determined only by the relative numbers of molecules or atoms of combustible gas and oxygen that are ionised .
Stepped ignition cannot occur after self-ignition has started , for the velocities of explosion measured by Dixon show no signs of it .
It must , therefore , occur before the establishment of the explosion wave , that is in the preliminary ionisation stage .
Condenser discharge of extreme rapidity is most favourable to its formation ; the impulsive discharge of the present work also brings it out in acetylene and cyanogen .
The fact that flat-based curves closely resembling fig. 4 have previously been found for both hydrogen and carbon monoxide with much slower circuit break sparks , would lead to the conclusion that the rate of ionisation of both of these gases in the act of ignition is relatively slow , though their explosion waves , once established ( which are dominated by the great thermal energy set free ) , are faster than in methane .
vol. xcn.\#151 ; A , 2 a Prof. W. M. Thornton .
Dr. Bones discovery of the greater affinity of oxygen for methane than for hydrogen , together with the present curves , may then be additional proof that ionisation precedes combustion , so far as the form of the ignition curve for disruptive discharge is an indication of the relative rates of ionisation in the different mixtures .
The wave front of an explosion wave in a closed vessel : is not drawn along by preparatory ionisation but driven forward by the translational energy of the flame and products of combustion behind it .
11 .
Propane .
Ignition was in this case so difficult that the gap had to be increased to 4 mm. between platinum points .
The curve of fig. 5 is not unlike hydrogen PER CENT OF PROPANE IN AIR and carbon monoxide .
There is a step at 4 per cent. , combustion to CO2 being at 3'96 , and a remarkable cusp at 6 per cent. , verified many times .
Combustion to CO is at 5*56 , and it would seem that propane , like methane , though e\amp ; sy to burn to CO in explosion , is hard to ignite to CO by impulsive sparks .
There was a step at 6 per cent , in condenser-spark ignition .
The Ignition of Gases by Impulsive Electrical Discharge .
391 12 .
Pentane .
The curve ( fig. 6 ) is very like hydrogen , free from singular points .
The limits of horizontal transmission are 1*35 and 4*5 per cent. In the present 1-0 i 5 2.0 2-5 3 0 3 5 4o ^5 50 5-5 6 0 PER CENT OF PENTANE INMR case , 1*5 per cent , could not be ignited , and , though there was a clear approach to an upper limit at 4*5 per cent. , the mixture was readily ignited up to 5*5 .
Above 4'5 a burning cap appeared where the spark had passed , diminishing as the richness of the mixture was increased .
The most inflammable mixture is 2*75 to 3 per cent. , that for perfect combustion being 2*51 .
The descending branch and base produced intersect at 2*6 per cent. The curve is identical in form with that obtained by continuous current break-sparks .
Since hydrogen and pentane are similar , and propane intermediate between the methane and pentane types , it suggests that the ignition of methane is abnormal , rather than that of hydrogen .
As a further test of this the limits of inflammability are of interest .
13 .
Limits of Inflammability of the Paraffins .
Wheeler has shown that the lower limit of inflammability of all the paraffin series up to pentane is inversely proportional to their calorific Prof. W. M. Thornton .
values.* It is , however , possible that both upper and lower limits depend as much upon the relative number of oxygen atoms in the mixture .
The limits are as follows ( Table I):\#151 ; Table I. Lower , L. Upper , U. Oxygen , n. nV .
Per cent , for ( 2\#187 ; \#151 ; 1 .
) Hydrogen , H2 9*0 72 -0 1 72 0 _ Methane , CH4 Ethane , C2H6 5*6 14-8 4 59 -2 5*55 3 T 10 -7 7 74-9 3*08 Propane , C3H8 2T7 7 35 10 73 -5 2*12 Butane , C4H10 1 -55 5-7 13 74 -1 1 -62 Pentane , CgH^ 1 *35 4-5 16 72 '0 1*31 In the fourth column is the number of oxygen atoms required for complete combustion of a molecule of the gas .
The product of this and the upper limit is nearly the same for all but methane , which should have another atom of oxygen to bring it into line .
The upper limit of inflammability is ( with this exception ) inversely proportional to the number of oxygen atoms required for complete combustion , irrespective of whether they combine with carbon or hydrogen .
That is to say , the action of the combustible gas is molecular and not in the first place atomic .
The upper limit of inflammability of the paraffins is reached when the volume of combustible gas is twice that for perfect combustion , as shown in Table II .
Table II .
Mixture .
Gras in air .
i Observed upper limit .
2CH4 + 04 2C2H6 + Or per cent. 17 -2 14 -3 10 5 10 *7 2C3H8 + O10 7*6 7*35 2C4H10 + 013 5*9 5*7 205H12 + O16 \ 4*9 4*5 On the other hand when the volume of oxygen is twice that required for perfect combustion ignition fails at the lower limit .
When , however , there is one atom less than this , so that the mixture corresponds to ( 2n\#151 ; 1 ) atoms of oxygen to a molecule of combustible gas , ignition is just possible .
There is a close coincidence between the lower limit for horizontal transmission and * " The Lower Limit of Inflammation of Mixtures of the Paraffin Hydrocarbons with Air.'* By M. J. Burgess and E. Y. Wheeler , ' Chem. Soc. Journ. , ' vol. 99 , p. 2013 ( 1911 ) .
The Ignition of Gases hy Impulsive Electrical Discharge .
393 these mixtures , as shown in Table I. In this case methane agrees with the others .
14 .
Ethylene .
The ignition of ethylene is unique amongst the gases examined , in that the richer mixtures are easiest to ignite .
' Its lower limit is here between 5'5 and 6 per cent. , its upper limit at 17 per cent , ( see fig. 7 ) , combustion to CO\#171 ; is at amperes l iO II 12 .
13 1-4- IS 16 17 PERCENT OP ETHYLENE IN AIR 6*5 , to CO at 9*4 per cent. The mixture C2H4 + 03 = 12*1 per cent. , and the three flat stages are approximately symmetrical about the mixtures having 06 , O4 and O3 respectively .
The lower limit is then just below ignition to CO2 ; the upper limit corresponds to C2H4-f 02 = 17*1 per cent , in air .
There is no reaction with less air than this .
Ignition of ethylene is with these sparks easiest when ozone is most readily formed around the combustible molecule ; next when two molecules Prof. W. M. Thornton .
of oxygen , and lastly three , collide most frequently with it .
It is a remarkable illustration of the control of ignition by ionised oxygen .
15 .
Acetylene .
This is an example of the methane type with a lower limit just below 3 per cent , and an upper limit at 48 per cent. From 5 to 20 per cent , the smallest spark which could be made with the gap used caused ignition .
At 20 per cent , there is a remarkable step , which is emphasised by using a short spark-gap .
The three curves A , B and C , fig. 8 , show the influence of gap AMPERES 15 SO 2J5 30 35 A-S 50 PER CENT OF ACETYLENE INAiR .
length .
When it is 1*5 mm. no spark or ignition is obtained with less than 0-6 ampere in the primary circuit ; with 11 mm. it is 0*3 ampere , with 0*8 mm. 0'25 ampere , and the rise of current in the step at 20 per cent , is in the three cases 0*6 to 1*5 , 0*3 to 3*0 , 0*25 to 5*0 amperes respectively .
Two things are here evident , first that when a short gap is used the upper limit may be less The Ignition of Gases hy Impulsive Electrical Discharge .
395 than that found with a longer one , provided that there is stepped ignition ; second that with a long gap the steps might be quite obliterated , since the effect of lengthening it is to raise the first flat and to lower the succeeding ones .
The gas in curves B and C is the same , well purified and passed through a freezing mixture .
The step with one gap is at 20 per cent. , with the other at 25 .
This movement of the step has been observed in the case of methane and is most probably due to the strong first spark which passes forcing the 20 per cent , step towards 29'2 the next possible step here .
It is midway between 21-6 and 29'2* Above 45 per cent , there is local burning but not true explosion .
The influence of gap length is that the fewer the molecules there are between the poles the more important the critical collision frequency becomes .
At 22 per cent , carbon is thrown down by the explosion in heavy clouds , below this much less .
The following mixtures appear to be critical , the 03 mixture having , as with ethylene , most influence on the form of the curve:\#151 ; Table III .
Mixture .
Gas in air .
C5H.J + 0^4 per cent. ' 2*86 7*6 21 *6 29 *2 45 *4 Lower limit .
Step .
Step .
Upper limit .
2C2H2 + Ojo 2C2H2 + O3 2CnHo + 02 ... 2C2H2 + 0 " .
16 .
Gavion Monoxide .
There is a general resemblance of the carbon monoxide curve ( fig 9 ) to that of hydrogen .
Its limits are 9'5 and 70 per cent. , and the mean base line passes through the origin .
To avoid any possible poisoning action between the platinum poles and the gas , they were fitted with carbon pencil points , having a 1-mm .
gap , between which the discharge passed .
The slope of the base , measured in amperes per unit percentage of gas and per unit length of spark-gap , is now 0-06 , not very different from that of hydros which was 0-05 .
The salients in the curve were always well established .
' e mixture for CO + 03 is 12-1 per cent. , the most easily ignited acetylene and ethylene .
' :en , as in * See also " Condenser Spark Ignition , " loc. tit .
, p. 19 .
39,6 Prof. W. M. Thornton .
amperes 30 35 PERCENT OF CARBON MONOXIDE IN AIR .
17 .
Cyanogen .
The ignition of cyanogen is perhaps the most suggestive of all the gases examined .
Its lower limit , with impulsive sparks , is at 7*7 per cent. , the upper at 38 per cent. ( fig. 10 ) .
Starting from the lower limit , there is first a deep dip as if to a minimum at 8 per cent. This is followed by a unique rise and a descent by a step , as in ethylene , to a flat stage between 12 and 17 per cent. There is a rise at 30 per cent , and another at 35 per cent. , followed by the upper limit .
The most interesting feature is the clear role of atomic oxygen in the formation of steps .
Table IY .
Mixture .
o/ c2n2 .
Gas in air .
c2n2+o5 5 per cent. 7*6 Lower limit .
C2N2+04 4 9*3 Step A. C2N2 + O3 3 12 2 " B. C2N2 + 02 C2N3 + 0 2 17 *1 " 0 .
1 29 -2 " D. 4C2N2 + 02 2 35 *4 " E. 3C2N2 + 02 | 38 *0 Upper limit .
The reaction at the upper limit is 3C2N2 + O2 = 2C2N2 + 2CO + N2 .
The Ignition of Gases hy Impulsive Electrical Discharge .
397 AMFELRE .
S \ 1 y Fi g.lQ ' Ej A 1 D .
J 1 u j 1 _ y J |7 i I 1 L 0 5 IO 15 20 25 30 35 40 45 PER CENT OF CYANOGEN IN AIR 18 .
Coal Gas .
The high efficiency to which gas-engine ignition has been brought is made possible by the fact revealed in fig. 11 , that the same electrical ignition is sufficient for all mixtures .
The curve is that of methane .
In the present case the lower limit is at 9-5 per cent. , that of hydrogen in air .
The upper limit is at 29 per cent. The gas is more sensitive to ignition than methane and in magnitude of current approaches hydrogen .
The flat base is of the greatest importance in gas-engine practice .
As a working substance a mixture of methane and hydrogen is almost ideal .
The steps may be possibly due to some action on the poles , though care was taken to remove deposit .
vol. xcn.\#151 ; A. Prof. W. M. Thornton .
amperes 6 I * O ___________ ______________________ , --5 lO 15 20 2.5 30 PER CENT OF COAL G^S IN / MR 19 .
Hydrogen and Methane .
A mixture of equal volumes of pure hydrogen and methane has the curve of ignition given in fig. 12 .
It differs from coal gas only in the more rounded AMPERES PERCENT OF COMBUSTIBLE GAS ^ + F g 1 .
t -J l(v* n .\#151 ; The Ignition of Gases by Impulsive Electrical Discharge .
399 approach to the upper limit .
This is probably owing to the absence of unsaturated hydrocarbons of the ethylene type , which , as shown in fig. 7 , are most inflammable in rich mixtures , and would possibly have the effect of making the corner sharper .
The limits are just below 8 per cent , and above 16 per cent. Ignition follows methane .
This is a striking confirmation of Bone 's measurements of the relative affinities of methane and hydrogen .
It shows further that they hold in the very earliest stage of explosion .
20 .
Types of Electrical Ignition of Gases .
It is now possible to make a preliminary survey of the types of electrical ignition , as illustrated by the curves , having critical electrical conditions for ordinates , percentage of combustible gas in air for abscissae .
There are four , shown in fig. 13 .
First in order of interest and of simplicity is that invariably FlG .
I3 TVPE5 OF ELECTRICAL IGNITION found with condenser discharge .
This is characterised by extreme rapidity ; it is , in fact , one of the most rapid forms of physical activity .
By it the first atomic groupings , following and caused by the initial ionisation but preceding the establishment of self-ignition , are made visible as if by the spark itself .
This type is occasionally found with impulsive coil discharge and is .prechemical .
, In the second type the steps are smoothed out and the curves have an inclined base passing through or nearly through the origin .
The difficulty of finding sufficient ionised oxygen to start combustion occurs here not in steps but uniformly as the percentage of oxygen is diminished .
It occurs equally whether the combustible atom is hydrogen or carbon .
This type is found with impulsive discharge in about half the cases , in the continuous current break-spark ignition of the paraffins and alcohols , in both continuous and alternating current ignition of carbon disulphide , in the alternating 400 The Ignition of Gases hy Impulsive Electrical Discharge .
current ignition of hydrogen , and the continuous current ignition of carbon monoxide.* It is nearly the same whatever the metal of the poles.f The third type can be either placed here or regarded as the most fundamental type of all .
The argument for placing it between the last type and that of Class 4 is based on the clear transition from one type to the other , as the metals of the poles are changed from copper to iron , nickel , aluminium , and platinum .
It is also found in the differences between continuous and alternating current ignition of hydrogen and in carbon monoxide .
In its complete form , with sharp corners and steep sides , it is independent of any chemical combination , and this is a reason for regarding it as the fundamental type .
It depends only upon the electric strength of the mixture or the ionising power of break-sparks .
This type is characteristic of ignition of methane by impulsive sparks , of hydrogen by continuous current break-sparks .
The fourth type is found in the alternating current ignition of the paraffins and alcohols , and in both the alternating and continuous current ignition of benzene .
It has been shown that the relative influence of the metal of the poles on ignition by alternating current is to be explained by their rates of heating .
It follows that , since alternating current ignition is the extreme type of slow ignition and condenser discharge of rapidity , the curves of fig. 13 cover the whole range , and that the type for any given gas depends upon the rapidity of transfer of electrical activity from the circuit to the gas .
Whether there is any change of this with pressure remains to be examined .
21 .
Summary .
The ignition of gases by impulsive discharge is considered first as a function of sparking distance .
It is shown that the shorter the distance the greater the spark , so that the volumes of the least igniting sparks are , in a typical case , the same for all spark lengths .
Ignition may occur with intense momentary brush discharge , generally with the true disruptive spark .
The products of combustion are found to be ionised and to carry a positive charge .
The gases examined were mixtures in air of hydrogen , methane , propane , and pentane ; ethylene and acetylene ; carbon monoxide and cyanogen ; coal gas and a mixture of equal volumes of hydrogen and methane .
Hydrogen , propane , pentane , and carbon monoxide rise gradually in difficulty as the * See " " Che Electrical Ignition of Gaseous Mixtures , " loc. cit. , figs. 2-7 .
t " The [ Reaction between Gas and Pole in the Electrical Ignition of Gaseous Mixtures , " loc. cit. , figs. 1 and 4 .
Atmospheric Electrical Variations at Sunrise and Sunset .
401 percentage of oxygen is reduced ; methane is ignited by the same spark whatever the percentage of gas may be , acetylene and cyanogen have the stepped atomic type of ignition , ethylene is more inflammable in rich mixtures .
Hydrogen and methane in equal volumes are ignited as methane in type , hydrogen in magnitude .
The limits of inflammability of the paraffins are shown to be reached , the upper limit when there is twice the volume of combustible gas to that in the mixture for perfect combustion , the lower limit when the volume of oxygen is twice that for perfect combustion less 1 atom to the molecule .
The ignition of coal gas is through methane .
Four types of electrical ignition are given , covering all from the most rapid to the slowest rate of discharge from the poles .
The work gives direct evidence that ignition begins by ionisation of the oxygen of the mixture .
Investigation of Atmospheric Electrical Variations at Sunrise and Sunset .
By E. H. Nichols , B.Se .
, A.B.C.Sc .
( Communicated by Sir Napier Shaw , F.R.S. Received March 11 , 1916 .
) The scheme of investigation described in the following paper was suggested by the scheme of sunrise and sunset observations formulated in 1913 by the British Association Committee for Radiotelegraphic Investigation .
As the phenomena of wireless transmission are supposed to be primarily associated with the upper atmosphere , any intimate connection between the phenomena here detailed and those exhibited by wireless is unlikely , but it is possible that the two sets of results may throw some light on one another .
As the periods near sunrise and sunset are attended by more conspicuous variations in the intensity of atmospherics or " strays , " special observations were taken at these times .
The instruments used were the Wilson compensating gold-leaf electroscope* and two Ebert electrometers.f The former gave the conductivity , and the air-earth current was obtained by combining this with the potential observations obtained from the Kelvin water-dropper .
The conductivity measured is usually considered to be due to the positive * ' Proc. Camb .
Phil. Soc./ vol. 13 , p. 184 ( 1906 ) ; 'Meteorological Office Memoirs/ No. 7 .
t 'Phys .
Zeit./ vol. 8 , No. 8 , p. 246 ; vol. 8 , No. 16 , p. 527 ; vol. 10 , No. 8 , p. 251 .
VOL. XCII.\#151 ; A. 2 I
|
rspa_1916_0025 | 0950-1207 | Investigation of atmospheric electrical variations at sunrise and sunset. | 401 | 408 | 1,916 | 92 | Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character | E. H. Nichols, B. Sc., A. R. C. Sc.|Sir Napier Shaw, F. R. S. | article | 6.0.4 | http://dx.doi.org/10.1098/rspa.1916.0025 | en | rspa | 1,910 | 1,900 | 1,900 | 7 | 176 | 4,289 | http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1916_0025 | 10.1098/rspa.1916.0025 | null | null | null | Meteorology | 45.852042 | Tables | 18.310432 | Meteorology | [
2.986023426055908,
-46.17842102050781
] | Atmospheric Electrical Variations at Sunrise and Sunset .
401 percentage of oxygen is reduced ; methane is ignited by the same spark whatever the percentage of gas may be , acetylene and cyanogen have the stepped atomic type of ignition , ethylene is more inflammable in rich mixtures .
Hydrogen and methane in equal volumes are ignited as methane in type , hydrogen in magnitude .
The limits of inflammability of the paraffins are shown to be reached , the upper limit when there is twice the volume of combustible gas to that in the mixture for perfect combustion , the lower limit when the volume of oxygen is twice that for perfect combustion less 1 atom to the molecule .
The ignition of coal gas is through methane .
Four types of electrical ignition are given , covering all from the most rapid to the slowest rate of discharge from the poles .
The work gives direct evidence that ignition begins by ionisation of the oxygen of the mixture .
Investigation of Atmospheric Electrical Variations at Sunrise and Sunset .
By E. H. Nichols , B.Se .
, A.B.C.Sc .
( Communicated by Sir Napier Shaw , F.R.S. Received March 11 , 1916 .
) The scheme of investigation described in the following paper was suggested by the scheme of sunrise and sunset observations formulated in 1913 by the British Association Committee for Radiotelegraphic Investigation .
As the phenomena of wireless transmission are supposed to be primarily associated with the upper atmosphere , any intimate connection between the phenomena here detailed and those exhibited by wireless is unlikely , but it is possible that the two sets of results may throw some light on one another .
As the periods near sunrise and sunset are attended by more conspicuous variations in the intensity of atmospherics or " strays , " special observations were taken at these times .
The instruments used were the Wilson compensating gold-leaf electroscope* and two Ebert electrometers.f The former gave the conductivity , and the air-earth current was obtained by combining this with the potential observations obtained from the Kelvin water-dropper .
The conductivity measured is usually considered to be due to the positive * ' Proc. Camb .
Phil. Soc./ vol. 13 , p. 184 ( 1906 ) ; 'Meteorological Office Memoirs/ No. 7 .
t 'Phys .
Zeit./ vol. 8 , No. 8 , p. 246 ; vol. 8 , No. 16 , p. 527 ; vol. 10 , No. 8 , p. 251 .
VOL. XCII.\#151 ; A. 2 I 402 Mr. E. H. Nichols .
Investigation of Atmospheric vertical current flowing to earth , and thus only about one half the total conductivity ; * but there is some difference of opinion on the subject .
The two Ebert instruments were used to record the simultaneous values of the positive and negative charges per c.c. of air .
About 100 observations at sunset have been obtained , each consisting of three 5-minute periods before , and three 5-minute periods after , sunset .
Monthly mean values have been worked out , and these are compared with the values obtained at 3 p.m. on corresponding days , which will indicate the general effect of diurnal variation on the electrical quantities ( Table I ) .
The experiments were made at Kew Observatory , except during August and September , 1914 , when they were performed at Eskdalemuir .
The winter results , being few in number , are grouped together , and include one observation in October , three in November , three in December , and one in February .
The figures in the column " Before sunset " refer to the mean value for the 15 minutes preceding sunset ; and similarly " After sunset " denotes the mean for the 15 minutes following sunset .
The natural inference from the Table is that at Kew the ionic charges are practically the same during 15 minutes before sunset and at 3 p.m. It would have been more satisfactory to have corrected these sunset observations for diurnal variation by a similar process to that adopted later for the potential gradient data , but the corrections would have been small , and could not be found with sufficient precision from the limited number of hourly observations of diurnal variation that have been obtained at Kew .
There is , generally speaking , a marked decrease in all the electrical quantities after sunset .
If we investigate the summer and winter results , the average sunset effect shows little difference for the two seasons , there being a mean decrease of about 20 per cent , after sunset ( see Table II ) .
These results show that the solar effect at sunset is at least as strong in the winter months as in the summer .
The value of the conductivity was also calculated for each 5-minute observation from the Wilson instrument , and similar values were also obtained for the electric charges , which for convenience were expressed in arbitrary units .
The mean values of these quantities obtained at Kew and Eskdalemuir ( fig. 1 ) show that there is no sudden change at any definite period in the 15 minutes preceding or following sunset , but there is a gradual decrease in all the elements .
The curves for Eskdalemuir are not so smooth as for Kew , owing to the fewer number of observations .
As regards the monthly results , fche conductivity variation was most regular for July , 1914 , and winter , 1914-15 , while June at Kew and September at Eskdalemuir are remarkable * Lutz , ' Luftelektrischer Messungen in Munchen/ p. 342 .
Table I.\#151 ; Sunset Observations compared with 3 p.m. Observations ( 15-min .
periods ) .
Electrical Variations at Sunrise and Sunset .
Conductivity x 1028 E.M.U. After sunset .
0 N O C5 O CD OHO0CONN H CO CO id CO H s 01 885 738 2 00 Before sunset .
( M lO ( U \#169 ; N Oi ( N CO rH !
\gt ; .
I'- 00 CO CO 1\#151 ; 1 CO CO CO ^ H H to Ol CO 1125 732 00 Ol 05 At 3 P.M. CO O H \#171 ; ^ 05 W CO ^ H \lt ; N \lt ; M !
\gt ; .
CO CO CO \#169 ; t\gt ; \#169 ; H N to CO " F 1101 796 00 TF 05 .5 .
S 2 \#163 ; x s \#171 ; .
1 a g ft i. | 3 13 After sunset .
^OiN\#169 ; lOOC5 tO t\gt ; t\gt ; Oi X CO Cl CO 1 1 1 Before sunset .
00 ^ X CO \lt ; M 00 CO to X l\gt ; Cl H CO ^ rH rH J\gt ; 1 1 1 Ph CO 76 99 102 104 97 50 65 to 00 II 1 Negative charge per c.c. x 1020 E.M.U. After sunset .
11ISSSS NNHN s Ol 236 255 to rF \lt ; M Before sunset .
1 I 1 CO tO tF \lt ; M 1 1 1 to O O LO ^ CO \lt ; M CO 05 Ol CO 319 440 C5 CO * CO 1 1 I CO CO ^F 1 !
1 o oq oi oo CO CO CO 400 361 00 CO Positive charge per c.c. x 10M E.M.U. After sunset .
C5 CO 05 00 00 \#169 ; 00 O -t H ^ X ^ H CO ^ to rf CO T ?
CO rr* 622 562 \lt ; N 05 to Before sunset .
OlXXN\#169 ; HX \#169 ; ^ 1^ CO \#169 ; \#169 ; ^ ^ CO CO QC CO CO tF 00 to 838 771 s 00 At 3 r.M. C5 f- ^ to 00 01 05 00 T-l Tjl |\gt ; .
CO ''F CO \#169 ; 0 00 CO Tjt T ?
C5 00 to 645 540 \lt ; M 05 to No. of observations .
XO^OHXIO H H rH 1 00 t ?
rH rH 1 Month .
Kew .
Mar. , 1914 April " May " June " July " Winler ( 1914-15 ) Mar. , 1915 Mean Kskdalemuir , Aug. , 1914 Sept. " Mean 2 i 2 Mr. E. H. Nichols .
Investigation of A tmospheric Table II.\#151 ; Values for 15-min .
Period after Sunset as Percentage of Values for 15-min .
Period before Sunset at Kew .
Month .
Positive charge per c.c. Negative charge per c.c. Air-earth current .
Conductivity .
Winter\#151 ; Mar. , 1914 : 66 \#151 ; 93 80 Oct.-Feb .
, 1914-15 ... 94 90 79 75 Mar. , 1915 93 82 63 58 Mean 84 86 78 71 Summer\#151 ; April 69 \#151 ; 94 101 May 76 ?
\#151 ; 92 82 J nne 89 59 76 84 July 73 71 76 76 Mean 77 65 84 86 -5 Sunset +5 +10 +l5 -15min-10 -5 Sunset +5 Positive ioo charge percc .
( arbitrary ' 90 units ) Negative *00 charge per cc .
( are bitrary* ] 90 units ) Conductivity in e.m.u. XI025 Kew .
Eskdalemuir .
Variation of Electric Charges and Conductivity at Sunset Electrical Variations at Sunrise and Sunset .
405 in that the decrease in the negative charge is so pronounced , especially before sunset .
A number of sunrise observations have been taken ( Table III ) , including six at Kew and seven at Eskdalemuir , in a similar manner .
After sunrise there appears to be a slight increase ( 5 per cent. ) in the conductivity , a decrease in the positive charge of 9 per cent. , and the negative charge of 23 per cent. , of the value before sunrise .
This indicates that the solar effect is not so pronounced at sunrise as at sunset .
Sunrise observations are subject to more uncertainty owing to the high relative humidity , which causes trouble with the insulation .
It was found that the most definite change took place in the negative charge for August , 1914 , at Eskdalemuir , showing a general decrease for the sunrise period .
Otherwise there appears to be a tendency for the electrical quantities to decrease till sunrise , and then increase .
Table III.\#151 ; Sunrise Observations ( 15-min .
periods ) .
No. of observations .
Positive charge per c.c. x 1020 .
Negative charge per c.c. x 1020 .
Air-earth current x 1018 .
Conductivity x 1023 .
Before sunrise .
After sunrise .
Before sunrise .
After ' sunrise .
Before sunrise .
After sunrise .
Before sunrise .
After sunrise .
Kew ( July ) ... 6 E.M.U. 496 E.M.U. 548 E.M.U. 183 E.M.U. 171 amps./ cm.2 .
48 amps./ cm.2 .
50 E.M.U. 422 E.M.U. 450 Eskdalemuir ( August ) ... 7 711 548 207 130 \#151 ; \#151 ; 735 764 Mean \#151 ; 603 548 195 150 \#151 ; \#151 ; 578 607 Analysis of Electric Potential Curves for Kew Observatory.\#151 ; The continuous records used were from the Kelvin water dropper during 1912 and 1914 .
The data for 1913 were not used , as the results were not considered reliable owing to disturbances introduced by structural alterations in the main building .
The curves were measured at the exact time of sunrise and sunset , and at 15 , 10 , and 5 minutes before and after each event .
This was done for every day of the month except when there were obvious disturbances due to rain , or defects in the record .
In a few cases , when fog is recorded with abnormal variations of potential , readings have been omitted .
The means for the month , first obtained in millimetres from the curves , are converted into volts per metre in the open by the appropriate factor , and from these the annual mean for the years 1912 and 1914 is deduced .
This is corrected for the diurnal variation by using the means for 1898-1912.* The process adopted * C. Chree , 'Phil .
Trans.,5 A , vol. 215 , p. 133 ( 1914 ) .
406 Mr. E. H. Nichols .
Investigation of Atmospheric was to plot the values of potential gradient for the three hours nearest the sunrise or sunset time , and to draw a smooth curve through the three points \#151 ; e.g. , if sunrise was at 6 h. 10 m. , the hours plotted would be 5 h. , 6 h. , 7 h. The correction at the hour of sunrise or sunset is supposed to be zero , as relative values are all that is required .
The ordinates of the curve are measured for the three 5-minute intervals before and after sunrise or sunset , noticing that the correction is reversed in sign .
The corrections are larger in the winter months , the explanation being that the range is much greater at this time .
For June no correction is necessary .
The mean correction for the year is a few volts : but as it is of the same order as the actual sunrise and sunset change , it is important to see if the correction obtained from using other years , 1912 and 1914 , produces any appreciable difference .
Although the monthly means for these years are much less regular than for the series of years , they give similar corrections , the summer correction being smaller than the winter , while the annual mean correction is practically identical in all three cases .
The monthly mean values indicate generally an increase in potential both for sunrise and sunset , this being more noticeable in the winter months .
Considering the results of the two years for sunrise , an increase in potential after sunrise is found for 15 months , when the means of values before and after sunrise are compared .
For seven months there is a decrease , and lor two months ( July , 1912 , and July , 1914 ) there is no change in potential .
For the sunset observations there are 20 months giving an increase of potential , and four months a decrease .
Thus the increase in potential is more marked for sunset than for sunrise , and agrees with other observations which show a more definite decrease of conductivity and electric charge at sunset than at sunrise .
It is generally observed that in wireless investigation of " strays , " while there is usually a tendency to increase during sunset , anomalous results are more frequently obtained near sunrise .
One would expect a priori that any change would be more marked in summer .
Although this is the case for the electric charges and conductivity , it is not true for the potential .
This is clearly shown in the seasonal means ( Table IV ) .
For the winter there is a well marked increase in the potential .
For the equinoxes it is less marked , especially in 1914 , while for the summer it is either negligible or there is a decrease of potential , as appears in the corrected value for sunrise .
The mean annual variation for sunrise and sunset ( fig. 2 ) shows a small but definite increase in potential , even when corrected for the diurnal variation .
There iSjio indication of any sudden change near sunrise or sunset , but the potential appears to be very steady just at sunrise and a few minutes before sunset , while it increases most rapidly just after sunset .
Table IV.\#151 ; Seasonal Variation of Mean Values of Potc Electrical Variations at Sunrise and Sunset .
05 o \#169 ; ^cc rH \gt ; .2 *3 a Mean after sunset .
p Cl CO 0 1 s CO 368 -5 363 255 -3 252 339 -4 335 478 -3 475 P VO Cl P I CO CO 1 CO VO CO Ol CD | CD Ol 1 Ol Ol p CD | cc 1 V oo VO CO J=2 S CO CO CD CO VO 00 VO _1_ VO 00 CO rH P , VO VO P Ol \lt ; M .
M J\gt ; COO VO CD Cl VO P CM .
CO 01 CO vo CD i CD Cl P CO P .
vo g CO T CO CO + CO CM r CM CO r CO p r p CO ' CO 01+01 CO + CO S.s P Cl o Cl 00 Cl X H CD I CO O CD sF CD 1 VO iH CD \#187 ; 0 P r CO ft- VO \lt ; M I- i ft- P 00 CD P 1 CO 00 P P CD e CD CO CD tree i VO + 3 CO 1 CO CO 1 CO CM 1 OJ CO 1 CO P * p CO 1 CO Ol 1 Ol CO 1 1 CO A S.s Cl CO i CD Cl Cl VO P CD i CD P \#187 ; o 0 \#151 ; l 1 P ft. 1 CO iH CO P ft- i r\#151 ; p VO Cl P 1 CO CD CO CO CD i CD CO P Cl CD l \#187 ; 0 o QQ + 3 CO 1 CO CO 1 CO CM 1 CM CO 1 CO p 1 p CO 1 CO Ol 1 Ol CO 1 CO ? !
3 m \#166 ; f .s ' 00 00 ft ft- 04 VO CD l CD CM VO H rH CD ( CO M P 1 CO ?
H T 00 H o 1 x CO Ol rH p 1 p O rH Cl CD i vo H 01 Cl CD l VO + 5 CO l CO CO 1 CO CM 1 CM CO 1 CO p 1 p CO 1 CO 01 1 Ol CO 1 CO a VO o VO CO CO CO O CD Ol P n S Ol CM \lt ; Cl O M p CD \lt ; o 5 - p p BP O p 01 CD \lt ; 01 D CD vO O vo \#163 ; \#187 ; CO CO CO CO \lt ; M CM CO CO P p 7 PC0 CO Ol 01 CO CO -5 min. p 00 rH + VO CO 359 + 2 361 00 P CM + 1 249 ft- 1 CM CO M Cl .
Ol + CO 00 - VO p + 1 459 333 + 2 335 rH i CD Ol + 1 262 rH l VO CO + 2 353 -10 min. CD CO CO + o CO 354 + 5 359 00 P CM + 3 251 CD CM CO + 4 330 VO VO p + 3 458 O VO VO to .
CO CO ^ CO Ol CD Ol + 3 265 Cl .
p CO + 4 353 -15 min. Cl CD CO VO + 1 ?
CO 345 + 8 353 00 p CM + 5 253 3 CO + 6 327 458 VO CO 4- S3 + P 323 + 8 331 Ol CD Ol + 5 207 00 p CO + 6 354 S ^ 8 48-C co ft- VO Cl O VO VO vO i P CM CD CM O 1 CD rH VO CD t cd o Cl ft- co i x O VO VO i1 CO 5 Ol vo 1 VO o fo ^ 03 S on p 1 CO CM 1 \lt ; M rH 1 r\#151 ; \gt ; M 1 Ol p ' P 01 I 01 rH 1 rH CO 1 CO Mean before sunrise .
p CO + 5 CO 238 + 4 242 VO CD rH + 1 166 259 + 4 263 vO CD P ft- Ol .
ft-+ p 262 + 4 266 is rH rH 00 + 2 vo Cl \lt ; M + 4 299 S.s 1^ Q rH CD Cl NXD VO | p P CD CO rH CD ft- Cl | CD oo Zj ft-ci *7 oo rH 00 CO ft- 1 CO 00 VO CO vo I VO O *T| + a p 7 CO \lt ; M 1 CM i\#151 ; 1 1 rH M .
Ol P 1 ^ Ol 1 Ol rH 1 rH CO 1 CO \#169 ; S.s rH 1\gt ; 1 p Cl VO CM p | p P CD CM CM i rH VO CD 1 so r-J Cl ft- p l 00 00 VO CO CD 1 CD s Ol vo I VO o VO rH 1 O 0Q + a p 1 CO CM \#171 ; CM rH 1 rH CM 1 Ol p 1 p Ol 1 Ol rH 1 rH CO 1 CO 3 3 OQ vo b Cl CO p Cl VO ( M CO P .
p Cl VO rH 00 1 W cd Ol VO 1 \lt ; 0 Ol 00 CO Cl O 01 00 ft- 1 CD VO vo rH P | VO o ^3 + a 00 1 CO CM * CM r\#151 ; 1 1 iH CM .
Ol p 1 p Ol .
Ol iH * rH CO 1 CO S s 00 00 o 00 00 CO CO POP s O CD P CD o S p ft- p O ft ' Cl Cl CD O CD CD VO CD O VO Cl Cl Cl O Cl OQ " S 00 CO \lt ; M CM rH rH CM 01 p p Ol Ol rH rH \lt ; M \lt ; M io a i , h s CO 00 00 CO ( M VO CO CD CO O CD CM CD 01 P .
CO p CO ft- CD 01 00 CO .
CD VO vo VO O vo 00 Cl + 1 1 a CO + CO cS + Si i\#151 ; 1 rH CM + Ol p + p Ol+Ol rH r\#151 ; l \lt ; M -10 min. p CO + 00 CO 238 + 4 242 00 CD rH + 1 169 260 P P 1 CD + Ol p CO p ft- rH .
ft-^ P 262 + 4 266 cc vo rH + 1 159 VO Cl CM + 4 299 -15 min. 00 CD CO + 10 00 CO P ft- i-1 CO .
P ( M + CM VO CD rH + 2 167 CD VO Ol + 6 262 456 + 10 466 257 + 7 264 Cl VO rH I9T Z + 3 CM CD 1+ M 1 CO* for diurnal g 01 ; i s .
* 01 i g : oi : g : \#169 ; p* : g : \#169 ; : Is : : \#169 ; : g : \#169 ; ; g : \#169 ; s - a . .
a .
a .
a * a . .
a .
a .
a 1 rH g .S TS I 'll 1 It i-S-S ll o o Cl rH ; o o \#169 ; o ^ 111 1 .ii 1 o 5 ii 1 g S g So'-S ~ o o 111 Is 01 01 S fc fc ss o o 5QOO Year Corre\lt ; Corre H* \#169 ; 01 .8 S3 fc K O O ROQ J4S 1 \#163 ; S Is ?
_ *4 S O o CQ O O \amp ; B \#163 ; \amp ; S3 Mr. J , Px'oudman .
Sunrise Sunset -15 min.-IO -5 -I5min.-I0 uncorrected corrected uncorrected corrected Mean Potential Variation at Sunrise and Sunset ( Kew , 1912 and 1914 ) .
It is hoped thate- a detailed study of the synchronous variation of the atmospheric electrical quantities with the integral intensity of " strays " in wireless phenomena may be possible at Kew Observatory in the near future .
On the Motion of Solids in a Liquid Possessing Vorticity .
By J. Proudman .
( Communicated by Prof. H. Lamb , F.R.S. Received March 28 , 1916 .
) 1 .
The following investigations were undertaken at the suggestion of Mr. G- .
I. Taylor as an extension of some of his own.* The equations of motion of any system of solids in a liquid which moves without vorticity were obtained by Lord Kelvin by a method based on that of ignorable co-ordinates in ordinary dynamics .
They are of Lagrange 's type , and were afterwards obtained by various writers !
by an adaptation to hydrodynamics of Lagrange 's original method .
Lamb 's work leads to some hydrokinematical relations which we shall put in evidence below .
For the rotational problems discussed in the present paper , an attempt to obtain a Lagrangian function has only been successful in one case .
This case is that to which Taylor 's principal results refer , viz. , the two-dimensional motion , with uniform vorticity , which at infinity reduces to a rotation about an axis .
That a Lagrangian function exists in this case is obvious from Taylor 's results . .
* An account of these investigations has not yet been published .
The subsequent references are to a MS .
which Mr. Taylor very kindly showed the author .
t See Lamb , ' Hydrodynamics,5 3rd Edit .
, Art .
136 .
|
rspa_1916_0026 | 0950-1207 | On the motion of solids in a liguid possessing vorticity. | 408 | 424 | 1,916 | 92 | Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character | J. Proudman|Prof. H. Lamb, F. R. S. | article | 6.0.4 | http://dx.doi.org/10.1098/rspa.1916.0026 | en | rspa | 1,910 | 1,900 | 1,900 | 1 | 13 | 346 | http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1916_0026 | 10.1098/rspa.1916.0026 | null | null | null | Fluid Dynamics | 82.745034 | Tables | 11.171735 | Fluid Dynamics | [
49.03916549682617,
-32.03562545776367
] | ]\gt ; from the solids only , is where is the moment of momentum , about the axis , of the relative motioq of the solids .
The contribution from the liquid is taken over all the liquid , which is equal to in our customary notation , where denotes the component of along the outward-drawn normal to the boundary of a solid .
Now we might express the motion of the solids by means a function ; and although this would not be a harmonic function , it could be taken equal to at the surfaces of the solida If , then , the density of solids were uniform , and equal to , their contribution ( 26 ) would be FroIn this we see that the actual contribution from the liquid .
is eqnS and opposite to that of a set of solids of uniform density , occupying always * the positions of the actual solids .
The total contribution to is therefore . .
of is zero for , while the coefficient of is .
We obtain , on using ( 61 ) , Similarly , we may obtain .
( 7$ 10 .
Methods similar to those of the preceding section may be used to the motion of a body which moves irrotationally relative to the rotating axa By this we mean that the body remains fixed relative to a set of axes themselves always remain parallel to the fundamental rotating axes , but whose origin moves in any manner .
The most general motion of a sphere may be regarded as of this type , when points on its surface are 1lot required to be identified .
These two sets of rotating axes we shall refer to as the fundamental and the secondary axes .
Lt denote the components at time of the velocity of the liquid relative to the fundamental axes , at a point whose co-ordinates relative to the secondary axes are .
Then , the motion being small , the equations remain valid , but we have now
|
rspa_1916_0029 | 0950-1207 | An active modification of nitrogen. -VII. | 438 | 450 | 1,916 | 92 | Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character | Hon. R. J. Strutt, Sc. D., F. R. S. | article | 6.0.4 | http://dx.doi.org/10.1098/rspa.1916.0029 | en | rspa | 1,910 | 1,900 | 1,900 | 13 | 233 | 4,945 | http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1916_0029 | 10.1098/rspa.1916.0029 | null | null | null | Thermodynamics | 38.087407 | Electricity | 35.482075 | Thermodynamics | [
-0.4857960641384125,
-47.6320686340332
] | An Active Modification of Nitrogen.\#151 ; VII.# By the Hon , R. J. Strutt , Sc. D. , F.R.S. , Imperial College , South Kensington ( Received April 10 , 1916 .
) S 1 .
Introduction .
In previous papers attention has chiefly been paid to the properties of active nitrogen when produced .
The present one deals almost entirely with the circumstances of its production by the electric discharge .
The jar discharge is much the most efficient , but does not lend itself easily to quantitative investigation .
It is not easily maintained steady for any length of time , but there is a more fundamental difficulty than this , for measurements of current and potential with the jar discharge do not admit of any simple interpretation .
Each discharge lasts for a time which is very short compared with the intervals between discharges , and , when it does occur , it is oscillatory .
For these reasons attention has been given to the steady discharge obtained from a direct current dynamo machine .
This yields much less active nitrogen than the jar discharge , but still enough to admit of satisfactory observations oil many points .
The machine employed was made by Messrs. Evershed and Vignoles .
It consists of three magneto generators in series , direct driven by a motor .
At full speed the output is 15 milliamperes at 5000 volts .
This voltage was in excess of what was usually required .
Part of it was dropped on a steadying resistance , and it was further reduced by diminishing the speed of the driving motor .
The nitrogen used in these experiments was commercial bomb-nitrogen , allowed to stand over phosphorus , and then dried by phosphorus pentoxide .
It contains enough foreign gas to give the necessary catalytic action.f S 2 .
Various Regions in the Luminous Discharge .
It was of interest to compare the yield of active nitrogen by the various regions of the discharge , Crookes dark space , negative glow , Faraday dark space , and positive column .
For this purpose the apparatus of fig. 1 was set up .
The discharge was in a tube A , 18 mm. in diameter , between aluminium disc electrodes B and C , maintained at a fixed distance apart of 130 mm. by means of three thin glass rods , as shown .
The system was moved up and * I , ' Roy^TSoe .
Proc. , ' A , vol. 85 , p. 219 ; II , ibid. , vol. 86 , p. 56 ; III , ibid. , vol. 86 , p. 262 ; IV , ibid. , vol. 87 , p. 179 ; V , ibid. , vol. 88 , p. 539 ; VI , ibid. , vol. 91 , p. 303 .
t See YI , p. 312 .
An Active Modification of Nitrogen .
down at pleasure by a steel rod screwed into the lower ( cathode ) disc , and passing through a barometric column below .
It was necessary to cover the lower side of the cathode with a mica washer , and the upper part of the steel rod with a glass tube , in order to prevent discharge from these surfaces , and limit it to the space between B and C. Connection to the upper electrode C ( anode ) was made by a spiral spring of thin copper wire , as shown .
A regulated stream of nitrogen entered at D , and was drawn out by a Oaede molecular air pump at E , passing transversely across the discharge .
On its way to the pump the gas passed through the length of the observation tube E , in which the intensity of the glow could be estimated .
This tube was viewed end on , its length being about 30 cm .
perpendicular to the plane of the figure .
It was blackened on the outside everywhere except at the observation end , to screen off stray light from the discharge tube .
The eye was applied to a cardboard tube about 6 inches long , fitted over the end of the observation tube .
These precautions were necessary , since the afterglow luminosities to be estimated were somewhat feeble .
It was found that the intensity of the active nitrogen glow ( measuring probably the square of the number of active nitrogen molecules present in the observation tube ) depended very much on which part of the discharge was brought opposite the openings D , E. The results are best indicated -diagrammatically .
In fig. 2 the various features of the discharge at 4*5 mm. pressure are shown to scale , beginning with the narrow Crookes dark space on the left , and above them a curve , the ordinates of which are equal to the estimated glow intensities on an arbitrary scale .
-Fig* 3 gives similar data for 1*4 mm. pressure , when the dark space and negative glow have broadened out considerably .
The scale of intensity is r Hon. R. J. Strutt .
again arbitrary , and not the same as that of the previous figure .
The current passed was about 15 milliainperes in each case .
\#166 ; Fig. 2 .
Pressure , 4*5 ' mm. mercury .
Distances from cathode\#151 ; End of Crookes dark space , 1 mm. End of negative glow , 7 mm. End of Faraday dark space , 22 mm. End of positive column ( anode ) , 130 mm. Fig. 3 .
Pressure , 1*4 mm. mercury .
Distances from cathode\#151 ; End of Crookes dark space , 3 mm. End of negative glow , 50 mm. End of Faraday dark space , 70 mm. End of positive column ( anode ) , 130 mm. It will be noticed that the yield of active nitrogen is greatest in the neighbourhood of the cathode .
It diminishes as we proceed along the negative glow , falling almost to zero in the Faraday dark space .
It then rises again as we enter the positive column , along which it is constant .
It would be of interest to compare the yield of active nitrogen from the Crookes dark space with the yield from the region immediately outside it ; but this was not found practicable .
At the higher pressures difficulty arises from the narrowness of the Crookes dark space .
At pressures low enough to make this space say 1 cm .
broad , no active nitrogen afterglow can be detected at all ; and even apart from this , diffusion acts very freely at such An Active Modification of Nitrogen .
low pressures , and would tend to mix up the gases from different portions of the discharge , thus obscuring the question at issue .
S 3 .
Wide Discharge Tubes Compared with Narrow .
The next point investigated was the relative efficiency of wide and narrow discharge tubes .
The arrangement was as in fig. .
4 , the positive column passing successively through a tube A of 15 mm. and a tube B of 6 mm. diameter .
It was possible to pass the stream of nitrogen through either A or Fig. 4 .
Hon. R. J. Strutt .
B at pleasure , by turning the three-way stopcock C. The course of the gas stream is shown by the arrows .
The observation tube for the glow was as before .
It was found that the intensity of the glow was much greater , about double , when the narrower tube was in use .
These tubes were not narrow enough to appreciably restrict the flow of gas , thus we may conclude that the same quantity flowed per second through each .
The velocity of the stream is greater in the narrow tube , and therefore the gas remains in it for a shorter time , but in spite of this the yield of active nitrogen is notably greater .
Experiments were made at the same time to compare the potential gradients in the wide and narrow portions of the tube .
The pairs of wires DE , FGf , could alternatively be connected with an electrostatic voltmeter by means of a suitable mercury key of high insulation .
It is generally admitted that though this method is unsatisfactory for exploring the potential gradient in the Crookes dark space , it gives trustworthy results in the positive column .
The mean of several consistent readings gave for the potential gradient in the narrower tube 87*8 volts per cm .
and in the wider one 86*6 volts per cm .
The current was 13 milliamperes , and the pressure in the tube about 6 mm. of mercury .
Under these conditions the afterglow produced had about double the intensity when the gas passed through the narrower tube .
These relations were not appreciably altered when the electric current was commutated .
It is , therefore , indifferent whether the ( positive ) electric current travels in the same direction as the gas stream or in the opposite direction .
It will be seen that the potential gradients were very nearly the same in the tubes A and B. Previous experimenters who have made similar measurements have usually found a distinctly higher potential gradient in the narrower tubes .
The current in these experiments is much larger than has generally been used , and the nitrogen probably purer , for the continuous flow of gas prevents contamination by gases given off by the electrodes .
These circumstances may account for the difference .
At all events , under the conditions used , the potential gradient in the narrow tube is but very little higher than^that in the wider one .
Consequently the larger yield of active nitrogen cannot be attributed to the potential gradient .
It would seem rather to be connected more directly with the greater current density .
The An Active Modification of Nitrogen .
great superiority of jar discharges in generating active nitrogen may perhaps be considered to fall into line with this : for the duration of the jar discharges as observed in a rotating mirror is extremely small compared with the intervals between successive discharges , and therefore the instantaneous current density very high .
S 4 .
Effect of Varying Length of Discharge Traversed .
Destruction of Active Nitrogen in the Discharge .
The current was sent between fixed electrodes A and B , fig. 5 .
The stream of gas , however , could be introduced at various points along the length of the positive column of the discharge .
It emerged at C , where the glow-intensity was examined .
If , for instance , it was desired to compare the intensity of the glow when the gas traversed the lengths DC or EC , a three-way stopcock was arranged so as to introduce the stream of gas at D or E alternatively , with rapid and easy transition to and fro by turning the stopcock .
The other apertures were stopped while this test was being made .
Then the stopcock , which was attached merely by short thick-walled rubber connections , was transferred to a different pair of apertures and the comparison repeated .
In this way it was established that with a tube 1*2 cm .
in diameter , gas pressure 6 mm. , current 15 milliamperes , distinctly more effect was produced by sending the gas 12 cm .
along the positive column than by sending it only 6 cm .
; but 12 cm .
was about the useful limit , for 24 cm .
of length did not give distinctly more effect than 12 cm .
The fact that a limit of useful length is reached in this way distinctly indicates that the discharge can not only produce active nitrogen , but can also destroy it .
It vas , however , thought to be of interest to prove this more directly .
An experiment for this purpose is shown in fig. 6 .
The gas stream enters near the cathode A. It traverses the positive column in the tube B , 4 mm. diameter , in which a considerable amount of active nitrogen is generated .
At C it emerges to a wider tube , along Lw B Fig. 5 .
Hon. R. J. Strutt .
which it passes to the observation vessel F , where the afterglow intensity is observed .
Either D or E can he made anode , the exchange being quickly TO PUMP NITROGEN Fig. 6 .
effected by a suitable switch .
When D is in use the stream of gas made active in B has to traverse the positive column in the wide tube DC , and this has the effect of partially destroying the active nitrogen formed in B* For it is found that the afterglow is less intense in F when D is anode than when E is anode .
This can only mean that the discharge in DE has a destructive effect .
As we have already seen , in a long tube the concentration of active nitrogen reaches a limiting value , which must indicate that a point has been reached where the rate of destruction is equal to the rate of formation .
For discharge in the wide tube this limiting concentration is lower than for the narrow one ; thus the discharge in the wide tube lowers the concentration instead of raising it .
A second form of experiment illustrates the point still more strikingly .
The gas stream traverses in succession two tubes , A and B ( fig. 7 ) .
In A it is made strongly active by a jar discharge , and , if this tube alone is in action , a very strong afterglow is obtained in the observation tube C. But , if an independent uncondensed discharge ( steady current from dynamo machine ) is passed through B , the glow in C is almost destroyed , to be restored when the current through B is broken .
This experiment is the same in principle as the last^tme , but , by taking advantage of the greater efficiency of the jar discharge , the effect is made still more striking .
It will be seen that the amount of active nitrogen generated under given An Active Modification of Nitrogen .
conditions depends on complicated conditions .
The rate of formation and the rate of destruction are both involved , and it may be that these do not vary together when the character of the discharge is altered .
The comparison is simplest when only a thin stratum of discharge is traversed , as in the experiments of S 2 .
In this case the rate of formation is the important factor .
S 5 .
Traces of Oxygen Affect the Afterglow Profoundly .
Do they Simultaneously Affect the Discharge Potential ?
Since the production of active nitrogen is profoundly influenced by the presence of a foreign gas such as oxygen , * it seemed of interest to determine whether or not such an addition would influence the discharge potential .
It was already known from the investigations of Warburgt that a trace of oxygen affects the cathode fall of potential in nitrogen considerably , but it was desirable to repeat the experiment with simultaneous observation of the afterglow intensity , so as to see if the same minute quantity of oxygen as suffices to produce the best afterglow would also affect the cathode fall .
The nitrogen used in this experiment was purified in the manner described in YI , p. 306 , with one slight modification .
Instead of using the liquid alloy of sodium and potassium to remove oxygen , sodium alone was used ; the sodium was dry , i.e. it had never been stored in oil .
The glow was reduced very greatly , though , as before , not completely .
Such nitrogen was allowed to pass through the discharge tube , and a small admixture of oxygen , amounting to 1/ 820 of the flow of nitrogen , could be admitted or shut off at pleasure .
For details I refer to the former paper .
J * YI , p. 308 .
+ 4 Wied .
Ann. , ' vol. 40 , p. 1 ( 1890 ) .
f VI , pp. 307-8 .
Hon. R J. Strutt .
For the experiments on the cathode fall of potential , the discharge tube had a long platinum cathode with an auxiliary platinum electrode about 1 cm .
from it ; the potential difference between this and the cathode could be read on an electrostatic voltmeter .
The positive column was confined in a narrow tube , and the afterglow intensity could be observed as usual .
It was found that the cathode fall was affected in a notable manner by the oxygen admission , which at the same time brightened up the afterglow to a marked extent .
The following were a series of readings , taken alternately , with the oxygen stream on and off:\#151 ; off . .
270 273 273 275 275 \/ \/ \/ \/ on . .
380 340 345 345 The effect of oxygen is seen to be very marked .
The current was reduced by resistance so that the negative glow only covered a small part of the cathode , and its value was 0*6 milliampere .
Thus the afterglow was feeble , though sufficient for observation .
It is to be observed that the active nitrogen responsible for the afterglow was chiefly produced in the positive column of the discharge , not at the cathode .
The absolute values of the readings quoted do not agree very well with the careful measurements of the cathode fall made by Warburg .
The matter was not pursued far enough to make it desirable to insist much on this difference .
My object was to observe simultaneously the effect of small oxygen admixture on the cathode fall and the glow intensity .
This was abundantly attained .
A few attempts were made to repeat this experiment admitting a trace of ethylene instead of oxygen .
This , as I showed formerly with jar discharges , has the same effect as oxygen in brightening up the afterglow .
But it was found that the introduction of a hydrocarbon made the readings of the cathode fall of potential altogether irregular , so that the original reading could not be recovered when the hydrocarbon admixture was shut off .
This is probably due to charges produced in the cathode surface by chemical action of the hydrocarbon .
Some similar experiments were made on the fall of potential in the positive column , between two platinum wires sealed in , 4 cm .
apart , in a tube 5 mm diameter .
In these experiments it was not necessary to restrict the current and it was increased to 15 milliamperes .
The nitrogen was at 5 mm. pressure in the tube .
The following are some readings alternately with and without an^oxygen admixture of 1/ 820 of the nitrogen .
210 on 207 off , 208 on , 205 off , 205 on .
Mean , 208 on , 206 off An Active Modification of Nitrogen .
52*0 volts per centimetre with oxygen , 51*5 " " without oxygen .
Thus there is no measurable effect of oxygen admission on the fall of potential in the positive column or on the current , but as usual it produced great increase in the afterglow intensity .
In this experiment the active nitrogen was entirely produced in the positive column , since this was the only part of the discharge traversed by the gas stream .
Yet the electrical conditions in the positive column do not seem to be affected by the slight oxygen admixture , which greatly enhances the afterglow^ .
S 6 .
Active Nitrogen at Atmospheric Pressure .
The formation and properties of active nitrogen as described in previous papers of this series are most advantageously examined at low gaseous pressures , say 5 mm. of mercury or less .
Under such conditions the effects are very spectacular , and can be shown with brilliant effect to large audiences .
At higher pressures the phenomena are much less conspicuous , but it is not without interest to trace them at atmospheric pressure .
This can be done without difficulty .
Fig. 8 shouts the arrangement which has been found most suitable for the purpose .
Leyden jar sparks , maintained by means of an induction coil , pass between the iron wire electrodes A , B , which maybe , say , 1 cm .
apart .
These wires are situated axially in a silica tube of , say , 4 mm. diameter , and they are carried on brass fittings adapted to the silica tube with indiarubber connections as shown .
The silica tube has a small lateral hole , halfway between the electrodes .
This hole is about 1*5 mm. diameter , and is drilled with a diamond .
A sheath of copper foil , perforated to correspond with the hole , surrounds the outside of the silica tube .
Its object is to cut off the dazzling light of the spark .
The silica tube is placed in a bottle ( see figure ) .
A supply of nitrogen is connected to the side tube D ; a cylinder of commercial nitrogen will do , if one is selected which is pretty free from oxygen , x The nitrogen stream passes through the region of discharge , and issues from the Fig. 8 .
Hon. R. J. Strutt .
hole , displacing the air in the bottle , so that the issue from the hole enters a nitrogen atmosphere .
The jet issuing from the hole shows the characteristic orange colour of the active nitrogen afterglow .
Its length was about 15 mm. under the experimental conditions used .
The interaction of active nitrogen and acetylene , to yield the cyanogen flame which forms so conspicuous a demonstration at low pressures , can readily be shown at atmospheric pressure with the arrangement described .
It is only necessary to deliver some acetylene into the bottom of the outer vessel so that the issuing jet of glowing nitrogen comes in contact with it .
The orange jet at once changes to lilac , and shows the cyanogen spectrum , exactly as at low pressures .
The experiment may , perhaps , be of interest to those who desire to see something of the phenomena , but who have not the use of a suitable motor-driven air pump for working at low pressures .
The luminous jet at high pressures is only about 15 mm. long , as already mentioned .
At low pressures , on the other hand ' , it may be readily made to extend to a distance of many metres , if long tubes are provided .
The question arises , what is the cause of this great difference in the time during which the gas remains luminous .
There seems to be no doubt that it is due to the destructive effect of the dense gas on the active nitrogen contained in it .
If the hole in the side of the quartz tube is made specially small , it is possible to maintain an approximate vacuum in the outer vessel into which it discharges , while still supplying nitrogen at atmospheric pressure to the spark-gap inside the quartz tube .
In this case the jet lengthens out , and the gas remains luminous throughout the connecting tubes leading to the pump .
It is evident , therefore , that the short duration of the afterglow when the jet emerges into the open is not due to any inherent peculiarity of the active nitrogen generated in the spark at atmospheric pressure , but rather to the conditions in which it is placed after formation\#151 ; that is to the high density of the surrounding gas .
Early experiments* demonstrated that certain gases , oxygen for example , produce a marked destructive effect on the glow of active nitrogen , even at low pressures .
It is probable , however , that ordinary nitrogen itself has a similar though smaller effect .
Such an effect may be supposed to depend on the active nitrogen molecules coming into contact with inert nitrogen molecules , and this will happen more often as the density of the latter is increased .
Thus there is no difficulty in understanding the short life of active nitrogen when contained in nitrogen at atmospheric pressure .
The longest duration of active nitrogen , on the other hand ( which may * I , p. 224 ; II , p. 56 .
An Active Modification of Nitrogen .
reach in extreme cases to half-an-hour ) , is observed when the electrodeless discharge , which admits of pressures as low as 1/ 10 mm. , is used .
In this case a minimum of inert nitrogen is present .
Returning to the experiments at atmospheric pressure : the discharge of the active jet into air with its contained oxygen destroys it very rapidly indeed .
Thus little can be seen of the phenomena if the jet discharges into the open .
S 7 .
Scattered Metal from the Cathode in a Stream of Active Nitrogen .
The well-known disintegration of the cathode is , of course , limited to the uncondensed discharge\#151 ; it does not occur with the jar discharge , in which the cathode dark space with its attendant phenomena are not developed .
During the studies on the uncondensed discharge described earlier in this paper , the idea suggested itself of using this cathode disintegration as a method of evaporating the metal into the stream of active nitrogen , to show the development of the metallic spectrum.* Of several heavy metals tried , copper showed the effect best .
The copper cathode should be sheathed in a quartz tube , f leaving 1 cm .
protruding .
This quartz sheath , as shown in fig. 9 , A , is cemented with sealing wax into a lateral tube .
The stream of active nitrogen produced in the narrow tube B Fig. 9 .
sweeps past the copper cathode , carrying the disintegrated or evaporated metal with it .
The nitrogen pressure in the tube is somewhat high , 5 to 10 mm. .
A tongue of green light is seen extending 10 cm .
or more down stream from A along the tube C. This shows the copper line spectrum , excited by active nitrogen , just as in those cases where the stream of active gas is led over a fragment of heated metal .
The latter method , which succeeds * I , p. 224 .
t The tube gets heated , and the effects to be looked for are masked by the sodium light developed , if glass is used .
VOL. XCII.\#151 ; A. .
2 M An Active Modificatioyi of Nitrogen .
very well with mercury , cadmium , zinc , magnesium , and the alkali metals , is scarcely applicable to copper , on account of the high temperature^ needed to evaporate it .
S 8 .
Summary .
( 1 ) The production of active nitrogen in various regions of the steady discharge has been studied .
It is greatest near the cathode , falls off to a minimum in the Faraday dark space , and increases again in the positive column to a value which is constant along that column , but less than that at the cathode .
( 2 ) With a given value of the current , much more active nitrogen is obtained from the positive column in a narrow tube than in a wide one .
The difference between the potential gradients in the narrow and wide tubes is not large enough to plausibly account for the different yield of active nitrogen , which must rather be connected with the current density .
( 3 ) The yield of active nitrogen comes to a limit as the length of positive column traversed by the gas is increased .
This is shown to be due to a destructive action of the discharge , which , beyond a certain concentration , destroys the active nitrogen as fast as it is produced .
( 4 ) A trace of oxygen ( or almost any other admixture ) is known to greatly increase the yield of active nitrogen .
The amount of oxygen required to do this considerably increases the fall of potential at the cathode , but it does not measurably affect the fall of potential in the positive column .
( 5 ) Active nitrogen is produced by the spark at atmospheric pressure .
That the phenomena are so much less striking than at low pressures is due to the destructive action of the surrounding gas on the active nitrogen after it is produced .
( 6 ) The metal scattered from a copper cathode when the discharge passes can be made to emit its line spectrum in a stream of active nitrogen .
|
rspa_1916_0030 | 0950-1207 | A hypothesis of molecular configuration in three dimensions of space. | 451 | 462 | 1,916 | 92 | Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character | Sir William Ramsay, K. C. B., F. R. S. | article | 6.0.4 | http://dx.doi.org/10.1098/rspa.1916.0030 | en | rspa | 1,910 | 1,900 | 1,900 | 6 | 149 | 4,206 | http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1916_0030 | 10.1098/rspa.1916.0030 | null | null | null | Fluid Dynamics | 37.488676 | Atomic Physics | 28.433758 | Fluid Dynamics | [
-14.557483673095703,
-61.611900329589844
] | 451 A Hypothesis of Molecular Configuration in Three Dimensions of Space .
By Sir William Ramsay , K.C.B. , F.E.S. ( Received April 1 , 1916 .
) It is now almost universally acknowledged that the valency of an element is due to its being associated with one or more electrons .
The mechanism of chemical combination was sketched by me in the Presidential Address to the Chemical Society* in the sentence : \#151 ; " If it be conceded that a salt differs from its solution only in so far as the mobility of the solution permits of transfer of ions , the transfer of an .
electron from the sodium to the chlorine must take place at the moment of combination .
Symbolised , if we write E for electron and simplify the reaction , dealing for the moment with an atom and not with a molecule of chlorine , we have EHa + Cl = NaECl .
Here the electron serves as the bond of union between the sodium and the chlorine .
... If it be desired to , form a mental picture of what occurs , let me suggest a fanciful analogy which may serve the purpose : it is that an electron is an amoeba-like structure , and that EHa may be conceived as an orange of sodium surrounded by a rind of electron ; that on combination the rind separates from the orange and forms a layer or cushion between the Na and the Cl , and that on solution an electron attaches itself to the chlorine in some similar fashion , forming an ion of chlorine .
It will be noticed that the E fills the place usually occupied by a bond ; thus Na\#151 ; Cl. It happens providentially that the bond and the negative sign are practically the same ; Ha\#151 ; Cl may be supposed to ionise thus , Na(\#151 ; Cl ) , the negative charge or electron remaining with the chlorine .
" It is proposed in the present paper to elaborate this conception , and to attempt to show by help of models the kind of mechanism which may be concerned when two or more elements form a compound .
Before proceeding further , however , in order that there shall be no misunderstanding , it should be stated that the subject of this memoir is not directly connected with what may be called the permanent constitution of the atom .
There is a strong consensus of opinion that an atom consists of a congeries of electrons ; .
it is supposed by some that there is a central positive nucleus which holds them in place ; these electrons are undoubtedly in rapid motion , and it will * 4 Chem. Soc. Trans. , ' 1908 , p. 781 .
Sir W. Ramsay .
A Hypothesis of be assumed that unless they are under disturbance from collisions , when there will be slight oscillatory deformation , they move in circular orbits .
The " Zeeman effect " is due to a hastening of these orbits by magnetic influence .
We have not to do with these electrons ; as a whole they constitute what may be termed the essential outworks of the atom , determining its interaction with other objects .
Their positions and relationships have been studied by several investigators ; to avoid laborious calculations one has used magnetised needles passing through discs of cork floating in water , another has employed electrified spheres of metal hanging from a support .
These discs or spheres group themselves into a triangular form if there are three such ; into the form of a square , or of a triangle with a disc or sphere in the middle , if there are four ; and so on .
It is suggested that these groupings imitate those of the electrons in the atom .
Apart from such constitutional electrons there appear to be attached to each atom one , two , three , four , or five\#151 ; rarely six , seven , or eight\#151 ; electrons more loosely connected , which determine the valency of the atom .
They differ from the " constitutional " electrons in so far as they are removable without disturbing the groupings which determine the essential structure of the atom as a whole .
It appears probable , however , that the constitutional electrons are also removable ; in fact , there is such removal from all radioactive elements when they lose a / 3-corpuscle ; but then these radioactive elements are fundamentally altered , they cease to conserve their qualities , and they change into other forms of matter .
Whether the elements not recognised as radioactive are capable of similar transformations is not yet fully elucidated ; evidence , however , has been accumulating that transformation can under favourable conditions be detected .
Such fundamental changes as are occasioned by the loss of a / 3-particle are irreversible \#151 ; i.e. } they occur too far removed from an equilibrium to leave any opportunity for recombination ; the original matter has never yet been reconstituted by addition of a yS-particle .
But the changes which take place when a valency electron is lost or gained are observed to occur in quantity in the reverse direction , and reach an equilibrium ; they form the familiar phenomena of the change of an atom into an ion , or vice versa as opportunity offers .
Bor the purpose of this investigation then , in which we do not concern ourselves with the inner structure of the atom , it will be considered as a sphere .
But the valency electron ( if there is only one ) will be supposed to revolve round that sphere .
A procession of electrons in rapid circular motion functions like a current of electricity in a circular coil of wire .
Molecular Configuration in Three Dimensions of Space .
453 Hence the system atom plus electron can be imitated by the system ball plus coil of wire carrying a current .
Kammerling Onnes has recently shown that if a current be induced in a coil of lead wire at 1*7 ' absolute , the current persists for many hours .
Here we have , through absence of electric resistance , a close imitation of what is attempted by the device to be described .
Experiment shows that when a current is passed through two parallel wires , in the same direction through each , these wires attract each other .
Conversely , when a current passes in one wire in the opposite direction to that in a parallel wire , these wires repel one another .
Should the current-bearing wires be not parallel to each other , they tend to come together by the attraction , which is greater where they are closer .
If rigid current-bearing coils be substituted for the straight wires , then the resultant action between them is most simply expressed by saying that it produces a motion which increases for each coil the number of lines of magnetic force which thread through it in agreement with the lines of its own field .
It is convenient to describe a current through a circular coil as " clockwise " or " counter-clockwise , " as viewed from some specified point .
There is a complete equivalence as regards external forces between a plane coil of wire through which a current is passing\#151 ; or its analogue , a stream of electrons revolving in a circular orbit\#151 ; on the one hand , and a uniformly magnetised magnetic shell whose boundaries coincide with those of the coil , on the other .
Thus a flat current-bearing coil and also a stream of electrons revolving in a circular orbit may be regarded as the equivalents of a thin disc-shaped magnet of which one surface is composed of north and the other of south poles .
This well-known conception will be found convenient in considering the attractions and repulsions produced by currents passing through coils of wire ; the one side of the coil may be termed the " northseeking,1 " or , more briefly , the " north " side , and the other the " south " side .
Certain assumptions will now be made on which the theory of valency will be based .
First , it is supposed that the path of the electron round the atom , which is taken as spherical , is not in a great circle , but that its orbit is a smaller circle parallel to some equatorial plane fixed in the atom ; it may be imagined that this path is forced on the valency electron owing to the balance of forces from the asymmetry of the more rigid distribution of constituent electrons represented here by the sphere.* The point of view from * If the structure were symmetrical around the centre , these orbital electrons would , as in familiar theories , be distributed in rings in an equatorial plane , and are illustrated by the groupings of magnetic needles in a plane .
Sir W. Ramsay .
A Hypothesis of which the electron is defined as clockwise , or anti-clockwise , as the case may be , is the nearer pole of the orbit on the sphere .
Second , the circular orbits of different valency electrons need not necessarily have all the same diameters .
Third , it will be assumed that some electrons may , owing to necessary conditions of stability , revolve clockwise , while others may have an anticlockwise path , relative to the nearest pole on the sphere as defined above .
It will also be assumed that atoms in which the path is clockwise are what is known , from the chemical point of view , as electro-negative ; such atoms us those of sodium , calcium , etc. ; while , if the path of the electron round the atom is anti-clockwise , the atom belongs to the class including chlorine , oxygen , etc.\#151 ; the class termed electro-positive .
In fig. 1 a sketch is given of a monovalent atom of the former class ; in fig. 2 , of an electro-positive monovalent atom .
The first figure is a front , the second a side , view .
A molecule of hydrogen consists of two atoms .
How are they kept together ?
Each atom may be supposed to belong to the class depicted in .
fig. 1 ; both atoms possess an electron rotating clockwise .
This question Fig. 1 .
Fig. 2 .
was in a sense answered by experiment .
The model of the atom consisted of a " ping-pong " ball ; it is a hollow sphere of celluloid , very light and fairly rigid .
At each end of a diameter a brass cup was glued , and from the convex centre of each cup a fine needle projected ; these were carefully centred , so that the ball rotated on them as an axis .
To represent the electron , a coil of silk-covered wire was glued to the side of the ball , at right angles to its equator ; one end of the wire of the coil was attached by solder to one needle and the other to the other needle .
One of the needles was pivoted in a shallow glass cup , containing a liquid alloy of tin and mercury ; the other passed through a perforation in a copper cup , also containing tin amalgam ; it was found that in this position the ball was free to rotate with very little friction when placed with the axis vertical .
The coil of wire was counterbalanced by an idle* coil , so that the centre of gravity of the ball should be in the centre of the sphere .
From each cup a wire was led to a switchboard Molecular Configuration in Three Dimensions of Space .
455 consisting of paraffin cups containing mercury which could be connected by bridge wires in any desired way , and also with the two poles of a battery .
By changing the poles , the current could be taken through the wire in the clockwise or anti-clockwise direction as desired .
Two such spheres were placed alongside of each other , with their axes of rotation parallel , as near each other as the position of the coils would permit .
The appearance of these balls is shown in fig. 3 .
For diagrammatic purposes it is better to depict these balls with their attached coils in plan , looking vertically down on the upper needle ; the coils may then be represented as chords to the circles .
The direction of the current may be denoted by the letters C or AC , clockwise or anti-clockwise ; the coil is to be looked at from the front .
The electrons on two atoms of hydrogen may then be imagined to be rotating clockwise ; how will the balls place themselves as regards each other ?
This is shown in fig. 4 ; it is the stable position .
There is also a Fig. 4 .
Fig. 5 .
Sir W. Ramsay .
A Hypothesis of metastable position , shown in fig. 5 ; that the ball should stay in that position at all is due to the friction of the bearings .
* If the current through the coil attached to the left-hand ball be clockwise , the ball representing hydrogen , and that through the right-hand coil be anti-clockwise , as representing chlorine ( supposed to be a monad , the other affinities being ignored for the moment ) , then the position taken by the two balls is that shown in fig. 6 ; it is the only stable position ; it is also depicted in fig. 3 .
C AC In figs. 4 , 5 , and 6 the dotted lines with arrows indicate the manner in which the lines of either coil thread through the other ; and it will be seen that the north pole of one solenoid is always connected with the south pole of the other solenoid .
A figure similar to fig. 4 represents also the position taken when both currents are anti-clockwise ; it may be conceived to represent the valency electrons in the molecule CI2 .
There is , of course , also a tendency towards the metastable position shown in fig. 5 .
Before passing on to consider the behaviour of dyad atoms , we may regard the halogens ; in what respect does chlorine differ from bromine , iodine , and fluorine ?
If fig. 6 be looked at , it is seen that the diameters of the circular paths of the electrons have been made equal .
This is pure guess-work ; but if they are equal , and if the velocity of the electron attached to the hydrogen atom is equal to that of the electron attached to the chlorine atom , the periods of rotation of both electrons will also be equal .
It may be , however , that the circumference of the circle traversed by the chlorine electron is less or greater than that traversed by the hydrogen electron ; and if so , then it is probable that the electrons attached to an atom of fluorine , bromine , and iodine would differ not only from that of chlorine in this respect , but also from each other .
The attractive force of a coil depends directly on the amount of ^electricity which passes through it per second\#151 ; translated into the language of electrons , on the absolute number of electrons which pass any point of the coil per second .
Similarly , the steady or mean part of the Molecular Configuration in Three Dimensions of Space .
457 attractive force which a rotating electron can exercise* will depend on the number of times it passes a given point on its orbit per second .
Of two electrons possessing equal linear velocity , that one with the smaller orbit will represent the stronger orbital current , while the attractive force depends on current and area jointly ; if they have equal orbits , that one with the greater linear velocity will have the greater attractive force .
It would be reasonable to suppose that while the greatest force is exercised by an atom of fluorine the least force or " affinity " is to be ascribed to iodine ; and the cause of their difference may be of the nature of that mentioned above .
Taking an atom of oxygen as typical of a dyad atom , it is to be noticed that its two electrons are each moving in an anti-clockwise path relative to the nearest pole , and will therefore repel each other , for they rotate in different hemispheres , and therefore in different directions .
Such an atom is shown in fig. 7 .
They would naturally be assumed to take such a position that their AC AC Fig. 7 .
planes of rotation would be parallel to and equidistant from the same great circle .
* It nmst be noted that the present investigation deals only with the magnetic forces of the revolving electrons .
Following the method introduced by Gauss into physical astronomy , the charge of each electron may be considered as spread along its orbit so that the quantity on any arc is proportional to the time the electron is in that arc ; this representation will give the steady mean forces of affinity , leaving out rapid fluctuations arising from the varying position of the electron .
The former include exactly the magnetic forces due to electric currents as here investigated : but there are also other ( usually greater ) forces due to the static attractions between the charges as thus spread round their orbits .
In ordinary galvanic currents the latter forces are compensated by other electrons of the opposite sign revolving in the orbit in the other direction , and an adjustment of similar kind may be understood as introduced here .
Or we may note that each negative ring-change must have a compensating positive charge in the nucleus , when the atom as a whole is uncharged , and these two together form a doublet having an electiic field roughly of the same general type as the magnetic field of the current , but ah\ a } s of the AC kind ; so that the present experimental procedure , employing coils of iffeient numbers of convolutions , is still suitable for general elucidation of* the problem .
458 Sir W. Ramsay .
A Hypothesis of The molecule of oxygen has the formula O2 ; two atoms must lie alongside each other ; there is no alternative .
There appear from experiment to be two almost equally stable positions : those shown in figs. 7 and 8 .
The former of these differs little from the hydrogen molecule as shown in fig. 4 ; it appears , on the whole , to be less stable .
Fig. 8 gives the alternative position ; it is to be remarked that the proximity to each other of the two north poles makes the resulting lines of force of oval shape .
'AC A( Fig. 8 .
Experiments have been made with systems of three balls , which may be conceived to represent O3 , ozone ; the electrons are supposed to revolve clockwise .
These may occupy two positions ; they may form a straight line , or they may be arranged as an equilateral triangle .
Both were tried .
The more stable form of an arrangement in line is shown in fig. 9 .
The position reminds one of that of two hydrogen atoms , combined to form a Fig. 9 .
molecule , as in fig. 4 .
A less stable form is that given in fig. 10 .
Both these exhibit all the electrons rotating in an anti-clockwise direction .
Fig. 10* may be compared with fig. 8 ; the planes of the electrons are similar .
It is usual for chemists to picture a molecule of ozone as a closed Molecular Configuration in Three Dimensions of Space .
459 system ; in this ease the atoms of oxygen are apparently all dyads .
If they are arranged in a row or chain , then the middle atom of oxygen must act as non Fig. 10 .
a tetrad ; in fact , the compound might be termed an " oxide of oxygen .
" But this idea does not apply to the figure shown ; inasmuch as each atom of oxygen carries only two electrons , all atoms are represented as dyad ; no experiment has been made with a tetrad atom .
Fig. 11 .
A model has been constructed , however , which reveals the configuration taken by three atoms of oxygen placed at the apices of an equilateral triangle .
As before , all paths of rotation of the electrons are taken as anti-clockwise .
The position of two of the atoms is similar to that assumed in fig. 7 by two atoms of oxygen ; that of the electron-path in the third atom is approximately at right angles to those of the other two .
It is obvious that not much disturbance would be caused by the disruption of the molecule and the formation of three molecules of oxygen from two of ozone .
The next molecule to be considered was the water molecule .
The two Sir W. Ramsay .
A Hypothesis of atoms of hydrogen , with the clockwise direction of their electrons , place themselves in juxtaposition to the anti-clockwise electrons of the oxygen atom , with this result : the configuration is a stable one and difficult to disturb .
With the conventional configuration H\#151 ; O\#151 ; H , the position of the atoms is given in fig. 12 .
s O s H n Fig. 12 .
Removing an atom of hydrogen , so as to leave O\#151 ; H , gives the structure shown in fig. 13 .
s o s n h It is convenient to add here the usual formula for chlorine monoxide , Cl\#151 ; O\#151 ; Cl ; it is shown in fig. 14 ; there are two alternatives , of which the SOS Fig. 14a .
Fig. 14b .
Molecular Configuration in Three Dimensions of Space .
461 former appears to be the more stable .
Hydrogen hypochlorite , H\#151 ; 0\#151 ; Cl , on the same plan , gives the arrangement shown in fig. 15 .
Fig. 15 .
Hydrogen hypochlorite and chlorine monoxide , arranged with the atoms at the apices of an equilateral triangle , give the form shown in fig. 16 .
Fig. 16 .
These have in some measure analogy with " triangular " ozone , or hydrogen dioxide .
Attempts with four balls did not succeed well ; the forces are not sufficient to adjust equilibria against the friction of the needle , except in one or two special cases .
Thus , an atom of nitrogen situated at the centre of an equilateral triangle , the corners of which are occupied by three hydrogen atoms , takes up a stable configuration , similar in its way to that of the oxygen and hydrogen atoms in " linear " water .
The hydrogen electrons all 'lie parallel each to a corresponding nitrogen electron .
The result is shown in fig. 17 .
In conclusion I wish to point out that this is an experimental research .
Having postulated a certain structure for some simple atoms , an attempt has been made to ascertain in what manner the atoms would arrange themselves 462 Molecular Configuration in Three Dimensions of Space .
relatively to each other in the molecule .
It is hardly necessary to insist that two-dimensional schemes cannot do more than feebly illuminate the .
structure Fig. 17 .
of molecules existing in three dimensions ; again , that the necessity in mechanical models of preventing the lateral motion of the atoms , and so of adjusting by wires or otherwise the spatial relations between them , removes the actual configurations taken up by such models still further from actuality .
Still , all progress in our knowledge of molecular structure has been made by first simplifying the problems to be solved .
A scheme in three dimensions , to be manageable , must be on broad simple lines ; whether simplification in this case has been carried so far as to destroy all real analogy between such models and molecular structures which may actually exist in nature , time alone can show\ I have to express my warm thanks to Prof. Worthington and to Sir Joseph Larmor for useful criticism .
|
rspa_1916_0033 | 0950-1207 | Further determinations of direct osmotic pressures. | 477 | 492 | 1,916 | 92 | Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character | Earl of Berkeley, F. R. S.|E. G. J. Hartley, B. A. | article | 6.0.4 | http://dx.doi.org/10.1098/rspa.1916.0033 | en | rspa | 1,910 | 1,900 | 1,900 | 6 | 98 | 2,738 | http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1916_0033 | 10.1098/rspa.1916.0033 | null | null | null | Thermodynamics | 29.593739 | Biochemistry | 28.983732 | Thermodynamics | [
-18.14383316040039,
-29.07052993774414
] | ]\gt ; Earl of Berkeley and E. G. J. Hartley .
cyanide solution the membrane was less permeable to a new solute .
new observations on cane sugar ( and one or two other substances ) were therefore so arranged that each was preceded by either a definite experiment on a ferrocyanide or by merely putting pressure on a solution surrounding the membrane ; in either case the apparatus thoroughly washed out before it was filled with the solution about to be exalnined .
( 2 ) A number of observations on " " dynamic\ldquo ; osmotic pressure*are also recorded .
These were made for two reasons : first , there were hopes that we could correlate the " " solution leak\ldquo ; rate , that is , the amount of solute passing through the membrane in unit time , with the rate at which water passed through under a given pressure , and so obtain a correction ; and , secondly , we wished to make further observations on this method as applied to dilute solutions .
Unfortunately the connection between " " tion leak\ldquo ; and " " water rate\ldquo ; turns ont to be nor have we been able to find any other means of the effect of this leak ; there is , however , more promise in the second of the above reasons , as will be seen in the Appendix .
It may be mentioned that these experiments are uot yet complete .
For osmotic pressures under 25 atmospheres the special deadweight apparatus in ' Phil. Trans , vol. 209 , p. 319 , was used .
The density determinations were carried out in flasks with graduated necks , as mentioned in ' Phil. Trans vol. , p. 180 .
PART 1 .
The on Cane-Sugar Solutions.\mdash ; Most of the experiments were made on pure cane\ldquo ; sugar chased from the Army and Navy Stores and on " " mineral water crystals\ldquo ; provided by Messrs. Tate .
At a later date Messrs. Tate kindly gave us a supply of specially pure mineral water crystals ; we are glad to have an opportunity of thankmg them for this , and for the care they took in seeing that it reached us in a fresh and uncontaminated condition .
It may at once be stated that no difference could be detected in these three qualities by osmotic pressure methods ; further , some of the mineral water crystals were dissolved in water and precipitated by alcohol , the resulting product gave ( within the limits of uncertainty as to the concentration , see below ) the same osmotic pressure as before .
As a further check on possible unknown sources of error two samples of Kahlbaum 's purest sugar wefe examined .
See 'Roy .
Soc. Proc , vol. 82 , pp. 271-275 .
Earl of Berkeley and E. G. J. Hartley .
whilst the previous work on Oxford sugar gave atmospheres .
discrepancy is probably due to the presence of an impurity of.smaller molecular weight in the Oxford sugar ; we have no data for an exact estimate of its effect ; the fact that the observed osmotic pressures deviate from Boyle 's Law by about 100 per cent. would indicate that the influence of an impurity in these solutions would be greater than in more dilute ones .
Table III ives the final results ( these are plotted in Diagram 1 ) .
As already stated , we have not succeeded in getting a satisfactory correction for the " " solution leak We therefore tabulate the mean values ( giving double weight to those with no leak or only a trace ) of the experiments in which the solution leak was less than .
of Further Determinations of Direct Osmotic Pressures .
483 The range of our experiments overlaps Prof. Morse 's work , and his values , reduced to our weight concentration , we give for comparispn .
The reduction was obtained by plotting the numbers on a large scale , and by means of the steel ruler apparatus described by one of a curve was drawn through the points .
The osmotic pressures corresponding to our weight concentrations were then read off the graph .
It will be noticed that the two sets of observations do not agree , the deviation increasing as the osmotic pressure decreases , and at the lower values it appears to be greater than either of our experimental errors .
We are unable to suggest any adequate reason for this discrepancy , but it is noteworthy that the graph of our results when produced towards the origin passes much closer to that point than Prof. Morse 's .
In this connection , it may be mentioned that in 'Phil .
Trans , vol. 206 , p. 505 , we point out a disagreement between Prof. Morse and ourselves in the osmotic pressure of a solution containing 282 .
per litre .
We are pleased to find that in his latest published results Prof. Morse ( who curiously enough does not refer to our work ) has been able to bring this observation into line with ours ; possibly we may meet with similar good fortune in the cases now under discussion .
The Equilibrium Pressure of -Methyl Glucoside Sotutions.\mdash ; The substance was purchased from Messrs. Kahlbaum , and was purified by filtering the concentrated solution through a porcelain filter and repeatedly recrystallising .
During these operations care was taken that the solutions were never heated above C. The observations are given in Table Iy ( the best lts are plotted in Diagram 1 ) , where the columns are numbered as in Table I , and have the same significance .
The water content of the crystals was determined in the same way as with sugar .
'Phil .
Mag vol. 24 , pp. 668 ( 1912 ) .
Further Determinations of Direct Osvnotic Pressures .
485 Column ( 4 ) gives , as before , the " " solution leaks These are derived as follows : glucoside which had penetrated the membrane was given three days to difluse out of the porcelain into the water filling the tube , it was then washed out , evaporated to dryness on a water-bath , and weighed ; the process was repeated a second time and even a third time if judged .
In several cases the residue first obtained was ignited , and the ash , which was assumed to be derived from a trace of copper sulphate ( the tubes are always stored in very dilute copper sulphate solution ) , was weighed .
A determination of the non-volatile matter in the water was also made .
These two determinations afford a means of estimating the actual quantity of glucoside in the residue , and this is the quantity tabulated .
Attempts were made to determine the -methyl glucoside by means of 's solution ; although a satisfactory method was worked out for the pure substance in as dilute a solution as .
per cubic centimetre , yet when applied to the residues above mentioned , which give still more dilute solutions , the results were quite unreliable .
From an inspection of the Table it is obvious that the experiments are not so satisfactory as with cane sugar .
Equilibrium Osmotic Pressures of Isodulcite and -Tetramethyl Solutions.\mdash ; The isodulcite , purchased from Messrs. Kahlbaum , was purified by recrystallisation .
Some difficulty was experienced in determining the water content , as the crystals , when under .
atmospheric pressure , melt in their water of crystallisation to form a glass which cannot be dehydrated without decomposition .
The difficulty was avoided ( but the esults are not so satisfactory as with cane sugar ) by dehydrating in a vacuum .
The apparatus designed for this purpose is shown in the figure .
A stoppered ( stopper not shown ) weighing bulb , containing a known quantity of powdered cystals , fits into the lubricated grobnd joint in the jacket C. Mercury followed by sulphuric acid is run round the stem of , and the side tube is connected to an exhaust pump .
is sealed off when a good vacuum is reached , and the whole apparatus is placed in an oven .
Cold water is circulated through : the jacket and the temperature of the is raised cautiously to the Earl of Berkeley and E. G. J. Hartley .
melting point of the crystals ( between 70 and C. ) and held there most of the water is driven off ; further heating to about until the is constant is then out .
The tetramethyl ferrocyanide was prepared as already described by one u It was recrystallised from chloroform , the chloroform of crystallisation driven off by gentle heat and then recrystallised from water .
The water content ( the salt contains two molecules of water of.crystallisation ) was obtained by means of complete analyses of samples withdrawn from the powdered salt at the time of making up the solution .
The results for the two substances are tabulated in Table .
The headings to the columns have the same signification as before , and Column ( 8 ) gives the densities of the solution at C. As neither the isodulcite nor the methyl feYrocyanide are soluble enough to give large osmotic pressures , no further experiments were made .
PART 2 .
Table gives the results for the ferro- and examined .
columns ( 1 ) to ( 7 ) inclusive have the same significance as for Table I. Column ( 8 ) gives the value of the osmotic pressure as calculated from Boyle 's Law , on the assumption that the salts are not ionised .
Column ( 9 ) the densities of the solution at C. The weight concentrations in Column ( 1 ) are calculated for the anhydrous salt , and all cases the water content has been determined either directly or * E. G. J. Hartley , 'Journ .
Chem. Soc vol. 97 , pp. 172 , 1732 ( 1910 ) .
Earl of Berkeley and E. G. J. Hartley .
From the osmotic pressure results for the magnesium ferrocyanide , taken in conjunction with the fact that the salt is ionised , it would seem probable that some at least of the molecules are associated .
None of the other solutions give any indication of this .
Table gives the results of a further search for association in solution , together with details as to the solutions ( marked ) the osmotic pressures of which have already been published .
Column ( 1 ) ives the volume concentration , i.e. , the number of grammes of anhydrous salt per litre at C. ; in most cases the salts were analysed for their water content .
Columns ( 2 ) to ( 5 ) , inclusive , bear the same gnificance as in previous Tables .
Column ( 6 ) gives the Boyle 's Law osmotic pressure , Column ( 7 ) the densities of the solutions at C. In Table it will be noticed that the osmotic pressures of the following salts , magnesium sulphate , magnesium chromate and zinc sulphate , are all lower than Boyle 's Law .
Now all these salts are ionised , and we therefore be certain that some association has taken place .
If Compare RaouIt , ' Tonometrie ' ( Scientia Series ) , p. 90 .
Earl of Berkeley and E. G. J. Hartley .
magnesium silicofluoride is appreciably ionised it also can be added to list .
We have already shown that the ferrocyanides of calcium and strontium are associated ; tbus all the salts hitherto found to be are constituted with a dyad base and dyad acid radicle , and were it not the outstanding case of magnesium camphorate ( further experiments this salt at somewhat higher concentration would seem to be desirable ) might state that this points to a general law .
On the other hand , both the and the tetramebhyl ferrocyanides the latter see Appendix ) normal values for the molecular hence , if we may assume that the methyl radicle is equivalent to an metal , the evidence derived from the osmotic pressures does not confirm previous that potassium ferrocyanide is associated .
APPENDIX .
The experiments detailed below were made not only to try the but also for the purpose of determining the molecular weight of the what insoluble substance , tetramethyl ferrocyanide .
In the course of the experiments on the " " dynamic\ldquo ; osmotic pressures , was noticed that very often the water rate before and after putting equilibrium pressures on the solutions differed considerably ; possibly membrane alters during the experiment ; obviously an alteration in bility would account for our failure to obtain a satisfactory solution correction , it also affords an explanation of the poor results for the dynamic\ldquo ; osmotic pressures .
The following method gets over some of the difficulties , and seems to afford a convenient and rapid means of determining weights , or , if these be known , small osmotic pressures .
A solution of cane sugar is made up of about the same molecular tration as that of the substance to be examined , and both solutions at C. The osmotic pressure apparatus ( with the porcelain tube with water ) is set up in ice , and is so arranged that it can be without disturbance .
The sugar solution is poured in , and the rate at the level in the water-gauge falls is noted ; this rate , when corrected " " guard-ring leak , be regarded as the standard rate R. The then washed out of the apparatus and its place taken by the new 'Phil .
Trans , p. 336 ( 1909 ) .
See E. G. J. Hartley , " " A Case of Isomerism.in the Methylated ' Journ. Qhem .
Soc vol. 103 , p. 1196 ( 1913 ) .
This " " guard-ring leak\ldquo ; is mostly due to the passage of water through the caused by the hydrostatic pressure of the water in the gauge .
492 Further Determinations of Direct Osmotic essures .
and the new rate obtained .
Let and be the molecular weights the sugar and the unknown substance respectively , and and volume concentration .
Then A tabular statement of the two sets of experiments is given on All the rates are measured with the water-level as near the same height possible , and frequent measurements of the guard-ring leaks were Each measurement on the unknown solution is both preceded and by a measurement on cane-sugar , and for calculating the mean of values thus obtained has been used .
It should be mentioned that the rates do not come to a steady state until about half an hour has elapsed from the time of filling .
The numbers given are the mean of three consecutive values , and represent millimetres ( on graduated water-tube ) moved over in 15 minutes .
The volume of 1 cm .
the tube is The accuracy of the above is about 2 per cent. , but we think the experimental error would be reduced if the apparatus were designed specially the work ; and there seems to be no reason why still more dilute solutions* should not give equally good results , in which case this manner of determining molecular weights would be more expeditious than any other known method , not excepting that of freezing-points .
lt may not be out of place to point out that the solution of cane-sugar of .
per litre has a -point lowering of C. The accuracy of 2 per cent. on this means an estimation of the temperature to 1/ 1000o .
With the best Beckman thermometers is but an approximation , for it is not generally realised that there are corrections of this magnitude due to column , change in barometer , other causes .
* In " " dynamic\ldquo ; osmotic pressures Proc we were able to get very fair results with solutions containing as little as 2 .
of sugar to the litre .
|
rspa_1916_0034 | 0950-1207 | The transmission of electric waves around the Earth's surface. | 493 | 500 | 1,916 | 92 | Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character | H. M. Macdonald, F. R. S. | article | 6.0.4 | http://dx.doi.org/10.1098/rspa.1916.0034 | en | rspa | 1,910 | 1,900 | 1,900 | 1 | 3 | 92 | http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1916_0034 | 10.1098/rspa.1916.0034 | null | null | null | Formulae | 80.840967 | Biography | 5.039973 | Mathematics | [
68.81279754638672,
-45.641849517822266
] | ]\gt ; here the summation is extended on both sides .
In order to leffect the aummation a knowledge of the zeros of the expression , : required ; this expression is an integral function of , and its zeros are continuous with the zeros of , which have been discussed in the former communication , the zero of is given by therefore the zero of , Again where when that is , , or Now , to the order of approximation required , , or and therefore that is .
or
|
rspa_1916_0037 | 0950-1207 | On the determination of gravity at sea (note on Dr. Duffield\#x2019;s paper). | 517 | 528 | 1,916 | 92 | Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character | Arthur Schuster, Sec. R. S. | article | 6.0.4 | http://dx.doi.org/10.1098/rspa.1916.0037 | en | rspa | 1,910 | 1,900 | 1,900 | 1 | 6 | 155 | http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1916_0037 | 10.1098/rspa.1916.0037 | null | null | null | Fluid Dynamics | 44.105845 | Tables | 38.430597 | Fluid Dynamics | [
-7.084236145019531,
-34.528236389160156
] | ]\gt ; 518 Prof. A. Sc over the cross-section are respectively energies are most suitably expressed by stands above the equilibrium position H. ( the rate at which the volume ( is equal to .
Hence the mean squar across the section is joined together of length etc. , am kinetic energy in the vessel is If one of the cross-sections be small contribute the share to the kine FIG. 1 .
it alone need be taken into considerati general expression for the present .
As regards the potential energy , we ta ] column of mercury in its position of equ has entered the tube , the upper leve .
through a distance , being the cr against gravity is therefore of the air in the upper part of the diminished by , and the pressure become small , .
The done in the of the average pressure and$l , and the total of
|
rspa_1916_0038 | 0950-1207 | On the magnetic shielding of large spaces, and its experimental measurement. | 529 | 549 | 1,916 | 92 | Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character | Ernest Wilson, M. Inst. C. E., M. I. E. E.|J. W. Nicholson, M. A., D. Sc.|Dr. J. A. Fleming, F. R. S. | article | 6.0.4 | http://dx.doi.org/10.1098/rspa.1916.0038 | en | rspa | 1,910 | 1,900 | 1,900 | 1 | 34 | 881 | http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1916_0038 | 10.1098/rspa.1916.0038 | null | null | null | Fluid Dynamics | 52.366986 | Electricity | 21.080073 | Fluid Dynamics | [
47.87685775756836,
-42.25728988647461
] | ]\gt ; respectively ( inner ) and ( outer ) , wiffi within the material , the preceding conditions give relations Let , then depending for a thin shell mainly on and not .
Moreover , , depending mainly on .
For a large permeability and a thin , we may write where is the thickness of the shell , and terms of relative order neglected .
In experiments described subsequently , is about If a second order is required , in general \amp ; k that These equations connect the constants in a convenient form at points just within two successive air spaces , and they are equivalent to recurrence formulae .
If they are developed further for thin shells of the order to which these experiments relate , approximately , , and within an error not exceeding about 2 per cent. , We may now write down the reourrence formulae in a convenient form .
Let and be the values of and just within the air spaaee bounding the inner surface of the shell , then where whereeffectivelyThe ratio iwhich atio i : The best illustration of the mode of calculation is a direct numerical Suppose , for example , we build up a series of shells , starting with a radius of 30 cm .
, and the thickness of the shells and air spaces is in each case 2 cm .
, the initial permeability of each shell being 100 .
Then , neglecting the second order , , nd so on , while planes in relation to the direction of the earth 's field does not account for the reversal of sign of the internal field in the case of the four complete shells .
For more dspecially in ( d ) , the field which leaks through the first junction plane is incident on the solid mass of the xt shell except at two single points only , and therefore should not appreciably leak into the next shell .
The same considerations come into play in the interior shells .
It seems fairly evident , therefore , that the effect is due to permanent magnetisation of the outer shell , and in a later section this supposition is verified .
The approximately horizontal portions shown on Curves 4 , , in the neighbourhood of , are due to the tendency of the earth 's field to preserve the right against the opposing forces .
It will be noticed that in all the experimehts with the planes of junction identical , the relative positions of the shells are the same on account of the axis of the inductor .
Any change in the position of this axis would have involved further perforation of the shells , and consequent increase in the leakage .
This important variable was for this reason not tested .
with Magnet Coils .
total area of shell .
The average outer surface of a shell is cm.2 and the circumference of a diametral section is ) cm .
The thickness of leakage space varied between and 4 mm. , with an average cm .
The orrespondin ratio is ) Thus the leakage actually found for four shells is four times as as might have been expected for one by this rough argument , which is evidently therefore inapplicable , and leakage fields must therefore be guarded against in such experiments thoroughly than has usually been thought necessary . .
An inductor which practically fills the internal space is of course necessary in the estimation of the true average value of the leakage , which is by no eans unifo1m throughout the space .
Using the results obtained for one , two , and three shells without demagnetisation , the intensities in the shielded fields are as follows:\mdash ; lower order .
a The leakage through air spaces in a magnetic shield has been studied , and found to be more important than is usually supposed .
Although plarisation of the shells still exists to a small extent , it is not of sufficient magnitude to affect any of the conclusions which have been reached .
The leakage field can , in fact , be completely isolated from other fields .
4 .
It is now possible to examine the behaviour of iron under practically no magnetic force .
The Period of a Resonator with Circular Aperture .
By F. PURYER WHITE , St. John 's College , Cambridge .
( Communicated by Lord Rayleigh , O.M. , F.R.S. Received June 23 , 1916 .
) In a paper on\ldquo ; The Theory of the Helmholtz Resonator , Lord Rayleigh has carried the determination of the wave-length of the fundamental aerial vibration a spherioal vessel with a small circular perforation to a second approximation , obtaining the result .
, ( 1 ) where is the radius of the sphere , the small radius of the aperture , and the volume of the sphere .
To obtain this value he assumes a form for the velooity over the apertureand adjusts it so as to lead to agreement , to a corresponding approximation , in the values of the velocity potential derived therebom over the agerture inside and outside , so to provide for
|
rspa_1916_0039 | 0950-1207 | The period of a spherical resonator with a circular aperture. | 549 | 555 | 1,916 | 92 | Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character | F. Puryer White|Lord Rayleigh, O. M., F. R. S. | article | 6.0.4 | http://dx.doi.org/10.1098/rspa.1916.0039 | en | rspa | 1,910 | 1,900 | 1,900 | 2 | 30 | 748 | http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1916_0039 | 10.1098/rspa.1916.0039 | null | null | null | Fluid Dynamics | 60.122904 | Tables | 24.255049 | Fluid Dynamics | [
46.395896911621094,
-42.537681579589844
] | ]\gt ; lower order .
a The leakage through air spaces in a magnetic shield has been studied , and found to be more important than is usually supposed .
Although plarisation of the shells still exists to a small extent , it is not of sufficient magnitude to affect any of the conclusions which have been reached .
The leakage field can , in fact , be completely isolated from other fields .
4 .
It is now possible to examine the behaviour of iron under practically no magnetic force .
The Period of a Resonator with Circular Aperture .
By F. PURYER WHITE , St. John 's College , Cambridge .
( Communicated by Lord Rayleigh , O.M. , F.R.S. Received June 23 , 1916 .
) In a paper on\ldquo ; The Theory of the Helmholtz Resonator , Lord Rayleigh has carried the determination of the wave-length of the fundamental aerial vibration a spherioal vessel with a small circular perforation to a second approximation , obtaining the result .
, ( 1 ) where is the radius of the sphere , the small radius of the aperture , and the volume of the sphere .
To obtain this value he assumes a form for the velooity over the apertureand adjusts it so as to lead to agreement , to a corresponding approximation , in the values of the velocity potential derived therebom over the agerture inside and outside , so to provide for which replaces ( 19 ) and ( 23 ) .
We shall retain terms in , which occur only in ( 2 ) above and in which is used in place of ( 22 ) .
The effect of these small corrections on the velocity potential is to change the term in the external value ( 24 ) to and to add a term ; the internal value remains unchanged .
On pp. 270-1 , the determination of the constant in equation ( 34 ) may be at first sight not entirely convincing .
We can verify as follows:\mdash ; This formula , although erfi lie , the Now the approximate result shows that is at most of the same order as ; hence neglecting terms of higher order than ( out ) .
( 5 ) We have .
Hence Lord Rayleigh approximates to these series and obtains ( p. 271 ) the value Thusthe ooefficient of in ( 5 ) above is being the angle POA , and the second integral is , ( 9 ) * wheoe is given by i.e. .
( 10 ) The integral is thus .
( 11 ) The third integral is is proportional to the constant potential of the bowl , and in fact , from tb result in the electrostatic problem as given in Maxwell , is equal to Thus , to the order required , , using ( 11 ) .
Hence neglecting terms of higher order than ( 13 ) This result has been verified by actual integration , but the work is somewhat long .
Collecting up our results , the integral ( 7 ) gives This is to be zero , as far as terms of order ( kc)6 , which gives .
( 15 ) Equation ( 15 ) is to hold for all values of , hence , and From this , using only the first three terms , and neglecting , we get , which is Lord Rayleigh 's approximation .
Substituting this in ( 16 ) , We get , as far as Also we have .
( 20 ) .
If , the amplitude of vibration is reduced in one period in the ratio In this case .
( 21 ) On SOme Determinations of the Sign and Magnitude of Electric Discharges in Lightning By C. T. R. WILSON , M.A. , F.R.S. , Observer in Meteorological Physics at the Solar Physics Observatory , Cambridge .
( Received June 3 , 1916 .
) The sign and magnitude of the electric charges transferred from the atmosphere to the earth in lightning flashes are of interest , not only in themselves , but also as having to be taken into account in any attempt test whether there is a balance in the interchange of electrical charges lxtween the atmosphere and the surface of the earth .
As is well known , the evidence at present available appears to show that on the whole an
|
rspa_1916_0040 | 0950-1207 | On some determinations of the sign and magnitude of electric discharges in lightning flashes. | 555 | 574 | 1,916 | 92 | Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character | C. T. R. Wilson, M. A., F. R. S. | article | 6.0.4 | http://dx.doi.org/10.1098/rspa.1916.0040 | en | rspa | 1,910 | 1,900 | 1,900 | 6 | 227 | 6,159 | http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1916_0040 | 10.1098/rspa.1916.0040 | null | null | null | Electricity | 51.646191 | Tables | 20.251889 | Electricity | [
4.204566478729248,
-57.879817962646484
] | ]\gt ; Electric in Flashes .
This gives ( 18 ) and the wave-length is .
( 19 ) Also we have .
( 20 ) If , the amplitude of vibration is reduced in one period in the ratio In this case .
( 21 ) / On Some of the Sign gnitude of Electric in Lightning Flashes .
By C. T. , F.R.S. , Observer in Physics at the Solar Physics Observatory , Cambridge .
( Received June 3 , 1916 .
) The and magnitude of the electric transferred from the atmosphere to the earth in flashes are of interest , not only in themselves , but also as having to be taken into account in any attempt to test whether there is a balance in the interchange of electrical charges between the atmosphere and the surface of the earth .
As is well known , the evidence at present available appears to show that on the whole an excess of positive electricity passes from the atmosphere to the earth as a result of conduction by ions and convection by charged aindrops .
I am not aware of the existence of any data on which more than the roughest estimate of the magnitude of lightning discharges could be based .
Schuster , arting with two by Pockels of the maximum * Schuster , ' Progress of Physics 1908 .
' 'Met .
Zeitschrift , ' p. 40 ( 1901 ) .
Mr. C. T. R. Wilson .
On the Sign current , measured by means of ibs magnetising effect , and taking 1/ 1000 second as the duration of a flash , estimates the quantity brought down by a discharge as about 10 coulombs .
It hardly seems possible to use systematically a direct method for the measurement of lightning , i.e. , to induce the discharges to traverse any form of measuring apparatus .
The most promising method would seem to be that of making absolute measurements of the sudden changes produced in the vertical electric field at a given point of the earth 's surface by lightning flashes in the neighbourhood .
A measurement of the difference between the vertical electric force immediately before and immediately after the flash at a sufficiently number of points would us a measure of the discharge ; for the total resulting displacement current must be equal and opposite to the current passing from the atmosphere to the earth in the discharge .
Although it is hardly practicable to carry out this method in its ideal form , there are two ways in which we may make approximation to it .
If the sole object of our investigations were the solution of the general problem of the part played by lightning discharges in the interchange of electrical charges between the atmosphere and the earth , we simply accumulate , over a long period , and at as many places as possible , measurements of the instantan eous changes of fiela1 due to lightning , and thus eventually obtain an approximation to the total charge transferred from the atmosphere to the earth in lightning discharges in a known time .
We may , on the other hand , measure the changes of field due to htning occurring at known distances from the place of observation .
It is with the results obtained by this method of study that this paper deals .
Let us consider the case of a lightning flash in which a charge of electricity , derived from a certain region of the atmosphere , passes to earth .
The resulting in the electric field at the place of observation i.e. , the difference between the vertical force at before and after the discharge , is due to the disappearance of the charge which occupied the A and of the induced charge on the surface of the ground .
The effect of the latter is most conveniently considered by substituting for it the of Q. The surface of the earth is assumed to be an equipotential surface before and after the discharge .
Treating the earth as a spherical conductor and applying the method of images , we know*that a charge at the point in the atmosphere , ethsr with the indqced charge , produces at a vertical force , , .
J. J. son , ' Elements of Electricity and Magnetism , ' p. 146 .
Magnitude of Electric in Lightning .
557 where is the radius of the earth , is the distance of from the centre of the earth , and is the distance Op ; or , putting .
The factor differs from unity by less than one part in a thousand : even when is as great as 10 kilom .
We may thus negiect the effect of curvature , all with which we shall be concerned being small compared with the radius of the earth .
The charge of an element of volume surrounding any point at a above the has its image at at an equal depth below the surface ; the and at and have the same effect for all points ) ground as the at and the induced on the surface of the ground .
If is the distance Op , the vertical electric force at due to and its image is change in the vertical force at the point due to the discharge of to earth is , where is the charge removed from an element of volume at a height and a distance .
from O. If has been symmetrically distributed in concentric spheres about centre , or if it has all been derived a region whose dimensions small compared with , the distance of that point from , we may substitute for , being the mean height from which the is derived .
QH is the electric moment of the discharge .
If then we are able to measure the changes of field due to distant lightning discharges and also the distances of these discharges , we may deduce their electric moments .
With several observing stations it would be possible to localise the discharges by the magnitudes of the observed of field at the different places .
The results discussed in this paper were obtained by obselving the time-interval between the occurrence of each sudden change of field and the beginning of the succeed- ing thunder .
It was found possible to apply this method up to distances of more than 20 ( on one oocasion of 30 ) kilom .
The distance measured in this way is not as defined above , but ( on the assumption that the discharge is vertical ) , the .
distance to the point where the discharge enters the ground .
The distance may be taken as indistinguishable from if is large , e.g. , 10 times H. For such distances we may put , where-F is the sudden of field .
For smaller distances ( if we assume that the electricity discharged in the htning had been so distributed that we may regard it as been concentrated at a point ) , where is what we may call the uncorrected moment of the discharge .
The height which the discharge takes place is unknown , but we Mr. C. T. R. Wilson .
On the Sign and might expect to get information about the average height by accumulating sufficient data to enable us to find how varies with the distance .
The observations which have already been made appear show that in certain storms the successive discharges are very much alike both as regards the height from which they have come and the quantity of electricity discharged .
In such a case it is possible to deduce and , and therefore also , from the manner in which the sudden of electric force depends on the distance of the discharge , just as in the corresponding netic problem we might find the moment of a magnet as well as the distance between its poles by observing the magnetic force produced by it at different distances in its equatorial plane .
us now suppose that the discharge is not to earth but between two regions , A and , of the atmosphere .
As a result a charge is transferred from A to B. The change of the vertical field at the point is now the difference between the field due to the charge when at A and at respectively , the effect of the induced charge on the round being as before obtained by substituting for it an equal charge at and , the images of A and B. We may again as a first approximation to the actual problem treat the charge as being concentrated at its " " centre of mass\ldquo ; before and after the discharge , i.e. treat the as if it took place between two points , and , in the atmosphere .
The change in the vertical electric force at is then equal to , where are the distances of from and respectively , and are equal to and being the heights of A and above the round .
If the discharge is vertical and at a sufficient distance , we may put approximately , and the change in the vertical force at becomes wlJereM is the electric moment of the discharge .
It is plain that in the case of the discharge between two points in the atmosphere the sign of the change of field due to a discharge depends on whether or is the greater .
If , for example , we had a series of vertical discharges , all between the same two heights in the atmosphere , in a storm over the place of observation , the sign of the change of field would be reversed when the discharge took place at a distance such that was equal to .
It should be noticed that when the discharge is between two points in the atmosphere the interval between the discharge and the beginnir4 of the thunder is not a measure of , the distance from to a point below the discharge , but more nearly of the distance to the nearest ehd of the discharge , i.e. of Magnitude of Electric Discharges in Lightning Fllashes .
559 Method Employed in the Investigations in Atmospheric Electricity at the Solar Physics Observatory .
The observations on the sudden changes of the electrical field due to lightning flashes were made with apparatus which had been designed to measure also the electric field at the earth 's surface and the current from the atmosphere to the ground , including both that due to conduction by ions and that due to the electric carried by rain or other form of precipitation .
The method may be regarded as a development of one described some years ago.* This depended upon an insulated conductor at zero potential by means of \ldquo ; compensator\ldquo ; whose measured the which had to be iven to the conductor to keep its potential zero : ( 1 ) when first exposed to the earth 's electric field by the removal of an earthed cover , ( 2 ) while kept exposed , and ( 3 ) when again covered .
In the method now to be described the compensation is automatic and the may , therefore , be made self-recording .
The principle of the method will be understood by reference to the .
A is a conductor whose flat upper surface is on the same level as the surrounding ground .
It is supported on insulators but connected to earth through an instrument indicated rammatically at , whose reading is a measure of the quantity of electricity which has traversed it , and which is of such a nature that the potential of A is never allowed differ appreciably from zero .
A type of capillary electrometer described later was found suitable as the instrument .
is an earthed conducting cover .
With in position A is uncharged .
If is removed a charge flows through into A from the earth , identical in and magnitude with that on any equal area ( correction being made for the ) of the surrounding flat ground .
The resulting change of of is thus a measure of the * C. T. R. Wilson , ' Roy .
Soc. Proc , vol. 80 , p. 537( Magnitude of Electric Discharges in Lightning Flashes .
561 while nearly level , is slightly convex , the fall of level not exceeding 2 feet at a distance of 40 feet from the test-plate in any direction .
There are no trees nearer than 100 yards ( 91 metres ) , and the nearest house is the farm- house , about 180 yards ( 165 metres ) away .
The grass in the immediate neighbourhood of the test-plate was kept short .
The electrometer and other necessary apparatus is housed in a zinc-roofed wooden hut , feet cm .
) in area , and having a maximum height in the middle of the roof of feet ( 260 cm It is placed with its longer side in an E.-W .
direction , the centre of the hut feet ( 1403 cm .
) due north of the centre of the test-plate .
The roof is in metallic FIG. 2 .
connection with a copper lightning conductor connected to a large copper earth-plate .
For the measurements other than those to it seemed desirable to make the exposed conductor approximate in character to a portion of the earth 's surface , isolated to enable the it to be measured , but otherwise differing as little as possible from the surrounding ground .
It consists of two earth-filled circular sieves , one resting on the top of the other , cm .
in diameter , and having together a depth of 18 cm .
, supported on three insulators in a concentric pit cm .
in diameter and 45 cm .
deep .
The sieves are completely filled with earth , the upper surface of which is on a level with the surl.ounding ground .
An air-gap cm .
wide separates the wooden rim of the upper sieve from the sides of the pit , which has a lining of wood , made out of a barrel with both ends sawn off .
The effective area of the exposed surface of the test-plate , taken as the mean of that of the mouth of the pit and of that of the sieve , is 2220 sq .
cm .
Magnitude of Electric Discharges in Lightning Flashes .
563 sieves have beeu able to absorb the rain falling on them .
No appreciable error is , however , likely to be introduced , even if the exposure be continued after water begins to drip from the under surface of the earth-filled sieves , the potential being always maintained at zero by the electrometer within one- or two-thousandths of a volt .
In measuring the potential gradient by observing the in the electrometer reading on removing or replacing the earth-connected cover , it is assumed that the latter and the surface of the test-plate are at the same potential .
With a vertical distance of 10 cm .
between the surfaces , potential difference of 1 volt would give a 10-per-cent .
error in potential gradient of 100 volts per metre .
Any error of this kind due to contact potential differences will be small when both surfaces are of earth , connected to the ground by copper wires , with copper plates at each end ; considerable error will be introduced if one only of these plates is of some other metal .
Measurements of the sudden changes of radiant due to discharges , with which we are concerned in the present paper , are unaffected by the sources of error which we have been considering . .
Given a suitable electrometer , and in particular one which is dead-beat and sufficiently rapid in its action , such measurements are very easily made .
It is not really essential for this purpose that the electrometer should have the property , postulated above for the instrument , of automatically maintaining the conductor connected to it at zero potential .
An electrometer of the gold-leaf or stretched-fibre type may be used .
In this case a sudden change of the earth 's field ] cause the electrometer to indicate a sudden change of potential , where is the charge which would have passed from the exposed conductor to the ground if it had been earth-connected , and is the capacity of the exposed conductor , electrometer , and connecting wire .
For the measurement of smaller changes in the electric field , such as are produced by very distant lightning discharges , a second exposed conductor on which the charge for a given potential gradient was more than 30 times as great , was arranged to be available as an alternative to the flat testplate .
It consists of a copper sphere , 30 cm .
in diameter , held when in use at a height of 480 cm .
above the round , and at a distance of 407 cm .
to the west of the nearest end of the hut .
An iron pipe , 14 feet ( 427 cm .
) in length and 5 cm .
in external diameter , serves to support the sphere and to protect the wire connecting the sphere with the electrometer .
The sphere is c , arried at the end of a brass tube , 22 mm. in diameter , projecting 39 cm .
beyond the top of the iron pipe , from which it is insulated by plugs of sulphured ebonite .
To the lower end of the Magnitude of Electric Discharges in Lightning flashes .
at the same potential by them together by a wire , the mercury and acid in the capillary are tlisplaced through a distance in the FIG. 3 .
direction from A to , then the surface of A in contact with the acid has been increased by an amount , while that of is diminished by an equal amount .
The positive charge on the surface of the mercury in contact with the acid is increased in A and diminished in by where is the capacity per unit area of the mercury-sulphuric-acid surface and is the contact potential difference between the liquids .
The negative charge on the acid in contact with A has been increased and that in contact with diminished by the same amount .
A quantity of electricity has therefore flowed round the closed circuit in the direction of displacement of the .
The reversible action of the capillaly electrometer is well known and was described by Lippmann in his early papers .
displacement may be produced by applying a pressure difference between the ends or by inclining the tube ; it may equally well be effected by momentarily insertin a small electromotive force in the circuit .
In each case the displacement is a measure of the quantity of electricity which has traversed the electrometer .
If we remove the short-circuiting wire and connect with the earth , then any charge given to A will cause a displacement that the acid column moving until the potential of A is reduced to zero .
The movement of the instrument when used to measure a in this way is extremely rapid and is completely dead-beat .
While the electrometer is ( in its ideal form ) without control when its terminals are connected together , it has an extremely strong , purely electrical , control on open circuit , the liberated by even a very small displacement a potential difference between A and , and consequent rence of surface tension between the two mercury-sulphuric-acid surfaces , sufficient to exert a considerable opposing force .
The constant of the instrument is readily determined by connecting it to a condenser of known capacity and charging the condenser through the Magnitude of Electric Discharges in Lightning Flashes .
567 the actual potential gradient by momentarily replacing the cover were positive and ranged between 100 and 200 volts per metre .
Sign of Change of Field.\mdash ; Of the 33 discharges observed , gave positive and 18 negative changes of field .
Magnitude of Change of Field.\mdash ; This varied from 50 to 760 volts per metre .
Distance of Discharges.\mdash ; Towards the end of the time during which the observations lasted , the intervals between the discharges became sufficiently great to admit of the timing of the interval between the individual discharges and the thunder which followed .
In the four observations made in this way the time-intervals varied between 45 and 60 seconds , corresponding to distances of from 15 to 20 kilom .
; the change of field produced by each of these four discharges was negative .
Electric Moments of the Discharges ( Uncorrected ) .
these four the values of in elecbrostatic measure were : , and , the distances being 20 , 17 , 17 , and 15 kilom .
AUGUST 21 , 1914.\mdash ; Observations made with sphere and gold-leaf electrometer .
Obselvations lasted from 5 to P.lf .
The potential gradient both at the beginning and end of the observations was positive , and about 120 volts per metre .
Sign of C'hange of \mdash ; Of the 39 discharges observed , 13 produced positive and 23 negative changes of field , the remaining 3 being cases of double or multiple with a re-ultant little from zero .
Magnitude of Changes of From 1 volt to volts per metre .
Distance.\mdash ; Measured in the case of three discharges , and 33 kilom .
Electr ( Uncorrected).\mdash ; The values of corresponding to these distances were , and Owing to the frequency of the there was room for some uncertainty in the identification of the thunder resuIting from a given discharge .
AUGUST 12 , 1915.\mdash ; The observations were made with the flat test-plate and the capillary electrometer .
The observations began about 12 .
, and were discontinued at 12.50 .
Sign of Changes of Field.\mdash ; Positive in 30 cases , negative in 4 .
Magnitude of es of Field due to Discharges.\mdash ; From 1000 to volts per metre .
tcvnce.\mdash ; Observations were obtained of the distances of all the 34 discharges .
They ranged from to 10 kilom .
Mr. C. T. R. Wilson .
On the Sign Discussion of the R\amp ; sults .
The observations are as yet too few for drawing any general conclusions as to the direction of the electric current in lightning discharges .
It is , howeve of interest to note that in the series of storms of August 12 to August 15 , 1915 , the direction of the current was upward in nearly all the If we leave out of consideration the results obtained when the discharges were nearer than 5 kilom .
, the values obtained for are , with few exceptions , comprised between and being measured in electrostatic units and in centimetres .
The values obtained continue to increase with tlre distance , esting that even the more distant discharges may have been too near to admit of being taken as appr.oximately equal to , the electric moment of the discharge .
The results of the observations made in the storm of August 15 , 1915 , are of special interest on account of the systematic way in which increases with ( fig. 5 ) .
It is difficult to believe that the electric moments can themselves have varied in any regular way with the distance of the discharge from the observer ; it is much more natural to assume that was independent of this distance , and to interpret the regularity as implying that the lightning flashes of this storm were approximately alike both as regards their vertical and the quantity of electricity discharged .
The nature of the variation of with is in facG in reement with this view .
Assuming that discharges all of equal amount pass from the same height in the atmosphere to the earth , we have seen that The curve I of fig. 5 is obtained by plotting the calculated values of agai1nst , assuming .
and electrostatic units coulombs .
This fits the observations very well .
The one point which lies far from the curve is at so nearly wics the height of the curve as to suggest that it may represent the bined result of two nearly simultaneous discharges .
We , on the other hand , suppose that each discharge was entirely in the atmosphere and that it might be arded as passing between two points one vertically above the other at heights and , approximately the same for all the discharges .
The distance given by the thunder observations must now be take .
as representing , that between the observer and the lower extremity of the discharge .
Curve II ( fig. 5 ) represents the calculated values of plotted against Magnitude of Electric Discharges in Lightning Flashes .
571 , when kilom .
, kilom .
, electrostatic units coulombs .
This again represents fairly accurately the results of the observations .
Observations of discharges at shorter distances would at once have distinguished between the two hypotheses , for the second one involves a reversal of the change of field for distances less than 5 kilom .
The value which has to be assigned to to make the curves fit the observations is , however , practically identical in the two cases .
It was noted at the time that the thunder was of the growling kind which one is inclined to associate with discharges which do not reach the surface of the earth .
The most natural interpretation of the results of the observations would thus appear to be that the discharges of this storm took place within the thunder cloud , and that they were of great vertical extending almost throughout the whole height of the troposphere .
It is perhaps worthy of note that the curve obtained by putting , also fits the observations fairly well if we exclude those of discharges at distances exceeding 15 kilom .
; the value which has to be assigned to to make the curve fit the observations is , it will be noticed , almost unchanged .
While , therefore , the observations leave room for some uncertainty as to the heights in the atmosphere between which the discharges occurred , is little doubt that the quantity of electricity discharged in each htning flash of the storm was about electrost , atic units ( coulombs ) .
The momentary electric currents constituting the discharges in this storm were upwards in nearly all cases .
This may be interpreted as , indicating that the falling rain drops of the thunder cloud were positively charged , leaving behind them a negative charge in the upper part of the cloud and , if they reached the ground , an excess of negative electricity in the cloud as a whole .
The lightning discharges were continually tending to neutralise the electric field produced .
The lightning may have reached the earth , or may not have extended below the cloud , or both kinds of discharges may have occurred .
At reat distances , owing to the smallness of in compal.ison with H2 , the instantaneous effects on the potential gradient at the surfaoe of the ground would be similar for both kinds of disclJal.ge , the longer ] laving , however , a somewhat larger effect on account of its greater moment .
The difference in the effects would increase with diminishing distance , of the effect due to the shorter discharge finally reversed .
Now three of the discharges observed took place in two stages , as was shown by the nature of the movement of the meniscus ; in each case the results can be explained by regarding the two stages as having consisted ( 1 ) in the discharge from the upper to the lower part of the cloud , ( 2 ) from Mr. C. T. R. Wilson .
On the Sign and the lower part of the cloud to earth , the first moyement of the electrometer resenting the discharge in the cloud , the total resultant displacement being the effect of the whole discharge from the upper part of the cloud to earth .
The of field recorded in observations Nos. and 7 for distances of and kilom .
each took place in two steps , both positive ; in observation ( 1 ) for a distance of kilon ) .
it consisted of a negative change of 500 volts per metre , followed by a positive change of 1500 , leaving a positive balance of 1000 volts per metre .
The results obtained in the storm of August 12 , 1915 , and represented in fig. 4 , show much less regularity .
Yet , while the points representing do not here all lie approximately on one curve , they appear to converge , as the distance is diminished , towards zero for a distance of about kilom .
This is the result to be expected if the discharges were all from a height of about 7 kilom .
, while the quantity discharged by the different flashes varied between 10 and 50 coulombs .
The observations are seen to be practically all contained between the two curves I and III , which have been calculated for and coulombs , the in each case being 7 kilom .
The mean of these vahues of is practically identical with that found for the discharges of the storm of August 15\mdash ; about 30 coulombs .
Curve II represents the case coulotnbs , the height being as before , 7 kilom .
The values deduced for the heights of the upper ends of the lightning discharges are surprisingly high ; indeed , the curve which best fits the observations of August 11 1915 , is obtained on the assumption that the .
came from a height of 15 kilom.\mdash ; considerably above the lower limit of the stratosphere .
It would be premature to conclude that the discharges really came from heights above 10 kilom .
Errors of observation or variations in the acter of the discharges may have occurred in a sufficiently systematic way to increase the values of for the greater distance aIId to diminish them for the smaller , and so lead to an over-estimate of the There is one factor in the problem which has thus far in the present paper been ignored\mdash ; conduction in the upper } ) here .
If we were to assume the atmosphere above a certain height to be a good conductor , we should have to consider not merely one image ( replacing the induced charge on the ground ) but an train of images of the discharge .
It is easily seen that the chan ge produced in the potential ooradient by a discharge to the earth would be thereby increased for the greater and diminished for the smaller distances , thus causin , over-estimate of the heights .
But if the lower limit of the conducting strata were at a height amounting to even a very small number of times that of the upper limit of the lightning discharges , the effect would Magnitude of Electric Discharges in Lightning be relatively very small except at distanoes greater than the height of the conducting layer .
It is unlikely that the requisite high conductivity could under normal conditions extend sufficiently low in the atmosphere to be an important factor in the problem .
There is , however , the possibility that the electric force produced in the atmosphere at no very great height by a lightning discharge below it might exceed that required to cause ionisation by collisions .
A lightning flash might thus be accompanied by a high level discharge extendingas a sheet ( possibly visible as sheet htning ) throughout the whole region in which the electric force and the pressure lay within the proper limits .
Even , however , at a height of 40 kilom .
the pressure is still nearly .
of mercury , and the maximum change of electric field at this height , due to a htning discharge comparable with those of which measurements have been made ( having for example an electric moment of electrostatic units ) , would only amount to 1 or 2 volts per centimetre .
Such discharges would thus probably be confined to somewhat higher levels than 40 kilonL ; they would then affect but little the change of field at the earth 's surface resulting from lightning flashes except at comparatively great distances .
Little need be said about the observations in the storms other than those of August 12 and 15 , 1915 , as these were the only ones in which any considerable number of measurements of the distances were made ; those of the previous year especially , however , to show that it is by no means true of all storms that the prevailing direction of the electric currents in the lightning discharges is upwards .
The values found for the quantity of electricity discharged in flashes are not much in excess of Schuster 's estimate of 10 coulombs to which reference was made at the inning of this paper .
His conclusion , that the balance in the interchange of electric charges between the atmosphere and the earth is unlikely to be influenced to any important degree by lightning , is not substantially affected by substituting 30 for 10 coulombs .
Perhaps the most instructive way of stating the matter is in terms of the interchange over the whole surface of the globe .
The total current flowing from the atmosphere to the earth a result of the normal potential gradient and atmospheric ionisation ( if we may take the results of observations at comparatively few points as giving a fair average for the whole surface ) is , as Simpson*has pointed out , of the order of 1000 amperes .
Thus about yhtning flashes , each carrying a charge of 33 coulombs from the 'Nature , ' December 12 , 1912 .
VOL. XCII.\mdash ; A. 2 Prof. J. C. McLennan .
On the Ionisation atmosphere to the earth , would be required every second to neutralise the total conduction current .
The whole resultant effect of a thunderstorm in increasing or diminishing the atmospheric may possibly be comparatively small , the lightning discharges neutralising almost completely the currents due to precipitation .
It would be interesting to have measurements of both the htning discharges and the charges brought down by precipitation for the same storm .
I have to thank Prof. Newall for advice on many points in all stages of the work .
I should like also to acknowledge the help I have received from Mr , Stanley , who has constructed the greater part of the apparatus .
To Mr. Crow I am indebted for help in the construction of various forms of capillary electrometer ; these were made and tested at the Cavendish Laboratory .
On the of Magnes other on their Absorption By Prof. J. C. McLENNAN , F.R.S. , University of Toronto .
( Received July 17 , 1916 .
) [ PLATES 7 AND 8 .
] 1 .
Introduction .
In a paper recently published by the writer , the single-line spectrum of magnesium , experiments were described in which it was found that when magnesium vapour in a vacuum was bombarded by electrons it was possible if the electrons possessed the requisite amount of kinetic energy to cause the vapour to emit a radiation consisting of the single spectral line .
At the time these experiments were made and the paper was written it was not known by the author whether this line was the first member of the series whose frequencies are given by or of the series * McLennam , ' Roy .
Soc. Proc , vol. 92 , p. 305 ( 1916 ) .
In the symbolic equation frequencies are given by , where is Rydberg 's number , has a fixed value either integral or one of the numbers , etc. , and has successire integral values , each one giving the frequency of a member of the
|
rspa_1916_0041 | 0950-1207 | Obituary notices of fellows deceased. | 0 | 0 | 1,916 | 92 | Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character | J. J. T.|H. H. T.|G. D. L.|F. W. D.|T. E. T.|O. J. L. | article | 6.0.4 | http://dx.doi.org/10.1098/rspa.1916.0041 | en | rspa | 1,910 | 1,900 | 1,900 | 3 | 268 | 8,779 | http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1916_0041 | 10.1098/rspa.1916.0041 | null | null | null | Biography | 55.494191 | Astronomy | 13.352847 | Biography | [
34.890254974365234,
80.95755767822266
] | ]\gt ; ii Notices of deceased .
famous club were , however , then and it came to an end in 1876 .
He took his degree in the Mathematical Tripos of 1876 as Third Wrangler , bracketed with Mr. Trimmer , of Trinity College , a very brilliant.man who suffered from persistent ill-health and died within a few months of taking his .
As Dr. Glazebrook and Dr. Shaw both raduated in the same Tripos and Lord Rayleigh was the additional Examiner , Physics was well represented on this occasion .
After degree Pointing came back for a short time to the Owens College , which was now in the buildings it at present occupies , and demonstrated in the Physical Laboratory under Prof. Balfour Stewart , who had succeeded Jack as Professor of Natural Philosophy shortly before Poynting 's departure for On his election to a Fellowship at Trinity College in 1878 , Pointing returned to Cambridge and began , in the Cavendish Laboratory under Clerk Maxwell , those experiments on the mean density of the earth which were destined to occupy so much of his time for the next 10 years .
He remained at unti11880 , when he was elected to the Chair of Physics in Mason College , Birmingham ( now the University of Birmingham ) , which had just been this post he held until his death .
The year that he went to , he married the daughter of the late Rev. J. Cropper , of Stand , near Manchester .
He threw himself whole-heartedly into the arduous duties connected with the of a new Uniyersity , the preparation of his lectures and the equipment of the physical laboratory , and , as was his wont , without any bustle or hurry he soon had efficiently .
And so in the efficient discharge of his duties as a Professor , in successful original research , in the fulfilment of municipal duties , the time passed placidly on , the only cloud on an almost idyllic domestic life being his somewhat indifferent health , the first threatenings of the disease from which he ultimately died .
To see if a country would suit his health better than a town one , the Poyntings nloved from Edgbaston to ] Hill , Alvechurch , a house about 12 miles out of Birmingham .
There was a small farm attached to the house and Pointing entered into most heartily , though I am afraid he did not de1ive much pecuniary profit from it .
But even farming when the agricultural depression was most acute could not impair his good temper or ruffle his equanimity .
If the farm did not yield money , it gave new interests and experiences , and if something was always going wrong , at any rate it drove away monotony .
The quietness and simplicity of the life were thoroughly to the taste of Mrs. Pointing and himself .
Life in the country too gave free scope to his taste for Natural History , in which he always took great interest ; he was a keen and excellent observer , and a favourite contention of his was that physicists were somewhat too much inclined to confine their ) to expel.iments made in the laboratory and did not sufficiently avail themselves of the opportunities of studying the physical phenomena going on in the sky , the sea , and earth .
The taste for Natura 1 John Henry Pointing .
History was a family one ; his younger brother , the late Mr. F. Pointing , was an excellent ornith 1 , devoting himself especially to the study of the of British birds , of which he made most careful and accurate water-colour drawings\mdash ; some of these have been reproduced in his book The Eggs of Briti sh Birds .
' The stayed at Foxhill until 1901 , when , his health much improved , they returned to Edgbaston .
His life at this time was a busy one , for in addition to the work demanded from him as the head of a large and successful School of Physics , he aoted as the Dean of the Faculty of Science , was a Justice of the Peace , and for some time Chairman of the Birmingham Horticultural Society .
He had also to plan and superintend the erection of a new phvsical laboratory when his department was transferred from its old quarters to the new buildings of the University of Birminghanl .
He went with the British Association to Canada in 1907 , when it met at Winnipeg , and gave one of the evening lectures ; his subject was the Pressure of Light , on which he had been for several years .
He went the trip to Vancouver and back and seemed thoroughly to enjoy the visit .
The pressure of light was also the subject of a lecture which he gave in Trench at Paris before the French Physical Society at Easter 1911 .
In the spring of 1912 a severe attack of influeIJza was followed by a recrudescence of diabetes , a disease from which he had suffered for some time , and he was ordered to take a long rest ; he was , in consequence , away from Birmingham for two terms .
On his return to Birmingham he seemed much better , he took an active part in } meeting of the British Association held there in September , 1913 , and he and Mrs. Pointing entertained a party of physicists at their house in Ampton , and it then seemed as if he might hope to enjoy many years of useful work .
Another attack of influenza in the spring of 1914 brought on a very severe attack of diabetes , and he died on March 30 , 1914 .
It is difficult to attempt to say what Pointing was to his friends without terms which must appear gerated to ttJose who did not know him .
He had a genius for friendship , and a sympathy so delicate and acute that whether you were well or ill , in high spirits or low , his presence was a comfort and a delight .
During a friendship which lasted for more than thirty years , I never saw him cvry or impatient and never heard him say a bitter or unkind thing about man , woman or child .
He took pleasure in many , in music , in literature , for } was a lover 'of books and a collector in a modest way , in novels of all kinds , good and bad .
He was fond of the country , and especially of North Wales , where he spent most of his vacations , but happiest of all ] at home with his family .
Throughout his life he took considerable interest in Philosophy , and a discussion of the philosophical basis of sics formed part of his Presidential Address to Section A at the Dover of the British Association .
Views similar to those he there expressed are now ] ) by many ; he had his years before , when but few in country agreed with them .
The excellence Obituary Notices of FellovJs deceased .
of his work received many recognitions , though not in my opinion so many as it deselved .
He was elected a Fellow of the Royal Society in 1888 , received a Royal Medal in served on the Council to 1911 and was VicePresident in 1910-11 .
He received the Adams Prize from the University of Cambridge in , the Hopkins Prize from the Cambridge Philosophical Society in 1903 .
President of Section A when the British Association met at Dover in 1899 and was President of the Physical Society in 1909-11 .
He was in great request as an Examiner in Physics and no one excelled him at this work , his long experience of students , his judgment and common sense , the charitable view he took of the limitations of a student 's knowledge , and the fact that he was never afraid of setting easy papers , made him an eminently fair and discriminating examiner .
He was very successful as a teacher of students of all kinds , those who only took Physics as a subsidiary subject as well as those who made it their life 's work , he inspired these with an enthusiasm for research and .
with some of his own skill in accuracy of measurement and in the tlJoroughness of their work .
SCIENTIFIC WORKS .
This may be divided into four groups : studies on gravitational attraction , ( b ) on the change of state , ( c ) on the transl.er of energy in the netic lield , and ( d ) on the pressure of light .
tional Aitraction .
His experiments on the mean density of the earth were commenced in Cambridge in 1878 but it took twelve years ' steady work before he obtained a result with which he was satisfied .
The method used was to measure the attraction veen two known masses A and by suspending A from one of the arms of a balance of the ordinary type and finding the increase in weight produced when was underneath it .
The , balance used in the later experiments was one built specially for the experiment by Oel.tling and had a beam 123 cm . .
With a balance of this size the difficulties arising from air currents proved very formidable .
Pointing fully recognised the advantage of Boys ' short torsion balance method in this respect and said that if he were designing the apparatus , instead of using an exceptionally large balance for the sake of being able to suspend large masses , he should go to the other extreme and make the apparatus as small as possible .
At the same time , as he points out , the magnitude of effects produced by the air currents made their detection easy , whereas they might have been overlooked and not allowed for had they been smaller .
The final ults ( ' Phil. rans .
, vol. 182 , p. 565 , 1891 ) he obtained for , the mean density of the earth , and , the gravitational were John Henry Poynting 's long ation incidentally added considerably to our knowledge of the technique of accurate With the co-operation of Gray he made a series of most } ) ments Phil. Trans to see if the attraction bebween two quartz crystals was the when the axes of the crystals were parallel when they were crossed .
The method he used was a very ingenious application of the principle of forced oscillations , which , so effective that , one sphere was only about 1 cm .
in diameter and the other about 6 , the experiments showed that the attractions in the two positions could not differ by as much as 1 part in 10,000 .
Later he made with Phillips a series of experiments to see if weight depended on temperature , as in his experiments a balance of the ordinary type ; the result of these was ( ' Proc. .
Soc vol. 76 , p. 445 , 1905 ) that between C. and 10 C. the in is not greater than 1 in and between C. and C. it is not so great as 1 in per 1o C. Change of State .
The problem of the change of was one which he took especial interest , and it was the subject of one of his earliest papers Phil. , vol. , p. 32 , 1887 .
His way of picturing this change was to suppose that from the surface of a liquid or solid particles were continually free , so that through each unit of area of the surface there was a constant escape of molecules .
This loss was balanced by the ) assage from the vapour above the solid some of the gaseous particles struck ainsC its surface , so that when there equilibrium the flow out from the liquid or solid was balanced by the flow inward the gas .
The proportion aseous molecules which after striking the surface passed across to the solid or liquid state he assumed to be the same for a solid as for a liquid and to be independent of the temperature , so that it could be measured by the vapour pressule .
Thus at the same temperature the flow across water would be to the vapour pressure of water , that across ice to the vapour pressure of ice , thus ice could only be in equilibrium with water when the vapour pressure over ice is equal to that over water .
Pointing supposed that the mobility of the molecules in liquids and solids is increased by pressure\mdash ; the pressure as it were squeezing the molecules out : the amount of the increase depending on the density of the substance , diminishing as the density increases .
Thus , if pressure increases the escape of the molecules from a liquid , a liquid under pressure will evaporate more freely , and so for it to be in equilibrium with its vapour the vapour pressure must be than that over the normal liquid ; from the equilibrium between water and its vapour in a capillary tube , he found that if is the increase in the vapour pressure produced by applying a pressnre to the liquid , , where is the density of the vapour and that of the liquid .
Pointing applied this conception of mobility to the case of solutions , taking the view that the molecules of the salt formed with some of the vi Obituary Notices of Fellows deceased .
water molecules and thus diminished their mobility diminishing the number of water molecules which passed from the liquid state through ach unit of area of surface per second .
The mobility of pure water is thus greater than that of the solution , so that if the two are separated by a semi-permeable membrane more molecules will pass from the water to the solution than from the solution to } water , and the water will flow into the solution .
To prevent this flow the mobility of the molecules of water in the solution must be increased by the application of a pressure that will make the mobility of the solution equal to that of pure water ; this pressure is the osmotic pressure .
Since under this pressure the mobility of the solution is equal to that of pure water the vapour pressure in equilibrium with the pressed solution will be the vapour pressure over pure water , so that another delinition of osmotic pressure would be the pressure required to raise the vapour pressure over the solution to that over pure water .
On the assumption that the presence of one molecule of salt to of water would diminish the mobility of the water in the proportion of , which would be the case if a molecule of salt imprisoned one and only one molecule of water , showed that the osmotic pressure on his theory would be the pressure exerted by the salt molecules if they were in the gaseous state and occupying the volume of the solution .
Though this theory does not connect the electrical properties of solutions with the properties associated with osmotic pressure so readily as the dissociation theory , it is so simple and fundamental that it helps to give vividness and .
definiteness to our picture of the processes operative in solutions .
ansJer of Energy .
The researches by which Pointing is most widely known are those published in the papers " " On the Transfer of Energy in the Electromagnetic Field\ldquo ; Phil. Trans and\ldquo ; On Electric Currents and the Electric and Magnetic Induction in the Surrounding Field\ldquo ; Phil. Trans .
He says in the first paper , " " The aim of this paper is to prove that there is a general law for the transfer of energy , according to which it moves at any point perpendicularly to the plane containing the lines of electric and magnetic force , and that the amount crossing unit of area per second of this plane is equal to the product of the two forces multiplied by the sine of the angle between them divided by 4 , while the direction of the flow of energy is that in which a right-handed screw would move if turned round from the positive direction of the electromotive to the positive direction of the magnetic intensity He shows from the equation of the electromagnetic field that the rate of increase in the energy inside a closed surface is equal to where is an element of the closed surface , the direction cosines of the normal to the surface , the components of the electromotive intensity , and those of the magnetic force .
This expression may be .
Vlll Notices of ellows deceased .
the current through the wire were an one with very high frequency the electric force near the wire would be at angles to it .
In this case the would flow parallel to the wire but outside it .
In the second paper Pointing , taking the view that the electromagnetic field consists of ibutions of lines of electric and magnetic force , discusses the question of the transfer of energy from the point of view of the movement of these lines .
He applies the same considerations to the question of the residual charge in Leyden jars in his fascinating and instrnctive paper on Discharge of Electricity in an Imperfect Insulator ( ' Phil. Mag vol. 5 , 1886 , p. 419 ) .
Poynting 's vector occurs as a quantity of fundamental importance in theories of netic action in which the subject is approached from a point of view somewhat different from the one he adopted .
It appears , for example , as a measure of the momentum per unit volume when the electromagnetic field is regarded as a mechanical system and the properties of the field as the result of the laws of motion of such a system .
It appears , too , when we magnetic force as the result of the motion of tubes of electric force , the direction of motion of these tnbes being parallel to Poynting 's vector .
of Iight .
For some years before his death Pointing devoted much attention to the question of radiation and the pressure of light .
On the theory of this subject he ished Phil. Trans a very valuable paper , in the first part of which he discusses the application of the fourth-power law of radiation to determine the temperature of planets ( in this he found afterwards he had been anticipated by Christiansen ) .
Among other interesti1lg results he arrived at the conclusion that the temperature of Mars must be so low that life , as we know it , would be impossible on its surface , this result was criticised by Lowell , but Pointing xinCained his ground in a paper published in the ' Philosophical Magazine , ' December , 1907 .
The second part of the paper in the ' Philosophical Iransactions ' contains investigations of the repulsive force between two hot spheres hich arises from the radiation from the one tending to repel the other .
He showed that if the bodies are in radiation equilibrium with the LQun at the distance of the Earth from it , the repulsive effect will be greater than the gravitational attraction between them if their radii are less than cm .
, if their density were that of water ; if they were made of lead the corresponding radius would be cm .
Thus if Saturn 's ings consisted of very small particles it is possible that the effect of radiation make them repel instead of attract each other .
He considers at the end of the paper the effect produced by radiation on the orbits of small bodies round the Sun and shows that this would ultimately cause them to fall into that body .
To quote his own words : ' The Sun cannot tolerate dust .
With the pressure of light he drives the finest particles altog away from his system .
With his heat he warms the larger particles .
They give out this heat again and with it some of that energy which enables them to withstand Henry Pointing .
ix his attraction .
Slowly he draws them to hi1nself and at last they unite with him and end their separate existence ( ' essure of Light , ' ' Bomance of Science ' Series .
) He made important contributions to the experimental side of the subject , thus with Dr. Barlow he established the existence of the force produced when light is reflected from a surface at which there is some absorption , and also the existence of a torque when light passes through a prism .
They also succeeded in demonstrating the existence of the ecoil from light of a surface giving out radiation : an account of these experiments was given in the Bakerian Locture for 1910 Proc. .
These ations involved the detection of exceeding minute forces and gave ample ope for Poynting 's in devising methods and apparatus .
He had exceptionally good mechanical instincts and an excellent knowledge of the capabilities of instruments ; the result was that ths apparatus he designed was always simple and effective .
In addition to papers published in scientific journals and the Transactions of Society he wrote ' The Mean Density of the Earth : The Adams Prize Essay for 1893 , ' ' The Pressure of Light ' Romance of Science ' Series ) and The Earth ' ( Camblidge UniversiCy Press ) .
Of the ' Text Book of Physics ' written in conjunction with J. J. Thomson he wrote the whole of the volume on Sound and Heat and of the first volume of Electricity and and the chapters on Gravitation in the Properties of Matter .
His writings exhibit to the full the clearness , simplicity and ness which was characteristic of all his work .
J. J. T. JAMES FRANCIS TENANT ( 1829-1915 ) .
LIEUT .
EBAL JAlIES F. TENANT , C.T.E. , , was born at Calcutta January 10 , 1829 , being the eldest son of Captain ( afterwards BrigadierGeneral ) James Tenant , of the Artillery , who comman the Artillery during the last Sikh War and received the K.C.B. for his services .
The son entered the service of the East India Company , after the usual training , in June , 1847 ; a beautiful little sextant , which he used throughout his life to excellent purpose , bears the inscription : " " Presented at the Public Examination on June 11 , 1847 , to Gentleman Cadet James F. TeIlnant by the Honourable Court of Directors of the East India Company as a mark of the Court 's approbation of his attainments in Mathematics while at the Military Seminary He landed at Calcutta as 2nd Lieutenan6 in the Bengal Engineers in March , 1849 , was promoted 1st Lieutenant in 2nd Captain in 1858 , 1st Captain 1862 , and so through other promotions to full Colonel on the last day of 1878 .
He seems to have been attached from the time of his landing in India to the Great Trigonometrical Survey .
The magnificent reports of this Survey have apparently not yet been indexed , so that it is not easy to trace the history of individuals , though full details of personnel are given under the heading of each operation .
In vol. 2 , p. 12 , we read that the Karachi longitudinal series was completed in four field seasons , ending in April , 1853 , by Captain A. Strange , " " with occasional Qtance from Mr. C. Lane and Lieutenant J. T. ( sic Tenant A later reference shows that the T. is a misprint for F. , and since the interval of four seasons carries the date back to 1849 , the year of Tennant 's landing in India , it may be presumed that he this work at once .
He was then put in charge of a part of the Great Indus series , starting at the Karachi base , and carrying the survey 90 miles to the north in , adding another 96 miles in 1855-6 .
He was then transferred to the Jogi Tila series ( meridian ) and did 60 miles , before the outbreak of the Mutiny ] him to volunteer for active service in August , He was appointed to the Delhi Field Force as Field Engineer , and afterwards Garrison Engineer , was transferred to Lucknow in 1858 , and was attached to that force during the siege of Lucknow , being mentioned in General Outram 's roll of officers deserving honourable mention at the siege .
There is a letter from him in ' Mon .
Not .
R.A.S. , ' vol. 18 , p. 287 ( June , 1858 ) , relative to the instruments of the Lucknow Observatory , which opens thus : The writer of fiis notice has been privileged to see the statement of service drawn up by ColoneI Tenant in 1882 .
It is remarkable , as tricks of memory , that these important dates are there quoted one year wrong , putting the Mutiny in 1858-69 !
James Tenant .
" " I believe I was the only member of the Society present at the capture and occupation of Lucknow , and I think possibly some account of what has been the fate of the observatory and instruments may , though almost all hope of the latter ever being found , be not The following paragraph from vol. 2 , p. 17 , of the Survey , ' referring to these dark times , is of peculiar interest to us at the present moment .
" " Though in this liod the operations had to suspended for some years , in several quarters , in consequence of the troubles caused by the Mutiny of the Bengal Army , whiJe all India was distracted by war and tumult\mdash ; these works of science and peace advanced steadily , though at a slower rate of progress than would otherwise have been possible ; the surveyors were transferred from districts where they would certainly have been murdered , to others where they probably would not be , and , as it happily turned out were not , murdered .
Several of the Military Officers quitted the survey temporarily , and served at the siege of Delhi , the relief of Lucknow , and in various actions against the rebels ; others had the more trying duty to perform of remaining to continue the work of the survey , when they would rather have joined their , in the struggle on which the fate of the British Empire in India was depending .
When it was nearly all over , Lord Canning , the -General of India , wrote a letter to Colonel Waugh , acknowledging his reports of the operations of this Survey , from which the following paragraph has been extracted:\mdash ; " " ' I cannot resist telling you , at once , with how much satisfaction I have seen these papers .
It is a pleasure to turn from the troubles and anxieties with which India is still beset , and to find that a igantic work , of permanent peaceful usefulness , and one which will assuredly take the highest rank as a work of scientific]abour and skill , has been steadily and rapidly progressing , through all the turmoil of the last two years.\ldquo ; ' In the latter part of operations were commenced on the [ Gurhagarh Series , Meridian ] at the north end during , by the Rahun Party , under Major Tenant , the country through which the latter series lay being too disturbed from the effects of the mutiny to admit of its being continued without risk to the safety of the instruments , and the members of the survey employed\ldquo ; ( vol. 4 , p. 7 , F ) .
But the breakdown in health of Captain Jacob , Director of the Madras Observatory , led to the appointment of Major Tenant as temporary Director ( October , 1859-October , 1860 ) pending the selection of Mr. N. R. Pogson , who reached India early in 1861 .
Tenant apparently did not return to survey work , and the noteworthy incidents in the remainder of his career centre in the observations of the total eclipses of 1868 and 1871 , and the transit of Venus in 1874 .
He officiated as Master of the Mint in Calcutta on various occasions , and was ultimately in permanent charge from January 18 , 1876 , to February 6 , 1882 , when he retired and came to England .
He became a constant attendant at the meetings of the Royal Astronomical Society , served on the Council Xll Obituary Notices of Fellous deceased .
1885-1894 , and was President in 1890-91 .
He was elected S. in after the successful observations of the eclipse of 1868 .
Apart from the eclipse work , Tennant 's astronomical papers call for Iittle notice at this day .
His first paper , presented to the oyal Astronomical Society soon after his election to its Fellowship in , dealt with a method " " of relieving the weight of the moving portion of an altazimuth and is characteristic both of the man and the times .
His suggestion was to obtain " " hydraulic relief\ldquo ; by means of an oil reservoir .
He was an alert observer , reluctant to accept an instrument as finally satisfactory ; and though nothing seems to have come of his gestion at the time , he had the pleasure , many years later , of his friend , Dr. A. A. Common , use " " hydraulic relief\ldquo ; successfully in the mounting of his huge five-foot equatorial .
In subsequent papers Tenant considered improvements for the sextant , the transit , the chronometer , the prime vertical transit , the pendulum , and even the tables of arithms necessary for use with all of them .
He was ungrudging of labour , and spent the leisure of his retirement in Engand in compiling a useful table of the positions of 400 or 500 observatories with the parallax factor for each ; or computing the orbits of various comets ; or tracing the formation of telescopic images by numerical methods .
It would serve no good purpose to follow these activities in detail here , for the sympathetic attention they once obtained is passing away , if it is not already gone , with those who solved the problems pressing for solution half a century ago .
A single instance will suffice to remind of the change that has come over astronomical work .
In one of his papers , as late as 1875 , Tenant calls attention to three stars within of the Pole , which Groombridge noted as of 6 magnitude .
Apparently more stars near the Pole were wanted for survey work , and it was to find that these three were not to be seen in the instruments used .
Were they , perhaps , variable ?
TenIlant 's only resource was to call attention to the matter in the hope that further observations might throw light on it .
Nowadays it is perfectly easy for us to turn to half a dozen catalogues , all of which show that 's estimates are two magnitudes in error , while as regards variability ( though the evidence can , of course , never be complete ) the presumption is strongly against any sensible change .
We have almost forgotten how little was known about casual stars half a century ago .
There is , however , another side to Tennant 's work which reveals more of his qualities .
His alertness made him a pioneer in new regions that are still explored .
The eclipse of 1868 marked an epoch in the history of solar work : it has become famous by giving Janssen*the clue which Sir Norman Lockyer independently made the same discovery , and thongh he only observed the chromosphere lines after the eclipse results became known in this country , the instrument means of which they were observed was in the hands of the maker before the eclipse took place , and there is no reasonable doubt that he would have seen the lines even though they had not been observed during eclipse .
James Francis Xlll enabled him to see the chromosphere in full daylight .
It was Tenant who first called attention to the favourable nature of this opportunity nearly two years beforehand , in a paper to the Royal Astronomical Society .
He calculated the requisite data : he was entrusted by the Government , on the recommendation of the Royal Astronomical Society , with the general ements for tion , and he carried them out successfully .
Moreover , he showed the true spirit of enterprise by his anxiety to use the raphic method , then comparatively new : and here , is hard for us to ealise what it meant to override strong traditions eYen some prejudices ) , and to facc the ditficulties of wet-plate .
He did not make the actual exposures himself , though that had been his first intention when he had the promised assistance of LieutenaIlt ( now Colonel ) Herschel to take charge of the spectroscope : on the latter being detached for duty elsewhere , Tenant reluctantly took charge of the spectroscope .
hi1nself , but he instructed the photographers in the necessary operations , initiating that system of drill which has become a regular feature of eclipse work .
[ The novelty of such work at the time is illustrated by a footnote in Tennant 's report .
on the desirability of a good supply of tools !
] The showed only the merest traces of Corona , a failure which , from subsequent experience in 1871 , Tenant ascribed to the haze obscuring the sun .
But this did not prevent spectroscopic observations by Tenant ( who found the spectrum continuous ) , and polariscopic by Captain Branfill , ( who found strong polarisation ) , and the former accordingly summed up his conclusions as follows:\mdash ; First : Corona is the atmosphere of the Sun , not self-luminous but shining by reflected : The Great Horn ( prominence ) certainly was composed of incandescent vapours , and probably all the brilliant protuberances are the same .
We have so little quarrel with these statements to-day that it is almost difficult to read them with interest .
But the environment of the time was strangely different .
Many astronomers still thought that the corona was a terrestrial , or perhaps a lunar phenomenon , a view which was thened by the observations made in Aurerica at the 1869 eclipse .
For one the Americans found its light unpolarised .
This will suffice to show that Tennant 's observations and conclusions were at least a useful contribution on the tTht side at a critical time .
In view of the " " contradictions which the American eclipse of 1869 had produced , and to reconcile these , if possible Tenant observed the eclipse of December 1871 , this time with Captain Herschel 's help , as also that of Mr. J. B. N. Hennessey and Captain J. Waterhouse , to whom the raphs were entrusted , with a success which has become famous .
It was recognised that the light of the corona was not wholly reflected ; but we may fairly ascribe Tennant 's failure to see the bright lines in 1868 to the same haze which obliterated the corona from the photographs .
The conditions in 1871 were clearly much better .
xiv Obituary Notices of Fellows The transit of Venusin 1874 was a piece of congenial work for Tenant .
After this his duties took a more business-like form until his return to England .
When the Astrographic Conference of 1887 was called , he was very naturally one of the British delegates .
As President of the Royal Astronomical Society he delivered an address on the work of Sir G. H. Darwin , there being no medallist in his first year of office .
As already intimated , he was keenly intel.ested in the large reflecting telescopes set up by Dr. Common at Ealing , and always ready to work out any special mathematical problem which arose in the course of the work .
For the last 20 years he has not attended scientific meetings .
He died on March 6 , 1915 , at the ripe of 86 .
H. H. T. WILLIAM JAMES SELL , 1847-1915 , WILLIAM JAMES SELL was born in 1847 at Cambridge , and had his early education at one of the primary schools of his native town .
There his personal character and rapid progress in learning soon attracted the notice of the master .
His scientific education at the chemical laboratory of .
John 's College , where , at the age of 14 , he was employed by the Professor of Chemistry .
At that time this laboratory , maintained by the College and , with great liberality , placed at the disposal of the University Professor , was the only place in where raduates could get any instruction in practical chemistry .
Subsequently in 1866 , when the University provided some rooms for a students ' laboratory , Sell became lecture assistant to the Professor of Chemistry .
He was one of those who knew how to take pains and soon made himself proficient in his duties , and became the professor 's right hand in his efforts to establish a school of chemistry .
Ihose were days of small , when the University had little money , and when the prejudice against physical science may be gathered from the words of an eminent literary professor , who said that the University was no more called on to teach practical chemistry than to teach shoe-making .
Sell 's heart was in his scientific work , and the students , mostly beginners , acknowledged the help he freely gave them in the difficulties of manipulation .
He had married in 1870 , and , as soon as circumstances permitted , he matriculated in the University as a member of Christ 's College , and with characteristic courage set to work , in vaqation and in the evenings when the laboratory was closed , to learn Latin and Greek , of which , heretofore , he knew nothing .
He passed all the preliminary examinations without one failure , and in 1876 obtained William James Sell .
xv first class honours in Natural Science at the final examination for the B.A. degree .
Having this proof of his qualification for , he now changed his position in the laboratory and took up the posl of Demonstrator , and on the retirement of Dr. Hicks ( afterwards Bishop of Bloemfontein ) , succeeded him as principal Demonstrator , and retained that post to the end of his life .
To the way in which he fulfilled the duties of his position the laboratory owes much of its prosperity , its rapid expansion , and the after success of those trained in it .
Never making difficulties himself , he nevertheless did not belittle the difficulties of others , and was most and patient in his endeavours to remove them .
His love of doing everything well , and his unwillingness to take for granted anything of which the truth could be tested experimentally , were reflected in the work which he superintended , and had a prevailing influence on his pupils .
His teaching , however , was not confined to , for he was always ready , wherever a gap appeared , to try and fill it to the best of his ability .
Such gaps were frequent in the early days when the resources of the University were unequal to meet the ever-recurring demands made by the rapid development of physical science and Sell came to be really an efficient assistant professor , taking a full share of the lectures and of all the instruction in chemistry .
The Uniyersity never properly recognised what he did .
He ought to have been yiven the office of Reader in Chemistry .
Sell himself was so modest , and so free from any kind of self-assertion , that his merits and his work were little known outside the laboratory , and when a movement was initiated to get him appointed Reader , it was not denied that he had a good claim , none a better , but the authorities seem to have thought , because readerships were demanded in other dopartments and the University had not the means of them all , that the easiest course was to refuse them all .
Sell never made any complaint of being unappreciated .
All that was done for him was to give him a University Lectureship with a stipend of a year , and he frankly accepted it .
Notwithstanding his close attention to official duties , he found some time for original researches in more than one line .
Of these , the most important were a long series of iuvestigations on pyridine derivatives , which were the subject of more than a score of papers published in the ' Transactions of the Chemical Society of Lond ' In some cases he was assisled in this work by one or other of the Junior Demonstrators , and their names appear as joint authors of the published papers .
Iu others he was sole author , and the thoroughness of the work is characteristic of him .
Many new products were obtained and their properties carefully observed .
Of these there are hardly any of which he t.ailed to establish satisfactorily the chemical constitution ; and the whole form a substantial addition to Chemical Science .
Interesting communications by him on the salts of a base containing chromium and urea were published in the ' Proceedings of the Royal Society , ' and on colloid solntions of ferric and other phosphates iu the ' Proceedings of the Philosophical Society .
' Obituary Notices of Fellows deceased .
In 1900 he was elected a Fellow of the Royal Society of London , and in 1906 he took the degree of Doctor in Science in Cambridge .
His personal character is pretty well indicated in the foregoing remarks .
His colleagues all testify to his loyalty in the cause of the advancement of learning , and to the ] , but unobtrusive , way in which he assisted them whenever occasion called for it ; and nlany of his pupils own , not merely how much they learnt from him , but the affection with which his personal influence inspired them .
G. D. L. ARTHUR AUWERS , 1838\mdash ; 191 THE life work of Auwers consisted largely in the co-ordination of astronomical observations .
Since the time of Bradley , 1755 , and particularly in the nineteenth century , the positions of many thousands of stars have been determined at many observatories .
Not only are the obseryations ffected by accidental errors of very different amounts , but they are also liable to systematic errors .
The determination of these systematic errors and the value to be attached to different observations is of more difficulty .
and importance than would appear at sight .
The reason for this is that the stars are all in motion inter se , and that the proper motions or movements of the stars are of as great importance as their relative positions at a given epoch .
As these angular movements are comparatively small , considerable increase in the accuracy with which they may be determined is secured by careful discussion and refinement of the observations .
Particularly is this necessary for determinations of precession , solar motion or systematic movements among the stars .
Three astronomers , Auwers , Newcomb , and Boss , rendered pre-eminent service in this work during the last 50 years .
Ihanks to their efforts the positions and movements of the brighter have been determined with great accuracy , by making use of the best observations and those which are most free from systematic error , spread over as wide an epoch as possible .
The positions of these stars have then been used to derive the systematic errors of many star catalogues , which have thus become available for the more accurate determination of the positions and movements of many thousands of fainter stars .
Friedrich Julius Arthur was born at GoCtingen on September 12 , 1838 .
His astronomical career began at the observatory of that University in 1856 .
As a student of astronomy he made meridian observations of comets and minor planets , varying his occupation by an Arthur xvii occasional computation of orbits .
In addition he was interested in variable stars , whose importance had been brought prominently forward by elander .
Auwers made observations of many of the variables then known , the famous stars Ceti and Lyrae , and discovered the variability of several other stars , among others of Orionis and Iauri .
It was also his fortune a few years later to discover a new star , " " Nova Scorpii In 1859 he was appointed assistant at the Obseryatory of Konigsberg , scene of Bessel 's labours from 1810 to 1846 .
He remained at sberg only three years , but in this short time determined the parallax of Lal Ursae Majoris , and 61 Cygni with the famous heliometer with which Bessel had determined the parallax of 61 Cygni in 1838 .
He also made an exhaustive investigation of the irregularities in the proper motions of Sirius and Procyon , to which Bessel had drawn attention and attributed to the presence of massive but invisible companions .
These companions discovered many years later , and the periods and other elements of ' orbits determined by Auwers were closely verified .
From 1862 to 1866 Auwers was an assistant at the Obseryatory at Gotha .
Here he added to his determinations of stellar parallax by that of Groomb 34 by observations of transits with an equatorial at the two periods of parallactic elongation .
The result was very satisfactory and agrees closely with modern photo , raphic determinations .
While at Gotha he published in 1865 his first important contribution to fundamental astronomy .
This consisted in the establishment of Fundamental System of Declinations\ldquo ; and a determination of the systematic corrections required by different to bring them into harmony with it .
The basis of system tions is the mean of 13 catalogues dating from 1820 to 1860 , including those of Bessel , Struve , Argelander , Pond , Henderson , Johnson ( Si .
Helena ) , and Airy .
The proper motions were obtained by comparison with dley ' positions for as given in Bessel 's ' Fundamenta Astronomiae .
' In 1866 Auwers was appointed a member of the Academy of Scienccs and changed his residence from Gotha to Berlin .
He commenced the work of the re-reduction of Bradley 's observations about this time and pursued it ssiduously for 10 years .
Bradley 's observations were made at Greenwich from 1752 to 1760 , with a new transit instrument cllld quadrallt , both executed with great care and skill by Bird .
After death the observations passed into the hands of his executors , and were finally presented to the University of Oxford .
Forty-three years after Bradley 's death they were published by the University in two folio volumes , the first of which ] , edited by Hornsby , appeared in 1798 , and the second , edited by The observations as published were u1treduced .
In 1807 Olbers his copy to Bessel , who undertook their reduction and published the results in 1819 in his ' Fundamenta Astronomiae .
' The progress of astronomy in the first half of the nineteenth century , to which this work contributed , made a further and more complete reduction of Pradley 's observations both possible and able .
Auwers made the re-reduction with VOL. XCII .
XVIII Notices of deceased .
characteristic thoroughuess .
He obtained Bradley 's manuscripts and went through them figure by figure .
The mean position for was calculated for each observation , and numerous ertOl .
S were detected by the comparison of the erent observations of the same star .
The instrumental errors were , and particular care was devoted to the relative position of the clock-stars so that the intervals be correct for stars distant from one another in right asceusion .
Similar care was lavished on the determination of the index errol .
S of the .
For this purpose Auwers educed 1 observations of .
85 stars made by Bradley with the enith sector .
He supplemented these by a series of observations made by Maskelyne between 1768 and 1786 , and a series made by Bradley at Wanstead .
In this manner he compiled a catalogue of the zenith distances of 130 stars distributed over the 24 hours of ascension , which served to points for all the quadrant observations .
This re-reduction gave accurate positions for the epoch 1755 of 3268 of the htest stars observable in the latitude of -observation of the at Greenwich their positions for the epoch 1865 , and a comparison of the observations proper motions with great accuracy .
The whole work was published in volumes ) the Academy of Sciences .
Vol. , giving the catalogue for and the proper motions , appeal'ed in 1888 ; vol. 2 , yivin the ] of separate observations , in 1882 , and vol. the delails of the reduction , in .
The Gold Iedal of the AsGronomical Society was awarded to Auwers in 1888 .
The President of the Society , ) aisher , expressed in his address the meant of onomers on this great work as " " admiration of the manner in which the most refined skill has been combined with the most patient care in its performance\ldquo ; .
Soon after its formation in 1865 the Astlononlische Gesellschaft decided to form a of all stars down to the ninth magnitude between limits of and dec. It was considered that this great project would be carried out most efficiently and economically by making the observations differential .
The construction of the catalogue on which the obseryations should depend was entrusted to Auwers .
He took the Pulkowa catalogue of as a standard with proper motions obtained from comparison with Bradley .
With this provisional system he compared other catalogues and deduced systematic corrections them .
Applying these corrections to the various , he derived new positions and proper motions for each star from all the observations , thus obtaining the greatest accuracy for each star , .
the fundamental catalogue systematically that of Pulkowa 1865 and Bradley ) .
This catalogue was published in 1878 , and was the system of star places adopted by the Berliner bnch .
' Later it was extended from dec. to dec. to serve fur the ones nbsequently added to of the lstronomische Gesellschaft .
The system of declinations of Auwel .
S ' catalogue was
|
rspa_1916_0042 | 0950-1207 | On the ionisation potentials of magnesium and other metals, and on their absorption spectra. | 574 | 583 | 1,916 | 92 | Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character | Prof. J. C. McLennan, F. R. S. | article | 6.0.4 | http://dx.doi.org/10.1098/rspa.1916.0042 | en | rspa | 1,910 | 1,900 | 1,900 | 8 | 176 | 5,557 | http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1916_0042 | 10.1098/rspa.1916.0042 | null | null | null | Atomic Physics | 88.462748 | Electricity | 5.312582 | Atomic Physics | [
1.2783000469207764,
-71.49138641357422
] | 574 Prof. J. C. McLennan .
On the Ionisation atmosphere to the earth , would be required every second to neutralise the total conduction current .
The whole resultant effect of a thunderstorm in increasing or diminishing the atmospheric charge may possibly be comparatively small , the lightning discharges neutralising almost completely the currents due to precipitation .
It would be interesting to have measurements of both the lightning discharges and the charges brought down by precipitation for the same storm .
I have to thank Prof. Newall for advice on many points in all stages of the work .
I should like also to acknowledge the help I have received from Mr. Stanley , who has constructed the greater part of the apparatus .
To Mr. Crow I am indebted for help in the construction of various forms of capillary electrometer ; these were made and tested at the Cavendish Laboratory .
On the Ionisation Potentials of Magnesium and other Metals , and on their Absorption Spectra .
By Prof. J. C. McLennan , E.R.S. , University of Toronto .
( Received July 17 , 1916 .
) [ Plates 7 and 8 .
] 1 .
Introduction .
In a paper recently published by the writer , * on the single-line spectrum of magnesium , experiments were described in which it was found that when magnesium vapour in a vacuum was bombarded by electrons it was possible if the electrons possessed the requisite amount of kinetic energy to cause the vapour to emit a radiation consisting of the single spectral line \ = 2852'22 A.U. At the time these experiments were made and the paper was written it was not known by the author whether this line was the first member of the series whose frequencies are given by v = ( 1*5 , S)\#151 ; ( m , jpg ) , f or of the series * McLennan , ' Roy .
Soc. Proc.,5 A , vol. 92 , p. 305 ( 1916 ) .
t In the symbolic equation v \#151 ; ( n , X ) - ( m , Y ) , the frequencies are given by " = X)r-[\#187 ; + Y+y(\#187 ; , Y)F N " E ?
dlerg ' ' " umb " ' " h- * a"d value either integral or one of the numbers 1*5 , 2*5 , 35 , etc. , and m has successive integral values , each one giving the frequency of a member of the series .
Potentials of Magnesium and other Metals .
whose frequencies are represented by v = ( 1'5 , S)\#151 ; ( m , P ) .
Since the single line spectra of mercury , zinc and cadmium consisted of the single spectral line whose frequency is given by v = ( 1*5 , S)\#151 ; ( 2 , it was assumed that the line X = 2852-22 A.U. also had a frequency represented by this formula .
On the basis of this assumption it was deduced from well-known data regarding the magnesium series spectra that the wave-length of the line whose frequency is v = ( 1'5 , S)\#151 ; ( 2 , P ) should be approximately X = 2073-36 A.U. As in some experiments made by the writer , in collaboration with Mr. Evan Edwards , * it had been shown that the absorption spectra of the vapours of mercury , zinc , and cadmium consisted of bands at lines whose frequencies were given by v = ( 1'5 , S)\#151 ; ( 2 , p2 ) , and v \#151 ; ( To , S)\#151 ; ( 2 , P ) , it was expected that the absorption spectrum of magnesium vapour would also exhibit bands at X = 2852-22 A.U. and X = 2073-36 A.U. Wood and Guthrief had already noted absorption by magnesium vapour at X = 2852-27 A.U. , but as no other absorption band had been found with this vapour an attempt was made to look for it at X = 2073-36 A.U. In making the examination a small quartz spectrograph with low dispersion was used , and it was found that a sharp clearly defined band came out at what appeared to be X = 2073-36 A.U. This result was therefore taken as indicating that the assumption that the frequency of the line X = 2852"22 A.U. was given by v = ( P5 , S)\#151 ; ( 2 , ^2 ) , was correct .
A few weeks ago , however , the attention of the writer was very kindly drawn by Prof. F. A. Saunders , of Vassar College , to an inaugural dissertation by Lorenser of Tubingen , of which there appears to be as yet but one copy in America , in which it was established that X = 2852"22 A.U. was the first member of the series v = ( 1"5 , S)\#151 ; ( m , P ) , and X = 2026-46 A.U. the second member of the same series .
With this information it was easy to deduce that the line whose frequency was given by v = ( 1-5 , S)\#151 ; ( 2 , p2 ) , must have the wave-length X = 457P38 A.U. With this knowledge it followed that if magnesium vapour acted as regards absorption in a manner analogous to the vapours of mercury , zinc and cadmium , bands should appear in its absorption spectrum , at X = 45 71 " 38 A.U. , X = 2852-22 A.U. , and possibly at X = 2026-46 A.U. and at still higher members of the v = ( l-5 , S)\#151 ; ( m , P ) series .
The absorption of magnesium vapour was , therefore , re-examined by the writer , and the following paper contains an account of these experiments and of others which followed on from them .
* McLennan and Edwards , ' Phil. Mag. , ' vol. 30 , p. 695 ( November , 1915 ) .
t " Wood and Guthrie , ' Astrophys .
Journ. , ' vol. 39 , No. 1 , p. 211 ( 1909 ) .
Prof. J. C. McLennan .
On the Ionisation 2 .
Absorption Spectrum of Magnesium Vapour .
In making these experiments a large Hilger quartz spectrograph , type C , possessing high dispersion was used .
Some metallic magnesium was placed in the centre of a steel tube about 3 cm .
in diameter and 20 cm .
long .
The ends of this tube were provided with crystal quartz plates sealed in with wax .
The tube was highly exhausted by a Gfaede pump and when a low vacuum was reached the metal was vaporised by heating the centre of the tube with a blowpipe , the ends of the tube being kept cool by wrappings of cloth kept soaked with water .
Some difficulty seems to have been experienced in photographing lines in the magnesium emission spectrum in the neighbourhood of X = 2000 A.U. on account of their feeble intensity , for , although the existence of the line X = 2026*46 A.U. was predicted by Lorenser , Saunders appears to have been the only one who as yet has observed it .
Some difficulty was also experienced by the writer in obtaining a photograph of it with ordinary or panchromatic plates .
When , however , the Schumann plates , recently put on the market by the Adam Hilger Company , were used , it was found that the line came out clearly and with considerable intensity .
The upper spectrum in fig. 1 was obtained with the light and from a spark in air between magnesium terminals and the lower one with the light from a magnesium arc of the type already described in a previous communication by McLennan and Henderson.* The second spectrum in the figure is that of the light from a spark between zinc terminals in air , while the third is that of the light from an arc between magnesium terminals in air .
The line X = 2026*46 A.U. , it will be seen , comes out clearly in both the spark and arc spectra of magnesium and practically coincides with the last line in the zinc spectrum , an exceedingly strong line , whose wave-length is given by Saundersf as X = 2026*19 A.U. It is of interest to note that the arc spectrum of magnesium in air show 's a strong reversal at X = 3838 A.U. and a fainter though well marked one at X = 2852*22 A.U. The fourth spectrogram in fig. 1 , which was obtained with the light of the magnesium arc in vacuo , was taken on a plate sensitive to the green , which was specially made for me by Dr. Mees of the American Kodak Company .
On account of the strong intensity of the line X = 2026*19 A.U. in the zinc spectrum , and its close proximity to the magnesium line X = 2026*46 A.U. , the spark spectrum of zinc in air was used in looking for the absorption of * * McLennan and Henderson , ' Roy .
Soc. Proc. , ' A , vol. 91 , p. 485 ( 1915 ) .
t Saunders , ' Astrophys .
Journ. , ' vol. 43 , No. 3 , p. 239 ( 1916 ) .
Potentials of Magnesium and other Metals .
this line by magnesium vapour .
The light from this spark was sent through the steel tube described above which contained the magnesium vapour , and photographs were taken of the spectrum when the tube was both strongly and gently heated .
Two of the spectrograms taken in this way are shown in fig. 2 .
The upper reproduction is that of the ordinary zinc spark in air with the light sent directly into the spectrograph , the second w~as obtained with vapour of low density , and the third when the tube was strongly heated .
In the second spectrogram it will be seen that while the intensities of all the lines are much lessened , absorption at A = 2852*22 A.U. is clearly marked .
The intensity of the line X = 2026T9 A.U. is also very greatly diminished .
In the third spectrogram the line X = 2026*19 A.U. has completely disappeared and absorption is widespread in the neighbourhood of X = 2852*22 A.U. Repeated attempts were made to see if absorption by magnesium vapour could be obtained at X = 4571*38 A.U. , but in no case was any trace of it observed .
Fig. 3 shows the results of one of these attempts .
The upper photograph was obtained with the light from an incandescent Nernst filament after it had passed through magnesium vapour of high density , and the lower one with the light from the zinc spark after passing through the same vapour .
Absorption at X -= 2852*22 A.U. , it will be seen , is well marked in the second spectrum , but there is no trace of it at X = 4571*38 A.U. in this photograph or in the spectrum of the light from the Nernst filament .
As far as all these experiments go , then , absorption by magnesium vapour was obtained only at X = 2852*22 A.U. and at X = 2026*46 A.U. , the first and second lines in the singlet series v = ( 1*5 , S)\#151 ; ( mf P ) .
3 .
Single-line Spectrum of Magnesium .
In a previous communication some experiments by the writer were described in which it was found that if magnesium vapour in a vacuum were bombarded by electrons the vapour could be made to emit a radiation consisting of the single spectral line X = 2852*22 A.U. , provided the electrons possessed the requisite amount of kinetic energy .
Since it has been shown that the frequency of this line is given by v = ( 1*5 , S)\#151 ; ( 2 , P ) , and since with mercury , zinc , and cadmium vapours the frequency of the spectral line in their single-line spectra is given by v = ( 1*5 , S)\#151 ; ( 2 , ^ ) , the experiments were repeated to see if the magnesium vapour could not be made to emit the line X = 4571*38 A.U.\#151 ; frequency ( 1*5 , S)\#151 ; ( 2 , p % ) .
The apparatus used was the same as that described by McLennan and Henderson.* Potential differences , gradually increasing , were applied between the Wehnelt cathode\#151 ; a * McLennan and Henderson , 'Roy .
Soc. Proc. , ' A , vol. 91 , p. 485 ( 1915 ) .
Prof. J. C. McLennan .
On the Ionisation tungsten filament\#151 ; and the vapour , but no radiation characteristic of the magnesium spectrum was obtained until a voltage of approximately 5 volts , was reached .
With this applied potential difference the spectral line X = 2852*22 A.U. came out strongly .
Repeated experiments failed to bring out either the line X = 4571*38 A.U. or the line X = 2852*22 A.U. until the electrons were given kinetic energy , corresponding to something like 5 volts .
With potential differences higher than 5 volts , the line X = 2852*22 A.U. was the only one which came out on the plates until the arc struck , which it did when the applied potential was about 7*5 volts .
When the arc struck , the many-lined spectrum of magnesium was obtained .
The reproductions in fig. 4 show , firstly , the many-lined arc spectrum of magnesium , and , secondly , the single-line spectrum with the spectral line X = 2852*22 A.U. alone .
This was obtained with an applied potential of 5*9 volts .
The third spectrum was obtained with an applied potential of 2*2 volts , and , as it shows , the only radiation recorded was that which came from the incandescent tungsten which constituted the Wehnelt cathode .
The spectrum shown in fig. 5 was obtained with an applied potential of 5*9 volts , using a Hilger quartz spectrograph , Type C , and it shows only the line X = 2852*22 A.U. It is interesting to note that the potential fall which was necessary to bring out the line X = 2852*22 A.U. was close to that given by the quantum relation Ye = liv , for if in this relation we insert the frequency of the line X = 2852*22 A.U. we find that the value of V comes out 4*28 volts .
Moreover , the arc striking voltage , 7*5 volts , by the quantum relation connotes the frequency of the line X = 1626*66 A.U. , which is very close to X = 1621*7 A.U. , the last line in the singlet series given by X = ( 1*5 , S)\#151 ; ( ra , P ) .
This last result is also of special interest , for it coincides with what was obtained with mercury , zinc , and cadmium vapours .
With these the arcing voltage was also practically that which corresponded to the frequency of the last line in the v = ( 1*5 , S)\#151 ; ( m , P ) series , i.e. } the frequency v = 1*5 , S. 4 .
Ionising Potentials of Magnesium .
In the experiments with mercury , zinc , and cadmium vapour , bombarded by electrons , it was found that the line whose frequency is given by v = ( 1*5 , S ) \#151 ; ( 2 , p2 ) , was the one which came out most easily .
Moreover , with mercury vapour , Frank and Hertz* showed that the least applied potential difference which would bring out this line was 4*9 volts , and theyf also * Frank and Hertz , ' Yerh .
d. Deutsch .
Phys. Ges .
, ' vol. 11 , p. 512 ( 1914 ) .
t Frank and Hertz , 'Yerh .
d. Deutsch .
Phys. Ges .
, ' vol. 10 , p. 457 ( 1914 ) .
McLennan .
Roy .
Soc. Jlroc .
, A , vol. 92 , Plate 7 .
Fig 2852.22 A.u. Fig. 5 .
Potentials of Magnesium and other Metals .
579 showed , by direct experiments , that for electrons to ionise mercury vapour they must have kinetic energy at least equal to that acquired in a fall of potential of 4*9 volts .
This voltage it will be remembered also is that given by the quantum relation for the frequency of the line X = 2536*72 A.U. , the well known line in the single-line spectrum of mercury .
In so far then as mercury , zinc , and cadmium are concerned , the ionising potential would appear to be deducible from the quantum relation by the use of the frequency v = ( 1*5 , S ) \#151 ; ( 2 , p2)- With magnesium vapour , however , the matter appears to be different , for the spectral line which came out most easily was the one whose frequency is given by v = ( 1*5 , S ) \#151 ; ( 2 , P ) , and not the one whose frequency is given by v = ( 1*5 , S)\#151 ; ( 2 , if ) ( X = 4571*38 A.U. ) .
Moreover , McLennan and Thomson* have shown recently that the magnesium radiation emitted by a Bunsen flame supplied with the vapour of this metal consists of the single line X = 2852*22 AU .
In none of their experiments was any trace of the line X = 4571*38 A.U.f observed .
It would seem , therefore , that the line which is most easily stimulated in the magnesium spectrum is X = 2852*22 A.U. McLennan and KeysJ have also shown that when a Bunsen flame , fed with magnesium vapour , emits the line X = 2852*22 A.Lh , it is strongly ionised as well .
From all these experiments then it wmuld appear that the ionising potential , with magnesium vapour as with mercury , zinc , and cadmium vapours , can be obtained by a direct application of the quantum relation , and'using the frequency v = ( 1*5 , S ) \#151 ; ( 2 , P ) , of the line X = 2852*22 A.U. , it comes out as 4*28 volts .
5 .
Ionising Potentials of Calcium , Strontium , and Barium .
De Watteville , S in a paper on " Flame Spectra , ^ has shown that if the spray of aqueous solutions of salts of calcium , strontium , and barium , be fed into a Bunsen flame , the latter emits a spectrum consisting of but a single line .
For calcium the wave-length of this line is X = 4226*91 A. U. , *for * * * S * McLennan and Thomson , infra , p. 584 .
t It should be stated here that Eder and Yalenta , in their ' Atlas Typischer Spektren , ' refer to experiments in which it was found that the radiation from a Bunsen flame fed with what appears to have been metallic magnesium consisted of light of the wavelengths X = 5183*79 , 5172-87 , 5164*49 , 4571*38 , 3336*82 , 3332*33 , 3330*04 , 3097*00 , 3093*09 , o 2852*22 A.U.^ Living and Dewar , 'Boy .
Soc. Proc. , ' p. 189 ( 1881 ) , also found the line X = 4571*38 A.U. among others , including X = 2152*22 A.U. , in the spectrum of the light from burning magnesium in air .
X McLennan and Keys , infra , p. 591 .
S De Watteville , 'Phil .
Trans./ vol. 204 , p. 139 ( 1904 ) , and 'Comptes Bendus , ' vol. 142 ( 1906 ) .
Prof. J. C. McLennan .
On Ionisation strontium it is X = 4607'52 A.U. , and for barium X = 5535-69 A.TJ .
Moreover , Eamage* has found that Bunsen flames fed with the pure vapours of these respective metals , or with the spray of aqueous solutions of their salts , also emit monochromatic radiations of the wave-lengths mentioned .
Further , Lorenser , in the dissertation referred to , established the fact that these three lines are the first members of the series spectra of these three elements given by v = ( l-5 , S)\#151 ; ( to , P ) .
It would seem , therefore , that the frequency given by v \#151 ; ( 1*5 , S)\#151 ; ( 2 , P ) , is the one most easily stimulated in atoms of calcium , strontium , and barium , as well as in the atoms of magnesium .
Following the same argument as that just presented in the case of the element magnesium , it would seem likely , therefore , that the ionising potentials for the three metals mentioned will also turn out to be deducible from the quantum relation Ye = liv , by using the frequency v = ( 1'5 , S ) \#151 ; ( 2 , P ) .
If this surmise should prove to be correct it would follow that the ionising potential for calcium is 2-89 volts , for strontium 2-65 volts , and for barium 2-20 volts .
Table I. Element .
Ionising potential .
Bemarks .
Helium* volts .
20 *5 Direct experiment .
Neon* 16 *0 tt \#187 ; Argon* 12 *0 \gt ; \gt ; j\#187 ; Hydrogen* 11*0 a \gt ; ) Oxygen* 9*0 ft ft Nitrogen* 7*5 tt ft Mercury 4*9 ft tt Zinc 3*96 Deduced from single-line spectrum .
Cadmium 3*74 t ) ft tt Magnesiumf 4*28 tt ft n Calcium 2*89 tt tt tt Strontium 2*65 tt tt tt Barium 2*20 tt tt tt ** Frank and Hertz , ' Ber .
d. Deut .
Phys. Oes./ Heft 2 , p. 44 ( 1913 ) .
f If it should turn out by later experiment that for magnesium , calcium , strontium , and barium the fundamental frequency is given by v = 1*5 , S \#151 ; 2 , instead of by v2 \#151 ; 1*5 , S \#151 ; 2 , P , then the ionising potentials of magnesium* calcium , and strontium would be respectively 2*67 volts , 1*86 volts , and 1*77 volts , the line possessing this frequency for the spectrum of barium not being known .
In the present communication , as well as in two previous ones , the writer has endeavoured to extend the field opened up by Frank and Hertz by their experiments with mercury vapour .
With metals possessing high vaporisation temperature it is difficult , if not impossible , to apply direct methods to * Eamage , 1 Eoy .
Soc. Proc./ No. 459 , vol. 30 , p. 1 ( 1901 ) .
Potentials of Magnesium and other Metals , the determination of such a magnitude as the ionisation potential .
The evidence which has been accumulated so far , however , seems to show that in the frequency of the spectral line constituting the single-line spectrum of an element , we have a magnitude which , through the agency of the quantum relation Ye=hv , gives us the ionisation potential with ease and great accuracy .
Up to the present the ionisation potential has been determined by direct experiment for but seven of the elements , and by the method of single-line spectra it has been deduced for six others .
With mercury it has been determined both by direct experiment and by the application of the quantum relation to the frequency given by the single-line spectrum of this element .
In Table I , the results obtained up to the present by both methods are collected .
6 .
Experiments with Thallium Vapour .
From the evidence collected so far , it would appear that either the frequency given by v = ( 1*5 , S ) \#151 ; ( 2 , p2 ) , or that given by v = ( 1*5 , S)\#151 ; ( 2 , P ) , is the one to look for in the spectrum of an element in endeavouring to ascertain its ionising potential .
The radiation from a Bunsen flame fed with the vapour of an element , the absorption by the vapour , and the bombardment of the vapour by electrons , are three agencies which have proven useful in revealing one or other or both of these frequencies in the spectra of seven of the elements .
For thallium neither of these frequencies is known .
Experiments by McLennan and Thomson* showed that the radiation from a Bunsen flame fed with thallium vapour consisted of light of the wave-lengths X = 5350*65 A.U. , and X= 3775*87 A.U. But these are the first members of the well known second subordinate doublet series given by i/ = ( 2 , ( m , s ) , and v = ( 2 , \#163 ; \gt ; 2)\#151 ; ( m , s ) .
Wood and Guthrief found that the absorption spectrum of pure thallium vapour consisted of well defined bands at X = 3230 A.U. , X = 3092 A.U. , X = 2530 A.U. , and X = 2380 A.U. , and that when mercury vapour was added to that of thallium the only band which appeared was at X = 2380 A.U. , and that with a moderate amount of thallium in the absorption tube all these bands , except X = 2380 A.U. , disappeared when mercury was added .
Increasing the quantity of thallium , they found , caused this band to reappear , and then , finally , to'become much stronger than with pure thallium .
On again adding mercury other bands also appeared which were not found with pure thallium .
Among these were bands corresponding to emission lines at X = 2580 A.U. , X = 2768 A.U. , and X = 3776 A.U. * McLennan and Thomson , infra , p. 584 .
t Wood and Guthrie , ' Astrophys .
Journ. , ' No. 1 , vol. 29 , p. 211 ( 1909 ) .
Prof. J. C. McLennan .
On the Ionisation In some experiments which were made by the writer , by the method adopted in photographing the absorption spectrum of magnesium , the only absorption which was observed in the region between X = 6000 A.U. and X = 1900 A.U. , with low vapour density , was at X = 3775*87 A.U. At this wave-length the absorption consisted of a narrow sharply defined band .
When high vapour densities were used , narrow diffuse absorption bands appeared at approximately X = 3230 A.U. and X = 3000 A.U. as well .
No absorption was observed at X = 2768 A.U. , X = 2580 A.U. , X = 2530 A.U. , or at X = 2380 A.U. As mercury vapour is known to absorb at X = 2536*72 A.U. and at X = 2338 A.U. , it is just possible that the absorption observed by Wood and Guthrie with thallium vapour in the neighbourhood of these two wavelengths was due to the presence of mercury in their absorption tube .
As the second member of the series spectrum of thallium given by v = ( 2 , p\)\#151 ; ( m , s ) , has the wave-length X = 3229*88 A.U. , the absorption observed by Wood and Guthrie at X = 3230 A.U. is accounted for .
Just what the absorption observed by them at X = 3092 A.U. means is , however , not very evident .
This wave-length has not as yet been associated with any series in the spectrum of thallium .
It may possibly be related to one or other of the series v = ( 1*5 , S ) \#151 ; ( 2 , p2 ) , , and v = ( 1*5 , S)\#151 ; ( m , P ) , but this does not seem likely , for any evidence which we have points to the probable occurrence of all the members of these two series in the extreme ultra-violet .
The method of electronic bombardment has not as yet been applied to the vapour of thallium , but experiments in this direction are now in hand , and it is expected that some information will soon be obtained , which may not only indicate the significance of the occurrence of absorption at X = 3092 A.U. , but which may also enable one to definitely locate the wave-lengths in the spectrum of thallium , whose frequencies are given by v = ( 1*5 , S)\#151 ; ( 2 , pf ) , and v = ( 1*5 , S)-(2 , P ) .
7 .
Summary of Results .
1 .
The absorption spectrum of non-luminous magnesium vapour in a vacuum consists of narrow sharp bands at X = 2852*22 A.U. and X = 2026*46 A.U. These lines are the first two members of the singlet series whose frequencies are given by v = ( 1*5 , S ) \#151 ; ( m , P ) .
2 .
When magnesium vapour in a vacuum is bombarded by electrons , no radiation characteristic of the spectrum of this metal is emitted until the electrons possess kinetic energy equal to that which would be acquired in a fall of potential of approximately 4*5 volts .
With a field corresponding to 5*9 volts the spectrum obtained consisted of a single line X = 2852*22 A.U. Potentials of Magnesium and other Metals .
With this voltage the line came out with strong intensity .
When a field of 2*2 volts was used no radiation characteristic of magnesium was obtained .
3 .
No indication of the line X = 4571*38 A.U. was obtained under electronic bombardment until the electrons possessed sufficient kinetic energy to cause the arc to strike .
The arcing voltage was approximately 7*5 volts .
This , by the quantum theory , corresponds to the frequency of the line X = 1626*66 A.U. , which is very close to X = 1621*7 A.U. , the last line in the series given by v = ( 1*5 , S)\#151 ; ( m , P ) .
With the vapour of mercury , zinc , cadmium , and magnesium , the arcing voltages appear to be connected by the quantum relation with the frequency ^ = 1*5 , S. 4 .
As the simplest Bunsen flame spectrum of magnesium vapour consists of the single line X = 2852*22 A.U. , and as the vapour in the flame when emitting this radiation has been shown to be ionised , it would appear that the ionisation potential of magnesium vapour also follows the quantum theory law , and is given approximately by 4*28 volts .
5 .
Arguments have been presented in the paper which support the view that while the ionising potential for mercury , zinc , and cadmium may be deduced by the quantum theory by the use of the frequency represented by v = ( 1*5 , S ) \#151 ; ( 2 , p2 ) , in the case of magnesium , calcium , strontium , and barium the frequency which must be used is given by v = ( 1*5 , S ) \#151 ; ( 2 , P ) .
6 .
The absorption spectrum of non-luminous thallium vapour , with low densities , consists of a narrow sharp band at X = 3775*87 A.U. , and with high vapour densities of this band and somewhat diffuse ones at X = 3230 A.U. and X = 3000 A.U. Of these the line X = 3775*87 A.U. is the first member of the second subordinate doublet series given by v = ( 2 , s ) } and X = 3230 A.U. is the second member of the second subordinate doublet series given by v = ( 2 , p\)\#151 ; ( m , s ) .
No sign of absorption was observed at X = 5350*65 A.U. , the first member of the second subordinate series v = ( 2 , pi)\#151 ; ( m , s ) .
The frequencies given by v = ( 1*5 , S ) \#151 ; ( 2 , p2)\gt ; and v = ( 1*5 , S)\#151 ; ( 2 , P ) , have not as yet been located in the spectrum of thallium .
The author , in concluding , wishes to acknowledge his indebtedness to his assistants , Mr. J. F. T. Young and Mr. H. R. Lindsley , for help in the photographic work and in the quartz and glass blowing .
|
rspa_1916_0043 | 0950-1207 | On the Bunsen flame spectra of metallic vapours. | 584 | 590 | 1,916 | 92 | Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character | Prof. J. C. McLennan, F. R. S.|Andrew Thomson, M. A. | article | 6.0.4 | http://dx.doi.org/10.1098/rspa.1916.0043 | en | rspa | 1,910 | 1,900 | 1,900 | 3 | 129 | 3,323 | http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1916_0043 | 10.1098/rspa.1916.0043 | null | null | null | Atomic Physics | 83.375916 | Thermodynamics | 9.518651 | Atomic Physics | [
6.002696990966797,
-49.7791748046875
] | 584 On the Bunsen Flame Spectra of Metallic Vapours .
' By Prof. J. C. McLennan , F.K.S. , and Andrew Thomson , M.A. , University of Toronto .
( Received July 17 , 1916 .
) [ Plate 9 .
] 1 .
Introduction .
In seeking to solve the problem of the structure of atoms , especially of the more complex ones , it is of great importance to know what are the simplest or fundamental spectra which such atoms are capable of emitting .
Information regarding such fundamental frequencies for the atoms of some metals has been obtained from investigating the characteristics of both the absorption and emission spectra of vapours of these metals .
For example , McLennan and Edwards* have shown that , with the non-luminous vapours of mercury , zinc and cadmium , narrow absorption bands are obtained , using moderate vapour densities , with lines whose frequencies are given by v = ( 1'5 , S)\#151 ; ( 2 , ^2)\gt ; f and v = ( L5 , S ) \#151 ; ( 2 , P ) , The first of these is the frequency of the first member of Paschen'sJ combination series v = ( 2 , p2)\#151 ; ( m , S ) , and the second is the first member of the singlet series v = ( 1*5 , S ) \#151 ; ( m , P ) .
Moreover , oneS of us has also more recently shown from absorption experiments that for magnesium atoms the frequencies v = ( 1*5 , S)\#151 ; ( 2 , P ) , v = ( 1*5 , S ) \#151 ; ( 3 , P ) , and possibly also'those of still higher members of the series v = ( 1*5 , S)\#151 ; ( m , P ) , are the fundamental ones .
With this metal the frequency v = ( 1*5 , S)\#151 ; \gt ; ( 2 , p2 ) , does not appear from experimental evidence as yet available to be fundamental .
c It has also been shown by McLennan and Henderson|| that the simplest spectrum which the vapours of mercury , zinc , and cadmium in a vacuum can be made to emit under bombardment by electrons consists with each of the metals of the single spectral line whose frequency is given by V ' * McLennan and Edwards , 'Phil .
Mag. , ' vol. 30 , p. 695 ( November , 1915 ) .
t In the symbolic equation v = X ) \#151 ; ( ra , Y ) , the frequencies are given by ' V = p \#151 ; \#151 ; \#151 ; =-----------rpr-p- , where N is Kydberg 's number , n has a fixed [ ra + X+tf(M , X)]a [ m+Y+y(m , Y)]2 ' J s value , either integral or one of the numbers 1*5 , 2*5 , 3*5 , etc. , and m has successive integral values , each one giving the frequency of a member of the series .
X Paschen , ^ Ann. der Phys. , ' vol. 35 , p. 860 ( 1911 ) .
S McLennan , supra , p. 574 .
|| McLennan and Henderson , 'Roy .
Soc. Proc. , , A , vol. 91 , p. 485 ( 1915 ) .
On the Bunsen Flam , e Spectra of Metallic Vapours .
585 v == ( 1*5 , S)\#151 ; ( 2 , p2)- With magnesium , on the other hand , one of us* still later has shown that the simplest spectrum which can be obtained of magnesium vapour in a vacuum by means of electronic bombardment is given by v = ( 1*5 , S)\#151 ; ( 2 , P ) .
For mercury , zinc , and cadmium vapours , then , the frequency v = ( 1*5 , S)\#151 ; ( 2 , p2)\#151 ; and probably also = ( P5 , S ) \#151 ; ( 2 , P)\#151 ; appears to be the fundamental one , while with magnesium it is in all probability v = ( 1/ 5 , S)\#151 ; ( 2 , P ) .
As the electrical conditions in flames are probably simpler than those which obtain in the electric arc or spark ; one should expect that , in flame spectra of the elements , the fundamental frequency would come out relatively with specially strong intensity .
Charles de Watteville , f in a number of papers on flame spectra , has pointed out that , if a Bunsen flame be fed with the spray of salt solutions of a number of different elements , the spectrum of the flame with some of the elements consists of a single strong line , and with others of a single strong line accompanied by a number of very much fainter ones .
These strong lines for the different metals , with their frequencies , are given in Table I. Table I. Element .
Frequency v \#151 ; 1 *5 , S \#151 ; 2 , / ?2 .
Frequency v - 1 -5 , S-2 , P. A.U. A.U. Mercury A = 2536 *72 \#151 ; Zinc A = 3075 *99 \#151 ; Cadmium A = 3260 -17 \#151 ; Magnesium* \#151 ; A = 2852 *22 Calcium \#151 ; A = 4226 -91 Strontium \#151 ; A = 4607 *52 Barium \#151 ; A = 5535 *69 * Lorenser , ' Inaug .
Diss .
, ' Tubingen , 1913 .
This Table , it will be seen , emphasises the view that for mercury , zinc , and cadmium , the fundamental frequency is given by v = ( 1*5 , S ) \#151 ; ( 2 , p2)\gt ; while for magnesium , and probably also for calcium , strontium , and barium , it is given by v = ( 1*5 , S)\#151 ; ( 2 , P ) .
Some earlier experiments made by Gouy , J with salts sprayed into a flame , also confirm this view with respect to zinc and cadmium .
* McLennan , supra , p. 574 .
t De Watteville , ' Phil. Trans. , ' vol. 204 , p. 139 ( 1904 ) ; and ' Comptes Rendus , ' vol. 142 ( 1906 ) .
+ Gouy , ' Ann. de Chimie et Phys. , ' vol. 18 ( 1879 ) .
Prof. J. C. McLennan and Mr. A. Thomson .
Observations have also been made by Hartley* and by Ramagef on the Bunsen and the oxy-hydrogen flame spectra of some nineteen of the elements .
With mercury no characteristic lines were observed with either of these flames .
With zinc , cadmium , and magnesium , spectra consisting of a number of lines came out with the oxy-hydrogen flame , but no characteristic spectra were obtained when the Bunsen flame was used .
With calcium , strontium , and barium , however , the single spectral line whose frequency is given by z/ = ( l*5 , S ) \#151 ; ( 2 , P ) , i.e. the fundamental frequency , came out strongly with the Bunsen flame , while the same line and several others in addition came out when the oxy-hydrogen flame was used .
In the experiments of Hartley and of Ramage , the vapours of the pure metals as well as of the salts of these metals were used in studying the flame spectra .
De WattevilleJ reports that he was unable to detect any characteristic line of the mercury spectrum in photographs taken of the spectrum of the flame of a Bunsen burner into which there was blown the spray from solutions of metallic mercury in nitric acid .
The only investigators who appear to have observed the line X = 4571*38 A.U.\#151 ; frequency^ = ( 1*5 , S)\#151 ; ( 2 , p2)\#151 ; in the flame spectrum of magnesium are Living and Dewar , S and Eder and Valenta.|| The former found in the spectrum of the light from magnesium burning in air a number of lines , among which those of the wave-lengths X = 4571*38 A.U. and X = 2852*22 A.U. came out with relatively strong intensity .
The first-mentioned line they state was always narrow and sharply defined .
Eder and Valenta in their experiments found that a Bunsen flame fed with magnesium emitted a spectrum consisting of the lines X = 5183*79 , 5172*87 , 5164*49 , 4571*38 , 3336*82 , 3332*33 , 3330*04 , 3097*00 , 3093*09 , 3091*11 , and 2852*22 A.U. , together with other lines which they attributed to magnesium oxide and to impurities in the magnesium .
In their Atlas of typical spectra , IT however , they give a spectrum of the flame from a magnesium-fed Bunsen burner which shows but the single line X - 4571*38 A.U. of the magnesium spectrum .
As the Bunsen flame would appear to be the simplest possible means of exciting the fundamental frequencies in the atoms of easily volatilised metals the failure of Hartley , Ramage , and de Watteville to bring out these * * * S * Hartley , 'Phil .
Trans.,5 A , vol. 185 , p. 161 ( 1894 ) ; and 'Trans .
Dublin Soc.,5 N.S. vol. 7 , Part XII , p. 341 ( 1901 ) .
t Ramage , ' Roy .
Soc. Proc.,5 No. 459 , vol. 70 , p. 1 ( 1901 ) .
J De Watte ville , loc. cit. S Living and Dewar , ' Roy .
Soc. Proc. , ' vol. 32 , p. 189 ( 1881 ) .
[ | Eder and Valenta , ' Atlas Typischer Spektren,5 and ' Beitrage sir Photochemie und A Spektral-Analyse,5 S. 411 , 1904 .
IT Eder and Valenta , ' Atlas Typischer Spektren,5 Tafel III , No. 1 .
On the Bunsen Flame Spectra of Metallic Vapours .
587 frequencies by means of this agency in the case of the metals mercury , zinc* cadmium , and magnesium seemed rather remarkable .
It is not clear from the papers of Hartley and Eamage whether more than a casual examination was made of this point , but before accepting as final the conclusion which may be drawn from their results as to the probable impossibility of stimulating the fundamental frequencies , of these elements by means of Bunsen flames , especially in regard to mercury , zinc , and cadmium it was thought desirable by the writers to subject this matter to a closer inquiry .
This has now been done , with the result that it has been found possible to obtain with the Bunsen flame the fundamental frequencies mentioned of the spectra of mercury , cadmium , and magnesium , but up to the present it has not been found possible to obtain such with zinc .
2 .
Apparatus .
In the experiments two types of Bunsen burner were used .
One , shown in fig. 1 , consisted of an ordinary burner A , to which was attached at the top a steel close-fitting tubular cap BB , provided with a conical shaped cover C. * Fig. l. Fig. 2 .
Prof. J. C. McLennan and Mr. A. Thomson .
The metal to be vaporised was placed in the cup BB , and when the cover C was replaced and the burner lighted the flame of a blow^-pipe was directed against the cup .
The vaporised metal in escaping was thus made to pass directly into the flame of the burner .
The second form of burner used is shown in fig. 2 .
To the top of an ordinary Bunsen burner Q a brass cylinder KL , 3 8 cm .
in diameter and 8 cm .
high , was soldered .
The top was closed by a lid containing an aperture in the centre 1*8 cm .
in diameter , to which a small tube 0*5 cm .
high was attached .
Another brass cylinder , 2*8 cm .
in diameter and 7 cm .
in length , was supported in the centre and coaxially with KL by means of three asbestos plugs .
This inner cylinder contained a quartz tube F , 1 cm .
in diameter and about 8 cm .
in length , drawn off to a neck about 0*5 cm .
in diameter at the upper end .
A coil of manganin wire MN was wound round this tube , and the ends were led out through two openings fitted with small porcelain plugs in the bottom of KL .
A layer of asbestos paper was placed round the wire and then the whole space between the tube and the brass cylinder next to it was filled with plaster of Paris , which on solidifying kept everything rigid .
The top of the quartz tube F came just level with the mouth of the burner .
When the gas was lighted a large clear Bunsen flame was easily maintained above the mouth of the burner .
The metals to be vaporised were placed within the quartz tube F and the furnace was raised to whatever temperature was desired by supplying a current of suitable intensity to the circuit MN .
With each metal a fresh quartz tube was used and care was taken to thoroughly clean the burner before taking the photographs .
The photographs of the flame spectra were taken first with a small Hilger quartz spectrograph , type A , and afterwards with a larger one of the type C. 3 .
Bunsen Flame Spectra .
The spectrograms taken of the different spectra are shown in the plate at the end of the paper .
No. 1 is a reproduction of the spectrum of the clear Bunsen flame free from all metallic vapours .
No. 2 was obtained with mercury vapour .
In addition to the ordinary Bunsen flame spectrum this spectrogram shows that the mercury line X = 2536*72 A.U. came out strongly .
No. 3 is a spectrogram of Bunsen flame spectrum of cadmium vapour and was obtained with the flame burning very gently .
It shows the characteristic line X = 3260*17 A.U. No. 4 is the Bunsen flame spectrum of magnesium .
It shows the line X = 2852*22 A.U. faintly but clearly in addition to the free flame spectrum .
No sign of the line X = 4571*38 A.U. was found in any of the spectrograms taken with this metal .
No. 5 is the spectrum obtained with thallium vapour .
In this case the only characteristic On the Bunsen Flame Spectra of Metallic Vapours .
589 lines of the thallium spectrum which came out were X = 3775*87 A.U. and X = 5350*65 A.U. The former line was always much the stronger , but this may have been because the plates used were less sensitive to the green than to the ultra-violet .
No. 6 is a. reproduction of the spark spectrum of cadmium , and No. 7 the Bunsen flame spectrum of cadmium vapour obtained when the draught was slightly forced and the flame was burning vigorously .
As No. 7 shows that the line X = 2288*79 A.U. came out faintly on the plates in addition to the line X = 3260*17 A.U. under these circumstances .
With zinc vapour no characteristic lines were obtained .
Numerous modifications in the form of the burner were made and exposures were taken with them of varying duration , with the flame burning with different intensities , but in no case did the flame spectrum show any trace of the lines X = 3075*99 A.U. and X = 2139*3 A.U. or of any other of the zinc lines .
Just why the zinc vapour failed to show any spectrum when results were obtained so easily with the other metals is not very clear .
4 .
Discussion of Results .
" In view of the line X = 2288*79 A.U. coming out in strong flames with cadmium vapour , it was thought that possibly the analogous line in the mercury spectrum X = 1849*6 A.U. might come out as well .
No trace of it , however , was found on any of the plates .
It is known that both of these lines are strongly absorbed by the vapours of their respective metals , but , since the one came out , the other might have been expected to appear as well .
However , it must be remembered that the line X = 1819*6 A.U. is in the spectral region where the air begins to absorb very strongly , and it is possible that this effect combined with the action of the cool vapour in the flame to cut off all radiation of this wave-length which may have been emitted .
It is of interest to note that with magnesium no trace of the line X = 4571*38 A.U.\#151 ; frequency v = ( 1*5 , S)\#151 ; ( 2 , p2)\#151 ; was obtained .
Since the line X = 2852*22 A.U.\#151 ; frequency v = ( 1*5 , S)\#151 ; ( 2 , P)\#151 ; came out on the plates but feebly , it was scarcely to be expected that the line X = 2026*46 A.U. \#151 ; frequency v = ( 1*5 , S ) \#151 ; ( 3 , P)\#151 ; or others of higher frequency in the same series would have been obtained .
With thallium , as stated above , the lines X = 5350*65 A.U. and X = 3775*87 A.U. were the only ones which came out .
They are the first members of the second subordinate doublet series given by v = ( 2 , pi ) \#151 ; ( m , s ) , and v = ( 2 , _p2)\#151 ; ( ^ , s ) , and are therefore analogous to the doublet yellow lines in the spectrum of sodium .
The behaviour of thallium vapour in a vol. xcii.\#151 ; a. 2 z 590 On the Bunsen Flame Spectra of Metallic Vapours .
Bunsen flame , in so far as these experiments go , is exactly similar to the well known behaviour of sodium .
5 .
Results .
1 .
The results with mercury and cadmium vapours go to confirm the view that the frequency v = ( T5 , S)\#151 ; ( 2 , p2 ) , is a fundamental one .
The fact that the cadmium line X = 2288-79 A.U. came out in strongly burning flames also gives support to the view that the frequency v = ( T5 , S)\#151 ; ( 2 , P ) , possesses fundamental characteristics for cadmium atoms .
2 .
The experiments tend to support the view that , in the magnesium spectrum , the fundamental frequency is given by = ( 1'5 , S)\#151 ; ( 2 , P ) .
It is the one most easily stimulated in the spectrum of magnesium .
When the line X = 457P38 A.U. has been observed by other spectroscopists , it has always been accompanied by other lines , including in some cases that of wave-length X = 2852-22 A.U. 3 .
The results obtained with thallium failed to give any indication of the fundamental frequencies in the spectrum of this element .
It is probable that , with thallium , the fundamental spectral lines come far down in the ultra-violet region .
In conclusion , we wish to acknowledge the kind help of Mr. J. F. T. Young in taking some of the photographs .
McLennan and Thomson .
Roy .
Soc. Proc. , A , Plate 9 .
|
rspa_1916_0044 | 0950-1207 | On the ionisation of metallic vapours in flames. | 591 | 608 | 1,916 | 92 | Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character | Prof. J. C. McLennan, F. R. S.|David A. Keys, M. A. | article | 6.0.4 | http://dx.doi.org/10.1098/rspa.1916.0044 | en | rspa | 1,910 | 1,900 | 1,900 | 14 | 314 | 7,121 | http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1916_0044 | 10.1098/rspa.1916.0044 | null | null | null | Atomic Physics | 62.134116 | Thermodynamics | 19.493171 | Atomic Physics | [
5.914219856262207,
-50.044551849365234
] | 591 On the Ionisation of Metallic Vapours in Flames .
By Prof. J. C. McLennan , F.R.S. , and David A. Keys , M.A. , University of Toronto .
( Received July 17 , 1916 .
) 1 .
Introduction .
It has been shown by Frank and Hertz* and also later by McLennan and Hendersonf that when electrons possessing kinetic energy corresponding to a fall of potential of approximately 4*9 volts are allowed to impinge upon heated mercury vapour in a vacuum , the vapour emits a monochromatic radiation of wave-length X = 2536*72 A.U. R. W. Wood^ : has also shown that if light of this wave-length be projected in a given direction into heated mercury vapour in a vacuum , the phenomenon of resonance conies into play and a radiation of wave-length X = 2536*72 A.U. is re-emitted by the vapour in directions making all angles with that of the impinging light .
Quite recently too it has been shown by McLennan and Thomson^ that if mercury vapour be introduced into the flame of a Bunsen burner there issues from the flame in addition to the ordinary well-known light of the Bunsen flame the monochromatic radiation of wave-length X = 2536*72 A.LT .
These illustrations serve to show then that there are at least three distinct agencies by means of which the vapour of mercury may be brought into a state in which it is capable of emitting the characteristic monochromatic radiation of wave-length X = 2536*72 A.U. Frank and Hertz|| have also shown\#151 ; and it has later been confirmed by NewmanlF\#151 ; that mercury vapour is ionised when electrons are projected into it with a velocity equal to or greater than that acquired in a fall of potential of 4*9 volts .
This result would therefore suggest that whenever mercury vapour is brought into a condition to emit the monochromatic radiation X = 2536*72 A.U. , it is also ionised and should be capable of exhibiting electrical conductivity .
Some experiments made by Steubing** also seem to support this suggestion , for he found that mercury vapour could be made conducting by simply passing through it light of wavelength X = 2536*72 A.U. It would seem , therefore , if this suggestion should * Frank and Hertz , ' Verh .
d. Deutsch .
Phys. Ges .
, ' vol. 11 , p. 512 ( 1914 ) .
t McLennan and Henderson , ' Roy .
Soc. Proc. , ' A , vol. 91 , p. 485 ( 1915 ) .
X R- W. Wood , 'Phys .
Zeit .
, ' Jahrgang 10 , No. 13 , p. 425 .
S McLennan and Thomson , supra , p. 584 .
|| Frank and Hertz , ' Verh .
d. Deutsch .
Phys. Ges .
, ' vol. 10 , pp. 457-467 ( 1914 ) .
K Newman , ' Phil. Mag. , ' vol. 28 , pp. 753-756 ( Nov. , 1914 ) .
** Steubing , 'Phys .
Zeit .
, ' Jahrgang 10 , No. 22 , p. 787 .
2 z 2 Prof. J. C. McLennan and Mr. D. A. Keys .
turn out to be correct , that mercury vapour , when projected into a Bunsen flame , should become ionised and this ionisation should be made manifest by an increase in the ordinary conducting power of the flame .
Though numerous investigators have experimented upon the electrical conductivity of salts of different metals in flames , but few appear to have made a study of the conductivity of the vapours of the simple metals themselves .
Hittorf , * who investigated the conductivity of mercury vapour by heating the metal in a tube and passing the discharge from an induction coil through it , came to the conclusion that it was non-conducting .
Herweg , t however , found that the vapour of mercury did conduct , but later still BraunJ showed that mercury vapour when heated to 1000 ' C. did not exhibit any electrical conductivity .
Sir J. J. Thomson , S too , found that mercury vapour even at very high temperatures was a good insulator , a better one in fact than air , under similar conditions .
Strutt,11 who investigated the electrical conductivity of mercury vapour in an evacuated quartz tube heated to redness , also found it to be an insulator .
E. N. da C. AndradelT has shown that strontium vapour increases the conductivity of a Bunsen flame and he has also presented some facts and conclusions drawn from them which lead to the view that the positively charged carriers in a flame containing a strontium salt are the metallic atoms of strontium .
Pollok , ** using pure vapours in a heated vacuum tube , found that the vapours of metals and their chlorides such as cadmium , zinc , and mercury conducted the current with great ease .
From the rtsumi just given it will be seen that no definite conclusions can be drawn regarding the state of ionisation of mercury in a Bunsen flame which is radiating monochromatic light of wave-length X = 2536*72 A.U. In view of certain theories of atomic structure which have been presented by Bohrff and others , it is highly important to know whether mercury vapour which is in a condition to emit this radiation X \#151 ; 2536*72 A.U. is ionised or * * * S ** * Hittorf , 4 Wied .
Ann./ vol. 7 , p. 592 ( 1879 ) . .
t Herweg , 4 Wied .
Ann./ vol. 9 , p. 77 ( 1880 ) .
J Braun , 4 Zeit .
f. Phys. Chem./ vol. 13 , p. 158 ( 1904 ) .
S J. J. Thomson , 4 Phil. Mag. ' ( 5 ) , vol. 29 , p. 384 ( 1890 ) .
|| Strutt , 4 Phil. Mag/ ( 6 ) , vol. 4 , p. 326 ( 1902 ) .
m E. N. da C. Andrade , 'Phil .
Mag. ' ( 6 ) , vol. 139 , p. 15 ( 1912 ) , and 4Phil .
Mag. ' ( 6 ) , vol. 138 , p. 885 ( 1912 ) .
** Pollok , 4 Sei .
Proc. Eoy .
.Dublin Soc./ N.S. , vol. 13 , p. 209 ( 1911-13 ) .
++ Bohr , ' PlTil .
Mag. , ' vol. 26 , pp. 1 , 476 and 857 ( 1913 ) ; vol. 27 , p. 506 ( 1914 ) ; vol. 30 , p. 394 ( 1915 ) .
On the Ionisation of Metallic Vapours in Flames .
not , and in order to obtain information on this point some experiments were made by the present writers and the results of these are given in the following communication .
2 .
Preliminary Experiments with Mercury .
In making some preliminary experiments with mercury vapour a Bunsen burner A , fig. 1 , was surrounded by a large earth-connected iron cylinder BB for the purpose of screening off air currents from the flame .
The burner , which was provided at the top with a close .fitting tubular steel cup CC , was also connected to earth .
A sensitive D'Arsonval galvanometer , I ) , was placed upon an insulated stand and one of the terminals , E , was joined to one end of a battery of small storage cells , the other end of which was earthed .
Two carefully cleaned platinum discs , F and G , carried by insulating supports were held in position in the flame .
One of these , F , was joined to H , the second terminal of the galvanometer , and the other , G , was joined to earth .
The discs F and G were each 3 cm .
in diameter .
With this arrangement it was found that , as soon as the Bunsen burner was lighted with the tubular cup , CC , empty , the galvanometer showed a deflection which indicated that a current was passing through it and that the flame was conducting .
When the current was steady and a few drops of mercury were put into the cup , CC , an increase in the galvanometer deflection immediately took place .
The heat from the flame warmed the cup and this was sufficient to vaporise the 594 Prof. J. C. McLennan and Mr. D. A. Keys .
mercury and supply the flame with a stream of the vapour .
This increase in the current was taken as showing directly that the vapour in the flame was ionised .
In some additional experiments photographs were taken of the flame and it was always found when the cup , CC , was empty and free from mercury that the Bunsen flame spectrum alone was obtained .
When , however , mercury was introduced into the cup and the increased conductivity was exhibited , the single spectral line X = 2536*72 A.U. always came out on the plates in addition to the flame spectrum .
In no case was any trace of any other spectral line within the region between X = 6000 A.U. and X = 1800 A.U. obtained .
It was thought that possibly the line X = 1849*6 A.U. might have come out on the plates , even though feebly marked , but it was never observed .
In so far then as these experiments go the results indicate that the emission by the vapour of the monochromatic radiation of wave-length X = 2536*72 A.U. connotes ionisation of the vapour .
The experiments also support the view that when the vapour acquires the power to emit the radiation , it simultaneously acquires the power to conduct electricity .
Further , it follows , since for the stimulation of the mercury vapour to the emission of the radiation X = 2536*72 A.U. by electrons , it is necessary for the latter to have kinetic energy corresponding to a fall of potential of 4*9 volts , that the experiments described go to confirm the conclusion drawn by Frank and Hertz from direct experiment that 4*9 volts is the ionising potential of mercury vapour .
3 .
Further Experiments with Mercury .
With the apparatus used in the preliminary experiments it was found difficult to maintain the current through the flame steady for long periods of time , but after several trials the modification of the burner shown in fig. 2 was found to give very satisfactory results .
To the top of an ordinary Bunsen burner a brass cylinder , KL , 3*8 cm .
in diameter and 8 cm .
in height , was soldered .
The top was closed by a lid provided with an aperture 1*8 cm .
in diameter , into which there was inserted a short tube 0*5 cm .
in length .
Another brass cylinder , 2*8 cm .
in diameter and 7 cm .
, in length was held in the centre of the tube , KL , by means of three asbestos supports .
This inner cylinder contained a fused quartz tube , F , 1 cm .
in diameter and about 8 cm .
in length , drawn off to a neck about 0*5 cm .
in diameter at the ifpper end .
A coil of manganin wire , MIST , was wound round this quartz tube , and the ends were led out as shown in the figure through two openings in the cylinder , KL , fitted with small porcelain insulating plugs .
A layer of asbestos paper was wound round the coil of manganin wire , and then the whole space between the quartz tube and the brass tube next to it was filled On the Ionisation of Metallic Vapours in Flames .
595 with plaster of Paris , which on solidifying kept everything rigid .
The top of the quartz tube , F , came just level with the mouth of the burner .
When the H G\ Fig. 2 .
gas was lighted a large clear Bunsen flame was easily maintained above the mouth of the burner .
The two electrodes , A and B , were placed in the centre of the flame as shown in the figure , and the connections with the galvanometer and the battery were the same as before .
The burner and the screening iron cylinder , CD , were both kept well earthed .
With this form of burner mercury could be inserted in the quartz tube , and before a heating current was passed through the circuit a set of readings could be taken on the conductivity of the simple flame .
A steady current of sufficient intensity to bring the furnace up to a selected temperature could then be sent through the circuit , MN , and in this way a steady stream of mercury vapour could be supplied to the flame .
The conductivity of the flame could then be investigated under these conditions and the proportion contributed by the vapour ascertained .
With this form of burner it was found that exceedingly steady readings could be obtained , provided sufficient time was allowed to elapse after the heating current was turned on for the furnace to reach thermal equilibrium with its surroundings .
As the burner as well as the electrode A was earthed , it will be seen that part of the current in the flame always went to each of them .
This , however , made no difference , for the readings taken 596 Prof. J. C. McLennan and Mr. D. A. Keys .
were always comparative ones , the one set being taken with the free flame and the other when it was kept supplied with the mercury vapour .
In a particular set of experiments , which will serve to illustrate the conductivity of the mercury vapour in the flame , a series of readings given by the galvanometer was taken when the potential of the battery was varied from 5 up to 237 volts , and the flame was free of mercury .
A current of 5'5 amperes was then sent through the heating circuit , and when the furnace attained thermal equilibrium with its surroundings and the supply of mercury to the flame was steady , the second set of readings was taken with the same applied voltages .
Table I gives the results of this particular experiment .
The applied voltages are given in column I , and the galvanometer deflections without and with the mercury vapour are given in columns II and III respectively .
The differences between these readings are given in column IY , and they represent the measures of the conductivity contributed by the vapour .
Curves corresponding to the readings in columns II and III are given in fig. 3 , and the curve in fig. 4 represents the differences given in column IV .
From the form of the latter curve it will be seen that a saturation current was approximately obtained with the vapour when the applied potential was about 240 volts .
Tablft I.\#151 ; Mercury .
Voltage .
Deflection without Hg .
Deflection with Hg .
Difference due to Hg .
Column I. Column 11 .
Column III .
Column IV .
cms .
cms .
cms .
5 1 *3 2*4 1 *1 20 2*4 4*2 2*8 40 3*4 6*5 3*1 60 4*8 8*8 4*0 80 5*2 10 *2 5*0 95 5-9 12 *2 6*3 112 6*4 13 *2 6*8 132 7*2 13 *8 6*6 157 7*6 14*4 6 8 177 8*0 16 '8 8*8 197 8*6 17 *2 8*6 217 9*0 18 -0 9*0 237 9*8 20 '4 10*6 Chi the Ionisation of Metallic Vapours in Flames .
VOLTS Fig. 3 .
Fig. 4 .
4 .
Experiments with Zinc , Cadmium , Magnesium , and Thallium .
Zmc.\#151 ; In the paper on the flame spectra of metallic vapours by McLennan and Thomson* , it has been shown that , in their experiments on photographing the spectrum of a Bunsen flame into which a stream of zinc vapour was passed , no trace of any of the lines in the spectrum of zinc was obtained .
Although the intensity of the flame was made as high as possible , * McLennan and Thomson , supra , p. 584 .
Prof. J. C. McLennan and Mr. D. A. Keys .
nothing came out on the plates except the ordinary Bunsen flame spectrum .
This result was rather surprising , for , in a previous paper by McLennan and Henderson , * it had been shown that it was possible to make zinc emit a spectrum consisting of the single line \ = 3075*99 A.U. , when the electrons were projected into the vapour with kinetic energy acquired in passing through a fall of potential of about 3*96 volts .
Moreover , de Wattevilief and also Bamage , + found that , when sprays of solutions of zinc salts were sent into a Bunsen flame , this single line came out with great clearness .
It would seem , therefore , that it is comparatively easy to stimulate the zinc vapour to the emission of light of this wave-length , especially when it is associated with a salt of this metal .
In the experiments of McLennan and Thomson , however , as stated above , no trace of the line was obtained .
It should also be pointed out that the lines \ = 2536*72 A.U. and \ = 3075*99 A.U. are respectively the first members of Paschen'sS combination series v = ( 2 , p2)\#151 ; ( wi , S ) , || for the elements mercury and zinc , and that this was an additional reason for expecting that the zinc vapour in the flame would emit a radiation analogous to that emitted by the mercury vapour .
In view of this result , it became interesting to see if zinc vapour , when led into a Bunsen flame , would produce any increase in the conductivity of the latter .
The form of apparatus shown in fig. 2 was well suited to examine this point , for it was only necessary to insert a fresh quartz tube in the burner , and place pieces of the metal zinc in it instead of mercury .
It was found quite easy to vaporise the zinc by means of the heating circuit , and on doing this it was found that the presence of the zinc vapour in the flame made no difference to the conductivity of the latter .
A typical set of results is given in Table II .
The applied voltages are given in column I , and the deflections without and with the vapour in the flame are given in columns II and III .
The differences between the readings are given in column IV .
These two sets of readings are plotted in fig. 5 , and they show clearly that , for the range of temperatures investigated , the conductivity of the flame was quite unaffected by the presence of the zinc vapour in it .
The experiments with zinc vapour , therefore , go to show that , if the zinc vapour is not * McLennan and Henderson , ' Roy .
Soc. Proc./ A , vol. 91 , p. 485 ( 1915 ) .
t Be Watteville , 'Phil .
Trans. Roy .
Soc./ A , vol. 204 , p. 139 ( 1904 ) , and 'Comptes Rendus/ No. 142 ( 1906 ) .
X Ramage , ' Roy .
Soc. Proc./ vol. 70 , p. 1 ( 1907 ) .
S Paschen , 'Ann .
der Phys./ vol. 30 , p. 746 ( 1909 ) , and vol. 35 , p. 860 ( 1911 ) .
|| In the symbolic equation v \#151 ; ( n , X ) ( m , Y , ) the frequencies are given by ' - x)j- " [ " +y4ky ) ?
' " 'herc N " * ]"s .
a"d value , either integral or one of the numbers 1*5 , 2*5 , 3*5 , etc. , and m has successive integral values , each one giving the frequency of a member of the series .
M O I On the Ionisation of Metallic Vapours in Flames .
599 subjected to a stimulation sufficiently intense to cause it to radiate light of a wave-length \ = 3075'99 A.U. , it is not ionised .
Table II.\#151 ; Zinc .
Distance between Plates 0-8 cm .
Volts .
Without zinc vapour .
With zinc vapour . .
^ \#166 ; .
\#166 ; Difference .
Column I. Column II .
Column III .
Column IV .
cms .
cms .
cms .
6 1*6 1*5 -0*1 20 4 *9 4 3 -0*6 40 6*9 7*4 0*5 60 9*2 10-2 1 *0 78 11 *9 13*0 11 102 15 *6 15 *3 -0*3 120 15 *7 16 *4 0*7 140 19-2 18 *8 -0*4 161 19 *6 20 *4 0*8 181 21 *4 25 '2 3*8 201 22 -1 23 -0 0*9 221 31 -0 29 *1 -1 *9 239 25 *2 30 *6 5*4 e _i Q Fig. 5 .
Prof. J. C. McLennan and Mr. D. A. Keys .
Cadmium.\#151 ; In the spectrum of cadmium the lines X = 3260*17 A.U. and X = 2288*72 A.U. are specially important .
They are respectively the first members of the combination series v = ( 2 , p2)\#151 ; ( m , S ) , and of the singlet series v = ( 1*5 , S)\#151 ; ( m , P ) .
Moreover they are the only lines which are absorbed by non-luminous cadmium vapour in the region between X = 6000 A.U. and X = 1900 A.U. Further , Recording to de Watteville ( loc. cit. ) and Ramage ( loc. cit. ) the line X = 3260*17 A.U. is the only one which comes out in spectrograms of Bunsen flames fed with a spray of aqueous solutions of cadmium salts .
If electrons be projected into heated cadmium vapour in a vacuum tube with kinetic energy equal to that acquired in a fall of potential of about 3*74 volts , it is found that the vapour radiates light of the wave-length X = 3260*17 A.U. , and of this wave-length only .
Further , it has been shown by McLennan and Thomson ( loc. cit. ) , when using a burner similar to that shown* in fig. 2 , that if a stream of cadmium vapour be sent into the flame the line X = 3260*17 A.U. comes out quite strongly when the flame is burning , even wit/ h moderate intensity , and when the draught is forced and a larger supply of the gas provided , so that the flame burns strongly , the line X = 2288*72 A.U. comes out as well as the line X = 3260*17 A.U. However , when experiments were made by the writers , both with strong and with moderate flames , the conductivity was the same when the flame was supplied with cadmium vapour as when none of the vapour was present .
Contrary then to what was expected these experiments lend no support to the view that cadmium vapour is ionised when it is in a state which renders it capable of radiating light of wave-length X = 3260*17 A.U. or even of radiating light of wavelength X = 2288*72 A.U. Magnesium.\#151 ; In the spectrum of magnesium the line X = 2852*22 A.U. appears to be the one of special importance .
It is the first line , according to Lorenser ; * of the singlet series v = ( 1*5 , S)\#151 ; ( m , P ) .
It and also the line X = 2026*46 A.U. have been shown by one of usf to be strongly absorbed by non-luminous magnesium vapour .
It has also been shown by one of us ( loc. cit. ) to be the only line in the magnesium spectrum emitted by the vapour of this metal under bombardment by electrons with kinetic energy acquired in a fall of potential of from 4 to 5 volts .
Moreover , as de Watteville ( loc. cit. ) and Ramage ( loc. cit. ) have shown , it is the only line of the magnesium spectrum which comes out in the spectrum of a Bunsen flame fed with the spray of aqueous solutions of magnesium salts .
Living and Dewar* observed the line X = 4571*38 A.U. in the spectrum * Lorenser , ' Inaug .
Diss .
, J Tubingen ( 1913 ) .
t McLennan , supra , p. 574 .
X Living and Dewar , 4 Roy .
Soc. Proc. , ' vol. 32 , p. 189 ( 1881 ) .
i On the Ionisation of Metallic Vapours in Flames .
601 of the light from magnesium burning in air , and Eder and Valenta* also found it in the spectrum of the light from a Bunsen flame fed with magnesium powder .
Both of these pairs of investigators , however , found other magnesium lines as well in their spectrograms , and the evidence which their work offers , while emphasising the importance of the magnesium line X = 4571*38 A.U. in the magnesium spectrum , does not definitely point to its having altogether a fundamental character .
The evidence rather goes to show that it is possible to stimulate magnesium vapour to the emission of light of wave-length X = 2852*22 A.U. without an accompanying emission of light of wave-length X = 4571*38 A.U. , and that when the stimulation results in the appearance of X = 4571*38 A.U. in the spectrum , it is necessarily accompanied by the line X = 2852*22 A.U. It is the line X = 2852*22 A.U. which appears to be the fundamental one .
In view of the importance of this line in the spectrum of magnesium , it is of considerable interest to know whether or not magnesium vapour when it is in a state to emit the radiation is also in a state to exhibit electrical conductivity .
Our experiments , therefore , were extended to include a study of the conductivity of flames fed with the vapour of this metal .
The apparatus again used was that shown in fig. 2 .
In this case it was found that the conductivity of the Bunsen flame was greatly increased as soon as the magnesium vapour was sent into it .
It was also shown that simultaneously with the occurrence of the increased conductivity the vapour in the flame began to emit strongly the monochromatic radiation of wave-length X = 2852*22 A.U. The results of one of a number of sets of observations are recorded in Table III .
The applied voltages are given in column I , and in column II the galvanometer deflections before the vapour was sent into the flame .
In column III the deflections are recorded which were obtained when the furnace had reached thermal equilibrium and the flame was being fed with a steady stream of vapour .
Column IV contains a set of deflections obtained a few hours after the heating circuit had been cut off and the furnace had become cooled down to room temperature .
Column Y contains the differences between the readings in columns III and IY .
Curves representing these deflections are shown in fig. 6 .
It will be noted from the deflections in columns II and IV that the conductivity of the flame was much less before any magnesium vapour had been sent into it than what it was after the furnace had been cooled down and the supply of vapour cut off .
The explanation of this high residual conductivity of the flame caused some trouble at first but it was finally traced to the existence of a fine layer of magnesium oxide which had become deposited upon the electrodes while the * Eder and Yalenta , 4 Atlas Typischer Spektren , ' p. 18 .
602 Prof. J. C. McLennan and Mr. D. A. Keys .
Table III.\#151 ; Magnesium .
Distance between Electrodes = 0*85 cm .
Volts .
Without vapour .
With vapour .
Without vapour .
Difference : Column I. Column II .
Column III .
Cplumn IV .
Column V. cms .
cms .
cms .
cms .
6 1 *0 42 *5 14 *9 27 *6 20 1*9 148 *8 39 *7 109 *1 38 2*9 255 -0 67 *0 188 -0 58 3*9 357 *0 96 *7 260 *3 77 4-9 425 *0 121 *5 303 *5 101 5*5 505 *8 136 *4 369 *4 118 6*3 552 *5 156 *2 396*3 138 7*1 629 *0 191 *0 438 *0 152 7*6 663 *0 198 *4 464 *6 172 8*4 722 *5 208 *3 514 *2 190 8*8 726 *8 218 *2 508 *6 210 9*2 748 -0 231 *8 516**2 229 9*8 773 *5 243 *0 530 *5 flame was being fed with the vapour .
The differences between the readings in columns III and IV , namely , the numbers in column Y , may be taken , therefore , to represent the conductivity actually contributed by the vapour in the flame under steady conditions .
It is of interest to note that with magnesium as with mercury saturation was obtained with about 240 volts .
With magnesium it would appear then that when the vapour in the flame is in the condition to emit monochromatic radiation of wave-length X = 2852*22 A.U. it is also strongly ionised .
One cannot say definitely , however , that the conditions which determine the ionisation are the same as those which give the vapour the power to emit the radiation X = 2852*22 A.U. alone .
We have'seen that with cadmium vapour in the Bunsen flame it was possible to obtain the line X = 3260*17 A.U. and the line X = 2288*72 A.U. The line X = 2852*22 A.U. has been shown recently by Lorenser* to be the first line of the singlet series v = ( 1*5 , S ) \#151 ; ( m , P ) , and the line v = 2026*46 A.U. the second member of this series .
As pointed out above both of these lines characterise the absorption spectrum of magnesium vapour and it is possible that radiations corresponding to both of them and to other members of the series as well were emitted by the vapour-laden flame but that the intensity of the radiation of the members of the higher frequencies was too weak to leave any impression on the photographic plates .
All that can be said definitely is that the vapour in the flame was ionised and that at the same time it was strongly emitting monochromatic light of wave-length X = 2852*22 A.U* As indicated above the line in the magnesium spectrum * Lorenser , ' Inaug .
Diss.,5 Tubingen ( 1913 ) .
On the Ionisation of Metallic Vapours in Flames .
603 given by v = 2 , p2 \#151 ; 1-5 , S , and corresponding to the lines X = 2536-72 A.U. , X = 3076'99 A.U. and X = 3260T7 A.U. in the spectra of mercury , zinc , and Without Vapour volts Fig. 6 .
cadmium respectively is given by X = 4571-38 A.U. This line has been found in the arc spectrum of magnesium , and as already mentioned it has been found by some experimenters in the Bunsen flame spectrum of magnesium , but in none of the experiments made by us with the magnesium Prof. J. C. McLennan and Mr. D. A. Keys .
vapour-laden flames was any trace of the line obtained in the spectrograms taken .
Moreover , in some experiments made by one of us* some time ago and recently repeated it was found that when electrons were projected into magnesium vapour in a vacuum with gradually increasing velocities no trace of a spectral line was obtained in the light from the vapour until the electrons were given a speed corresponding to between 4 volts and 5 volts fall of potential .
When this speed was reached A , = 2852-22 A.U. came out strongly on the plates .
With still greater speeds no additional lines came out until the kinetic energy of the electrons corresponded to a fall of potential of about 7'5 volts .
When this potential was reached the arc suddenly struck and the many-lined spectrum came out .
Combining all these results it would seem that in the case of magnesium vapour , ionisation does not take place until the conditions are such as to enable the vapour to radiate light of wave-length X = 2852"22 A.U. If this be so it would appear that on the quantum theory the frequency of the line X = 2852-22 A.U. is the one which determines the ionising potential of magnesium vapour .
From the equation Ye = hv it would appear then that the ionising potential for atoms of this metal is 4'28 volts .
Thallium.\#151 ; Some experiments were also made on the conductivity of thallium vapour-fed Bunsen flames .
With this metal it was found that the presence of the vapour greatly increased the conductivity of the flame and that it was difficult to obtain a saturation current .
Table IV contains a set of readings taken with this metal and the curves in fig. 7 and 8 represent Table IV.\#151 ; Thallium .
Distance between Electrodes = 0-9 cm .
Yolts .
Without thallium vapour .
With thallium vapour .
Difference .
Column I. Column II .
Column III .
Column IY .
cms .
cms .
cms .
6 0*3 2*0 1-7 20 0*5 2-7 2*2 39 0*9 3 '6 2*7 59 1 *1 4*4 3*3 80 1*3 6*2 4*9 102 1 *45 6*8 5*3 120 1-5 8*0 6*5 140 1*6 9*4 7 *8 161 1 *8 11 -9 10*1 164 2*0 13*0 11*0 202 2 05 17 *2 15*1 222 2 2 24 *4 22 *2 243 2-35 31 *6 29 *2 1 * McLennan , 1 Roy .
Soc. l'roe .
, ' A , vol. 92 , p. 305 ( 1915 ) .
* On the Ionisation of Metallic Vapours in Flames .
them .
In taking these readings the sensitiveness of the galvanometer was greatly reduced .
At the same time as the readings were taken the spectrum of the flame was photographed and it was found that when the vapour was present in the flame the only lines in the spectrum of thallium which came out were those of wave-length \ = 5350*65 A.U. and \ = 3775*87 A.U. These lines are the first members of the second subordinate v = ( 2 , p\)\#151 ; ( m , s ) , and v = ( 2 , 22)\#151 ; ( m , s ) .
The lines whose frequencies are given by v = ( 1*5 , S)\#151 ; ( 2 , p2 ) , and v = ( 1*5 , S)\#151 ; ( 2 , P ) , are not yet known for the spectrum of thallium , and consequently one cannot be certain where to look for them .
They are probably , however , in the extreme ultra-violet region .
Had they been known or been found one might have deduced the ionising potential for thallium vapour provided it were shown to act in a vacuum in a manner YOL .
xcii.\#151 ; a. 3 A DE FLECTION Prof. J. C. McLennan and Mr. D. A. Keys .
an alogous either to the vapour of mercury , zinc , and cadmium or to that of m agn esium .
With thallium then the results show that the vapour of the metal increases the conductivity of a Bunsen flame , and that at the same time as the added conductivity is contributed radiations of the wave-lengths X = 535065 A.U. and X = 3775'87 A.U. are emitted .
It should be pointed o ut in this connection that Ramage , * who investigated the spectrum of Bunsen VOLTS Fig. 8 .
# flames into which metallic thallium or a spray of the aqueous solutions of thallium salts was injected , found the line X = 5350*65 A.U. to be the only one which came out in addition to the spectrum of the free flame .
5 .
Atomic Structure .
It was expected in undertaking these experiments to arrive at some definite information regarding the nature of the atomic structure of the * Ramage , 4 Roy .
Soc. Proc.,5 vol. 70 , No. 459 , p. 1 ( 1902 ) .
On the Ionisation of Metallic Vapours Flames .
607 metals investigated .
The results , however , are not conclusive .
According to the theory advanced by Bohr , * ionisation of an atom can only be said to take place when the disturbing agency causes one or more of the electrons in an atom to be projected out from the permanent electronic system beyond the outermost stationary or non-radiating orbit of the atom .
Such displaced electrons in returning to the permanent configuration could emit light of only one wave-length then if the atom possessed but at most one stationary or non-radiating orbit outside the permanent ones .
The theory of Bohr , however , hypothecates many of these stationary orbits even for atoms of the simplest structure .
It would follow then on this theory that if an atom emits light of but one wave-length it caiinot be said to be ionised .
The results of the experiments with mercury vapour would indicate that the theory is invalid , for the evidence goes to show that the radiation emitted by the atoms of the vapour was entirely monochromatic , and at the same time it supports the view that under these circumstance the vapour was ionised .
The results with zinc are inconclusive .
With cadmium , on the other hand , we find that the vapour in the flame emitted light of at least two wavelengths , and yet the vapour did not appear to be ionised .
This result supports Bohr 's conception of atomic structure .
The results obtained with magnesium vapour , just as those obtained with mercury vapour , are opposed to Bohr 's theory , for with this vapour in the flame we obtained ionisation of the vapour and at the same time an emission of radiation of apparently but one wave-length .
Finally , the results obtained with thallium vapour neither conclusively support nor definitely tend to invalidate the theory .
While the radiation emitted by this vapour in the flame , as observed by us , consisted of light of but two wave-lengths , the collateral evidence available does not altogether support the view that the radiation actually emitted under the circumstances was really confined to light of these wave-lengths .
It is possible and likely that radiation also took place in the spectral region beyond that which could be detected by a quartz spectrograph , which was the optical instrument used in this investigation .
The fact that ionisation of thallium vapour in the flame was observed cannot therefore conclusively be used for or against Bohr 's theory .
6 .
Summary of Results .
1 .
Mercury vapour which is fed into the flame of a Bunsen burner is ionised , and the radiation from the vapour consists of light of wave-length X = 2536-72 A.U. * Bohr , 'Phil .
Mag. , ' vol. 26 , pp. 1 , 476 , 857 ( 1913 ) ; vol. 27 , p. 506 ( 1914 ) ; vol. 30 , p. 394 ( 1915 ) .
Mr. R. C. Dearie .
Emission and 2 .
Zinc vapour , when injected into Bunsen flames , is not ionised , and does not emit any light characteristic of the spectrum of zinc .
3 .
A Bunsen flame which is supplied with cadmium vapour emits light of wave-length X = 3260*17 A.U. when the intensity of the flame is weak , and when burning strongly it emits light of wave-length X == 2288*79 A.U. as well .
The cadmium vapour in such flames does not appear to be ionised .
4 .
Magnesium vapour which is fed into the flame of a Bunsen burner emits light of wave-length X = 2852*22 A.U. , and the vapour in the flame is ionised .
The ionising potential for atoms of magnesium vapour appears to be 4*28 volts .
5 .
Thallium vapour , when it is fed into a Bunsen flame , becomes strongly ionised , and under these circumstances emits light of the wave-lengths X = 5350*65 A.U. and X = 3775*87 A.U. 6 .
The combined results of the investigation neither conclusively support nor definitely tend to invalidate Bohr 's theory of atomic structure .
Emission and Absorption in the Infra-Red Spectrum of Mercury .
By Raymond C. Dearle , M.A. , University of Toronto .
( Communicated by Prof. J. C. McLennan , F.R.S. Received July 17 , 1916 .
) Introduction .
In a previous paper by McLennan and Dearie , * it was pointed out that bands had been found in the absorption spectrum of non-luminous mercury vapour at X = 1849 A.U. , X = 2536*72 A.U. , and X = 2338 A.U. , but that nothing had been done up to the present in the way of investigating the infra-red region of this spectrum for characteristic absorption bands .
In the same paper an account was given of some measurements made on the infra-red emission spectrum of the mercury arc for the purpose of establishing the wave-lengths and intensities of the lines in that region .
The present paper deals first with some additional work on the relative intensities of these lines , and , secondly , with the absorption bands produced by passing-white light through non-luminous mercury vapour .
* McLennan and Dearie , 'Phil .
Mag. , ' vol. 30 , p. 683 ( 1915 ) .
|
rspa_1916_0045 | 0950-1207 | Emission and absorption in the infra-red spectrum of mercury. | 608 | 620 | 1,916 | 92 | Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character | Raymond C. Dearle, M. A.|Prof. J. C. McLennan, F. R. S. | article | 6.0.4 | http://dx.doi.org/10.1098/rspa.1916.0045 | en | rspa | 1,910 | 1,900 | 1,900 | 9 | 127 | 2,902 | http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1916_0045 | 10.1098/rspa.1916.0045 | null | null | null | Atomic Physics | 56.843489 | Thermodynamics | 13.907438 | Atomic Physics | [
5.99556303024292,
-49.83792495727539
] | ]\gt ; Mr. R. C. Dearle .
Emission 2 .
Zinc vapour , when injected into Bunsen flames , is not ionised , and does not emit any light characteristic of the spectrum of zinc .
3 .
A Bunsen flame which is supplied with cadmium vapour emits light of wave-length .
when the intensity of the flame is weak , and when burning strongly it emits light of wave-length .
as well .
The cadminm vapour in such flames does not appear to be ionised .
4 .
Magnesium vapour which is fed into the flame of a Bunsen burner emits light of wave-length , and the vapour in the flame is ionised .
The ionising potential for atoms of magnesium vapour appears to be volts .
5 .
Thallium vapour , when it is fed into a Bunsen flame , becomes strongly ionised , and under these circumstances emits light of the wave-lengths .
and 6 .
The combined results of the investigatio neither conclusively support nor definitely tend to invalidate Bohr 's theory of atomic structure .
Emission Absorption in the Infra-Red Spectrum of By BAYMOND C. DEARLE , M.A. , University of Toronto .
( Communicated by Prof. J. C. McLennan , F.R.S. Received July 17 , 1916 .
) INTRODUCTION .
In a previous paper McLennan and Dearle , was pointed out that bands had been found in the absorption spectrum of non-luminous mercury vapour at , and , but that nothing had been done up to the present in the way of investigating the infra-red region of this spectrum for characteristic absorption bands .
In the same paper an account was given of some measurements made on the infra-red emission spectrum of the mercury arc for the purpose of est.ablishing the wave-lengths and intensities of the lines in that region .
The present paper deals first with some additional work on the relative intensities of these lines , and , secondly , with the absorption bands produced by ) assing white light thrqugh non-luminous mercury vapour .
* McLennan and Dearle , ' Phil. Mag , p. 683 ( 1916 ) .
Ab sorption in the Infra-Red Spectrum of Mercury .
SPECTRUM .
In the paper by Prof. McLennan and myself ( loc. cit. ) on the infra-red spectrum of the mercury arc , it was shown that there was a disagreement between the values of the relative intensities of the lines and , as given by Paschen and by us .
According to the former , the line is the strongest in the arc spectrum of mercury , while in our ation the line was found to be somewhat the .
It was pointed out by Paschen*that , with low vapour-pressures , the intensities of the two lines were about equal , while an increase in vapour-pressure caused a relatively greater increase in intensity of the line Kuch and Retschinsky , in their measurements on the temperature of the mercury arc , found that an increase in current caused an increase in temperature , but did not affect the vapour-pressure , whereas an increase in voltage caused an increase both in temperature and in vapour-pressure .
In Paschen 's paper no mention is made of any variation in the voltage , but only of variations in current , so that , from the information given , it is not clear whether there was actually any variationl in the vapour-pressure in his lamp , or merely variations in the temperature .
In a later paper by Kuch and Retschinsky , was stated that , with temperatures the mercury arc , the lines of shorter wave-length were relatively than with lower temperatures , but no measurements were made on the line .
As this is analogous to the temperature effect for black body radiation , it seemed possible that the distribution of intensity in the lines of the spectrum might follow the usual form of the radiation curve .
This point was investigated by and later by with the result that it was established that lines belonging to the same series have their relative intensities arranged along a curve which is convex to the wave-length axis , that is , a curve the short-wave portion of an energy curve .
It was also that an increase in tempera- ture caused a relatively reater increase in the iutenbities of the wave-lengths than in those of the longer wave-lengths .
These relations , however , did not hold within a single triplet , nor among the lines as a whole .
All of the wave-lengths investigated lay within the region of the visible spectrum or in the ultra-violet , and no observations were made on the * F. Paschen , ' Ann. .
Phys vol. 27 ( 13 ) , p. 559 ( 1908 ) .
R. Kiich and T. Retschinsky , ' Ann. .
Phys vol. 22 ( 3 ) , pp. 695 , 602 ( 1907 ) .
R Kuch and T. Retschinsky , ' Ann. .
Phys vol. 22 ( 5 ) , pp. 852 , 866 ( 1907 ) .
S A. Pfliiger , ' Ann. .
Phys vol. 26 ( 4 ) , pp. ( 1908 ) .
L. Grebe , ' Phys. Zeitschr vol. 11 , pp. 1121-1122 ( 1910 ) .
Mr. R. C. Dearle .
Emission infra-red , that is , in the region where the maximum of an energy curve would be expected to appear .
The present investigation was undertaken to find ( 1 ) whether , in the infrared region , the relative intensities of the lines in a given series are distributed along an energy curve ; and ( 2 ) the effect of increased temperature and vapour-pressure on the relative intensities of the two lines and , which do not belong to the same series .
EXPERIMENTAL ARRANGEMENT .
The aJ ; rangement of the apparatus was the same as that previously described in the paper by Prof. McLennan and myself , except that the light from the mercury arc , instead of being focussed on the spectrometer slit by a concave mirror , passed directly through a quartz lens having a focal length of 20 cm .
For the determination of the intensities of the various lines as distinguished from the continuous radiation due to the heated quartz , the method was followed of drawing a cooling curve for the lamp after exti uishi the arc .
Greater precision was given to these measurements by taking logarithms of the galvanometer deflections and plotting these against elapsed time .
This gave straight lines which could be continued back Absorption in the -Red ectrum of Mercury .
to zero time very accurately .
An additional advantage of this method is that it was only necessary to take two readings with the galvanometer in order to obtain a complete curve .
An example is given below , the curves being shown in fig. 1 .
From the curve we get , for zero time , deflection hence , deflection due to radiation from the heated quartz mm. RESULTS .
The lines chosen for the first part of the investigation were those to the main series of single lines and the first three members of the series were used .
These are given by The lamp was run with two different energy consumptions with the following results : * In the symbolic equation the frequencies are given by , where is Rydberg 's number , has a fixed value either integral or one of the numbers , etc. , and has successive integral values , each one giving the frequency of a member of the series .
that they are steeper on the short-wave side , and the increase in energy is quite clearly relatively greater in the shorter wave-lengths .
The lack of sufficient points on the curve prevented the necessary accuracy for determining whether the maximum intensity shifts to the shorter wave-lengths for increase in temperature .
If this were so then the analogy to the energy curve would be complete .
It is interesting to note that the distribution of energy is governed by the actual wave-lengths of the lines and not by the order in which they occur in the series ; i.e. , although the first member of the series is and the second is , the lines are distributed along the energy curve , not in this inverted order , but in the order of their wave-lengths .
For the second part of the investigation the current in the lamp was kept constant at amperes , and the voltage.was varied so as to give an energy consumption in the lamp which from 150 to 250 watts .
For each of the applied voltages the intensity was measured on the line and on by the method described above .
The results are given in the Table below , the first column gives the energy consumption in watts , in the second column represents the intensity of the line and in column ives the intensity of the line .
The fourth represents the ratio of the two intensities in each case .
Absorption in the Infra-Red Spectrum of Mercury .
It will be noted from the last column that the relative intensity of the line to that of the line increases regularly with increase in energy consumption , or in other words , with increase in vapour-pressure in the lamp .
In all measurements with this lamp the line always appeared to be the more intense .
II .
ABSORPTION BY MEBCUIY As far as the author has been able to ascertain there has been no work done by previous investigators on the selective absorption by llon-luminous mercury vapour in the infra-red region .
It was at first intended to pass the light from a mercury arc through a layer of the vapour and examine the emergent radiation to find whether any of the lines in the infra-red spectrum were extinguished .
This method was abandoned , however , and the radiation from a Nernst glower was used instead of that from a mercury arc .
The principal advantages in this were the greater steadiness in the radiation secured , and the fact that a continuous spectrum was produced in which absorption bands would take the form of depressions .
Apparatus .
The apparatus used for these measurements was similar to that used in the Aevious work .
The spectrometer , thermopile , and galvanometer were unchanged , and the mercury lamp was replaced by the Nernst glower and the absorption cell .
The latter is shown in section in fig. 3 .
It is made entirely of fused quartz , is about 6 cm .
long and cm .
iu diameter , with a small reservoir ( C ) for the mercury underneath .
The ends were formed of two circular plates of clear fused quartz which transmitted the visible light with very little diffusion .
A small tube ( D ) at the top served to connect the cell with an exhaust pump .
The reservoir was first filled with clean dry mercury , which was boiled to eliminate all traces of water-vapour , and the cell was then exhausted to a pressure of .
few millimetres of mercury and sealed off .
When in use the cell was heated by means of an electric current applied to the walls of the reservoir and tube , temperatures as high as 19 C. being Mr. R. C. Dearle .
Emission used .
In order to obtain uniform temperature and hence constant vapour density , the cell was placed in a box and packed in powdered magnesia .
The ends were kept clear for the transmission of the radiation by means of two brass tubes projecting it from the sides of the box , as shown at BB .
It was found that on account of the radiation through these tubes , and the consequent lowering of the temperature at the ends of the cell , the mercury vapour immediately condensed on the end plates , thus cutting off the radiation very considerably .
This difficulty was overcome by putting a single turn of wire against each plate from the outside ( AA ) , and passing a current through these wires of sufficient strength to maintain the plates at a slightly higher temperature than the rest of the cell .
The light from the Nernst glower was first focussed on the slit of the spectrometer by means of a quartz lens ; then the cell and its containing box was placed in such a position that the radiation from the Nernst glower had to pass through the cell before falling on the lens .
After all the readings had been taken , the absorption cell was replaced by a plate of clear fused quartz similar to those forming the ends of the cell .
The intensity o the radiation was cut down by means of a diaphragm of Bristol board having a small hole cut in the centre , in order to make the Absorption in the Infra-Red Spectrum of Mercury .
galvanometer deflections comparable with those obtained when using the cell .
Readings were taken over the spectrum with this arrangement so as to find out whether anyaf the observed absorption bands might be due to absorption by the quartz itself .
RESULTS .
The range of wave-lengths studied was from to , and this region was investigated very thoroughly .
A great number of readings were necessary on each wave-length to obtain a satisfactory curve , and each set of readings was repeated over a period of several months .
The necessity for this lies in the unsteadiness of the zero point in reading the galvanometer deflections , which was due to the combined effects of local magnetic disturbances on the galvanometer and stray air-currents on the thermopile .
Despite these difficulties it was found that certain well-defined depressions occurred in every set of readings , while others were obtained which were not so well defined , sometimes appearing quite strong and at other times being scarcely detectable .
In the following Table are given all the wave-lengths at which absorption bands were observed and the characteristics of each one .
The wave-lengths of the emission lines as recorded in our previous paper are given for purposes of comparison .
The temperatures used varied from 14 C. to 19 C. , and an attempt was made to show that the strength of the weaker bands was dependent on the vapour.pressure within the absorption cell .
But within the limits of these temperatures the results were entirely negative .
Readings were then taken with the cell at the temperature of the room , about C. , and the resultant curves gave all the absorption bands as doubtful except those at and , absorption being quite distinct on both of these The final readings were taken , as described above , with a plate of clear quartz in the path of the radiation in place of the absorption cell .
Readings were taken over the same range of wave-lengths and a smooth curve was obtained with no evidences of any characteristic absorption bands .
-Red Spectrum of Mercury .
spectrum , but it is difficult to see how its presence could be detected , as the intensity of the line .
is so small as to require an exposure of at least one hour in order to produce an impression on a photographic.plate .
It has recently been shown by Prof. McLennan and Mr. A. Thomson that this same line is given out by mercury vapour in a Bunsen flame , and an attempt was made to see if the radiation of wave-length could be detected as well from such a source .
The experiments , however , failed to reveal any indication of the emission of such radiation .
SUMMARY 1 .
Emission .
1 .
It has been established that the relative intensities of the lines in an individual series lie along a curve analogous to an energy curve , not only in the region of short waves , but also in the long-wave region beyond the maximum of the energy curve .
2 .
The intensities of the series lines become relatively greater in the shorter wave-lengths with increase in temperature .
3 .
For the two lines , and , which do not belong to the same series , the intensity of the former becomes relatively greater for higher temperatures and increased vapour-pressures , although it is the line of longer 2 .
Absorption .
1 .
Evidences of absorption have been found with each wave-length for which there is an emission line in the mercury spectrum between and 1 .
2 .
Strong absorption was obtained on wave-lengths , and 1 .
3 .
Absorption was obtained at wave-lengths and , with very low 4 .
It has been shown that these two wave-lengths correspond to the first members of the series , and , respectively .
In conclusion , the author wishes to acknowledge his indebtedness to Prof. J. C. McLennan for gesting the investigation , and for his kind direction and helpful suggestions through its progress .
|
rspa_1916_0046 | 0950-1207 | The kinetic theory of simple and composite monatomic gases : viscosity, thermal conduction, and diffusion. | 1 | 20 | 1,916 | 93 | Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character | S. Chapman, M. A.., D. Sc.,|Sir J. Larmor, F. R. S. | abstract | 6.0.4 | http://dx.doi.org/10.1098/rspa.1916.0046 | en | rspa | 1,910 | 1,900 | 1,900 | 17 | 210 | 6,118 | http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1916_0046 | 10.1098/rspa.1916.0046 | null | null | null | Tables | 40.105724 | Fluid Dynamics | 37.130115 | Tables | [
37.01057815551758,
-36.208194732666016
] | ]\gt ; PROCEEDINGS OF TILI E ROYAL SOCIETY .
SECTION TEBMA TICAL AND SCIE NCES .
\mdash ; \mdash ; The Kinxtic Theory of Simple and Composite JIonatomic Viscosity , duclion , and Diffusion .
By S. , D.Sc .
, Fellow and Lecturer of Trinity Canlbridge .
( Communicated by Sir J. Larmor , F.R.S. ) ( Abstract .
* ) The mean-free-path phenomena of ases can be explained in a way by a very elementary form of the kinetic theory , but to dlo satisfactory mathematical treatment of them , yielding accurate numerical results , is less easy .
The difficulty varies to some extent with the nature of the molecular model chosen as .
It is curious that the adopLoion of particular model , viz. , a centre of force varying inversely the fifth of the distance , removes nearly all the analytical complications in the theor The first accurate treatment } viscosity , conduction , and lsion , Maxwell made possible by this fact , and it is remarkable that Maxwell ' theory requires ) knowledge of velocity-distribution function the state of the gas .
If the molecnles are of ( t1 ) * This abstract summarises two papers in the hiCal Tansactions , ' the received dealing with simple gases ( ' Phil. Tratls , vol. 216 , pp. 279-348 , 1915 ) , and the second ( received May 19 , 1916 ) with ] osite gases .
Tho two papers a1nplify and complete an earlier memoir ( ' Phil. Trans , vol. 211 , pp. 433 483 1911 , which contains a first ation to the present theo1y .
VOL. XCIII.\mdash ; A. Dr. S. Chapman .
The inetic Theory of there type , the function must be determined , a task wherein lies the ain ( lifflculty of the investigation .
It is , however , of more than mathematical to widen the basis of the theory , since Maxwell 's olecular model clocs not satisfactorily represent the molecules of ases .
The velocity-distribution function has been proved by mann to tisfy a certain integral equation , which Hilbert has shown to be to determine the iunction uniquely .
Loreutz solved an important enera form of this equation : while Pidduck* has obtained solutions of typical examples of the general case , and so deduced many interesting merical results to diffusion .
The present method , is not tsed on Boltzmann 's equation .
less direct , it seems to possess dvantages not shared by the other method , in that it yields results of complete formal enerality , which can be reduced to ical form with omparatively little arithmetical labour .
To comply with the pure mathematician , the results should be proved to be in conformity with Boltzmann 's equation .
Progress has already been made in this lirection , and has brought to light several theorems of much analytical i1lterest .
As the insertion of these would unsuitable in memoirs intended primarily to deal with questions of physics , they are eserved for a future OF MATIIE)[ATIOAL ]]TflOD .
( 1 ) Notation of of We consider a composed of a mixture of two sets of sy1lJmetri ; al molecules of masses in numbers per unit volunls The component densities , are consequently equal to .
The external force acting on each molecule ( and similarly for the molecules , with change of suffix throughout ) will be denoted by , or , vectorially , by , while the mean velocity of this group of lnolecules a will be denoted by or by .
The portions of either kind be denoted by , so that where evidently -k lesungen ube ] stheorie .
' vol. 1 , p. 114 ; Hilbet , 'Math .
Ann. ( 1912 ) ; Lorentz , 'Theory of Electrons , ' p. 268 ; Pidduck , 'Proc .
Lond. Math. Soc vol. 15 , p. 89 ( 1915 ) .
Also cf. Lunn , ' Bull .
Amer .
Iath .
Soc vol. 19 , ; , ' Phys. Zeit vol. 12 , p. 58 ( 1911 ) .
For convenience we shall suppose the heavier gas to be taken as that I.e. , at the point and at time Sirnple and Composite Monatomic suffix here , and throughout , refers t , o the composite as a whole .
Thus the mean mass , or external force per molecule , and the mean velocity of the gas as a whole , are given by equations of the type and so on .
Evidently , the total density , equal to , is also given by The suffix , together with a dash will relate to certain multiples of difference between the values of various data for the component gases .
we define by the equations , , By the equations , we obtain the expressions for original quantities , etc. , in of , and so It may readily be seen that the motion of can be analysed into a steady motion of the whole velocity together with a Dlotion of interdiffusion in which equal numbers second ) of the two roups of ulolecules are transported in opposite directions , the mean yelocities of the two eams b and .
The momentum of the common motion is , while the resultant momentum of the motion of ( due to the difference of molecular lnass ) is ; it is easily seen that , with the above definitions , As regards the resolution of the forces into multiples of and the first terms , ?
on and on ?
, represent forces which will inlpart a common acceleration to each group of lnolecules we may ippose this to modify the common elociCy c ) .
The remaining courpouents of and , when summed up over the or molecules of the corresponding roup , afford equal and opposite total forces such interdiffusing groups of molecules as we consider in ) will exert and opposite forces on one another , and the forces acting on the ( rrouPs must be and opposite if the motion of interdiffusion is to be iutained , or modified without impartiug any common velocity to then ] .
As for , it is introdnced for the sake of symmetry : denoting , clearly Dr. S. Chapman .
The Kinetic of We next consider motions of individual molecules .
The velocity of a typical molecule will be denoted by , or , when referred to the co-ordinate axes , or when referred to axes moving with the velocity appropriate to the given values of , by or .
Thus , the second equation referring to the molecules The mean value of any function of the molecular velocities will be denoted by a bar )laced ave the expression for the function .
Hence , by definition , or far , has denoted a vector quantity , and the equations it have been vectorial : henceforward it will denote ) amplitude of vector , so that is essentially positive , and The mean energy of the motion " " peculiar\ldquo ; to each molecule is clearly 1 , pe molecule , and we write where is the universal -constant .
These equations define and , will be termed the " " temperaturcs\ldquo ; of the component ases , which are not necessarily equal , though all the departures of the from the uniform state will be supposed small .
The nean hydrostatic pressures of the component and composite ases , and also and ( the temperatur of the composite ) are defined by Clearly The six pressure components , for the compo ent and osiCc gases are si1nilarly defined , e.g. , We aJso define , by the equations Sirnple and Composite Gases .
Evidently is a measure of the difference between the temperatures of the component gases .
( 2 ) The Velocity-Distribvtion When the gas is uniform , so that are constant , while , are zero , the function distribution of the components of velocity the molecules / assumes xwell 's well known form : These cleally satisfy the necessary conditions For the velocity distribution function in the slightly disturbed state we shall vrite where is a function , of the first order of smallness , which irlS to be letermined .
( 3 ) of Let be any function of the velocity components , of a molecule ; then is the aggregate value of QI summed over all the molecules in unit volume .
The equation expressing the analysis of the rate change of is called the " " equation of transfer\ldquo ; of .
It may readily be shown to The rate of is here analysed into ( a ) the part due to encounters veen the molecules themselves or with the others , ( b ) the part due to the passage of molecules into or out of the volume considered , and ( 3 ) that caused by the action of external foroes .
By assigning to the values unity , , or , we may obtain the equations of continuity , momentum , or energy , for the composite gas , since in these three cases , by virtue of the conservation of mass , momentmn , and we may eliminate Three special functions are important in the present theory .
By means three equations just mentioned , and by the of all second-order .
Jeans ' ' Dynamical Theory of Gases , ' ( 2nd ed Dr. S. Chapman .
The Kinetic Theory of quantities , the corresponding equations of transfer may be reduced following form : The equations define , and there are , of course , ilar quantities and so on , which a fined in like manner : .
In each of the above equations of transfer , as written , a multiple of is equated to certain " " external ' or mean data of the .
The reduction to this form requires no knowledge of the small deviation from Maxwell 's distribution law of molecular velocities , , of the function , but such is necessary for the calculation of onversely , however , the above equations for throw light on the form of ; in fact , if we assume that can be expressed as a power series in , we may in this way*infer that it will have the following The function is obtainable by changing the suffix 1 into 2 hout .
We express the functions , etc. , in power series which are conveniently written as follows:\mdash ; * The details of the deduction will be found in the papers , where it is shown how depends on q ) .
Simple and Compositc ' ' The dash ' after the sign of summation in is to indicate that is to be omitted from the numerical factor of the first ternl .
factors are arbitrary and not really necessary , since the coefficients are unknown , but their insertion is analytically advantageous .
Similarly it is convenient to denote the coefficients in ) , etc. ( which expressions correspond to , etc. , the natural change of suffix ) ; it is then necessary to distinguish between and and so on , even when The factors A , in can ) chosen at will , after which coefficients , become definite ; these remain determined .
ertain relations between them , however , hold good , in irbne of the conditions which ( with the suffixes appended ) satisfy .
These are readily seen to yield the , .
, In the last equation , and are entirely independent hence , if we eliminate , we can } ) arately equate their co-factors to zero , in the equation .
In this way the tionS 1 be Dr. S. Chapman .
inetic Theory of which also define and ; consequently , also , ( 4 ) .
means of the above expression for it is ossible to culate , the operation ( a ( and elaborate one ) in the luation of an octuple integral the variables which are required to specify an encounter two molecules .
Small quantities than the first are ected , and the expression for always consists of a linear series of the coefficients thti l into , etc. ; the factor of each in these .
series depends on , and and involves the of molecular i1lteraction during ncounter .
It is found possible to erfectl expressions for these factors , no particuIar of interaction has to as , sumed .
ting the value , of , so calculated , in the bove equations of ansfer , may } ) arately equate the on the two sides which contain thus obtain a number of , each of which is linear in one set of the cicnts c , or the factors as above stated , , definitely known functions of , and is au infinite sequence of such quations for each of coefficients , one cquation Corresp u to each ) , which takes all from to .
If we solve in same way as for lineal equations in 1 ' unknowns , ) we arrive at tions typified the equation : the cient of in equation of sequence of equations for , and denotes the determinant whose element while denotes the same determinanli with the elements of .
all replaced ) unit These determinants infinite in directions , the in each of the equations whence they are derived , j ) from to , while thu equations of transfer for provide a second infinite sequence of equations corresponding to the of from ) ) .
If we are a simple gns , so that do not appeal the determinants reduce to the more ordinary quadrant of the plane .
Simple Composite Monatomic Gases .
These general formulae for the coefficients , complete the determination of the velocity distribution function .
The mean value of any function of , can hence be calcuJated in the form of a linear series of these coefficients .
It remains only to add that any such linear series in the , or can readily be transformed into the quotient of an appropriate determinant by [ espeotively .
P-tRT TO TIIE ATlI ( 1 ) By I ( 1 ) and 1 ( 2 ) , total qStlre components , are given the significanc of and and comparin , these equations equations of pressure of a whose coefficient of viscosity is .
with At is clear that the composite behaves like a viscous fluid , that .
From 1 ( 3 ) , the it } ) that Hence ( taking the right-hancl terms rder)iffusion is ) roduced by ( 1 ) concentration gradient , or ill the relative of constituent ases ; ( 2 ) by external forces unequally per unit mabS on the two sets of molecules , and by variations in ( 3 ) the totad pressure , temperature of the composite .
If we write theI1 Dr. S. Chapman .
The Theory of and we may call , and DT respectively the coefficients of diffusion , forced diffusion , pressure diffusion , and thermal .
The definition of agrees with that usually iven for the coefficient of diffusion .
The other coefficients seem to be defined here for the first time .
If , as we supposed , the molecules are , the four coeflicients of diffusion are .
Ifence , in the case of pressure the avier gas will tend towards the direction of in case of thermal diffusion , the heavier gas wiJl tend towards the direction of decreasing vidently both pressure and thermal diffusion will in eneral take place the passage of sound through a composite such as air , the effects presumably comparable with those of ' and conduction been investigated by Stokes , Kirchboff , and of The equation of energy is the equation of transfer of .
On the separate equations for the two -components , the equation of energy for the ] , correct to the first order , is found .
Here is the })ecific beat at constant volume , Joule 's mechanical equivalent of heat .
terms , it will appear , } on viscosity , difl'usion , conduction .
If we these small effects , the equation may be written or , by the equation continuity , , or , or Thi is the law of adial)atic expan sionl of a monatomic ected Sirnpte Composite terms hence give the necessary corrections to this law , are due to the causes indicated .
The left-hand side represents the net rate of increase of energy of molecular agitation , being the increase corresponding to the temperature after allowing for the change due to adiabatic alteration of volume .
This net rate is analysed as follows , taking the various terms in order:\mdash ; ( a ) Work is done on the molecules by the external forces , in the motion of interdiffusion relative to the resultant stream velocity ( b ) The variation in the proportions of the molecules and , due to diffusion , produces a flow of energy of stream-motion , since The viscous forces cause dissipation of , represented by the third on the -hand side .
( d ) The fourth term epresents the effect of conduction , together with a hitherto unrecognised term due to diffusion .
Supposing , for simplicity , that there is no mass motion , the equation of becomes on substituting the values of and and substituting for in of and .
If , further , there is no diffusion , it reduces to the eqnn C } of conduction of heat with therlnal conductivity , where It appears also that the motion of interdiffusion is accompanied by a of heat proportional to the velocity of diffusion , a process which we term the " " thermal flux of difl.usion.\ldquo ; In the absence of conduction , forces , and mass motion , the equation of is thus seen to be where is , and is called the " " specific energy of diffusion Dr. S. Chapmall .
The Kinetic of ( 4 ) Inequylity oj the artial T In I we found that so that the temperatures of the component ases are unequal by an amount proportional to the of change of the ratio of their densities .
We will write the equation in the form being termed the anisothermal constant of diffusion .
Since is found to be positive , the of ] relative density is the hotter .
PART III .
THE RESULTS 1N IOUS SECIAL CASES .
( 1 ) In The various results arrived at in .
Part II are complete and perfectly eneral .
To be of service to natural philosophy , however , we must consider their values for selected particular molecular models , and in order to obtain uunlerical results we must be prepared to make successive approximations to the accurate fornrulae .
Our usual procedure in this Abstl'act will be to state the eneral form of the first approximation , and to determine the correction to further approximations only for special types of molecule .
The types which will be dealt with are ( a ) point centres of force varying inversely the power of the mutual distance ; ( b ) rigid elastic spheres ; and ( c ) elastic spheres surrounded by a field of attractive force .
The following notation must first be explained , in order that the .of this section l1lay be understood .
, , Here is the angle which the relative velocity of two molecules , , is an encounter in which is the distance their initial or final lines of undisturbed rectilinear motion , and is the ma nitude of their inirial or final relative velocity ; is the endre function of , of yree k. If both molecules are of same kind , or , the function to is or .
In the next equation , is affected the same suffixes as the fu1lction under the Simple Composite onatomic ( integral sign ; and clearly depend upon the molecular model the various models differing in respect of the dependence of on and / ? .
Again , ; in the latter the suffixes 11 , 12 , or 22 , are to be added to correspond to suffixes of on the left .
( Partic If the molecules are elastic spheres of radii , it may readily be shown that In these formula , or , more ooenerally , , where but not .
is a positive denotes .
When the molecules are power centres of force , the force at unit distance , it may be shown that 5 where I , , are pure numbers , depending on only .
* When , so that the molecules are Maxwellian , we may note that for all values of When the molecules are rigid elastic spheres surrounded by a field of attractive force , the latter may be allowed for very approximately ) additional factor in , a in , and a factor in .
Here , which known as Sutherland 's constant , is given by * They are the same as the quantities thus denoted in Jeans ' 'Dynamical Theor .
of abes , ' 2nd ed. , SS305 , et seq. is Sutherland 's diffusion constant ; when the gas is simple , 's constant of viscosity ( generally written C ) is , or .
S. Chapman .
The Kinetic Theory of where is the potential of the force between two molecules hen in contact ; and are similarly defined , and appear in the numerators of the additional factors in and By putting , and changing the suffix 2 into 1 hout , formulae for a composite gas reduce to those appropriate to a simple gas .
shall first deal with the latter .
viscosity of a The genel.al first approximation to the coefficient of viscosity of lnple gas is .
( 0 ) .
This result iveu and discussed in an earlier memoir , so that only the correction introduced by further approximations need be considered here .
In the case of elastic spherical molecules , the correction factor is purely llumerical , as also in the case of centres of force .
Successive approximations to the factor in the former instance are found to be , so that times the above result may be takeu as exact well within per cent. For nth power centl.es of force , , the correction factor is found to have the values corresponding to the typical values 5 , 9 , 15 , 25 and inity for In the case of elastic .
molecules , the correction factor yaries very slightly with temperature .
Typical values , to the values , 1 , for , are respectively , and .
Thus , in all cases , the first tion is close to the exact value .
( 4 ) of plc A first approximation leads to the result given in the earlier memoir just cited .
As in the case of viscosity , the correction consists of a numerical factor to be applied to the above result ; this factor is very nearly unity , being for rigid eiastic spheres , and for power centres of force varying from for ) rough the values for , 15 , and 25 , for Similarly for spheres , as takes the values ] , , the factor is found to equal , and respectively .
The corrections to the first approximation are 'Phil .
Traua , ' , vol. 211 , pp. 433-483 , SS17 , 20 1911 ) .
and Convposite latomic G ardly within the present experimental powers of measurement , and the simple , agrees well with the observed values for argon , heliuln , and neon .
( 5 ) Coefficient of first approximation to is .
This result first obtained by evin , and subsequently , independently .
in the earlier .
by present author , already cited .
Like the first approximations also to , and , it is an exact formula in the case of Maxwellian molecules , and in no other .
Maxwell obtained this expression for in his special case , though without a rigorous proof ; his method applied to other cases ( as by the authors ) leads only to the above first approximation , the error of which is in some cases considerable .
We shall vrite the correction factor introduced on a second approximation in the form .
Before considering the value of we shall examine some particular cases of our formulae which throw light on the accuracy of second approximation AVhen the mass and size of the molecules are ible compared with ithose of , an exact solution for is obtainable , as Lorentz first showed .
The first approximations to the correction factor in this case , when the luolecules are elastic spheres , are found to be converging to the value or .
If the molecules are ?
power of force , the correction factor is equal to which , when is 5 , 9 , , 17 , , has the respective values .
These results agree with Lorentz 's theory , and show that in this case , at auy rate , the first approximation to is seriously in error .
The next simplest case of a general character with which we can deal is that in which the molecules are identical in dynamical properties , mass , size , force ) , as , for instance , in the diffusion of a ) into itself .
Hence we shall in this case write .
for .
The correction factor is found to depend only on the nature of the molecule ; its values for power centres of force , when equals 5 , 9 , 17 , or , are respective]y , 1004 , , or , and the last value also corresponds to spherical molecules .
These are only first approximations , but would not be altered by further approximations by more than or .
The complete formula for rigid spherical molecules is Dr. S. Chaplnan .
Theory of correction factor in this case had been previously calculated approxilnately by Pidduck , who obtained thus to three decimal only ) in place of as above .
For the same type of molecule , we also have may be compared with an approximate result obtained by Jeans , using the \ldquo ; method , viz. , .
For other types of molecule , is a different multiple of ( 6 ) , of of The above first approximation to , it may be noticed , depends only on , and not at on the ratio .
Meyer disputed the independence of on the ratio of mixture , and developed a theory predicting considerable of as was varied .
results ed a small variation of , but much less than 's formula .
This suspicion on both Maxwell 's and Meyer 's theories ; it now appears that the former was correct , but failed to represent the facts because of the unsuitability of the molecu ] model .
A Maxwellian gas is the only one for which is indepcndent of ) .
correction factor to the above ap proximate formula is in every other case a function of We shall consider only the approximation to the correction ctor ; this is very nearly exact .
find that here is obtainable from the suffixes 1 and 2 .
The behaviour of of is easily studied when the olecules are rigid elastic spheres .
In this case ( renlembering conventio1l ) it appears that exceeds ) , and that exceeds .
Further , if , lave b ; the of equality correspond to the case , as in self diffusion .
This indicates why does nof depend on .
In the general case , if above condition is fulfilled .
Simple Composite Monatomic Gases .
and ] steadily decrease , as the proportion of molecules is increased , while , if it is not fulfilled , and ( and consequently also first increases and then decreases , as increases from to 1 .
Clearly , ths more equal the molecular masses , the more equal also must be the molecular radii , in order that the above condition may be fulfilled .
ards the magnitude of the correction factor , it is greater the more unequal the diameters and masses of the molecules , a maximum of , or , when and are infinite .
This is for rigid spherical molecules : for other types the is less , to zero in the case of Maxwellian molecules .
In other cases the factor appears always to exceed unity .
The nitude of the variation in ordinary cases , and the comparison of experiment with theory , may be from the following Table* ; the theoretical values of are so calculated as to make their mean agree with the mean of the experimental values , so that the theory is concerned only with the variations the mean .
The molecules are assumed to be spheres , a less simple model might prove still better .
It may be added that has improved Meyer 's theory of by taking persistence of velocities into account , and has thus much reduced Meyer 's predicted variations with they still remain twice or thrice as great as the observed changes .
Dr. S. Chapman .
The Kinetic Theory of ( 7 ) The first tion to the coefficient of thermal diffusion is where and In the case of Maxwellian molecules vanishes ( as also every approximation to it , as here , since for such a gas ) ; like the variation of with , thermal diffusion is a phenomenon which wholly disappears in this alone out of all typical ases , so that model is far from suitable physically , whatever its mathematical Thermal diffusion depends essentially on a difference of mass and structure between the molecules if and , etc. , vanishes , as the above first approximation also esCs .
The more unequal the molecules , the reater is .
Considering elastic spherical molecules , if but is very large , reduces approximately to thus nearly ) .
When both and are very ( Lorentz 's case ) ' where first , second , and third approximations to the numerical factor give , converging to nearly\mdash ; this also illustrates the degree of correction introduced on further approximations after the first , although the error of the latter is at its maximum for this specially unequal molecular pair ; the above formula is , moreover , true only so long as is not too nearly equal to 1 , since vanishes with always .
If nearly , which may be compared with the former case when , as illustrating the effect of the inequality between the molecular diameters when is very Pressure diffusion likewise depeuds on the inequality of the molecules ( of their masses only , however ) .
Thus .
The following Table illustrates the relative magnitudes of , Dp and for a few typical -pairs ( rigid elastic spherical molecules being assumed ) Simple and Composite Monatomic Ratio of ixtur .
In this connection we may also remark on the steady state of a without diffusion , under the influence of ( a ) external forces or ( b ) of a permanently maintained non-uniform temperature distribution .
In ) former case the pressure will , of course , be non-uniform .
The equations of diffusion show that a permanently non-uniform composition will thus be set up , case on the ratio or , and in ( b ) on .
Both cases are exemplified in the upper strata of the atmosphere , above the region of convection , and in a future note the effect of temperature $ radiant on atmospheric constitution will be indicated in detail ; it is less , however , than the effect of the pressure .
The influence of nonmiform temperature on composition has been verified , the proportions of two gases , found to differ in two bulbs kept at different temperatures and an open connection veen them ; a preliminary account of these experiments will appear shortly .
The magnitude of the effect is easily indicated by an example ; if and helium , or oxygen and hydrogen , are the gases , mixed in yinally equal , and the hot bulb is kept at 10 C. and the cold at C. , the heavier gttS will concentrate slightly in the cold bulb , 52 per cent. of it to per cent. of the lighter gas , instead of the original 50 per cent. to 50 per cent. , and vice vjrs at the hot bulb .
( 8 ) Viscosity JIixed Gascs .
The formulae for and in mixed gases are very complicated .
A first approximation to agrees with that given in my first memoir , but the first approximation to was there given wrongly , since , in ib , it was assumed that conduction could take place in a uniform gas without diffusion , which we have just seen to be impossible .
The correct formula is given in the second memoir here abstracted , but will not be reproduced in this place .
( 9 ) Inequality of the Temperatures of the nponent Gases .
This phenomenon has been shown to depend on , or the time rate of variation of the relative proportions of the component gases .
The following Mr. G. H. Livens .
On the example will illustrate its order of nitude .
Consider a composed initially of equal numbers of molecules which are similar to one another in mass and other dynamical properties ( since the phenomenon does not , like thermal diffusion , depend on molecular differences , this assumption may imately be made , in order to obtain a simple numerical illustration ) .
We will suppose that the gas is at normal temperature and pressure , and that the olecules are similar in mass and size to oxygen molecules , from one another in some other respects .
Then if the proportions are changing at such a rate that at the end of one second there will be 51 per cent. of one component to 49 per cent. of the other , a temperature difference of about one thousand-millionth of a degree Centigrade will be set up , the hotter gas being that which is in , ratio .
Thus equi- partition of energy is dibturbed only by a ible amount even in this rather extreme case .
On of Energy By G. H. LIVENS , The University , Sheffield .
( Communicated by Sir J. Larmor , F.R.S. Received September 19 , 1916 .
) 1 .
There still appears to be some uncertainty in the expression for the total energy of a magnetic field , and the mode of its separation into its fundam.ental constituents , as to the aether and the matter .
This is chiefly due to certain discrepancies of which exist in the results of the theory in its statical and dynamical aspects .
In the statical theory the energy is usually made to appear as though distributed over the field with the density , which corresponds to an ethereal density of amount , but in the dynamical theory the same expressions obtained with opposite signs .
In some quarters it is considered that there are difficulties of a fundamental nature involved in any attempt to remove this discrepancy , and several authors*have tried to construct a more consistent theory on a new basis .
The object of the present note is mainly to prove that it is possible to interpret the older and more usual form of the theory in a perfectly logical and consistent manner , so that the aforementioned discrepancy does not *Cf .
'Encyclopadie der mathematischen Wissenschaften , ' vol. 5 , Art .
15 , " " Electrostatik .
Magnetostatik\ldquo ; ( R. Gans ) , p. 338 , where full references are given .
|
rspa_1916_0047 | 0950-1207 | On the mechanical relations of the energy of magnetisation. | 20 | 27 | 1,916 | 93 | Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character | G. H. Livens|Sir J. Larmor, F. R. S. | article | 6.0.4 | http://dx.doi.org/10.1098/rspa.1916.0047 | en | rspa | 1,910 | 1,900 | 1,900 | 6 | 94 | 2,656 | http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1916_0047 | 10.1098/rspa.1916.0047 | null | null | null | Fluid Dynamics | 52.458044 | Tables | 26.688962 | Fluid Dynamics | [
34.50935363769531,
-35.36968994140625
] | ]\gt ; Mr. G. H. Livens .
On the example will illustrate its order of nitude .
Consider a composed initially of equal numbers of molecules which are similar to one another in mass and other dynamical properties ( since the phenomenon does not , like thermal diffusion , depend on molecular differences , this assumption may imately be made , in order to obtain a simple numerical illustration ) .
We will suppose that the gas is at normal temperature and pressure , and that the olecules are similar in mass and size to oxygen molecules , from one another in some other respects .
Then if the proportions are changing at such a rate that at the end of one second there will be 51 per cent. of one component to 49 per cent. of the other , a temperature difference of about one thousand-millionth of a degree Centigrade will be set up , the hotter gas being that which is in , ratio .
Thus equi- partition of energy is dibturbed only by a ible amount even in this rather extreme case .
On of Energy By G. H. LIVENS , The University , Sheffield .
( Communicated by Sir J. Larmor , F.R.S. Received September 19 , 1916 .
) 1 .
There still appears to be some uncertainty in the expression for the total energy of a magnetic field , and the mode of its separation into its fundam.ental constituents , as to the aether and the matter .
This is chiefly due to certain discrepancies of which exist in the results of the theory in its statical and dynamical aspects .
In the statical theory the energy is usually made to appear as though distributed over the field with the density , which corresponds to an ethereal density of amount , but in the dynamical theory the same expressions obtained with opposite signs .
In some quarters it is considered that there are difficulties of a fundamental nature involved in any attempt to remove this discrepancy , and several authors*have tried to construct a more consistent theory on a new basis .
The object of the present note is mainly to prove that it is possible to interpret the older and more usual form of the theory in a perfectly logical and consistent manner , so that the aforementioned discrepancy does not *Cf .
'Encyclopadie der mathematischen Wissenschaften , ' vol. 5 , Art .
15 , " " Electrostatik .
Magnetostatik\ldquo ; ( R. Gans ) , p. 338 , where full references are given .
lations of the Energy of even present itself .
It is shown that the whole difficulty arises partly from an unfortunate choice of ethereal vector , and partly also in the fact that the usual expression for the energy density in the statical case , although in complete agree1uent with the proper total , is not the proper expression to use in a consistent theory .
It has already been emphasised by Larmor*that the netic induction vector is by far the lnole suitable vector to use in defining conditions in the netic field of the aether .
In fact , in a strict theory , the tYnetic induction is the vector , and the netic force is an auxiliary vector derived in the process of the small molecular current whirls into their effectiye representation as a distribution of magnetic polarity .
We interpret all our results in terms of the netic induction , instead of the more usual netic force .
2 .
In the statical theory of tYnetism , the involved in the fnetic ption in any stationary field is to be considered as the potential of the sepal'ate poles of the elementary nets of which it is composed .
This is easily seen to be equivalent to a distribution of amount per unit volume at any place equal to , wherein I is the intensity of the polarisation produced at the , and is the intensity of force in the field , which in the present instance may be regarded as derived from an acyclic potential .
Of this the part , is alone concerned with the mechanical bodily forces on the netic media , of which it may be regarded as the potential function .
Tbis follows in the usual manner the principle of virtual work , which implies that the work done by such mechanical forces per unit volume in any small displacement of the body is ( IH ) , wherein , however , the internal constitution of the medium , as specified in its polarisation , is to remain unaltered during displacement , so that all the mechanical work is properly converted , and none of it off as energy of intrinsic deformation and consequently of effectively non-available character in the medium ; or it may be deduced from the fact that the linear forcive per unit volume on the medium , calcu- lated from first principles , is equal to , wherein is the usual Hamiltoni.an vector operator . .
his book Ether and Matter , ' and also the paper " " On the ynamic and Thermal Relations of the Energy of Magnetisation : Ro Soc. Proc vol. 71 , p. 229 ( 1904 ) .
The coutents of this latter paper suggested the developments sketched in the present note .
Mr. G. H. Livens .
On the Mechanical The remaining part of the total , or , represents work done by the internal elastic or motional forces } the setting up of the polarisations .
With sign changed it may be regarded as of effectively non-magnetic nature stored up in the medium on account of the polarisation induced in it .
3 .
Let us now examine the distribution of the total netic energy in the field on the supposition that it arises from a distribution of rigid magnetic polarity of density at any point .
The total energy may be calculated as the mechanical work done in building up the rigid magnetism radually in the presence of the isable substances , the induced magnetism simultaneously taking its appropriate value at any of the process .
Suppose that at any instant tlJe intensity of force at the typical field point is , then the work supplied by external systems in bringing up additional small } lent of polarity to each place the field is clearly equal to , the being taken throughout the field .
Now by definition of , where I is now reserved for the intensity of the induced polarity , so that Thus the total work done in establishing the field may be written in the form But if there are no sudden discontinuities in the field , and any such be treated as continuous rapid transitions , it is easy to prove*that ( S ) These follow in the usual way because the induction vector is always circuital , and the force vector in the present case is derived from an acyclic potential .
Thus the expression for the total in the field reduces to - .
*Cf .
Jeans , ' Electricity and Magnetism ' ( 1st Ed p. 387 .
Rdations of the Energy of Magnetisation .
The second integral in this last expression represents the internal elastic or motional energy stored up in the magnetic media on account of the polarity induced in them .
The first integral therefore represents the true netic potential energy of the system , and on a tentative theory could now be regarded as distributed hout the field with a density at any place .
Of this latter part of the energy the term in the polarisation represenvs of a purely local or intrinsic nature in the magnetic lnedia , whilst the other term represents the part of the that must be associated with the field in the aether .
4 .
Of the true potential in the field , - the part corresponds to the polarisations induced in the metic media .
It is concerned mainly with the fnetic attractions , or their equivalent mechanical forces , exerted by the field on the polarised media as a whole , of which it may be regarded as the potential function .
The remainder , or - , corresponds to the polarisation and is , in fact , the potential function of the mechanical reactions on the permanent uets vivino Since , this part may be written in the form , which , since in very stage of the process reduces to in reement with the result of S2 . .
When the induction follows a linear isotropic law , so that Mr. G. H. Livens .
On the we have and therefore and In this case the stored in the onetic media on account of the induced polarisation is whilst the of truly etic nature in the field is equal to the ralo of The total associated with the system is therefore sinlply equal to dv , and it may be as distributed the field with density if the constant local part in is omitted , as it would be mechanical theory .
At points of the field where there is no neGism this density is the same as , which is the expression usually derived , but the opposite .
The difference of arises from the fact that in the usual interpretation of these relations an expression is adopted for density which fers from that just deduced by zero total on the whole .
We next turn to the consideration of the circumstances in the more eneral type of magnetic field when there are linear colldlction currents as well as permanent nets and netisable media .
The work required in order to increase the typical current in one of conductors by the infinitesimal mount is in electroma ( fnetic units ; denotes the number of unit ) of induction which thread the circuit of J. Thus the totRl supplied by the batteries in starting the currents is where denotes a sum relative to the various linear currents and in the last expression the surface ralb for each circuit is taken .
a barrier surface usnal i , s derivable from a potential cy clic with respe the tiltiCe this proved by the usIlal .
to be to the vohlme integral taken the field .
inchde for generality hont Ihe field of intensity any } ) oint , and if current Hystem , additional nnonnt of } ' the internal the syenl Io .
Thus the total ) ) energy ) up in the telll is But if there are ) substances in the field , and if at any stage of the ) uilding up the system the intensity of the induced polarity is I , then It is then easy to prove that the total energy of the can be expressed in the fornl - .
The last term represents the increase in the intrinsic .
of the induced polarisations in the field and the first the increase of the purely tYnetic energy .
This latter part may be as distribu(ed through the field with the density at any point .
These results are identical with deduced case in S3 .
In the case when the netisation f ) a linear isotropic law the expression for the total in the field again reduces the simple expresses it as a with density at place , just as in the previous case .
7 .
Of the total purely ( tnetic nature stored ) in fiel of amount VOL. XCIII .
is ( '( JnRi n the rrents and in fact , ] tial function ( thi and of the of the magnets then .
A similar } nsforIJlation , } of that ) plied in S6 , S00YI shows that ] ) is to lf thele is ) about this is the oliy of total in the lield that is mechanically available .
Of rest of the ener( the part similarly concerlled with the rigidly netised masses , being , in fact , the force function of their mechanical interactions and the interactions of the held with them .
The remainder , 01 , is concel.ned in a way with the induced 8 .
we tate that in a general thatio of the energy netic field complete consistency is obtained by fnetic induction instead of the force as mdamental vector the theory .
This arises partly on of the main characteristic properties of that vector and artly from the fact that the total energy in the field be expl.essed in a form which exhibits it as consisting of the intrinsic the ) polarisations ether with an amount equivalent to a distribution with density differing from by the purely local term .
This latter part can only represent energy of a purely local or acter and in mechanical theory would be omitted entirely .
Moreover in tion , the total energy in the lield when the induction ollows a linear law is expressible in the form which is consistent with the value for the den ) in Irse there ( .
It is , haps , sary to emphasise the , throughout the preseut energy is treated as potential energy .
If it is desired , treat it etic e must be reversed .
In On the Relations of the Energy of .
27 dynamics it is the Lagrangian function that determines everything , so that , if a part of the energy is reckoned as kinetic energy , it has the opposite sig to what it would have if reckoned as potential energy .
The failure to recognise this difference in the two types of energy in the present instance appears to be the cause of much of the confusion in the subject .
The usual treatment of the relations of the magnetic field gives the same to a quantity which in the statical case is treated as potential energy and in the dynamical case as kinetic , and this apparent agreement of sign appears to satisfy most authors , so that the real discrepancy has rarely been noticed .
The present mode of treatment has actually been suggested by Cohn , * but he rejects it as unsatisfacto ) because it leads to opposite for kinetic and potential energies .
In another place Jeans comes up against the opposite , but reconciles them by finding that one of the expressions compared is incomplete by an amount which makes the signs the same .
On Phenomena relating to the Spectra of Hydrogen and Helium .
By T. B. MERTON , D.Sc .
, and .
J. W. NICHOLSON , M.A. , D.Sc .
( Communicated by A. Fowler , F.R.S. Received June 16 , 1916 .
) ( Abstract .
) In a previous paper the structure of broadened spectrum lines was investigated by a method involving the use of a neutral-tinted wedge as an accessory to the spectroscope .
The present communication deals with a method for the accurate determination of the raphic intensities of spectrum lines and the reduction of such intensities to absolute values by comparison with the continuous black-body radiation of the carbon arc .
These methods have been applied to a study of the relative intensity distribution in the spectra of helium and hydrogen under different conditions of excitation .
It has been found that under certain specified conditions tltere is a transfer of energy from the longer to the shorter wave-lengths in any given series , and that , under such conditions , the associated series , and in particular the Diffuse series , are relatively enhanced at the expense of the Principal series .
'Das Electromagnetische , ' p. 300 .
' Electricity and Magnetism , ' p. 432 .
VOL. XCIIL\mdash ; A.
|
rspa_1916_0048 | 0950-1207 | On phenomena relating to the spectra of hydrogen and helium. | 27 | 28 | 1,916 | 93 | Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character | T. R. Merton, D. Sc.|Prof. J. W. Nicholson, M. A., D. Sc.|A. Fowler, F. R. S. | abstract | 6.0.4 | http://dx.doi.org/10.1098/rspa.1916.0048 | en | rspa | 1,910 | 1,900 | 1,900 | 2 | 29 | 841 | http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1916_0048 | 10.1098/rspa.1916.0048 | null | null | null | Atomic Physics | 39.41375 | Formulae | 31.969263 | Atomic Physics | [
33.381160736083984,
-35.9921760559082
] | On the Mechanical Relations of the Energy of Magnetisation .
27 general dynamics it is the Lagrangian function L = T\#151 ; W that determines everything , so that , if a part of the energy is reckoned as kinetic energy , it has the opposite sign to what it would have if reckoned as potential energy .
The failure to recognise this difference in the two types of energy in the present instance appears to be the cause of much of the confusion in the subject .
The usual treatment of the energy relations of the magnetic field gives the same sign to a quantity which in the statical case is treated as potential energy and in the dynamical case as kinetic energy , and this apparent agreement of sign appears to satisfy most authors , so that the real discrepancy has rarely been noticed .
The present mode of treatment has actually been suggested by Cohn* but he rejects it as unsatisfactory , because it leads to opposite signs for kinetic and potential energies .
In another place Jeansj* comes up against the opposite signs , but reconciles them by finding that one of the expressions compared is incomplete by an amount which makes the signs the same .
On Phenomena relating to the Spectra of Hydrogen and Helium .
By T. R. Merton , D.Sc .
, and Prof. J. W. Nicholson , M.A. , D.Sc .
( Communicated by A. Fowler , F.R.S. Received June 16 , 1916 .
) ( Abstract .
) In a previous paper the structure of broadened spectrum lines was investigated by a method involving the use of a neutral-tinted wedge as an accessory to the spectroscope .
The present communication deals with a method for the accurate determination of the photographic intensities of spectrum lines and the reduction of such intensities to absolute values by comparison with the continuous black-body radiation of the carbon arc .
These methods have been applied to a study of the relative intensity distribution in the spectra of helium and hydrogen under different conditions of excitation .
It has been found that under certain specified conditions there is a transfer of energy from the longer to the shorter wave-lengths in any given series , and that , under such conditions , the associated series , and in particular the Diffuse series , are relatively enhanced at the expense of the Principal series .
* ' Das Electromagnetische , ' p. 300 .
+ ' Electricity and Magnetism , ' p. 432 .
VOL. XCIII.\#151 ; A. E Prof. W. H. Young .
It has also been found that the distribution of intensity found in certain celestial spectra can be approximately reproduced in the laboratory .
In any attempt to interpret the phenomena observed in connection with the Balmer series of hydrogen , it is necessary to know the particular type to which this series belongs .
In order to decide this point a study has been made of the separations of the components of lines of the Balmer series of hydrogen , and the mean values of the separations of the doublets constituting the lines Ha and Hp have been found to be respectively 0*132 A.U. and 0*033 A.U. These values are consistent with the separations appropriate to a Principal series , and the first is in precise agreement with the value deduced by Buisson and Fabry .
These results have been obtained by crossing a Lummer Gehrcke plate with the neutral wedge , and submitting the contours obtained to mathematical analysis , by means of which the distribution of intensity in the individual components , and the separation of the components , can be determined .
On Multiple Integrals .
By Prof. W. H. Young , Sc. D. , F.R.S. ( Received July 16 , 1916 .
) S 1 .
In the modern theory of absolutely convergent integrals , as distinct from the older Riemann theory , the difference between multiple and repeated integration falls to the ground .
Every multiple integral is equal to the corresponding repeated integrals , and the formulae involving such multiple integrals , even when expressed without the repeated integral notation , can be obtained by means of the repeated integration process .
To really grasp the distinction* between multiple and repeated integrals we have to take as independent variables functions of bounded variation ; more precisely , we have to replace the ensemble of variables { x , , ... ) by a single function of bounded variation , which , indeed , takes the place of the product of the variables xyz ... , the more general integration reducing to the ordinary when this product replaces the function in question .
I have already had occasion elsewhere to explain what is meant by a function of bounded variation of any number of variables , and to define * In the French language there is said to be , as yet , no word expressing this distinction .
|
rspa_1917_0001 | 0950-1207 | On multiple integrals. | 28 | 41 | 1,917 | 93 | Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character | Prof. W. H. Young, Sc. D., F. R. S. | article | 6.0.4 | http://dx.doi.org/10.1098/rspa.1917.0001 | en | rspa | 1,910 | 1,900 | 1,900 | 15 | 178 | 4,925 | http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1917_0001 | 10.1098/rspa.1917.0001 | null | null | null | Formulae | 78.593846 | Tables | 18.375335 | Mathematics | [
69.13438415527344,
-47.103126525878906
] | ]\gt ; Prof. W. H. Young .
It has also been found that the distribution of intensity found in certain celestial spectra can be approximately reproduced in the laboratory .
In any attempt to interpret the phenomena observed in connection with the series of hydrogerl , it is necessary to know the particular type to which this series belongs .
In order to decide this point a study has been made of the separations of the components of lines of the Balmer series of hydrogen , and the luean values of the } ) arations of the doublets ituting the lines and have been found to be respectively .
and .
These values are consistent with the separations appropriate to a Principal series , and the first is in precise agreement with the value deduced by Buisson and Fabry .
These results have been obtained by a Lummer Gehrcke plate with the neutral wedge , and submitting the contours obtained to mathematical analysis , by means of which the distribution of intensity in the individtlal components , and the separation of the components , can be determined .
On ultiple Integrats .
By Prof. W. H. YOUNG , Sc. D. , F.R.S. ( Received July 16 , 1916 .
) S1 .
In the modern theory of absolutely convergent integrals , as distinct from the older Riemann theory , the difference between multiple and repeated integration falls to the ground .
Every multiple integral is equal to the corresponding repeated integraIs , and the formulae , such multiple integrals , even when expressed without the repeated integral notation , can be obtained by means of the repeated ration process .
To really grasp the distinction*between multiple and epeated integrals we have to take as independent variables functions of bounded variation ; more precisely , we have to replace the ensemble of variables by a single function of bounded variation , which , indeed , takes the place of the product of the variables , the more general integration reducing to the ordinary when this product replaces the function in question .
I have already had occasion elsewhere to explain what is meant by a function of bounded variation of any number of variables , and to define * In the French language there is said to be , as yet , no word expressing this distinction .
On fultiple Integrals .
integration of any bounded function , and absolutely convergent integration of unbounded functions , with regard to such functions of bounded variation It will be sufficient here to call special attention to the fact that a function of bounded variation , for simplicity , let us say , of two variables , and , is expressible , to a value of the function pres , as the difference of two functions , which are monotone increasing in \ldquo ; in , and in , representing the positive and negative variations in the plane , increased by the differences of the variations along the axis of and along the axis of respectively .
There is , in consequence of the definition , a unique limit at each point for each of the four standard modes of approach , these four limits coinciding , except at points on a countable set of lines parallel to the axes at most .
The modes of approach here considered correspond to the four quadrants when the point is the origin , the lines corresponding and parallel to the axes being excluded .
The limits along these excluded lines may be different from one another and from the other four .
* Such functions , then , cannot in general be double integrals of ordinary functions of two variables , even if they are continuous .
The simplest case , one which constantly occurs in practice , is that in which the functions are not integrals , .
solely because they are not continuous .
This is the case , for instance , with the sum-function of the double Fourier series whose general term is , which is discontinuous at the origin and along the axes , and is the simplest type of double integral elsewhere .
The step taken in extending the theory of integration to that in which the ordinary variables are replaced by one or more functions of bounded variation , is for this very reason a matter to which no one who has occasion to use mathematical analysis can be indifferent , though he may be quite unaware of the existence of continuous functions of bounded variation which are not integrals .
The original idea of introducing integration with respect to a monotone function of a single independent variable is due to Stieltjes , and was employed by him exclusively in the case of continuous integrands .
Indeed , his definition fails in general with a less restricted hypothesis .
On the other hand , has given a definition depending on change of the independent variable , for integration of any bounded function with respect to a continuous function of bounded variation .
In my own theory , in which the treatment runs precisely parallel to that I have employed when the variable itself is the integrator ( that is , the function with respect to which we integrate ) , the integrand and integrator are both perfectly general , the latter being any function of * This could only be at the exceptional points already mentioned .
's method fails when there are more independent variables than one .
Prof. W. H. Young .
bounded variation , not necessarily continuous , and the former any bou'nded or unbounded function to which the process is applicable .
In the case in which the integrator is an absolutely convergent integral , we iain ordinary integrals , and I have utilised this fact on more than one occasion to obtain new theorems in ordinary integration .
In a recent paper , I have thus obtained eneralisation for any number of bless of the second theorem of the mean in Bonnet 's and other forms , as well as the formula for integration by parts in its most general form .
In such applications , certain fundamental theorems connecting ordinary integration with the more general type I have here in mind , are necessary .
Moreover , in the development of the new theory itself , a new type of theorem is required .
Whereas absolutely conyergent multiple integration with respect to the product is always expressible in the form of a repeated integral , this in general to be the case when the integrator is no expressible as the product of factors , each involving a single variable only .
It becomes important , therefore , to formulate tolerably wide conditions under which such a reduction of difficulty is possible .
In the present communication to the Society , I propose to give a brief account of some of the formula , which , from these two different , but closely allied points of view , are fundamental .
I by explicitly stating certain facts on which the theory of integration with respect to a function of bounded variation in two or more variables is based .
I have not introduced any discussion of integration with respect to a continuous function which is not of bounded variation .
Many of the formulae might be deduced from those of the present paper in the case when the rand is a function of bounded variation , but it seems advisable to reserve the discussion of this subject for a separate communication .
I have also it unnecessary to give the formulae for functions of more variables than two .
S2 .
The function with respect to which we integrate is supposed to be any function of bounded variation with respect to .
Every such function is , however , expressible in the form , where is the sum of the positive variations of with respect to respectively , each taken rectangle , the last two variations being taken along the axes of and , and being similarly defined for the ative variations .
On Multiple Integrats .
the definition it follows at once that only and , the positive variation and negative variation , taken , with respect to , contribute anything to the double integral with respect to , so thaC g is virtually expressible as ) difference of and , that is the difference of two functions , each of which is monotone with respect to , to and to It will be conyenient , therefore , to avoid repetition , to suppose that in the enunciation of our theorems , the function with respect to which we integrate ( integrator ) is itself such a function ( monotonely monotone increasing function ) .
It is clear from what has been said that there be no loss of generality in adopting such a course , except in cases where some additional special hypothesis is made with pect to the rator , which does not ipso facto hold for the functions of hich g is in the difference .
The condition that y ) is monotonely increasing with respect to is expressed as follows:\mdash ; , ( 1 ) and may be expressed in words by saying that the plane increment round an .
rectangle whose sides are parallel to the axes is positive , or more precisely by saying that monotone creasj with respcct to eith(of tlnj variables has ) increasing as the other varinble From these properties it follows that has a unique limit as we approach any particular point from one side or the other along the axes , or in any manner in each of the completely open quadrants .
Denoting the former four limits by , beginning with the horizontal hand axis , and proceeding round clockwise , and the latter four by beginning with the first , or -quadrant and proceeding clockwise , we have the inequalities ; ?
Hence also , that lies 'oetween and or ?
and , we can show that is continuous uith respect to , except possibly at point .
lying on a countable set of parallels to the axes of S3 .
The last result enables us to prove , as in the theory of functions of a single real variable , mutandis , that any simple or -function of can be expressed as the limit of a monotone sequence of simple or W. H. Young , " " Integration with Respect to a Function of Bounded Variation ' Loud .
Math. Soc. Proc Ser. 2 , vol. 13 , p. 139 ( 1913 ) .
Prof. W. H. Young .
-functions*none of whose discontinuities coincide with discontinuities of .
We have accordingly , as in the original theory , three methods of starting : ( 1 ) By the integral of general simple or -fnnction .
This will not be used in the present note .
( 2 ) By defining of sp jcial simple and -functions , whose continuiti arnot of .
The formula is that is where the fundamental rectangle is supposed divided up by lines parallel to the axes , the feet of which on the , -axis have abscissae , and on the -axis the ordinates in any convenient way such that all the discontinuities of lie on the dividing lines , none of which coincide with any of the set of lines parallel to the axes on which the discontinuities of y ) lie ; then denotes the constant value of in the interior of the rectangle whose left-hand bottom corner is , and is the value of y ) at ( 3 ) By defining of continuous functions .
The formula is Lt , where is any convenient point in the rectangle whose left-hand bottom corner is , and the rest of the notation has been already explained .
It may be shown that the rals we obtain are the same , whichever of the three methods we adopt .
The definition of the integral of a function which is the limit of a monotone sequence of functions whose yrals have been previously defined is ) it is the limit of the of functions the sequence .
validity of such a definitio1l follows as in one dimension , and we have , as in one-dimensional theory , the theorem that the is at the same time the lower bound of the ralsb of -functions greater than and the upper boun of the of -functions less than .
S4 .
We can now prove certain formulae for our double integrals with respect to .
The method of proof will in eneral consist in proving the * Such functions are constant in the interior of a finite number of rectangles into which the region of integration is divided by lines parallel to the axis .
On Multiple formulae from first principles for one or other of our two statldard forms ( 2 ) and ( 3 ) of the article , and then deducing the result by the method of monotone sequences , either by using generalised induction , or by deducing the truth of the formula for l- and -functions and applying the theorem mentioned at the conclusion of the preceding article .
We begin by establishing the following extremely important result:\mdash ; THEOREM.\mdash ; If is am absolutely convergent integral respect to ) , then , ( 4 ) anyJunctio of which is the , far function equal to the repeated differmtial coefficient of .
, wherever this differential coefficicnt , and equal to zero elsewhere .
Since the rectangle is the sum of the rectangles and minus the sum of the and , it follows that If then is a constant , say , the left-hand side of ( 4 ) is by definition equal to while the right-hand side , , has as has just been pointed out , the same value .
Thus the formula is true when is a constant .
Again , if is a simple or ?
-function of the special type , its integral with respect to , is the sum of the finite number of terms , by the formula ( 2 ) , each of which is the of a constant , and therefore , by what has been proved , is equal to the ordinary integral of that constant multiplied by over the corresponding rectangle .
all these terms , the equation ( 4 ) follows in this case .
But if the equation ( 4 ) holds for each of the members . .
of a monotone sequence , it holds for their function , since by definition limit , and is the limit of by a known theorem .
It follows , therefore , that the theorem is simple and -functions , as the limits of monotone sequences of these special functions , * See a forthcoming paper by the author .
Prof. W. H. Young .
is therefore true for general and -functions , as the limits of monOtone sequences of simple and -functions .
Hence eneralised induction the theorem is true for all functions which can be obtained as the limits of monotone sequences of functions , with simple and -functions .
This proves the truth of the formula ( 4 ) .
Similarly we may prove the more general theorem : \mdash ; If is integral of with respect to , is of of bounded variation , have .
( 5 ) We have in fact only to start from the identity and the argument is otherwise the same as before .
This eneral theorem , which I have not hitherto stated , even for functions of a single variable , is of very great use in practice , as it enables us to make in a very simple manner certain transformations in our integrals , which would otherwise scarcely occur to the worker .
S5 .
\mdash ; If th integrand is of one of the variables , the integration reduces to integration )respect to a .function of the other , in with the formula .
( 6 ) To prove this , let be a continuous function .
We then have , by Thus the formula is verified in the case considered .
Since , therefore , -hand and -hand sides continually eproduce themselves , when we let describe monotone ences , first of continuous functions , then of and -functions , which are the limits of such sequences , and so on , it follows that the formula holds all functions mathematically definable .
This proves the formula , using generalised induction .
If , however , we prefer to use the theorem alluded to at the end of S3 , we only use the above method to prove the ] for and ?
-functions , and then remark that is the upper bound of the rals of On JIuttiple Integrals .
-functions less than , and ( dg , being the integral of with respect to , is the upper bound of the integrals of the functions with respect to the same function ; since the formula ( 4 ) holds for in place of ( it ) , it therefore holds as it stands .
This proves the formula also .
Thus by either method the formula is verified by monotone sequences .
S6 .
.\mdash ; If the rrator g , the result integration with ?
to this given by following ( 5 ) provided only , , t ) poss)integral nith to Suppose first that ) a simple or ?
-function of the special type , whose discontinuities are different from any of those of .
Then , by , we have by ( 2 ) , , since is easily seen to be a simple function of the special type as .
This proves the formula in this case .
But if , f2 , , are functions forming a monotone sequence with as limit , we may integrate this sequence term-by-term with respect to the function J , so that And also similarly .
Denoting the function of represented by either side of the last equation by , and the function whose limit is taken on the right by , It is convenient here elsewhere to suppose positive in the proof .
; is no restriction , as we may always break up into the difference of two such functions .
Prof. W. H. Young .
increases or decreases with , according as does so , and therefore also describes a monotone sequence with as limit .
Therefore , as before , we may integrate term-by-term and write Now , supposing the equation ( 5 ) to hold for each of the functions , we have , with our present notat , ion , .
Proceeding to the limit with , and the results just obtained , we get therefore , which is identical with ( 5 ) .
If therefore the equation ( 5 ) holds for all the members of any monotone sequence of functions , it holds for the limiting function .
Thus , as before , the theorem is true , since it has been shown to hold for simple and -functions of special type .
\mdash ; If thw integramd contains ameter t to inside th , that is The proof of this theorem is the same as that in the ordinary theory of absolutely convergent integrals .
S7 .
We have already given in S5 the simplest case in which integration with respect to a function of bounded variation reduces to ordinary integration .
We prove the following further theorems:\mdash ; \mdash ; If is ( int respect to , then ( 6 ) where is any one of the derivates of , Jp ) with respect to .
In fact , denoting by the function which is equal to the differential coefficient with respect to of wherever this exists and is finite , and is zero , or has any other convenient values , at the remaining set of values of of content zero , we have .
*Absolutely convergent , or Lebesgue , integral .
On Multiple Integrals .
Now by the formula ( 4 ) , ' , and But change of order of integration is allowable on each side of the last equation* ; thus which may be written .
Using the expression already given for the integral of ?
this gives , which is identical with the formula to be proved .
In the theorem just proved the integration is reduced to lepeated integration first with respect to a function of bounded variation of one variable , and then with respect to the other .
From which cret THEOREM.\mdash ; If an o.ntegral lrith respect to and is integral with respect to a of bound omrifh .
resp to , then Here we have been able to go still farther all the tions employed are ordinary .
Again , without any assumption as to integrator , we can reduce to ordinary integration when the iegrand is a double integral .
The theorem , which is an immediate consequence of ( 4 ) when the formula for integration by parts for multiple integrals is employed , is as follows:\mdash ; ' ' Integration with respect to a Function of Bcunded Variation S32 , p. 148 .
Prof. W. H. Young .
TtlEOREM.\mdash ; If a double integral with respect to , then ' .
( 8 ) This theorem also from ( 6 ) by the formula for integration by parts for integration of fnnctions of a single variable .
S8 .
We shall now find it convenient to prove the following property of our rator g .
This is that the derivat of with respect to either are monotone asc ending ctions of the other variable .
In fact the relation ( 1 ) jves Let describe such a sequence of positive values with zero as limit that the right-hand side approaches its upper limit , the upper hand derivate of with respect to , say .
Then the left-hand approaches some limit or limits which are not greater than .
Thus .
imilarly , the sequence of values of so the left-hand side approaches its lower limit , the lower right-hand deriyate of with respect to , we .
This shows that both the hand derivates with respect to are monotone ascending functions of Similarly , taking positive and negative , in which case the symbol must , of course , be changed to in order that the plane increment may with the right-hand top corner , and proceed clockwise , we find that both the left-hand derivates of with respect to are monotone functions of By symmetry the sftme result holds when and are .
This .
therefore , proves the required result .
S9 .
If , in addition to having the property of being what we have called a monoto of , ( S2 ) , is an integral with respect , it is the integral of any one of its derivates with respect to .
These derivates agree and are finite except at a set of content zero of values of.r .
for of and , therefore , and are finite except at a set of values of of plane content zero .
Hence they ) and are finite except at a set of content zero of values of for jach fixed value of not to a certain set of content of values of .
Putting aside this exceptional On Muttiple lntegrals .
set of values of , therefore , it follows from S8 that , being con stant , exists and is finite except at a set of content zero of values of , and the values at the exceptional points be so that becomcs ascending function , defined for all values of With understanding therefore we may , when is an integral with respect to , not only write , but also we may rate a function with respect to being constant , and then rate the result with respect to , the exceptional set of content zero of values of ' at which the inside integral is undefined not the second ration .
With this understanding , we have the following theorem on the reduction to a repeated integral:\mdash ; \mdash ; If a monotonely monotone ascending function of and an ral with respect to , and therefore an integral with respect to of a monotone ncreasing function of ?
, we ' .
( 7 ) If is a constant , say , the theorem is at once seen to be true , for , by definition , the left-hand side of the equation is , and the -hand side is same , since , performing the inside integration , we get , writing for Hence , by the formula ( 2 ) , the theorem holds when is a simple l- or -function of the special type , for the integral is then a double summation of a finite number of such integrals with constant ) .
But any simple l-or -functions can be expressed as the limit of a monotone sequence of simple function of the special types just con- templated , say , , and we may integrate this sequence -by-term either with respect to , or first with respect to , being constant , and then with respect to Thus and also .
* This mode of regarding the matter is sufficient for the purpose of justifying the notation in equation 7 ) .
For fuller information with regard to the delivntes and repeated derivates of functions of bounded variation , see the forthcoming ) referred to in S4 .
Prof. W. H. Young .
But , by what we have already proved , .
From these three relations the required relation immediately follows .
Similarly , it now follows generally for any and ?
-functions , these being the limits of monotone nces of simple and -functions .
this the heorem generally by geDeralised induction , or , if prefer , as follows : the left-hand side of ( 7 ) is the upper bound of , where \ldquo ; y ) is any -function less than ; and the right-hand side of ( 7 ) is the integral with respect to of the upper bound of , which is the same as the upper bound of , so that integrating , with respect , and taking the bound , the upper of .
But we can find a for which J differs by as little as we please from , so that integrating with respect to and taking the upper bound , we see that the upper bound of , where is as small as we please .
From this the truth of the statement made at once follows .
But by what has been proved , so that the upper bounds of the two sides of this equation are also equal .
This gives us the equation ( 7 ) , and proves the theorem .
S 10 .
From the theorem of the article , we at once deduce the following : THEOREM.\mdash ; If is notoncly rtotone jnding function , an integral with respect to therefore an integral with respect to of a onotone increasing of , we hare , ( S ) provided the right-h side continuous On Multiple Integrals .
S 11 .
When the integrator , instead of the integrand , describes a sequence , the mere monotony of the sequence is not enough to ensure that the limiting process is allowable , that is , that the integral with respect to the limit is the same as the limit of the integral .
In this connection the theorem is of importance:\mdash ; THEOREM.\mdash ; If a function of , with respect to , to ?
1 , and to , and its triple ) of ' it is uith respect to , then .
( 9 ) From the hypothesis in the enunciation it follows that , is monotonely monotone increasing with resl ) to , supposing the triple increment of to be ) ositive .
For the function here considered is the limit , as positive values , of % ; , which is monotonely monotone increasing with respect to ) .
Hence if is a bounded function of , and is numerically and hence has the unique limit zero as .
This proves the theorem when is bounded .
When is not bounded , we denote by the fmlction which is equal to , where this is less than , and is elsewhere equal to as usual taken to be positive ) .
Making then .
, we see , by monotone sequences , that the theorem is true .
As a particular case of the theorem just proved , we have the THEOREM.is a'monotonely increasing of , and has , ( as limit , and generates such lonotone inrre decreasing sequence that reases , decreases , with ( 10 ) * This theorem may be utilised , among other wayS , in extending the theorem of Integration by Parts .
|
rspa_1917_0002 | 0950-1207 | On the order of magnitude of the coefficients of a fourier series. | 42 | 55 | 1,917 | 93 | Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character | Prof. W. H. Young, Sc. D., F. R. S. | article | 6.0.4 | http://dx.doi.org/10.1098/rspa.1917.0002 | en | rspa | 1,910 | 1,900 | 1,900 | 14 | 147 | 4,254 | http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1917_0002 | 10.1098/rspa.1917.0002 | null | null | null | Formulae | 78.69127 | Tables | 19.407314 | Mathematics | [
70.21690368652344,
-47.49193572998047
] | ]\gt ; On the Order of gnitude of the Coefficienls of a Fourier Series .
By Prof. W. H. YOUNG , Sc. D. , F.R.S. ( Received August 9 , 1916 .
) S1 .
Riemann 's theorem that the coefficients of a Fourier series converge to zero was shown by Lebesgne to still hold when integration is understood to be in the general sense now employed , absolutely convergent , or Lebesgue integration .
Little progress has , however , been made in the determination of the order of magnitude of the coefficients .
It has , indeed , been proved that , when the function has bounded variation , and are bounded functions of , and that , when the function is a continuous function of such a type as satisfies a condition of Lipschitz , and converge to zero , where is a positive number not greater than unity , depending on the particular Lipschitz condition satisfied by the function .
As regards the second of these results , involving the satisfying of a condition of Lipschitz , it is to be remarked that , in well-known series of the type and the functions of which they are the Fourier series do not , in any interfal containing the , satisfy any condition of Lipschitz , being , indeed , unbounded .
In the present communication I obtain a number of theorems corresponding to each of these two results , including them as particular cpses , and , at the same time , leading to the known properties of the simple sine and cosine series above referred to .
It will be remarked that the conditions supposed to hold in the neighbourhood of the origin and the remaining part of the interval of periodicity are different ; this .
is inevitable , if they are to be as wide as possible .
It might be , perhaps , supposed a priori that conditions of a far more general type would be adequate ; this is not , however , the case .
It is still more unusual for and to converge than it is for the Fourier series to converge .
Indeed , if the Fourier series converges at the origin , and converges to zero , the Fourier series must do more than ordinarily converge , it must converge to a Cesaro order of ative unity .
A similar statement holds good of the convergence of .
and when multiplied by a function of of lower order of magnitude than .
There is , however , H. Lebesgue , " " Sir la representation trigonometrique approchee des fonctions satisfaisant a un condition de Lipschitz 'Bull .
de la Soc. Math. de France , ' pp. .
of of the Coefficients of a Fourier Series .
43 theory of Ce convorgence of sucoessions to that for series , where consider instead of the convergence of , the arithmetical integral , or fractional , means of these quantities .
When this is done , more general results are possible .
For example , if the Cesaro is of a type greater than or equal to unity , only the nature of the function in a small neighbourhood of the origin matters , equally when we consider convergence or oscillation .
We can , however , no longer , in employing this theory , speak of the results obtained as referring to the order of magnitude of the coefficients of a Fourier series .
I propose , however , as they have an important application in the theory of Fourier series , to consider these questions on a subsequent occasion For simplicity of expression , the theorems have been stated for functions which are either odd or even .
It is hardly necessary point out that the results are perfectly general ; when is itself odd or even , is the even , and the odd , function which takes the place of in the theorems , and being then the coefficients of and in the Fourier series of S2 .
For completeness the theorem about to be given and the following one are stated generally , though information as to the older of the coefficients and is only given by the latter half of each .
* IBORBN \mdash ; If be the typical coeffic of the of functi of variation , then when convergence taken in the Cesaro manner , of any positive type wh ever ; moreover , convergence ordinary convergence if the funetion be an integral in every interval not containing the origin .
Let be the function in question , then Case 1 .
Let be an integral in every interval not containing the origin ; then by the Theorem of Rienlann-Lebesgue the first term of the expression just written down approaches zero .
* It should be remarked that the second half of Theorem 1 , if we assume the known properties of a function of bounded variation , reduces to the theorem which I have that of Riemann-Lebesgue .
It is inserted to preserve the parallelism between the Fourier series and its allied series .
The whole of Theorem 2 breaks new ground .
XCIIL\mdash ; A Prof. W. H. Young .
On the Order of Case 2 .
If be not such an integral , then the first term appro.aghe@ zero , when the convergence is taken in the CesAro manner , Witb any positive index , as is easily seen , does not do so in the ordinary manner .
In either case we reduce to the consideration of the second term .
This is numerically ; and therefore is as small as we please , if is continuous at the Bul even if is discontinuous at the origin , such a discontinuity could not affect this fact , since is zero at the origin .
Therefore in all cases the second term in our expression approaches zero , which proves the theorem .
THEOREM \mdash ; If be the typical coefficient of the Fourier series of an odd function of bounded variation , tlven ( jump at the in ) , the convergenoe is takoen in the Cesaro manner , of any positive type what ; moreover , the convergence is ordinary convergence if the totion be an infegral in every interval not containing the origin .
Let be the odd function of bounded variation .
Its Fourier series is unaffected by the values of at the origin and the extremities and and we may therefore with advantage suppose the value of at these points to be that given by summing the Fourier series of , namely zero , so that We then have , if be the typical Fourier coefficient of .
Case 1 .
Let be an integral in every interval not containing the origin ; then the first term iu the expression just obtained approaches zero as by the Theorem of Riemann-Lebesgue .
* In fact 2 oscillates boundedly for , and therefore boundedly when .
It follows that , if summed in the Cesaro manner , index .
This boundul sequence can by a known theorem be then integrated with respect term-by-tenm .
of the of a Fourier Series .
not be suoh an integral , then the first term approaches zero , as , provided the convergence be taken in any Cesaxo manner , index Thus only the second term needs consideration .
But this differs from by a quantity which is nuinerically ) where V ( x ) is the total variation of , by a quantity which is as small as we please , being chosen sufficiently small .
Thus ( jump at the origin ) , the convergence being in the Cesaro or ordinary manner , according as we have to do with Case 1 or Case 2 .
This proves the theorem .
S4 .
The former of the two preceding theorems enables us to prove immediately that the derived series of the Fourier series of a function of bounded variation converges ; more generally it converges with any negative Cesaro type on the positive side of .
The latter of our theorems gives us the corresponding theorem for the convergence of the allied series , involving the usual further condition .
The two theorems also show that , when is an integral in every interval not containing the origin , the convergence is ) .
In the second half of Theorems 1 and we may , both in the enunciation and in the proof , avoid the concept of function of bounded variation changing the condition that the function should have bounded variation into what is in our case the equivalent condition that the differeutial coefficient of the function should possess an absolutely convergent integral .
We divide the interval at the point .
We then have sin , for points of the completely open interval being by hypothesis an integral .
Indeed the right-hand side having by hypothesis a unique finite limit when , the same is true of the left- *This follows from the fact that ri oscillates boundedly for , and the rest of the algument is same as for Theorem 1 .
See a forthcoming paper by the author .
Cesaro summability of negative integral indices has apparently been regarded as offering difficulties of at least an inconvenient character .
In the theory of Fourier series this concept seems to me to be as indisas that of convergence .
far as they relate to ordinary convergence of Prof W. H. YOUDg .
On the Order of hand side , thus exists and is finite .
Also by the same equation approaches this limit boundedly , since the right-hand side is numericaUy Again where the last is numerically which is as small as we being chosen conveniently small .
Hence , as before , the required results at once follow .
S5 .
In the next two theorems the assumptions made render an absolutely convergent in every interval not containing the The following simple lemma is used in the proofs .
LEMMA.\mdash ; If is an absolutely convergent integral in the interval ( ) oos prow.ded in tloe latter case , e.g. , if is an odd function represented Fourier series .
We have in fact only to integrate by parts , and use the Tlieorem of , by which has the limit zero .
We now have the following theorem:\mdash ; THEOREM \mdash ; If is even function , in a the origin is such that a funxtion of varia , and in the remaining part of the interval is cm absdntdy ( jonvergent integral , then the coefficients of the derived series of Fourier serips of to a unique limit , , If is the typical Fourier coefficient of , we have ( no ) the nts of a Founer Series .
sin. o is the integral of , in the interval , for in this interval , not oontaining the origin , is bounded .
Now if we write for , we have , A is the upper bound of in .
Therefore certainly approaches zero as approaches zero , and therefore the same is true of being for the moment fixed .
Thus the limit on the right of reduces Using the Lemma ( S5 ) , we have therefore , by ( 1 ) ( nx ) , ( 2 ) where and is therefore a bounded function of in the whole infinite interval ) .
Now being an absolutely convergent in any finite interval , and a function of bounded variation , we may integrate by parts and write But as , except at , where its value remains zero , and the approach of to its limit is bounded .
Thus by a known theorem in the theory of integration with respect to a fimction of bounded variation , thus Lt which proves the theorem .
COR.an even , such that is a function of varrdion throughout the whole , then the theorem is true .
The integrals in are Lebesgue integrals , since has an onvergent integral from to , and is continuous .
Prof W. H. Young .
On the Order of S7 .
It will be noticed that , from and after the equation , in whtclS ffi absolutely convergent integral occurs , the proof consists merely in proving that this has the unique hmit .
Neglecting quantities which vanish when increases indefinitely , this is the expression for the sum of terms of the Fourier se.ries of ; we might , therefore , have simply quoted Dirichlet 's results here , and omitted the rest of the proof .
I preferred , however , to what is virtually a new proof of this theorem of Dirichlet 's .
The proof of the following theorem has been written out slightly differently from that of the theorem .
Had we pursued the same lines , would have taken the place of in the preceding in this sense , that we should have reduced the discussion to that of the absolutely convergent integral ) , and accordingly have proved that is effectively the sum of the first terms of the allied series of the Fourier series of .
We have , accordingly , in the course of the following proof shown incidentally that the allied series of a function ff of bounded variation converges to , provided only this limit exists .
This result had already been obtained by me by another method .
* S8 .
Analogous to the theorem of S6 , we have the following:\mdash ; THEOREM \mdash ; If is an odd having a definite limit as and such that , in a certain neighbourhood surrounding a function of bounded variation , while in the remaining part of the interval , itself an absolutely convergent integral , then the coefficients of the derived series of the Fourier series of converge to a limit , namely , In fact , writing for 2 , where , like , is an integer , and .
( 2 ) ' ' Konvergenzbedingungen fur die verwandte Reihe einer en heihe ' Munchener Bericht , ' June 10 , 1911 .
Magnituh of the of Fourier Series .
Also .
since is the of in the intsrval not containing .
the origin , for in this interval is bounded .
Here is a function of bounded variation .
Putting so that is an integral , we may therefore integrate the last term of ( 3 ) by parts , and write This is numerically , where is the total variation of from to , and may therefore be put , where Hence , using the Lemma ( S5 ) , the -hand side of ( 3 ) differs from by a quantity which vanishes when , and differs therefore from by a quantity which vanishes when .
Thus by ( 1 ) , ( 2 ) , and ( 3 ) .
remains , as , numerically .
But may be chosen as large as we please , therefore , 3 can have no other limit except zero , when .
This proves the theorem .
S9 .
Always provided that we ensure the vanishing in the limit of the portion of our expression due to the interval in the Theorems 3 and 4 , the problem of the order of magnitude thus reduces to that of determining the conditions oi convergence of the Fourier series of and of its allied series .
Corresponding to every known theorem regarding the convergence function must accordingly possess an absolutely convergent integral in : It be immediately cognised that this is the case in the theorems given below .
Prof H. Young .
On the Oroler of of such series , we have accordingly theorems relating to the order of magnitude of and With regard to the coefficient , it should be remarked that the extra condition for the convergence of the allied series , namely , the existence of the limit of a , reduces in the case of the , order of magnitude problems to the condition that should have a unique limit as Thus we have the following theorems which correspond to a test due to de la Vallee Poussin for the Fourier series , and my counterpart of it for the allied series .
\mdash ; If is an even function , and such that in a certain neighbourhood surroundin origin of variation , whilj in every interval not containing the is itsdf an absolutely convergent integral , th.en .
HEOREM \mdash ; If an odd function satisfying the same ) , and the further oorufiiion that exists , then .
Again , corresponding to tests due to myself , which I have recently simplified , we have the theorems : THEOREM \mdash ; If is an even function , and such that in certain neighbourhood the origin whpre is , while in the remaining part of terval is itsdf an absolutety convergent integral , then , fhis limit being supposed to exist .
THEOREM 8.\mdash ; If is an odd function , satisfying the same conditions as in satisfying the further conditim that Gveffi a fbumer Series .
ions .
of evidently render an absolutely oonvergent integral in every interval not containing the origin .
Thus all that is necessary to ensure that the argumentemployed in and 4 , and explained in S7 , is applicable is to.show that , in all the theorems of the preeent article , to zero as In the cases of Theorems 5 and 6 we have and therefore , since and are both summable in the whole interval , by hesis , has a unique finite limit as this limit cannot be other than zero , for if it were , ) would in the neighbourhood of the origin be of the order , and therefore not summable from to whereas the Fourier series considered is that of , which is accordingly summable from to In the cases of Theorems 7 and 8 , is bounded and therefore possesses an absolutely convergent integral in .
Also from the identity [ xf ] we deduce sinoe is an integral in .
But each of the integrals on the right exists iu the whole interval , tbererore the right-hand side of the last equation has aunique finite limit as ; hence also t has a unique limit , which , as before , must be zero .
S10 .
It will be noticed that , in the next theorems , bounded functions have taken the place of the functions of bounded variation in Theorems 3 and 4 .
That we could not formerly make this more general assumption is due to the fact that there is a sudden change as reaches zero when decreasing from unity .
Otherwise the two theorems which follow are precisely analogous to Theorems 3 and 4 , and constitute , like them , very wide generalisations of the properties of the familiar simple series of cosines or sines .
It should also be remarked that in this and in the following theorems up to Theorem 12 , we write the generalised condition of Lipschitz briefly .
The notation must be interpreted to mean , being a quantity which has finite bounds independent of and When is a quantity as small as we please , which occurs , for example , if the quantity employed is not the smallest at our disposal ( e.g. , when there is no smallest ) we use in place of O. Prof. W. H. Young .
On the Order of THEOliBM \mdash ; If is an even function a neighboufhood unding the origin is such that is boltnded fun ' a um'que limit as , and in the remaining part of nterval ( itself sati fies the condition of Lipschitz , then Moreover ; if in the Lipschitz condition be replaced S Let us put ) , where in the interval and is zero elsewhere .
Then satisfies our condition of Lipschitz hout the whole interval .
Therefore by 's result the theorem holds when for we substitute in the enunciation .
Hence it is only necessary to prove that the theorem is true when for we substitute Now in the interval we have , and if , in the function is bounded , therefore we have where is the bounded function hypothecated in the enunciation .
Therefore we may write nx tdt , since , where A is the upper bound of in ) , so that , and therefore also , for fixed , vanish as Now the interval of integration at the point 2 where is the upper bound of in ) .
Letting increase definitely this term is therefore numerically , which is we please , if is chosen conveniently large .
Magnotude the Ooefficimts of a Foutiet Series .
AlSo o undedly , Thus finally , letting first and then inorease indefinitely , , which proves the theorem iu both its parts .
S11 .
Similarly we have the following theorem:\mdash ; TnEOREM \mdash ; If is an odd function , which in a surrounding the origin is a bounded function a unique limit as in the remaining part of the itself the condition of Lipschitz , , Moreover , if in the Lripschitz condition be repfaced by , then .
It is , in fact , only necessary to follow the reasoning of the preceding article , taking the place of S12 .
We now proceed to give other generalisations of the properties of simple sine and co.sine series referred to at the end of S7 .
That we have convergence to zero due to the ct that whatever power of we take , there is no index which will make this just summable .
On the other hand , if a smaller index is used than , the example of the simple sine and cosine series shows that we must get and not O. THEOREM \mdash ; If is an even , which is such is integrable ( summable ) and in the of tlve interval itself satisfies the condition of Lipsehitz , then Moreover , if in the Lipschitz le replaced In fact , writing ) for ; and , therefore , as in the preoeding article , as Prof. W. H. Young .
On the Order of Thus we get , as in the proof of Theorem 3 , or rather in Theorems 5 , 7 , 9 , in accordance with the remarks of S9 , that the convergence of .
is irtually the same as .
of We now use the theorem of S8 , p. 439 of my paper " " On the Mode of Oscillation of a Fourier Series and of its Allied Series , \ldquo ; which tells us that this latter when divided by converges to zero .
Hence divided by converges to zero , that is THEOREM \mdash ; If is an odd Jies the same conduions as in Theorem 11 , The argument is precisely the same as that used in proving Theorem 11 , except that takes the place of Reasoning precisely analogous to that employed in the article quoted at the end of the preceding proof leads to the same order of magnitude of this integral as of the other integral , as is , indeed , pointed out in the article quoted , this integral related to the allied series as the other is to the Fourier series . .
In the next two theorems we use , instead of the condition of Lipschitz , the condition of Lipschitz-Dini , namely , the convergence being uniform for all values of , or as we shall for brevity write it .
THEOREM \mdash ; If is even function , which in such that is bounded , in remaining part of itself satisfies the condition of Lipschitz-Dini , , then Further , if in addition a unique limit as , then that is 'Lond .
Math. Soc. Proc Ser. 2 , vol. 12 .
Magnilu\amp ; the COefficients of a Fourier Series .
55 proof : of this theorem is precisely similar to that of Theorem 9 , using corresponding result of and S 3 , p. 436 of my paper\ldquo ; On the Mode of Oscillation of a Fourier Series and of its Allied Series TnmRB)\mdash ; If is an odd function , ing the same conditions as and if , in has a unique finite limit as , then Here , again , .
laces in the part of the integral considered due to the interval [ Added December , 1916.\mdash ; In a communication made to the Societe Helvetique , in August , entitled " " Sur les integrales multiples et les series de Fourier I remarked that I had occupied myself with the extension to multiple Fourier series of results obtained by myself and others with respect to Fourier series of a single variable , and that I had as yet not found any which did not hold mutatis mutandis in the general case .
This is also true of the results of the present paper .
] .
cit. , S 1 supra .
|
rspa_1917_0003 | 0950-1207 | The corrosion and electrical properties of steels. | 56 | 67 | 1,917 | 93 | Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character | Sir Robert Hadfield, F. R. S.|Edgar Newbery, D. Sc. | article | 6.0.4 | http://dx.doi.org/10.1098/rspa.1917.0003 | en | rspa | 1,910 | 1,900 | 1,900 | 14 | 220 | 4,429 | http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1917_0003 | 10.1098/rspa.1917.0003 | null | null | null | Electricity | 31.144023 | Measurement | 25.067815 | Electricity | [
-5.544431686401367,
-64.69935607910156
] | 56 The Corrosion and Electrical Properties oj Steels .
By Sir Robert Hadfield , F.R.S. , and Edgar Newbery , D.Sc .
( Received September 28 , 1916 .
) As long ago as 1899 , Caspari* showed that the condition that zinc should dissolve in an acid solution with evolution of hydrogen may be expressed in the form\#151 ; Single potential of metal + overvoltage \lt ; single potential of hydrogen electrode , ( a ) The single potential of zinc in a normal zinc sulphate solution is \#151 ; 0493 volt , and that of a hydrogen electrode in normal sulphuric acid is + 0*277 volt .
If a mixture of zinc sulphate and sulphuric acid be taken , the potential of the zinc will become more positive as the concentration of zinc sulphate increases , and the potential of the hydrogen electrode more negative as the concentration of the acid decreases .
Since the overvoltage of pure zinc is about 0*7 volt , conditions may be easily adjusted in this way so that solution is exactly arrested and the statement above then becomes an equation .
If a definite solution is used for a series of experiments , then the potential * of the hydrogen electrode is constant , and the tendency of the metal to dissolve will be measured by the fixed potential of this hydrogen electrode minus the sum of the overvoltage and the potential of the metal .
Denoting this " solution voltage " by the letter S , we may say generally that the condition that any metal shall dissolve with evolution of hydrogen in the given solution is S\gt ; 0 , and , further , that the rate of solution of the metal is approximately proportional to the value of S. In order to apply this method of reasoning to the problem of steel corrosion , two assumptions have to be made:\#151 ; ( 1 ) That the corrosion factor of a given steel is proportional to its rate of solution in a given acid .
( 2 ) That the rate of corrosion without evolution of gas is controlled by similar laws to that with evolution of gas .
If these assumptions are even approximately true , then it should be * ' Zeit .
Physik .
Chem. , ' vol. 30 , p. 89 ( 1899 ) .
The Corrosion and Electrical Properties of Steels .
57 possible to obtain a good estimate of the corrosion factor of a given steel by a simple measurement of its overvoltage and single potential in a given acid .
The work described in this communication was undertaken with the idea of examining how far , if at all , these assumptions were justifiable .
Varieties of Steel Used .
The samples of steel taken were 15 in number , all forged bars , 1 inch diameter and 5 inches long .
Discs of |-inch thickness were sawn off each bar , and a small segment of about 1 cm .
chord sawn off each disc .
The samples were numbered as follows :\#151 ; Steel No. Type of steel .
S.C.I. ... Pure iron .
2229 ... Carbon steel , low .
2228 ... Carbon steel , medium .
1618/ 2 ... Carbon steel , medium .
898 M/ 13 ... ... Silicon iron alloy .
3433/ 2 ... High chromium alloy .
1775 ... Nickel chromium steel , low carbon .
1795 C Nickel chromium steel , medium carbon .
1663 S ... Nickel chromium steel , high carbon .
3137 D ... Nickel chromium steel , high carbon .
3125 ... Nickel steel , 5 per cent. Ni .
3408 ... Nickel steel , 36 per cent. Ni .
1908 D ... Tungsten steel .
3435 ... Tungsten cobalt steel .
1109 D ... " Resista , " an alloy of 5 per cent. Mn an Full analyses , showing the compositions of these various steels , are given in the Table on p. 58 .
Overvoltage Measurements .
The small segments of steel were smoothed on an emery wheel and a uniformity of surface secured by rubbing on No. 1 emery cloth .
This uniformity of surface is necessary for comparative purposes , as the overvoltage is affected to a small extent by the nature of the surface.* A short copper wire was soldered to each and covered with white , hard sealing wax , leaving only 1 sq .
cm .
of the steel uncovered .
The overvoltage was then measured by the Back E.M.F. method , as described in ' Trans. Chem. So .
, ' vol. 105 , p. 2420 ( 1.914 ) , the electrolyte being N/ l H2SO4 .
Four series of measurements were made with current densities from 2 to 2000 milliamperes per square centimetre , and the averages of these four sets * Pring and Curzon , 'Faraday Soc. Trans. , ' 1911 .
CJ1 00 Summary of Analyses of Specimens .
Type of steel .
Steel No. Treatment .
'C .
Analysis .
c. Si .
S. P. Mn .
Cr .
Ni .
1 w. Co. Pure iron S.C.I. i !
As forged .03 .01 .013 \#166 ; 014 .04 1 | Carbon steel 2229 | .29 .31 .48 Carbon steel 2228 , , .50 .05 , .04 j Carbon steel 1618/ 2 .54 *16 1 -03 Silicon material !
898 M/ 13 T1 3 '05 .04.R .099 Chromium steel ( high Chromium ) 3433/ 2 775 ' Furnace .29 12 -84 | Nickel steel 3125 As forged .28 \#151 ; .50 5 -00 Nickel steel ... .
... 1798 H 830 ' Furnace .48 1 -35 19 *58 Nickel steel 3408 As forged .05 .05 .27 .08 .28 36 *38 Nickel chromium steel 1775 .
12 *13 1 *81 3 *41 h ickel chromium steel 1795 C 795 ' Furnace .34 .10 045 .041 .42 1 #79 3 *43 Nickel chromium steel 1663 S 795 ' Furnace .65 .12 .12 2 *00 2 *00 Nickel chromium steel .
3137 D 795 ' Furnace .66 .12 .12 2 *50 2 *75 u Resista * ' ( Fe-Ni-Mn alloy ) 1109 D As forged .60 5 -00 15 -00 Tungsten chromium steel 1908 D 795 ' Furnace .60 .20 4 \#171 ; qo 1V *0 Tungsten chromium cobalt steel \#166 ; - - - i 3435 775 ' Furnace .31 \#151 ; \#151 ; \#151 ; 3-62 J \#151 ; i 16-1 4-90 r R. Hadfield and I)r .
E. Newbery The Corrosion and Electrical Properties of Steels .
of readings are given in the following Table , the current density being given in milliamperes per square centimetre and the overvoltage in volts .
Current density .
S.C.I. 2229 2228 1618/ 2 .
898 M/ 13 .
3433/ 2 .
1775 .
1795 C. 2 0-24 0 23 0-20 0-21 0-22 0-26 0-20 0-18 4 0-25 0-23 0-21 0-21 0-22 0*26 0-20 0-19 6 0-26 0-23 0*22 0*21 0-22 0*26 0-21 0*19 10 0-26 0-24 0 22 0-22 0 22 0*26 0 21 0-19 20 0-27 0-24 0-22 0-22 0-22 0 26 0*21 0-19 50 0*27 0-24 0-23 0 22 0*22 0-27 0*22 0-20 100 0-27 0-24 0*23 0*22 0*22 0-27 0 22 0*19 200 0-27 0*24 0-22 0-22 0-22 0-27 0 22 0*19 400 0-28 0-24 0 22 0-21 0-22 0-27 0 22 0 18 1000 0-27 0-24 0 -21 0-20 0 21 0-28 0 21 0*17 2000 I 0 '26 0-23 0 21 0 19 0-20 0-27 0-20 0 16 Current density .
1663 S. 3137 D. 3125 .
3408 .
1908 D. 3435 .
1109 D. 2 0-19 0-19 0-18 0*20 0-21 0-21 0 19 4 0-19 0-20 0*19 0-22 0-22 0 22 0*20 6 0 20 0-21 0 19 0 22 0*22 0 23 0-20 10 0-20 0-21 0 -20 0 23 0 23 0*24 0-21 20 0-20 0-22 0*20 0 23 0-23 0 24 0*21 50 0*21 0-22 0-21 0-23 0-23 0 25 0-21 100 0-21 0-23 0-21 0*22 0-24 0-25 0-21 200 0 21 0*23 0-21 0-21 0-24 0 25 0-21 400 0 21 0-23 0-21 0-20 0-24 0*25 0 20 1000 0-21 0 23 0 19 0-18 0*23 0-25 0-19 2000 0-20 0-22 0-18 0-17 0-22 0 23 0-18 Single Potential Measurements .
After measuring the overvoltage , the electrodes were washed with ' distilled water , dried , and repolished with emery cloth as before .
The potential of each was then measured in a N/ l H2S04 electrolyte against a mercurous sulphate electrode containing the same solution .
Measurements were made by means of the same apparatus as used for overvoltage , the anode A being disconnected , and readings taken every minute for 5 to 10 minutes until constant for 3 consecutive minutes .
Measurements were also taken in an electrolyte consisting of N/ l FeSO* + N/ l H2S04 , but no appreciable difference was observed .
After deducting the difference of potential between a normal mercurous sulphate electrode and a normal hydrogen electrode , the following values were obtained for the single potentials of the steels against a standard hydrogen electrode :\#151 ; VOL. xcm.\#151 ; A , G Sir R. Hadfield and Dr. E. Newbery .
- -02 + 02 Criterion of Solubility ( By Electrical Method ) Orrjwed/ n dscerd/ hg Order .
+ - 14 3I37D I663S II09D I908D 898MI3 Fig. 1 .
Corrosion 12 t O II uj a 9o : D 0 .
\lt ; CO -20 .05 - 11090 I908D '"SC.1.3,370 \#151 ; Normal H2S04 , 72 hours .
\gt ; 1795 898MI3 Atmospheric , 10 weeks .
Fig. 2 .
The Corrosion and Electrical Properties of Steels .
61 Steel .
Potential .
Steel .
Potential .
Steel .
Potential .
S.C.I. volt .
-0-28 * 3433/ 2 Tolt .
-0-25 3125 TOlt .
\#151 ; 0 '19 * 2229 -0 26 1775 -0-21 3408 -0*06 2228 -0 21 1795 C -0-20 1908 D -0*19 1618/ 2 898 M/ 18 -0-25 1663 S -0-21 3435 -0-18 -0-25 3137 D -0*19 1109 D -0-16 In order to combine these measurements with the overvoltage measurements , the question arises as to what current density should be taken as standard .
Since the local currents set up during most forms of steel corrosion are probably very feeble , it is perhaps advisable to take the values for the overvoltage at the lowest current densities used .
On adding these overvoltages to the corresponding single potentials , we obtain the values of \#151 ; S* for each electrode .
These are arranged in order of magnitude in the following Table :\#151 ; No. Steel .
-S .
No. Steel .
-S .
volt .
volt .
1 3408 + 0-14 9 2228 -0*01 2 1109 D + 0-03 10 1775 -0*01 3 3435 -hO -03 11 1663 S -0*02 4 1908 D + 0-02 12 1795 C -0*02 5 3433/ 2 4 0 01 13 2229 -0*03 6 S.C.I. 4-0*01 14 898 M/ 13 -0*03 7 3137 D 0*00 15 1618/ 2 -0 04 8 3125 -0*01 Corrosion in Acid .
For these measurements , the larger segments of the discs cut off from the bars were used .
One face of each disc was smoothed down on a carborundum wheel , rubbed with emery as before , weighed carefully , and the remainder of the disc covered with a coating of wax .
All the discs were then laid , polished side up , on the bottom of a large glass dish , and 3 litres of N/ l H2S04 poured in , the temperature being 15 + 1 ' C. throughout the whole experiment .
After 72 hours the discs were removed , washed , the wax cleaned off , and the discs dried and weighed .
The loss in weight per square centimetre of exposed surface is given in the following Table:\#151 ; * While S measures the corrodibility , \#151 ; S measures the resistance to corrosion .
The Table is arranged in this way in order to correspond with the other Tables .
G 2 62 Sir R. Hadfield and Dr. E. Newbery .
Departure of Order of Merit Figures from those for Atmospheric Corrosion .
Electrical Criterion .
1109 D 1618/ 2 Acid Corrosion .
Fig. 3 .
Order of Merit\#151 ; Resistance to Corrosion .
( The Specimens are arranged in order of Resistance to Atmospheric Corrosion .
) dt/ nospheric Corros/ dc/ cf Corrosion f/ V S 72/ iaurs ) \#163 ; 7eetrico/ Criterion .
1663S II09D I908D Fig. 4 .
The Corrosion and Electrical Properties of Steels .
Steel .
Loss in grm. Steel .
Loss in grm. Steel .
Loss in grm. S.C.I. 0-024 3433/ 2 0*132 3125 0-314 2229 0-400 1775 0-062 3408 0-008 2228 0-142 1795 C 0-096 1908 0-564 1618/ 2 0-432 1663 S 0-182 3435 0-230 898 M/ 13 0 034 3137 D 0-088 Atmospheric Corrosion .
The steel bars from which the discs had been sawn off were placed in a horizontal row in a box with the worked ends protruding and left exposed to the laboratory atmosphere for 10 weeks during the months of May , June , and July .
At the end of that time none of the bars showed any appreciable rust except on the worked ends , and since patches on these ends had been polished by the rubbing action of the upper part of the saw , the variation in corrodibility of the polished and rough metal could be observed .
They were carefully examined with the aid of a Coddington lens and arranged in order of corrodibility , as follows :\#151 ; No. 1 " 2 v ) 3 \#187 ; 4 " 5 " 6 " 7 \#187 ; 8 " 9 " 10 \#187 ; 11 \#187 ; 12 " 13 \#187 ; 14 " 15 3433/ 2 Quite bright .
No rust .
3408 Faint , but uniform light brown coloration .
\#187 ; 3435 Bright , slight traces of rjist .
1109 D Bright , rusting a little more marked .
2228 Bright , patches of rust visible .
1618/ 2 Polished parts bright , large rust patches .
3125 Polished parts bright , larger rust patches .
1908 D Polished parts bright , rest covered with rust .
3137 D Polished parts black , rest covered with rust .
S.C.I. Polished parts black and partly rusted , rest quite rusted .
1663 S Polished parts black and much rusted .
1795 C Quite covered with rust , thin over polished parts .
2229 Quite covered with rust , polished parts not visible .
1775 Badly rusted , thick uniform coating .
898 M/ 13 Badly rusted , thick uniform coating .
The Table on p. 64 shows the order of resistance to corrosion of the steels as determined by these three methods .
If the object of experiments on corrosion be considered to be the determination of the alloys which best resist the action of the atmosphere , then the figures in the third column of the Table must be taken as standard , and those in the other columns judged as good or bad according to their nearness or otherwise to those in the third .
Reviewing the Table as a whole , in four cases the electrical and acid methods give identical results , in 10 cases the electrical method gives better results than the acid method , and in one case only ( No. 1618/ 2 ) , the acid Sir R. Hadfield and Dr. E. Newbery .
Steel No. Electrical method .
Corrosion in acid .
Atmospheric corrosion .
S.C.I. 6 3 10 2229 13 13 13 2228 9 9 5 1618/ 2 15 14 6 898 M/ 13 14 4 15 3433/ 2 5 8 1 1775 10 5 14 1795 C 12 7 12 1663 S 11 10 11 3137 D 7 6 9 3125 8 12 7 3408 1 1 2 1908 D 4 15 8 3435 3 11 3 1109 D 2 2 4 method gives a slightly better estimate than the electrical though both are wide of the mark .
This is evidently due to the presence of 1 per cent. Mn in the specimen , since this metal is only attacked slowly by the atmosphere owing to the formation of a protective oxide coating , while it dissolves with ease in acid and also has a high negative solution potential .
In four cases only does the electrical method agree with atmospheric corrosion , but the acid method only agrees in one case and the deviations are generally much greater with this method .
Notes on Individual Alloys .
S.C.I. , Pure Iron.\#151 ; The resistance of this to the action of acid seems to be connected with its high overvoltage , and its non-resistance to atmospheric corrosion may be due to the presence of some substance in the air which reduces the overvoltage .
After treatment with acid the surface was quite smooth but dull .
2229 , Low Carbon Steel.\#151 ; In this case only , all three methods agree in showing the alloy to be very liable to corrosion .
Large patches were eaten out by the acid .
2228 , Medium Carbon Steel.\#151 ; =Both electrical and acid methods underestimate the corrosion-resisting powers of this alloy .
The surface was pitted by the acid in patches .
1618/ 2 , Medium Carbon Steel , 1 per cent. \#151 ; This has already been referred to .
The surface was very deeply pitted and eaten into by the acid .
898 M/ 13 , Silicon Iron Alloy.\#151 ; The acid test in this case gives a very false impression as to the corrodibility .
The surface remained smooth and bright .
The electrical method gives a much better idea .
The Corrosion and Electrical Properties of Steels .
3433/ 2 , High Chromium Alloy.\#151 ; Here again , both methods greatly underestimate the corrosion-resisting powers of this alloy , the acid method giving the more incorrect estimate , the surface being decidedly pitted after treatment .
This was the only alloy which was quite unchanged by the atmospheric test .
1775 , Cr NiSteel , Low Carbon.\#151 ; The corrodibility is underestimated by the electrical method and very badly by the acid method .
After treatment with acid the surface was almost smooth .
With this exception , all the nickel steels have been well placed by the electrical method , while half of them are badly placed by the acid method .
1795 C was slightly pitted , 1663 S deeply pitted , and 3137 D left almost smooth by the acid test .
3125 , Nickel Steel , 5 per cent. Ni , was very badly attacked by the acid , specially round the edges .
Though the overvoltage is low , the negative single potential is also low , and hence the electrical method places this alloy much higher on the scale than the acid method , and nearer the value indicated by atmospheric corrosion .
3408 , Nickel Steel , 36 per cent. Ni.\#151 ; The low negative single potential of this alloy , due to the high percentage of nickel , places it easily first by the electrical method , and its appearance was quite unchanged by the acid test .
In the atmosphere the coloration produced is probably due to a thin protective coating of nickel oxide .
1908 D , Tungsten Steel.\#151 ; The ready solubility of this , and also of No. 3435 , which also contains tungsten , is surprising .
Both have fairly high overvoltages and low negative single potentials , and hence the electrical method gives a much better estimate of the corrosion-resisting powers .
1109 D , Manganese Nickel Steel.\#151 ; The figure for the acid test with this alloy is doubtful , as owing to the extreme toughness a disc could not be cut off , and the experiment was made with a small chipping .
Advantages and Disadvantages of the Electrical Method .
( a ) Advantages:\#151 ; 1 .
This method certainly gives a better estimate of the ability of an alloy to resist atmospheric corrosion than the acid immersion method .
2 .
When once the apparatus is fitted up a sample can be examined in 10-30 minutes , while at least two hours is necessary for the acid test .
3 .
By the addition of certain elements with the object of raising the overvoltage and of others with the object of lowering the negative single potential , there appears to be a better chance of attaining the ideal of a rustless steel than by merely trusting to a single measurement for determining corrodibility .
4 .
Very small samples , less than 1 grm. , may be used .
Sir R. Hadfield and Dr. E. Newbery .
( b ) Disadvantages:\#151 ; 1 .
The apparatus needed is much more complicated and expensive than that required for the acid test , and greater skill in manipulation is necessary .
2 .
The differences in the values of S obtained are not great enough for suitable grading of the alloys .
3 .
Slight errors in measurement may cause large differences of position in the corrodibility scale .
4 .
Where a large number of samples have to be tested at the same time , the acid immersion method can probably be worked more quickly , specially as the electrodes for the electrical method require careful preparation .
The overvoltage apparatus ( loc. cit. ) can be considerably simplified .
' The voltmeter V may be dispensed with , and the potentiometer P2 replaced by a sliding resistance coil .
A calomel or mercurous sulphate electrode may be used instead of the more troublesome hydrogen electrode , a unipivot galvanometer may replace the reflecting galvanometer and shunt Gf , and the cemmutator X can be fixed directly on the spindle of a small electromotor and driven easity at a high speed .
It may be better to use still lower current densities , say from- 0*1 to 10 milliampkres per square ' centimetre and extrapolate to find the overvoltage at zero current density .
Possibly also the measurement of the overvoltage and the single potential in a solution of a weaker acid such as acetic may give results more comparable with atmospheric corrosion and also give greater variation in the values of S obtained .
The liability to atmospheric corrosion is reduced by polishing the surface of a metal , owing to the fact that the overvoltage is raised , and it is generally true that any process or addition which raises the overvoltage of a metal also reduces its tendency to corrode .
The galvanising of iron is a case in point , zinc having a very high overvoltage .
There are , of course , so many different causes of corrosion that one cannot hope for a method which will give reliable information on corrodibility in all cases .
Again , referring to the comparison Table , we see that the electrical method only places one alloy more than four out , while the acid method makes nine such mistakes out of the 15 cases .
At the same time , in five cases the electrical method makes a mistake of four places , and this cannot be regarded as satisfactory .
It is hoped that the method may be further developed so as to give more reliable information .
Other points which might be considered are :\#151 ; ( 1 ) The average overvoltage .
( 2 ) The maximum overvoltage .
( 3 ) The current density required to produce maximum overvoltage , but ) The Corrosion and Electrical Properties of Steels .
conclusions deduced from such considerations would not have the same theoretical foundation as those obtained by the method already described .
It is evident that the assumptions made at the beginning of this paper are only fulfilled to a small extent .
The first is certainly somewhat wide of the facts if the given acid is N/ H2S04 .
It may be nearer the mark when some other acids are used , and it is possible that , with suitable choice of solvents , reliable information may be obtained with regard to corrodibility under different circumstances .
The present paper deals only with atmospheric corrosion , and the conclusions arrived at are not intended to apply to other cases ( sea water , strong acids , etc. ) .
The second of the two assumptions appears more justifiable than the first , as it is largely on this second that the electrical method is based .
The solution or corrosion of a metal is intimately associated with the exchange of electrical charges , and the tendency to corrosion is measured by the potential differences between these charges .
When the acid test is employed , the overvoltage of the sample is considerably lowered as soon as the surface becomes attacked , and local currents are set up due to slight non-homogeneity of the alloy , thus greatly increasing the rate of solution .
In the electrical method , the surface of the metal or alloy is quite unchanged during the overvoltage measurements if the current density is kept low , and is not appreciably affected by the five minutes ' acid immersion when the single potential is measured .
Hence the resistance of the alloy to the beginning of corrosion is determined , and it must , of course , be remembered that this is not usually the same after corrosion has once started .
There is no reason why the electrical method should not be employed with non-ferrous alloys and metals , but further experiment with different electrolytes is needed before any standardisation will be possible .
A recent paper by one of the writers of the present paper is given in the * Journal of the Iron and Steel Institute/ JSTo .
1,1916 , entitled " The Influence of Carbon and Manganese upon the Corrosion of Iron and Steel .
" Much useful information with regard to the effect of tap water and sea water is there presented .
|
rspa_1917_0004 | 0950-1207 | Monoclinic double selenates of the nickel group. | 68 | 72 | 1,917 | 93 | Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character | A. E. H. Tutton, D. Sc., M. A., F. R. S. | abstract | 6.0.4 | http://dx.doi.org/10.1098/rspa.1917.0004 | en | rspa | 1,910 | 1,900 | 1,900 | 5 | 71 | 2,290 | http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1917_0004 | 10.1098/rspa.1917.0004 | null | null | null | Atomic Physics | 54.788042 | Chemistry 2 | 18.979164 | Atomic Physics | [
-28.524860382080078,
-77.90332794189453
] | 68 Monoclinic Double Selenates of the Nickel Group* By A. E. H. Button , D.Sc .
, M.A. , F.E.S. ( Received November 23 , 1916 .
) ( Abstract .
) In this paper the results are given of the investigation of the double salts potassium nickel selenate , rubidium nickel selenate , csesium nickel selenate , and ammonium nickel selenate , each containing six molecules of water of crystallisation , forming the group of the series Iv2M(Se04)2,6H20 in which M is nickel .
The results are absolutely in line with all those already published for the complete monoclinic double sulphate analogous series with 6H20 , and for the isomorphous magnesium and zinc double selenate groups .
The morphological and physical properties exhibit the progression in accordance with the atomic weight of the alkali metal which has been so clearly brought out by the previous work , and the ammonium salt is shown conclusively to belong to the isomorphous series , and to exhibit the peculiar traits described in connection with the other ammonium salts of this monoclinic series already dealt with .
Symmetry.\#151 ; This is the same for all the four salts , as for all the other groups of double sulphates and selenates dealt with , namely , Class 5 , prismatic-holohedral , of the monoclinic system .
Crystal Elements.\#151 ; These are:\#151 ; Axial angle / 3 .
Axial ratios .
ct : b : c. KNi selenate 104 ' 27 ' 0 -7467 : 1 : 0 -5059 RbNi selenafce 105 20 0 7395 : 1 : 0-5031 NH4Ni selenate 106 17 0 -7395 : 1 : 0 -5048 CsJSii selenate 106 11 0 7288 : 1 : 0 *4993 The axial angle of the rubidium salt is almost exactly midway between the axial angles for the potassium and caesium salts , corresponding to direct progression with the atomic weight of the interchangeable alkali metals .
The axial ratios for the rubidium salt are also intermediate .
The axial ratios for the ammonium salt are very close to the analogous values for the rubidium salt , and the axial angle of the ammonium salt is nearly identical with that of the ccesium salt .
* For full paper see ' Phil. Trans. , ' A ( not yet published ) .
Monoclinic Double .
Selenatesof the Nickel Group .
Habit._Potassium nickel selenate and caesium nickel selenate exhibit characteristic habits , very distinct from each other , dependent on the relative development of the faces of two forms , the basal pinakoid c{001 } and ^{011 } .
In the case of the potassium salt c{001 } predominates , either conferring a tabular habit or , if the prism faces | ?
{ 110 } are fairly high , giving a flat top and base to the vertical prism ( which is parallel to axis c ) ; while the \lt ; ?{011 } faces form merely small side-corner truncations .
In the caesium salt , on the other hand , the faces of the basal pinakoid c{001 } form only more or less narrow elongated strips , with large ( / { Oil } faces on each side of them , the two forms , together with low and narrow faces of the clino-pinakoid Z\gt ; { 010 } , forming a prism parallel to the inclined axis a. rIhe rubidium salt exhibits an intermediate type , in which the faces of c{001 } and ^{Oil J are more or less equally developed .
The ammonium salt also usually resembles the rubidium salt , but its intermediate character has a wider range than the very distinctive intermediate type presented by rubidium nickel selenate .
Interfacial Angles.\#151 ; The interfacial angles of rubidium nickel selenate are intermediate in value between those of the analogous potassium and caesium salts , a progressive change of angle following the replacement of potassium by the heavier and still heavier atoms of rubidium and caesium .
Thirty-six quite different angles have been measured and compared , and the average values of the changes which they show for each replacement , and the maximum amount of change of angle , are given below :\#151 ; Replacement .
Average change .
Maximum change .
K by Rb 23 ' 57 ' K by Cs 47 119 !
K by NH4 45 110 Remembering that the atomic weights of the three metals are K = 38'9 , Rb = 84*9 , Cs = 131*9 , and that the increments of atomic weight are Rb \#151 ; K = 46 , and Cs\#151 ; K = 93 ( double 46 ) , it is obvious that the average and maximum increments of angles are directly proportional to the increments of atomic weight of the metals interchanged .
The ammonium salt proves its isomorphism , although not eutropism , by the fact that the average and maximum changes , when NH4 replaces K , are not quite so large as when caesium replaces potassium , that is , the change is of precisely the same order as for the metallic replacements , and not outside their limits .
Volume.\#151 ; The volume and dimensions of the unit cells of the structural space-lattice , relatively expressed by the molecular volume and the topic Dr. A. E. H. Tutton .
axial ratios , are , perhaps , the most important of all the morphological constants .
They are given below :\#151 ; Molecular volume .
Topic axial ratios .
X .
: KNi selenate , 206 *14 6 -1677 : 8 -2598 : 4 *1786 T ?
, hNi selenate 216 *96 6 -2533 : 8 4561 : 4 '2542 NK4N i selenate 216 *53 6 -2520 : 8 *4543 : 4 '2678 CsNi selenate 229 -17 6 -3317 : 8 -6878 : 4 *3378 The volume and dimensions of the unit cell are thus found to show a regular and somewhat accelerating progression from the potassium salt , through the rubidium salt , to the caesium salt , and the values for the ammonium salt are very close indeed to those for the rubidium salt .
The importance of this latter fact will be pointed out in the concluding paragraph of this abstract .
The Optical Ellipsoid.\#151 ; The ellipsoid , which graphically represents the optical properties , enlarges as potassium is replaced , first by rubidium and then by - caesium .
At the same time it rotates progressively about the symmetry axis b. Starting with the potassium salt , the ellipsoid is situated with one of its other two principal axes ( those which lie mutually at right angles in the symmetry plane ) not far from parallel to the vertical crystal axis c ; when the potassium is replaced by rubidium the ellipsoid rotates so that the axis in question moves away 3 ' further from the vertical direction , and when the rubidium is in turn replaced by caesium , the ellipsoid rotates in the same direction nearly 7 ' further , the progression being thus an increasing one .
For the ammonium salt the position is nearly truly vertical .
Optic Axial Angles.\#151 ; The optic axial angles have been measured for seven wave-lengths of light , and found to show a similar slightly increasing progression with the atomic weight of the alkali metal .
The optic axial angle for the ammonium salt is slightly larger than that for the rubidium salt .
Refractive Indices and Double Refraction.\#151 ; The refractive indices have also been determined for seven wave-lengths .
They also progress from the potassium to the caesium salt , the acceleration being , in this case , so considerable that a curious effect is produced by the simultaneous more direct progress ( almost in simple proportion ) of the double refraction which occurs .
The double refraction\#151 ; the difference between the and a indices for the same wave-length , sodium light being taken for the comparison\#151 ; is 0*0246 for KNi selenate , 0*0192 for KbNi selenate , 0*0175 for the NH4Ni salt , and 0*0094 for the CsNi salt .
The effect referred to is that , while the a and / 3 indices of Monoclinic Double Selenates of the Nickel Group .
the rubidium salt are higher than those of the potassium salt , in consequence of the first progression , the difference between the extreme indices is so curtailed by the second progression ( diminution of the double refraction ) that the y indices are just slightly less than those of the potassium salt , and the mean refractive index works out to be exactly the same for both potassium and rubidium salts .
Molecular Optical Constants.\#151 ; The true progression in refractive power is , however , best shown by the molecular refraction .
This , indeed , is probably the most important of all the optical constants , just as the volume and directional dimensions of the unit cell are the most important morphological constants .
The values in Gladstone units are given below:\#151 ; Molecular refraction .
a i8 y. Mean value .
A ( a + 6 + y ) .
KNi selenate 106 10 107 '96 111 -10 108 -39 RbNi selenate 112 -08 114 -07 116 -20 114-12 NH4Ni selenate 113*70 115-56 117-45 115 -57 CsNi selenate .
122 -90 124 '14 125 *03 124 02 The true progression with the atomic weight of the alkali metal is clearly shown by these constants , and the fact that the molecular refraction of ammonium nickel selenate is almost identical with that of rubidium nickel selenate is as impressive as , and is doubtless connected with , the closeness to identity of the volumes and directional dimensions of the unit cells of the similar space-lattices of the two salts .
Concluding Remarks .
In conclusion , two points from the above results may be specially emphasised .
Firstly , the remarkably quantitative manner in which the law of progression is indicated in the cases of the alkali metallic salts .
For it has been shown that the average and maximum amounts of all the changes in interfacial angles when potassium is replaced by caesium are exactly double those for the replacement of potassium by rubidium , corresponding precisely to the change of atomic weight , which is almost exactly double ( 93 to 46 ) .
That the ammonium salt is really isomorphous with the alkali metallic salts is proved by the fact that when ammonium is substituted for potassium the average and maximum changes of angle are no more , and , indeed , just slightly less , than if caesium were introduced instead of potassium .
The second point worthy of emphasis is the extreme closeness of the molecular volumes and the topic axial ratios of the rubidium and ammonium Dr. A. E. H. Tutton .
salts of the group , representing the volumes and edge dimensions of the unit cells of the monoclinic space-lattices of the two crystal structures .
The values thus indicate very perfect congruency and almost identity of the two structures .
It will be shown in a separate communication , immediately following this paper , that this result , in conjunction with the precisely similar facts observed concerning the ammonium and rubidium salts of every group investigated by the author , including the rhombic group of simple alkali sulphates , has an important bearing on the theory of valency volumes ; for that theory is entirely incapable of explaining it .
X-Ray Analysis and Topic Axes of the Alkali and their Bearing on the Theory of Valency Volumes .
By A. E. H. Tutton , D.Se .
, M.A. , F.RS .
( Received November 20 , 1916 .
) One of the most interesting facts brought to light in the course of the author 's crystallographical investigations of the rhombic sulphates and selenates of potassium , rubidium , caesium , and ammonium , and of the monoclinic double salts containing those simple salts in combination with the sulphates and selenates of dyad-acting metals ( Mg , Zn , Fe , Ni , Co. Mn , Cu , and Cd ) , is the approximation in structure which has invariably been observed between the rubidium salt of any group and the ammonium salt of that same group .
This striking fact is again emphasised by the results for the nickel group of double selenates* laid before the Royal Society on the same day as this present communication , and of which an Abstract immediately precedes this paper .
While considerable differences occur between the structural dimensions of the potassium , rubidium , and caesium salts of the group\#151 ; differences which have been shown to follow the order of the atomic weightsf * See ' Phil. Trans. , ' A ( not yet published ) .
t Instead of " atomic weights " we may substitute with equal validity " atomic-numbers " ( the numbers of the elements according to their sequence in the Periodic Table ) .
For the atomic numbers of K , Rb , and Cs are 19 , 37 , and 55 , and their differences are similarly related , Rb-K = 18 , Cs-Rb = 18 , and Cs-K = 36 or twice 18 .
Indeed , it is probable that there is an intimate connection between this crystallographic law of the author and the law of Moseley , that the properties of an element are defined by the atomic number , which is equal to the number of units of positive electrical charge in the atomic nucleus .
|
rspa_1917_0005 | 0950-1207 | X-ray analysis and topic axes of the Alkali sulphates, and their bearing on the theory of valency volumes. | 72 | 89 | 1,917 | 93 | Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character | A. E. H. Tutton, D. Sc., M. A., F. R. S. | article | 6.0.4 | http://dx.doi.org/10.1098/rspa.1917.0005 | en | rspa | 1,910 | 1,900 | 1,900 | 10 | 245 | 8,487 | http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1917_0005 | 10.1098/rspa.1917.0005 | null | null | null | Atomic Physics | 47.476401 | Tables | 21.048009 | Atomic Physics | [
-28.5612850189209,
-77.43653869628906
] | ]\gt ; Dr. A. E. H. Tutton .
salts of the roup , and edge dimensions of unit of the monoclinic space-lattices of the two crystal structures .
The thus indicate very perfect congruency and almost identity of the two ucCures .
It will be in a separate communication , immediately following this paper , that this esult , in conjunction with the precisely silnilal facts observed concerning the almnoniuln and rubidium salts of every ocrroup ated by author , including the rhombic group of simple alkali sulphates , has an important on the theory of valency volumes : ' that theory is entirely incapable of explaining it .
Analysi Topic Axes of the Sutphates , their on the Theory of Valency By A. E. H. TUTTON , D.Sc .
, hf .
A. , F.R.S. eceived November One of the most interesting facts brought to light in the course of the author 's ations of the rhombic sulphates and selenates of potassium , rubidium , caesium , and ammonium , and of the monoclinic double salts containing those simple salts in combination with the snlphates and selenates of dyad-acting metals ( Mg , , Fe , Ni , Mn , Cu , and Cd ) , is the approximation in structure which has inyariably been observed between the rubidium salt of any group and the ammonium salt of that same roup .
This striking fact is again emphasised by the results for the nickel roup of double selenates , before the Roy Society on the same day as this present communication , and of which an Abstract immediately precedes this paper .
While considerable differences occur between the structural dimensions of the potassium , rubidium , and caesium salts of the differences which llown to follow the order of the atomic * See ' Phil. ( yet published ) .
Instead of " " weights\ldquo ; we may substitute with equal validity " " atomic \ldquo ; ( the numbers of the elements according to their sequence in the Periodic Table ) .
For the atomic numbers of , Rb , and Cs are 19 , 37 , and , and their fferences are similarly related , , Cs-Rb , and Cs-K or twice 18 .
Indeed , it is probable that there is an intimate connection between this stall law of the author and the law of Moseley , that the properties of an element are defined by the atomic number , which is equal to the number of units of sitive electrical charge in the atomic nucleus .
X-Ray Analysis Axes of the .
Sulphates .
73 of the alkali metals , Rb , Cs , and , or twice 46 so that the rubidium salt is always lntermediate\mdash ; the ammonium salt has without exception proved to possess structural dimensions almost identical with those of the rubidium salt , the central member of the } ) .
By structural dimensions jlre meant directional dimensions and the total volume of the unit cell the spacelattice , the same type of which is common to the whole rhombic or monoclinic isomorphous series .
The total volume is represented by the nlolectlla volume ( the quotient of the molecular weight ) the density of the crystal ) , and the three directional dimensions of the cell in space are known as the topic axial ratios , or topic axes .
The basis the molecular volume ( molecular weight ' known ) is a very accurate determination of the density of the most perfect attainable crystal .
The topic axial ratios .
their calculation ( in addition to the molecular volume ) the crvstal elements ( crystal-axial crles and ) , which are derived from very accurate measurements of the external interfacial angles of perfectly developed crystals .
For a series of isomorphous , such as the ] ombic nornlal sulpbates of the alkali-metallic family roup of the periodic classification , , where may be potassium , rubidium or caesimn , there be no possible that the type of structure , that is of space-lattice , is identical .
Its sy1nnletry is the same for all the members of the group , but the dimensions of the cell vary progressively with the atomic weight or atomic number of the interchangeable alkali metals ; and the interfacial also differ htly and progressively , in accordance with very definite rulef , which have been established by the author .
When , however , we introduce the radiclc alnmoniunl , , instead of an alkali metal , and produce the isomorphous ammoniunl salt , the possibility has been suggested that the case may not be strictly comparable with the substitution of rubidium or caesium for potassiunt .
It is just conceivable that the observed nilarity of symmetry and crystal may be accompanied by a considerable up of the structure , such as , for instance , by the introduction of the extra atoms of in the form of new layers .
That is , it might be a case of a different sort of ructure being produced as regards dimensions and arrangement , but outwardly conforming to the same type of rhombic symmetry , with a fortuitous close similarity in external crystal angles .
Although , however , this is a possibility , it is highly improbable .
It is true that the quality of the isomorphism of ammonium sulphate is so far different from that betweell potassium , rubidium , and caesium sulphates as not to be subject to the Dr. A. E. H. Tutton .
of progression with the atomic weight or atomic number of the metal , for we are now dealing with a non-metallic radicle group .
The case is defined by saying that the ammonium salt , while truly isomorphous , does not to the sive " " eutropic\ldquo ; group of the metallic salts , the term eutropism having been applied to the isomorphism of strictly analogous nlembers of the roup ( their interchangeable elements belonging to the same family group of the periodic classification ) , which follow the law of progression with the atomic weight or atomic number of the interchangeabJe constituents both as regards morphological and physical ( optical and other ) con stants .
But the author has shown that although the ammonium salt is uot eutropic with the salts of the alkali metals , its molecular volume topic axial ratios are indeed strictly comparable with those of the alkali metallic salts .
That the ammonium salt is truly isomorphous with the alkali-metallic salts is strikingly shown by the fact that not is the type of symmetry identical and the axial ratios very close ( see Table on ) , but the average change of angle ( for 37 measured angles ) on replacing potassium by ammonium is not even quite so yreat as when potassium is replaced by esitlm , and the maximum of interfacial angle follows the same rule .
The angular change oh substituting ammonium for potassium is , however , naturally greater than when rubidium is introduced instead of potassium , for this latter ( Rb ) replacement gives rise to only half as much of angle as when caesium is introduced for potassium , in accordance with the law of progression for the alkali metals , which law is very beautifully and directly by this fact .
To make the point clear , the actual figures for the sulphates are given in the following short Table .
It should be remembered that the difference of atomic weight or of atomic number between and Cs is just double that between and Rb .
and Maximum Angular Changes .
For replacement of in by Precisely similar facts are shown in the monoclinic double sulphate and selenate series , in which the angular changes are much larger ; the precision with which the and maximum changes for the caesium replacement are double those for the rubidium replacement is truly remarkable , in every X-Ray Topic Axes of the Alkali Sulphates .
75 group investigated , while the ammonium replacement approaches in effect the caesium interchange .
( See Table in preceding Abstract , p. 69 ) .
If there had been some disturbance of the structure , such as would be provoked by the insertion of additional ]ayers , one would have expected much more disturbance of the interfacial angles than this , even had the type of symmetry been left unaffected , ( which would have been improbable ) .
Hence , there was every reason to that the internal structural dimensions also had suffered no crucial change , and that they were faithfully indicated by the topic axial ratios .
Now , when we make the comparison of these ratios and of the molecular volumes of the four salts we obtain the result stated at the opening of this communication , namely , that the values for the ammonium salt are almost identical with those of the rubidium salt .
This will be clear from an inspection of the Table on p. 79 .
From this , and from similar lips which have been observed by the author for the ammonium and rubidium salts of every group of double sulphates and selenates , it has been concluded that the structures of the ammonium and rubidium salts are not only similar but practically ruent .
If they could be inlagined as shadows ( noil-material ) and one such ghostly space-lattice could be moved over and through the other consequently without inter- ference , it could be brought into actual identity with that other .
Before proceeding to indicate the great significance of this , it should be stated that there is further independent information available to show that it is a real fact .
It has been shown by the author that the ammonium and rubidium salts , of the two great rhombic and monoclinic isomorphous series studied in detail , exhibit a remarkable facility for the formation of mixed crystals .
* The analogous potassium and rubidium salts , or the rubidium and caesium salts , show very little such tendency to crystallise together , and the potassium and caesium salts , which differ most in molecular volume and topic axial ratios , practically never crystallise together .
G. Wulff has also independently discovered the fact as regards potassium and rubidium sulphates , obtaining perfect mixed crystals of these salts , while he found potassium and caesium sulphates to be totally immiscible , which he attributes to the great difference in their molecular volumes ; he , too , obtained only very imperfect mixed crystals of either ammonium or rubidium sulphate Indeed the rhombic form of ammonium selenate ( which salt usually crystallises exceptionally in a monoclinic form , being dimorphous ) isomorphous with potassium , rubidium , caesium has only hitherto been obtained by the author in large crystals when admixed with more or less rubidium selenate .
It is for this reason ( inability to prepare the pure rhombic form ) that ammonium selenate is not included in this comparison .
'Zeitschr .
fur Kryst .
vol. 42 , p. 558 ( 1906 ) .
VOL. XCIII.\mdash ; A. Dr. A. E. H. Tutton .
with potassium or caesium sulphate .
Further , T. .
Barker has in beautiful series of researches , that the facility for forming overgrowth crystals or parallel growths of one salt of an isomorphous series on another is dependent on ruency of structure , as indicated by closeness of molecular volume and topic axial ratios ; and that the rubidium and ammonium salts of the same acid ( sulphates , chromates , and perchlorates were studied ) exhibit the property par excellence , while the corresponding potassium and caesium salts either form no such over- or parallel growths at all , or do so to a very low minimum extent .
Hence , we are compelled to conclude , the evidence being overwhelming , that the crystal structures of ammonium and rubidium sulphates ( and of the double sulphates or selenates containing these two alkali bases and the same dyad-acting metal ) are almost identical isostructural , that is ; congruent to a remarkable degree .
But this conclusion obviously means that the two atoms of rubidium are replaced by the 10 atoms of without any opening up of the structure .
In other words , the structure must either be already sufficiently open to permit of the insertion of the eight additional atoms , or the volume of the two ammonium radicle groups must be approximately the same as that occupied by the two rubidium atoms .
This conclusion has an important bearing on the valency volume theory of Barlow and Pope , as has been pointed out in the author 's memoirs .
No adequate explanation has been given of the difficulty .
The essence of the theory is that each valency in a given compound has the same volume , and that , therefore , the atomic volumes of combined elements are directly proportional to their valencies .
The theory is , of course , entirely inconsistent with Kopp 's idea of molecular volume .
Thus , in the two monadic potassium atoms are each supposed to occupy unit volume , the four dyadic oxygen atoms each to occupy two volumes , and the sulphur atom is , considered , somewhat arbitrarily , to also only dyadic and to occupy K two volumes ; the total volume thus be .
Similarly , the two rubidium and caesium atoIIlS in the isomorphous salts would occupy the same relative volumes of two out of twelve ; and the relative total volumes , as expressed directionally by the " " equivalence parameters\ldquo ; employed by Barlow and Pope ( who discard topic axial ratios ) , are also practically identical for the three salts .
The theory does not account at all for the considerable increase * Journ. Chem. Soc vol. 89 , p. 1120 ( 1906 ) , and 'Mineralog .
Mag vol. 14 , p. 235 , and vol. 15 , p. 42 Jo/ lrn .
Chem. Soc vo ] .
89 , p. 1675 ( 1906 ) ; vol. 91 , p. 1150 ( 1907 ) ; vol. 93 , p. 1528 ( 1908 ) .
X-Ray and Topic Axes of the Alkali Sulphates .
77 in molecular volume on passing from the potassium salt through the rubidium to the caesium salt , corresponding to the very considerable rise ( more than tripling ) in the atomic of the metal , and to the tripling of the atomic number , and indeed ignores it .
In their very first paper Barlow and Pope take*the case of the sulphates and selenates of potassium , rubidium , and caesium as an example of the working of their theory ; they omit all reference to ammonium sulphate , however .
They employ the author 's experimental data , and give a Table , which is reproduced below , of the " " equivalence parameters\ldquo ; , which they calculate like topic axial rabios , except that they use the sum of the valencies , the valency volume , instead of the author 's molecular volume to , gether with the author 's crystal-axial ratios .
It will appear from this Table that any one and the same parameter for the three different salts of each group ( sulphate or selenate ) remains almost unaltered .
average Barlow and Pope 's Equivalence Parameters difference shown by any one of the three parameters for the two extreme ( potassium and caesium ) salts of each group is less than 1 per cent. Indeed , the maximum difference over the whole six salts , that due to the replacement of sulphur by selenium , is only just 2 per cent. for the third parameter , and it is only 1 per cent. for the first parameter , and per cent. for the second parameter .
The real directional changes , however , as shown by the topic axial ratios ( Table on p. 80 ) , are 10 per cent. in either group , and 12 per cent. over the two groups from to , while the real change in total volume is as much as one-third .
In connection with this Table , Barlow and Pope say specifically that the interchangeable elements of the same group of the periodic system are represented by spheres of atomic influence of nearly the same size as compared with the sphere volumes of other constituents .
In the latest memoir , contributed by Mr. Barlow to the 'Mineralogical ' Journ. Chem. Soc vol. 89 , p. 1724 ( 1906 ) .
'Mineralog .
Mag vol. 17 , p. 314 ( 1916 ) .
Dr. A. E. H. Tutton .
Magazine , ' a disposition is shown , in referring to the first -ray results of Prof. , to admit that those results demonstrate the value of the constant , molecular olume .
For he states : " " When isomorphous substances of similar atomic composition are compared , close similarity of the pattern formed by the atomic centres of iven kind common to the compared bodies is associated with a marked difference of scale , viz. of actual dimensions .
Thus the distances the sulphur atoms in potassium sulphate will not be the same those separating the atoms in caesium sulphate ; corresponding dimensions of the two bodies will be approximately in the ratio of the cube roots of the respective molecular volumes Yet on the next , very ically , Mr. Barlow again recommends the use of the and Pope equivalence parameters to represent the changes , in which parameters not the molecular volume but the yalency volume ( identical for the whole series ) forms the volume factor , the result shown being consequently infinitesimal change .
Now , it will be at once apparent that if we replace by we shall , according to the valency volume theory , be replacing two unit volumes by 10 atoms of volume 14 , taking nitrogen at its lower triadic valency , and , therefore , as of volume 3 , and hydrogen as 1 , the whole salt then having a volume of 24 ; if nitrogen be pentadic , as is more logical and more in accordance with chemical facts , clearly four more units of volume must be added , making 28 .
That is , to the valency volume theory , and on the lower estimate , we double the volume , from 12 to 24 , on passing from rubidium sulphate to am1nonium sulphate .
This , however , has been shown by the author not to occur , but that , on the contrary , the volumes of the ammonium and rubidium salts are almost identical and closely congruent .
It has appeared to the author that in the -ray spectrometric analysis of crystals , brought to such perfection by Prof. W. H. and Mr. W. L Brag , * we have a new method of attack , which affords a crucial test of the validity , on the one hand , of the author 's conclusions based on his experimental results and the conceptions of molecular volume and topic axial ratios , and , on the other hand , of the valency volume theory of Barlow and Pope .
The author therefore ested to Prof. Brag that an X-ray analysis of the rhombic alkali sulphates and selenates would prove of extreme value ; Prof. happily concurred and arranged for such an analysis to be carried out in his laboratory , with crystals supplied by the author , many of them being the actual crystals employed in the author 's published investigations .
The ork has been carried out by Prof. A Ogg and Mr. F. Lloyd Hopwood , and a first paper of results has been published in 'Philo-rays and Crystal Structure , ' G. Bell and Sons , 1915 , 2nd edition , 1916 .
Topic Axes of the Sulphates .
79 sophical Magazine ' for November , 1916 , vol. 32 , p. 518 .
These results , it may be said at once , have proved conclusively that the atnmonlum and rubidium salts are , indeed , practically iso-structural , the actual dimensions ( absolute volumes and distances in space ) of the space-lattice elementary cells having been measured , and found to be precisely as closely identical as is indicated relatively by the molecular volumes and the topic axial ratios .
The dimensions for the potassium and caesium salts , moreover , are found to be considerably different , just as much so , in fact , as is by the molecular volumes and topic axial ratios for those salts .
The actual directional dimensions in space , as measured directly by the -ray spectroineter , are wonderfully close to the author 's values for the topic axial ratios .
These latter constants , therefore , are both justified and verified .
On the other hand , there can be no other conclusion than that the valency volume theory is not based on fact , and is fallacious , The actual numbers , both of the topic axial ratios and of the -ray spectrometric dimensions for the sulphates , are given in the accompanying Tables , an inspection of which cannot fail to be impressive and conclusive in the sense just indicated .
The important values to be compared are those in the right-hand portion of the second ( middle ) Table ( topic axes when for , ith the lengths of the sides of the unit rhomb in the third ( bottom ) Table .
The actual volumes in the last column of the bottom Table show very clearly the closeness of the volumes of the rubidium and ammonium salts , just as do the molecular volumes given in the first Table .
The actual lengths of the elementary cell edges given by Prof. and Mr. Hopwood , expressed in terms of cm .
, happen to be on the scale of 10 times greater than that of the relative distances given by the topic axial ratios ; indeed , if " " \ldquo ; be written after each of the author 's topic axial ratios when for , these latter relative values become converted Densities , Molecular Volumes and Crystal Axial Ratios ( Tutton ) .
Dr. A. E. H. Tutton .
Topic Axial Ratios Absolute Dimensions of Space-Lattice Cell ( Ogg and Hopwood ) .
into the actual distances in space .
Remembering this , the differences between the two sets of constants are wonderfully small , less than one in a thousand ( the actual differences varying from to per cent Too much stress must not be laid on this , however , as the actual numbers in the last resort depend on the angular values for the reflections observed in the X-ray spectrometer , a list of which is given by Prof. Ogg and Mr. Hopwood .
The agreement between these angles and tbose calculated from the figures in the third Table is amply adequate , however , to substantiate the facts stated .
The calculation of the of directly from the -ray measurements , given later on p. 83 as an example , afforded , for instance , the value , with a possible error not exceeding 1 in 500 .
Hence , the results are fully trustworthy .
The values given in the middle Table for the topic axial ratios , in which the unit is taken as the value for the first salt of the series , potassinm sulphate , are new ones now given for the first time , derived by use of the author 's latest determinations of the density of the crystals by the Betgers immersion method .
The values formerly however , which depended on the less trustworthy pyknometer density determinations , nowhere show appreciably greater differences from the -ray values , the boreatest being per cent. , as against per cent. in the case of the new values .
'Journ . .
Soc vol. 83 , p. 1067 ( 1903 ) .
Topic Axes of the Alkati Sulphates .
81 The formulae used in determining the topic axes of these rhombic crystals , referred to in the middle Table , were as under:\mdash ; where are the crystal-axial ratios and is the molecular volume .
They relate to the unit cell of ular rhombic form , that is , a rectangular brick-like block with three different edge-lengths , corresponding to the three crystal axes .
As topic axial ratios are relative , the author reduces them to their simplest form by dividing out by the value of the potassium salt , the first member of the series , the topic axial ratios in the case of this salt becoming then identical with the crystal-axial ratios .
Indeed , it has to be remembered that the topic axial ratios are in the same proportion to each other as the crystal-axial ratios , being modified correto molecular volume , so as to show how the latter is directionally distributed .
In the first paper on these sulphates , in the year 1894 , the author* pointed out that there was a considerable amount of evidence that the full crystal umit , the smallest edifice possessing the complete details of symmetry of the crystal structure and which ( considered as a point ) by its regular repetition affords the space-lattice , was composed of four molecules of .
Now , it is exceedingly interesting that Prof. and Mr. Hopwood find this to be a fact , indubitably indicated by their X-ray analysis .
The rectangular parallelepipedal cell , the edges of which are the of their measurements , is that formed by taking analogously situated atoms , whether these be metallic , sulphur , or oxygen atoms , one from each set of four molecules to act as their representative point .
In the author 's later papers the idea of the necessity for molecules at all in the crystal structure was not referred to , as the purely geometrical theory of crystal structure , now complete , regards the structure as essentially one of atoms .
But the author has always considered this to be carrying geometry too far , further than either the chemistry or the physics of the organised solid , the crystal , warrants .
It is a satisfaction , therefole , to find that the work of Prof. Brag and his colleagues now shows that there is a real advantage in and necessity for thus marking off the molecules , if only in order to obtain a correct idea of the structure which is essential to the crystal as such .
The work of Prof. Ogg and Mr. Hopwood is not yet complete as regards the details of the structure , but sufficient has been done to render it almost certain * Journ. Chem. Soc vol. 65 , p. 662 ( 1894 ) .
Dr. A. .
H. Tutton .
that the sulphur atoms are situated at the corners and centres of the faces of the unit cell , as shown in the accompanying .
Owing to the angles the centre of the face of the rhomb bounded by and edges being near , it is to be remarked that the sulphur atoms would thus exhibit a ) structure in planes parallel to the basal plane , the face ( 001 ) .
It is also stated in their paper as probable that the metallic atoms are also arranged in .
This is particularly interesting , for Fedorov has proposed a pseudo-hexagonal Arrangement of the sulphur structure for these rhombic ates , as being atoms in unit cell of spaceindicated by his crystallo-chemical analytical lattice of alkali sulphates .
of finding the method correct setting of crystals. .
In deference to this , the author*recalculated the topic axial ratios for such a pseudo-hexagonal space-lattice , using the new densities which had just been determined ; the points of the lattice were the same as for the rectangular lattice , but the diagonal distances between them were taken as forming four sides of the hexagon ( two equal pairs ) , along with one oi : the rectangular axial directions only , which furnished the other two sides ( one equal pair , but not quite equal to the others ) , such a lattice having angles of nearly exactly .
These facts are doubtless not unconnected with the remarkable manner in which the crystals often display a hexagonal ) sometimes by twinning ( as in the well-known triplets of potassium sulphate , which resemble short prisms doubly capped by pyramids ) , and sometimes by mere habit on the part of the crystals ( as in the case of the apparently hexagonal double pyramids of rubidium sulphate ) , the angles in the primary prism zone , formed by the faces of , being very nearly .
The pseudo-hexagonal topic axial ratios do not enable a comparison to be made with the measurements of Prof. and Mr. Hop- wood , hence the necessity for now hing the new values corresponding to the rectangular form .
The mode of arriving at the results of and Mr. Hopwood may be briefly described .
The actual distances between the centres of the atoms forming the corners of the rectangular elementary cell , or , in other 'Journ .
Chem. Soc vol. 87 , p. 1188 ( 1905 ) .
metallic or oxygen atoms may here be equally as well specified as the sulphul atoms , provided they are similarly analogously chosen , one from each set of four molecules ; for the same space-lattice applies in common , being formed by any representative analogous points , one from every structural uuit composed of four molecules .
-Ray Analysis Topic Axes of the .
83 words , the distances between the consecutive planes in each of the three sets of parallel planes of atoms corresponding to the faces of the three primary pinakoids ( 100 ) , ( 010 ) , and ( 001 ) , were obtained from the measurements of the angles of reflection of the -rays from these faces in reality from the interior planes of atoms parallel to the tces ) .
The now well-known equation is eluployed:\mdash ; where is the order of spectrum ( first , second , or third ) , is -length of the -radiation used ( in this case from a palladium anticathode ) , is the glancing angle of re{iection of the -rays , and is the distance in question between successive planes of atoms .
We have only to insert the observed value of the , the wave-length ( already determined by the use of the crystals best worked out by Prof. , such as the alkali chlorides , and confirmed by independent methods ) of the particular line of the of the radiation used , and the numerical order of the spectrum , in order at once to obtain the distance required .
For instance , when the value of for the line employed in the spectrum from the palladium anticathode used was , and the glancing for this radiation in the second order spectrum reflected from the ( 100 ) .
face of potassium sulphate was , the value of for planes of atoms parallel to this face was found to That this corresponds to a structural unit composed of four nlolecules is proved by the following:\mdash ; Molecular of , density Ratio of crystal-axes : 1 : NIass of the hydrogen atom Mass of unit rhomb of 4 molecules also grrIl .
Then from the known axial ratio values of we find cm .
, cm .
, cm .
Volume of unit rhomb The equality of the value of and that for obtained above shows that the assumption that there are four molecules of ] iu the elementary cell is correct .
Dr. A. E. H. Tutton .
The work in Prof. 's laboratory on the corresponding selenates .
has been interrupted for the present , but , as the author 's values for the morphological constants on the same rectangular basis as regards the unit cell will be required when it is resumed , they are given in the two Tables on pp. As ards the valency volume theory , there is now much evidence , from the work of other ators , that the theory can no longer be entertained .
It has always appeared to the author to be unlikely to represent the truth .
Until , however , definite experimental evidence of a decisive character was , such as that now afforded by the -ray analysis , the author has not felt justified in expressing his views .
It appeared most unlikely that a theory could be correct which does not admit the undoubted very considerable increase in volume ( one-third of its bulk ) which occurs on replacing potassium in potassium sulphate by caesium , the equivalence parameters of Barlow and Pope showing an almost negligible change , as already pointed out connection with the Table of these parameters given on p. 77 .
A considerable increase was in any case to be expected , corresponding to the increase in complexity and in material content of the atom ( probably by the addition of further rings or other distributions of negative electrons , in accordance with Moseley 's law ) , indicated by the rise in atomic weight from to , and of the atomic number from 19 to 50- .
Yet , while taking practically no note of this , the theory asserts that volume of the atom , of the low atomic weight 16 and atomic number 8 , is twice as Jreat as that of the caesium atom , or whatever alkali atom is present in combination with the oxygen .
Moreover , it has been possible to put forward the theory only by the aid of what cannot be called anything else than quite rrantable arithmetical manipulation of the crystal-axial ratios , the arbitrary dividing or multiplying of certain ratios by various numbers to suit the exigencies of the theory .
This manipulation has been defended by the authors of the theory and is maintained and used extensively by Barlow in the very latest memoir on the subject , justifiable on the ground that a certain amount of arbitrariness exists in the choice of the crystal axial planes .
It is argued that planes corresponding to the manipulated ratios may be considered equally as valid for axial planes as those chosen by the rapher who measured the crystals .
This contention , however plausible , is not to be substantiated .
There is always some good reason for the choice of particular planes for axial planes , such as the fact that these planes were the vastly predominating ones developed as faces , and were 'Mineralog .
Mag vol. 17 , p. 314 ( 1916 ) .
Analysis and Topic Axes of the Atkali Sulphates .
85 parallel or otherwise definitely related to the cleavage planes discovered Moreover , Fedorov*has recently indicated means by which the proper setting of a crystal , which involves the proper choice of axial planes , can be checked and in doubtful cases determined , so that there is no tYer any excuse for the incorrect choice of these fundamental planes .
In general , the decision afforded by Fedorov 's method is given in favour of simplicity and low indices for the other planes developed on the crystal .
Barker , who has made a special study of Fedorov 's method , and has worked in his laboratory at Petrograd , has shown , however , in typical cases taken from among those put forward by Barlow and Pope , that the new crystal elelnents arrived at their manipulations lead in to greater complexity of the indices of the other faces , in some cases , indeed , rotesquely so .
This indicates the inherent improbability that the manipulation was justifiable .
Barker has further shown that ninety of the hundred examples put forward by the supporters of the theory are tainted with this arbitrary and rrantable manipulation of the axial ratios .
Further , that on the most ) fenerous basis uot more than five cases out of the hundred can in any sense be regarded as .
in consonance with it , and not one of them actually demands the theory as the sole or even the best explanation .
A very important contribution to the subject has also been made by Prof. Theodore Richards Harvard ) in two memoirs dealing with the subject which he has made his own , the compressibility toms .
He shows that the valency volume theory is directly opposed to the results of his investigations , and that it leads to extraordinary and highly improl ) able conclusions .
Richards , indeed , can find no plausible reason why each valency in a given compound should have the same volume .
He gives one remarkable illustration of the impossible situation in which the theory lands its supporters , that the relationship between beIJzene and tetrabromobenzene .
There is no reason why all the remaining carbon and atoms in benzene should nearly double their volume when four atoms of bromine are substituted for hydrogen , as the valency volume theory demands .
The more reasonable explanation , as all Kopp 's work shows , is that the atomic volume of bromine in combination is much larger than that of , as we should obviously expect it to be from its much greater atomic complexity ; but they are the same , each of unit volume , according to the valency volume theory .
Richards shows , moreover , that the most striking argument advanced by * E. S. Fedorov , 'Crystallochemical Analysis ' ( Russian ) , 1914 ; 'Zeitschr .
vol. 53 , p. 337 , and vol. 54 , p. 17(1914 ) .
'Journ .
Chem. Soc vol. 107 , p. 744 1915 ) .
'Journ .
Amer .
Chem. Soc vol. 35 , ( 1913 ) , and vol. 36 , p. 1686 ( 1914 ) .
Dr. A. .
H. Tutton .
Barlow and Pope , derived from the results of Le Bas for the moleoular volumes of the liquids of normal paraflins just above their points , is an entire fallacy .
He shows that ( quite apart from the fact that these are liqnids and not solids , and that an arbitrary temperature is chosen for the comparison ) the agreement between the molecular volumes and the calculated on the -Pope basis of vol. vol. , is no better than would occur on almost any other assumption .
For instance , if the volume of the carbon be taken as twice that of the hydrogen , the agreement is practicaJly as , and if carbon be taken as five times hydrogen , the yreement is twice as good .
memoirs of ichards are particularly interesting , and relevant to the qnestions raised in this communication , as they deal specifically with the isophism of the ammonium and potassium salts .
He considers its explanation quite beyond thel.each of the valency volume theory , ives to ammonium nine volumes ( accordin , to ichards , but seven according to Barlow and Pope , who take arbitrarily as triadic instead of pentadic ) , but to potassium only one volume .
He finds it hard to see how any sort of netry could be ucted in the two cases under the circumstances .
The work on collpressibility of atoms , however , that the five atoms up the radicle possess about the same as the potassium ( or , better still , according to the author 's work , rubidium ) atom , and are compressed by their mutual aflinities into a shape not unlike that occupied by the compressed and distorted alkali metallic atom .
Richards finally shows that the volume occupied by a solid is dependent on the uriable forces come into play , and which are not arbitrarily determined but are inherent in the atoms , and that every change in affinity must ) roduce its corresponding change in volume .
On the other hand , Barlow and Pope assume that the spheres of influence of atoms expand and contract to fit their theory of valency volumes , for which there is no plausible reason .
Their theory takes account of numerous facts such as : that less cohesive elements have large molecular volumes and large compressibilities ; that isomers the more volatile are also the more compressible , are less dense , and possess less surface tension and greater coefficients of expansion ; that , in general , the exhibition of greater chemical affinity involves , reater diminution in volume ; and the very large internal pressures which must exist in solids .
Indeed , Richards concludes that the doctrine of ency volume is irreconcilable with a broader view of the nature of solids and liquids and the mechanism of chemical change .
Barlow and Pope replied* to the first paper of Richards , but after the : .
Amer .
Chem. Soc , p. 1675 ( 1914 ) .
-Ray Analysis Topic Axes of the Alkali Sulphates .
87 second they published only a short note , which the statement was made that a weighty reason rendered further discussion at that time 1914 ) f.utile , namely , that the last year or two a method for the practical determination of crystal structure has been developed by Laue , and W. H. and W. L. Brag , which gives every promise of ultimately leading to very precise information the arrangement of the atoms in a crystalline structure . .
Further discussion may well be postponed until the important developments which are pronlised have had time to mature This time would appear now to have arrived , and the results of Prof. Ogg and Mr. Hopwood , obtained in the laboratory of Prof. , have furnished the crucial test , which is decisively against the valency volume theory .
Careful study of the melnoirs of Barlow and Pope , and of the expedients emplo.yed therein , leads to the anticipation of the possibility of the suggestion being put forward , to explain the now inlcontrovertibly proved isostructure of ammonium and rubidium sulphates , that although there are 24 valency volumes in and only 12 in , the actual spheres of lniC influence in the former are on a smaller scale than in the latter , namely , on a one-half scale , thus in the total the same volutne .
Such an assumption , however , would be even more arbitrary than that denounced by Richards in the case of tetrabromobenzene ; or than that which they made concerning the replacement of in KI by ( according to which the volume of the iodine suffers a shrinkage of five-sevenths of the bulk which it occupies in the potassium salt ) , and which has been by Barker to be most unreasonable .
Indeed , the assumption would .
not be merely arbitrary , but positively absurd .
In the openino words of his last memoir , communicated to the Royal Society only very shortly before his lamented demise , Sir William stated : " " It is now almosG universally acknowledged that the valency of an element is due to its being associated with one or more electrons This idea as to the nature of valency , which assigns a practical meaning , that of an attaching electron or electrons , the valence-electron , to the older idea of a " " bond is one which is rapidly developing from the great progress now being made in our knowledge of the nature of the atom , due very largely to the researches of Sir J. J. homson , Sir E. Rutherford , van den Broek , Bohr , and Moseley .
Indeed , it is a natural corollary to the beautiful structure of the atom , as we now know it from these researches ; and especially from the revelation in the work of Moseley ( unhappily his last ) 'Journ .
Amer .
Chem. Soc vol. 36 , p. 1694 ( 1914 ) .
' Journ. Chem. Soc vol. 101 , p. 2496 ( 1912 ) .
' Roy .
Soc. Proc vol. 92 , p. 461 ( 1916 ) .
Dr. A. E. H. Tutton .
of the important function of the atomic number in corresponding to the positive nuclear charge , and thereby determining the number of negative satellite electrons in the electrically stable atom .
The idea of the valence-electron or electrons was most worked out by W. C. Arsem*in 1914 , and its logical outcome was to show that the valency of an atom is a natural result of the dynamic relations between molecules and the atoms of which they are composed .
We shall , doubtless , hear a reat deal more about this view of valency in the near future .
It is impossible to conceive , however , of any connection whatever between valency of such a nature and the volume of the atom or its sphere of influence .
On the other hand , the conception of atomic and molecular volumes , and their directional expression in topic axial ratios , is in complete harmony with this new knowledge of the structure of the atom .
Finally , the decisive result of the -ray analysis of the sulphates of the alkalis may be accepted as substantiating a truth which had already been indicated by a body of evidence , derived from all sides , namely , that the valency volume theory of Barlow and Pope has no foundation in fact .
On the other hand , the indications of the constants molecular volume and topic axial ratios , for the members of any isomorphous series of crystalline substances , are proved to express accurately the structural relations of such substances .
of Condusions .
1 .
An -ray spectrometric analysis of the orthorhombic crystals of the alkali sulphates , , where represents potassium , rubidium , caesium , and ammonium , carried out in the laboratory of Prof. W. H. by Prof. A. and .
F. Lloyd Hopwood , has indicated that four molecules of are contained in the unit rectangular cell of the space-lattice , as was suggested by the author in the year 1894 .
2 .
The atoms of sulphur occupy the corners of the rectangular cell and the middle point of each side ; they lie , therefore , in planes separated at distances equal to half the lengths of the sides .
The planes of sulphur atoms parallel to the ( 001 ) face ( the basal plane ) are of pseudo-hexagonal structure , the points ( atomic centres ) being arranged in nearly regular hexagons , a structure which has been suggested by Fedorov and adopted by the author ( Tutton ) .
The metallic atoms ( K. Rb , or Cs ) are also probably in nearly ular hexagons .
3 .
-ray spectrometric measurements , based on the accurate knowledge of -length of the -radiation employed ( a specific line in the radiation from a palladium anticathode ) , of the actual lengths ( absolute distances in ' Journ. Amer . .
Soc vol. 36 , p. 1655 ( 1914 ) .
X-Ra .
Analysis and Topic Axes of the Alkali Sulphates .
89 space ) of the edges of the rectangular orthorhombic cells of the spacelattice ( dlstances apart of the centres of the atoms in the three rectangular axial directions , or of the metallic or oxygen atoms , when similarly analogously chosen , that is , one from each set of four molecules to represent the crystal unit ) , agree perfectly with the topic axial ratios for these salts determined by the author .
A new series of the latter constants is now published for the ular space-lattice , based on later , more refined density determinations than those given in 1903 ; both the old and the new values are in excellent reement with the -ray measurementQ .
4 .
The congruency or close approximation to identity of the structures of rubidium and ammonium sulphates , indicated by the molecular volumes and topic axial ratios published by the autnol ( not only for these simple sulphates , but for every pair of double sulphates and selenates iu which the bases rubidium and ammonium , as in the example of ammonium nickel and rubidium nickel selenates brought forward in a separate paper* ) , is thus confirmed by absolute measurement by the -ray spectrometric method .
The absolute volumes of the unit cells of the space-lattices of the two salts are within 1 per cent. of identity , just as are the molecular volumes , and the absolute lengths of the three edges for the two salts are correspondingly close to each other , and in a manner precisely like that shown by the topic axial ratios .
5 .
It is thus fully substantiated that the constants molecular volume and topic axial ratios afford true indications of the relative volume and dimensions of the elementary space-lattice cells , in the cases of the crystal structures of isomorphous series .
6 .
As the volume of the unit cell of ammonium sulphate should be at least twice that of rubidium sulphate according to the valency volume theory of Barlow and Pope ( that is , if we assume triadic valency for nitrogen , since the sums of the fundamental valencies of and are respectively 24 and 12 ) , and more than twice if nitrogen be pentadic ( the volumes then being 28 to 12 ) , whereas the volumes of the unit cells of the two salts are now proved by direct -ray measurement to be nearly identical , it is obvious that the valency volume theory does not represent a law of nature .
A crucial test thus now been applied , and the decision is against the theory .
* See preceding Abstract .
|
rspa_1917_0006 | 0950-1207 | Address of the president, Sir J. J. Thomson, O. M., at the anniversary meeting, November 30, 1916. | 90 | 98 | 1,917 | 93 | Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character | Sir J. J. Thomson, O. M. | speech | 6.0.4 | http://dx.doi.org/10.1098/rspa.1917.0006 | en | rspa | 1,910 | 1,900 | 1,900 | 2 | 130 | 4,413 | http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1917_0006 | 10.1098/rspa.1917.0006 | null | null | null | Biography | 89.213197 | Thermodynamics | 3.831582 | Biography | [
39.069053649902344,
78.25731658935547
] | 90 Address of the President , SirJ .
J. , , at the Anniversary Meeting , November 30 , 1916 .
It is a pious custom , hallowed by long usage , that your President at the Anniversary Meeting should begin by paying , on behalf of the Society , tribute to the memory of those of our members who have been taken from us since our last Meeting .
This year our losses have been almost unprecedentedly severe , and are so numerous that it is impossible , in the time at our disposal this afternoon , to describe at all adequately the work those we have lost have accomplished , and their manifold claims to our respect ; for this we must look to the Obituary Notices which have been , or will be , published by the Society .
My words must be few and inadequate .
Shortly after the last Meeting , by the death of the Right Hon. Sir Henry Enfield Roscoe , we lost one who , for more than half a century , had been foremost in promoting the interests of Science and Education .
He was renowned not only for his researches , but also for his success as a teacher and expositor ; he organised at the Owens College , Manchester , a school which was for long the most important centre of research in chemistry in this country .
As a student at the Owens College in the seventies I have a vivid recollection of the influence he exerted on the development of what is now the Yictoria University of Manchester , as well as on the extension of the chemical industries of the district .
He was a wise and unbiased counsellor , ever ready to help in any project which he thought would improve the condition of the country .
By the death of Sir William Ramsay we have lost a chemist whose discovery of the rare gases in the atmosphere has been among the greatest contributions made by this country to science .
The founder of a great school of research at University College , a great teacher , a man of unbounded energy and remarkable independence of judgment , his loss , while full of vigour and ideas , has deprived English Science of one of its greatest personalities .
Dr. Henry Debus was a veteran of veterans among teachers of chemistry , and had been a Fellow of the Society for more than fifty years .
Prof. Silvanus Thompson had for long plnyed a prominent part in the development of electrical science in the country , he was a man with many gifts , literary and artistic , as well as scientific , a most successful teacher , and a remarkably clear expositor , whether with tongue or pen .
He had an unrivalled knowledge of the literature of physics , which enabled him to Anniversary Address by Sir J. J. Thomson .
91 render invaluable service to the Society as Chairman of the ' Catalogue of Scientific Papers .
' In Mathematics we have lost Dr. Benjamin Williamson and Prof. Esson , who combined with their mathematical knowledge powers of organisation and administration which made them play a great part in their respective universities .
The University of Edinburgh , as well as our Society , suffered a severe loss by the death of Sir William Turner .
In addition to being a great anatomist , he was a man of much influence and a very successful administrator , and was for many years foremost in all questions relating to Scottish universities .
Medical science has lost Sir Victor Horsley and Sir William Lauder Brunton .
Horsley was a pioneer in the surgery of the brain , and showed all the surgeons of the world how to operate on the brain and spinal cord .
He gave his life to help his country in this war , going to give much-needed help to our troops at the front in Mesopotamia , and there he died at Masara , in July .
Lauder Brunton was renowned for his contributions to medical science and for his skill as a physician .
The death of Dr. Keith Lucas through an accident , when flying , adds another name to the Roll of Honour of Fellows of the Royal Society who , during the war , have lost their lives in the service of the country .
At the beginning of the war he joined the Royal Aircraft Factory at Farnborough , and devoted his remarkable inventive power to making improvements in the equipment of aeroplanes ; in this work he was very successful .
He possessed unrivalled powers of design in physical apparatus for the investigation of physiological problems , and this faculty enabled him to make researches in regions of physiology which were beyond the reach of other workers .
He delivered the Croonian Lecture in 1912 .
His death leaves a gap in physiological science , and in the circle of his friends , which it will be difficult indeed to fill .
% Physiology has sustained another loss by the death of Prof. Brodie , of the University of Toronto , who made important investigations on the kidney , of which he gave an account in the Croonian Lecture for 1911 .
By the death of the Right Honourable Sir James Stirling , a Senior Wrangler , for many years a judge in the Chancery Division , and from 1900 to 1906 a Lord Justice of Appeal , we have lost a wise counsellor , and one who was ever ready to help the Society with his legal knowledge and experience .
Mr. Roland Trimen , a Darwin Medallist , and at one time Curator of the South African Museum , was well known both for his own researches in natural history and for his association with those of Darwin and Wallace .
VOL. xcni.\#151 ; A. I 92 Anniversary Address by Sir .
Thomson .
Dr. Scott , formerly Secretary to the Meteorological Council , had , been for long closely associated with the progress of meteorological science in this country .
Sir William Henry Power , K.C.B. , for some time Medical Officer to the Local Government Board , was a leading authority on the question of public health , and received the Buchanan Medal in 1907 .
There are few , if any , in this country who have done more than Sir William Power to advance the cause of scientific hygiene .
Sir Clements Markham was one of the veterans of Arctic exploration , and a former President of the Royal Geographical Society .
Prof. Judd was a distinguished geologist who was for long Professor at the Royal College of Science .
Prof. H. H. W. Pearson , whose name appears both in the list of newly-elected Fellows and the Obituary list , was an enthusiastic botanist , whose premature death will be a great blow to the progress of botany in South Africa , where he was a professor .
Mr. Charles Booth rendered great services to the country by his remarkably interesting and important investigations on Social Statistics .
By the death of Prof. Metchnikoff , a Foreign Member and Copley Medallist of the Society , Science has lost a great leader and France one of her most eminent citizens .
He will ever be remembered by his investigations on inflammation and on immunity to infective germs and the poisons produced by them .
To quote the words of Sir Ray Lankester , " he was especially honoured and revered by every Zoologist in the world , for it was to him that we owed the demonstration of the unity of biological science and the brilliant proof of the invaluable importance to humanity of the structure and laws of growth of the lower animals , which he had pursued from pure love of the beauty and wonder of the intricate problems of organic morphology .
" The death of Prince Galitzine and Prof. Backlund has deprived our ally Russia of two of the most prominent and distinguished of her men of science .
Prince Galitzine , who died shortly after election as Foreign Member , had , it is hardly too much to say , revolutionised the science of Seismology , while Dr. Backlund , the distinguished head of the great observatory of Pulkowa and renowned for his researches on Encke 's comet , had many warm friends in this country and rendered great services to the English astronomers who went to Russia to observe the eclipse in 1914 .
Besides those who have been removed by death from the roll of the Society , there are some who have lost their lives while fighting for their country , whom we had hoped at no distant date to welcome into the Society and thereby mark our appreciation of the services they had rendered to science .
Anniversary Address by Sir J. J. Thomson .
93 I can mention but two names : Mr. Geoffrey Smith , whose contributions to biology had marked him out as one to whom that science would owe much , and Prof. McClaken , the author of valuable investigations on the difficult problem of the Equipartition of Energy .
Of these and other young men of science fallen in the war we may say in the words of Dr. Montague James , " Many and diverse were the hopes and expectations we had formed for them , but every one of these has been surpassed by the event .
They have all been found capable of making the greatest denial of self that men can make ; they paid away their own life that the life of their fellows might be happy .
" During the past year the work of the Society as a body as well as that of its members individually has been concentrated on problems connected with the war .
The Physiological Committee has done important work on the food supply of the country .
The Engineering Committee have been busy with applications of their science to Naval and Military purposes ; the Chemical Committee with the preparation of substances of which the supply has been interrupted by the war .
The Society has been entrusted with the difficult task of selecting those chemists whose services could be employed more advantageously in chemical work than in active service at the front .
The Society has also compiled a register of trained scientific workers which has proved exceedingly useful in finding men competent to attack the many scientific investigations demanded by the war .
The National Physical Laboratory has during the past year been working at high pressure on investigations of great importance to the country at this crisis .
Apart from the work of the Society as a body , very many of our Fellows have since the war began been engaged with investigations directly connected with it .
The resources of almost every laboratory in the country have been employed on work intended to be of service to our Army or Navy .
The number and nature of these researches is striking evidence of the extent to which even the most recondite branches of science can find application in modern warfare .
Many of these investigations are of extreme difficulty , effects have to be detected amidst the noise of a battleship or the din of an engagement which it would formerly have been thought somewhat of a feat to measure in the quiet of a laboratory .
The work , too , has to be done as a race against time , and when , from conditions arising from the war , apparatus and assistance are very difficult to obtain .
I think the experience we have 94 Anniversary Address by Sir J. J. Thomson .
gained in the past two years points very strongly to the desirability of having as part of the permanent establishment of both the Army and Navy , special laboratories , properly equipped and in close touch with the services , whose work should be the discovery and development of applications of Physical , Chemical , and Engineering Science for Military and Naval purposes .
The cost of modern warfare is so great that the expense of these laboratories over long periods of peace would be more than recouped if they succeeded in saving a single battleship or ensured the success of an attack .
Second only in importance to questions connected with the successful prosecution of the war is the question how best to remedy those defects in our industrial organisation and educational methods which have been revealed under the stress to which the country has been exposed by the war .
Many of these are closely connected with science but they are no less closely connected with economic and political considerations .
For example , we have been taught by bitter experience that it is not safe to have regard to nothing but money profit in developing the industries of the country , we have to recognise that the possibility of the country being attacked by bitter and powerful enemies is one that cannot be lost sight of , and that when this happens it makes a great deal of difference to the strength of a country whether the energies of its people have been directed to production or to importing and selling on commission the productions of the enemy .
We cannot , however , produce everything , and the selection of what we should produce is a vital one and depends as much upon economic and political considerations as upon purely scientific ones .
It is , I think , important in any consideration of this subject to remember the duality of this question , for the kind of scientific training required for those who are to develop these industries will depend upon the industries selected , and we must arrange this training so that it is appropriate to the industrial conditions\#151 ; it is no use making ammunition if it will not fit the guns .
It may , for example , require some changes in our industrial organisation to get the full benefit of the application of scientific research to our industries .
There are probably but few firms in the country but would benefit from an increase in the research work they undertake , and this not only from the commercial value of the results obtained , but from the spirit of vigour , youthfulness , and independence which successful research brings in its train .
We must remember , however , that many of the most important lines of research in applied science may require such an expenditure of time and money as to be beyond the powers of any firms which have not quite exceptional wealth and resources , and even with these , the English impatience at any Anniversary Address by Sir J. J. Thomson .
expenditure which does not show a clear prospect of an early return , together with a wide prevalence of a lack of intensity of faith in the certainty of obtaining any results by the application of scientific methods , would make it difficult for even a powerful company to carry its shareholders with it in undertaking a research which might take many years ' labour and great expenditure before any profit was obtained .
It would seem that for research to have its full effect on our industries , associations must be formed among those engaged in any particular industry\#151 ; developments of the idea which is embodied in the old Trade Guilds and City Companies\#151 ; and that one of the primary functions of these associations should be research for the benefit of the industry , carried out in Institutes connected with the association .
There are fortunately indications that the formation of associations is already under consideration in certain industries .
We must be careful , however , and I think this might be regarded by the Royal Society as one of its most important duties , that the badly needed increase in research in applied science is not accompanied by any slackening off in research in pure science , that is , research made without the idea of commercial application , but solely with the view of increasing our knowledge of the laws of nature .
Even from the crudest utilitarian point of view , nothing could be more foolish than the neglect of pure science , for most of the great changes that have revolutionised or created great industries have come from discoveries made without any thought of their practical application .
It may seem paradoxical , but I think it is true , that , the more remote an investigation appears to be from the regions which appear most promising from the point of view of the established industrial practice of the country , the greater are the effects it may produce on the industries of the country .
Applied science may lead to reform in our industry , it is to pure science we must look for revolutions .
It is not the improvement of old ideas , but rather the discovery of new ones , which produces the most revolutionary effects .
It is often said that in this country we have been slow in seeing the possibilities , for industrial purposes , of new discoveries in pure science , and I am afraid there is some truth in the accusation .
One of the reasons for this is , I think , that there has not in the past been sufficient co-operation between the workers in pure science and those who are responsible for the control of our great industries .
By such co-operation I do not mean that the physicist or chemist should work himself at any industrial application of his discoveries ; he is wanted for other things , and there are others familiar with the industry who could work out the application far more effectively .
What I do mean is that , if possible application of a discovery occurred , say to a physicist , it should be easy for him to go to the proper quarters and be able 96 Anniversary Address by Sir J. J. .
to point out the possibility to those best able to carry it into effect .
Ome of the objects of the newly formed Conjoint Board of Scientific Societies is to promote closer union between workers in pure and applied science .
One difficulty connected with these plans for reconstruction after the war is , I am afraid , formidable .
They all require a large increase in the supply of able and well trained workers .
How , where are they to come from ?
Already before the war the demand exceeded the supply ; since the war training for the scientific professions has necessarily ceased , and many of those who had been trained have fallen .
We are faced with the position that the demand will be increased when the supply is below even the normal amount .
We must tap new sources of supply .
The only source I can see likely to yield an adequate number is the elementary schools of the country .
We must try if we cannot " comb " out , to use the word of the moment , from these schools all the boys able to profit by further training , and try to prevent them drifting into employment of secondary importance to the State .
There is at present lamentable leakage between primary and secondary schools , and also from the secondary schools themselves , for which the State is , to a considerable extent , responsible .
It considers with great care the kind of training to be given in our elementary schools , but when a child has been through this training it gives no guidance whatever as to how it can best be used for the service of State .
We want badly some machinery for instructing people what best to do with their children after passing through the primary school .
Something which will point out as simply as possible the callings open to them , the training required for these , the assistance which the State would give , if necessary , towards this training , and the opportunity for employment and remuneration after the training has been completed .
We want to make the advantages of secondary education much more tangible than they are at present .
The position with regard to the supply of adequately trained workers is critical , and calls for earnest and immediate attention .
I now pass on to the most gratifying part of our proceedings this afternoon , the award of the medals .
The Copley Medal is awarded to Sir James Dewar .
For more than fifty years he has been indefatigable and most successful in his efforts to increase natural knowledge .
In collaboration with Dr. Living he made long and most important series of spectroscopic investigations , which have recently been published in a collected form .
His well known long continued investigations on the liquefaction and solidification of gases have been one of the most striking features of modern science .
Hot only has he Anniversary Address by Sir J. Thomson .
97 taught us how to liquefy gases on a large scale , but he has made notable investigations on the properties of matter at the low temperatures which can only be obtained by their use .
His investigations on specific heats of elements at low temperatures , and those made with Dr. Fleming on the effects of low temperatures on the resistance of metals , have yielded most interesting and suggestive results .
Many of the most interesting and important investigations made in Physics in recent years would have been impossible but for his invention of the method of obtaining very high vacua by the use of charcoal immersed in liquid air or hydrogen .
The nation owes a debt of gratitude to Sir James Dewar for his unwearied work , which the Royal Society tries to acknowledge by awarding him the Copley Medal .
The Rumford Medal has been awarded to Prof. William Henry Brag for his researches into the nature and property of the rays from radioactive bodies and on other kinds of ionising radiations .
His experiments on a-rays threw a new* light on the nature of the absorption of a-rays by matter and showed that the a-rays from each radioactive transformation have a definite and characteristic range depending on their initial velocity .
Lately Prof. Brag , working in collaboration with his son , Mr. W. L. Brag , has made most important investigations on the interference spectra of X-rays reflected from crystals ; these investigations , which formed the subject of the Bakerian Lecture , 1915 , have led to a method of great beauty and power for the investigation of the molecular structure of crystals , which has already yielded results of the first importance .
A Royal Medal has been awarded to Prof. Hector Munro Macdonald for his researches in Mathematical Physics .
Prof. Macdonald is the author of an important series of papers on the diffraction of electrical waves by a large spherical obstacle , a problem which is of especial importance in connection with the transmission over the earth 's surface of the waves used in wireless telegraphy .
He has also made a valuable contribution to the theory of Bessel 's functions and has obtained results which promise to have important applications to some problems in Mathematical Physics .
His work has extended over a wide range , for , in addition to his work on electrical waves , he has made valuable contributions to Hydrodynamics , Elasticity , and Optics .
The other Royal Medal has been awarded to Dr. John Scott Haldane for the important contributions he has made to Physiology , especially on the 98 Anniversary Address by Sir J. J. Thomson .
subject of respiration .
His studies of the combination of carbon monoxide with haemoglobin have been fruitful in many directions .
They led him to the investigation of gas explosions in coal mines , which has had important results in the saving of life in mines .
He has also studied the effect of high temperatures under varying conditions of moisture on the human body , and was the first to lay down the definite conditions under which it is possible to withstand high temperatures or to work in them .
His work shows the rare combination of a wide philosophic insight into fundamental problems with the power of applying the knowledge gained from scientific researches to the every-day needs of the community .
The Davy Medal is awarded to Henri Louis Le Chatelier , who , as the result of much investigation , introduced the Le Chatelier thermo-electric couple and inaugurated a new period in the measurement of high temperatures .
In co-operation with M. Mallard he made extensive investigations on the ignition and explosion of gaseous mixtures , in which several principles of first-rate importance were established .
He was one of the pioneers in micrometallurgy and one of the first to introduce exact methods and clear ideas into the science of industrial silicates .
His work has been carried out in close relation to the practical application of science , and his discoveries have been of great industrial importance .
The Darwin Medal is awarded to Prof. Yves Delage for his important investigations on the development of Sponges and for his contributions to Biology and Zoology .
The Sylvester Medal is awarded to Prof. Jean Gaston Darboux , Perpetual Secretary for Mathematical Sciences to the Academy of Sciences , one of the most distinguished of contemporary French Mathematicians .
He has published work of the first importance on the Theory of Surfaces , the Theory of Partial Differential Equations , Kinematics , and the Planetary Theory .
The Hughes Medal is awarded to Dr. Elihu Thompson , one of the pioneers of Electrical Engineering , for his important contributions to that subject .
|
rspa_1917_0007 | 0950-1207 | Motion of solids in fluids when the flow is not irrotational. | 99 | 113 | 1,917 | 93 | Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character | G. I. Taylor, M. A.|Prof. H. Lamb, F. R. S. | article | 6.0.4 | http://dx.doi.org/10.1098/rspa.1917.0007 | en | rspa | 1,910 | 1,900 | 1,900 | 17 | 164 | 4,934 | http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1917_0007 | 10.1098/rspa.1917.0007 | null | null | null | Fluid Dynamics | 77.236247 | Measurement | 12.370674 | Fluid Dynamics | [
48.84410858154297,
-32.32695007324219
] | ]\gt ; Motion of Solids in Fluids when the Flow is not By G. I. TAYLOB , M.A. ( Communicated by Prof. H. Lamb , F.R.S. Received April 13 , 1916 .
) The chief interest in the results obtained in the following pages lies in the fact that a mathematical result has been obtained concerning the motion of solids in fluids which is vel.ified accurately when recourse is had to experiment , with real solids moving in real fluids .
This is so exceptional a circumstance that it is hoped that the interest which it ives to the mathematical work will serve to extenuate , to a certain extent , the clumsiness of the methods employed .
The problem solved is two-dimensional .
An infinite cylindrical body of any cross-section moves in a uniformly flnid with its generators parallel to the axis of rotation .
The stream lines and the reaction between the solid and the fluid are found .
Suppose that a stream function has been found which represents the irrotational motion of an incompressible fluid when a cylindrical solid several cylindrical solids ) of the required cross-section is moved in an assigned manner starting from rest in a fluid which has a given boundary or has a given irrotational motion at infinity .
is a function of the -ordinates of a point in a plane perpendicular to the axis of rotation , and , the time .
Since the motion is irrotational satisfies the relation everywhere , and at the solid boundaries , where represents the velocity normal to the boundary of a point on the surface of cylindrical solid moving in the fluid , and repr sents the rate of change in measured in a direction along the solid boundary .
These , together with the conditions at infinity , if the fluid is unenclosed , are the necessary and sufficient conditions for determining .
The components of velocity of the fluid are then and Now consider the function , ( I ) where is a constant both in regard to space and to time .
It satisfies the dynamical equations of motion , for , which is constant ; and it is the stream function of the fluid motion obtained when the whole system represented by is rotated with uniform yular velocity VOL. XCIII.\mdash ; A. Mr. G. I. Taylor .
Motion of Solids in about the origin .
The boundary conditions of the rotating system evidently satisfied if the cylindrical solids move relative to the rotating stem in same way that they moved relative to fixed axes in the case of the motion represented by .
Hence it appears that the system consisting of the cylindrical solids and the fluid in which they move may be rotated without the motion of the fluid relative to the rotatin system , provided the cylinders are constrained to moye , relative to the rotating system , in the same way that they moved , relative to fixed axes , when the system was not If , however , the solids are free to move under the action of their own inertia and of the pressure of the fluid , the rotation will make a considerable difference to the relative motion of the solids and the fluid .
It therefore becomes important to find the pressure at any poin Let be the pressure at the point in the irrotatlonal case , and let be the pressure when the whole system is rotated .
The equations for and are , ( 2 ) ' ( 3 ) where and are the components of velocity in the rotational motion .
The symbol has been used to represent the rate of change , at a point fixed in space , in the component of velocity parallel to a fixed direction which momentarily coincides with the axis of This is not the same thing as .
Since may be regarded as being known in terms of the co-ordinates and , referred to axes , and the time , represents the rate of in the component of the velocity of the fluid which is parallel to the rotating axis of at a point which moves with the axes .
It is evident that and To find the value of and , consider the rate of , at a point fixed in space , in the component of velocity parallel to a fixed direction which momentarily makes an angle with the axis : * It will be shown later that this proposition cannot be extended to the case of the three-dimensional motion .
Fluids when the not Irrotational .
The component of the velocity of the fluid parallel to this direction is After a short interval of time , , the co-ordinates of the fixed point relative to the axes are and The components of velocity parallel to the rotating axes ( which now make an angle with their previous positions ) are and The component of velocity parallel to the fixed direction is therefore .
The rate of change in velocity parallel to the fixed direction is therefore Putting we find and putting Substituting these values in ( 3 ) , subtracting equations ( 2 ) and substituting for and , it will be found that - and These equations may be integrated in the form .
( 4 ) At this stage it is easy to prove that the proposition proved on p. 100 cannot be extended to the case of three-dimensional motion .
Let be the components of the velocity of a fluid in irrotational motion .
Suppose that the motion defined by is possible .
Mr. G. I. Taylor .
tion of Solids in as before , it will be found that the pressure equations can be reduced to These are not consistent unless and are independent of ; that is , unless the motion is two-dimensional .
Let us now apply ( 4 ) to find the resultant force and couple which the fluid pressure exerts on a solid moving in a rotating fluid .
Let , and be the resultant forces and couple due to fluid on the solid in the case when the system is not and supposed to act at the centre of gravity of the area of the crosssection of the solid .
Let , and be the corresponding quantities in the case when the system rotating .
If represents the angle between the normal to the surface of the solid and the axis , then and are the co-ordinates of a point the surface referred to axes parallel to the axes of and , and passing through ; and the integrals are taken round the surface of the solid .
the value of given by ( 4 ) may be orated .
Thus ( 5 ) Now since .
Also where A is the area of cross-section of the solid , and are the coordinates of centroid .
Fluids when the Flow is ?
2 may be rated by parts .
It then ecomes ( 6 ) since .
evidently vanishes .
represents the velocity of the fl normal to the surface of the solid .
The boundary condition which must be satisfied by is where is the angular velocity of ) body .
Substituting iu ( 6 ) and that \amp ; d and , it will be found that The these rals vanishes and the second be written Now -A and , since , is centroid of the area of cross-section .
Hence from ( 5 ) ) Similarly it will be found that It will be noticed that and are the components of a ARE radially , being the distance of from the centre of rotation .
Also 2 and are the components of a force 2 AQ acting at right angles to the direction of motion of relative to the axes , the relative velocity of C. Now consider the couple due to rotation .
Substituting from ( 4 ) , .
Mr. G. I. Taylor .
Motion of Solids in Neglecting all terms which contain only powers of or of and integrating the second integral by parts , this becomes Now and ; also since leduces to The forces due to fluid pressure , which act on a body moving in an assigned manner in a rotating fluid , may therefore be regarded as being made up as follows:\mdash ; ( 1 ) The forces , and the couple which would act on the body if it moved in the same way relatively to the fluid at rest .
( 2 ) A force equivalent to acting towards the centre of rotation through C. ( 3 ) A force acting at in a direction perpendicular to the relative motion of and the rotating axes , and directed to the left if the rotation of the fluid is anti-clockwise .
We can solve any problem on the motion of cylindrical solids in a rotating fluid if we can obtain a solution of a similar problem respecting the motion of the solids in a fluid at rest .
Now , consider the forces and the couple which is necessary to apply to a solid body of mass , in order that it may move in an assigned manner relatively to axes .
Suppose that a force and a couple must be applied at its centre of ravity , in order that it may move in the assigned manner relatively to fixed axes .
The additional force which it is necessary to apply when the system is rotating uniformly with angular velocity may be shown to consist of a force perpendicular to the direction of the velocity of the centre of gravity relative to the rotating system , together with a force acting through the centre of ravity towards the centre of rotation .
* For they vanish when integrated round a closed contour .
Ftuids whoen the is not Irrotational .
It will be noticed that , if the position of the centre of gravity of the solid coincides with the centroid of its cross-section , and if the mass per unit length of the solid is equal to , that is to say , if the mass and the centre of gravity of the solid are the same as those of the fluid displaced , then these forces are the same as those which on the solid .
to the additional pressures in the fluid due to its rotation .
These considerations lead to the conclusion that , if a solid of the same density as the fluid be moved , a certain path by certain assigned external forces , then a uniform rotation of the whole system , the external force , makes no difference to the path which the solid pursues relative to the system .
This theorem applies only to the case of two-dimensional motion .
In the case of a finite cylinder , for instance , it seems almost obvious that pressures due to the rotation must fall off towards its ends .
It is natural to suppose , therefore , that the reaction of the fluid would not sufficient to hold a finite cylinder in its path when the whole system is rotated .
The case of a sphere in a rotating fluid presents considerable mathematical difficulties , but the initial motion has been ated by .
J. Proudmall , who has kindly conscnted to allow the author to make use of his results , , they are not yet published .
* He finds that , if sphere of volume starts from rest iu the fluid and moves with uniform velocity a straight line relative to the system , it is acted on initially by a force directed towards the centre of the rotation which is at a distance from the centre of the sphere ) by a force acting in a direction perpendicular to its path .
But in order a sphere of the same density as the fluid , that is , one whose mass is may nlove along a path relative to the system , it mnst be acted on by a force directed towards the centre of rotation and by a force perpendicular to its path .
The forces due to fluid pressure are not sufficient to supply the second of these .
If , therefore , the sphere were drawn the fluid by means of a string , it would not move in the direction } string was pulling it , but would be deflected to the left if the fluid were rotating clockwise , and to the if were anticlockwise .
On the other hand , if cylinder of the same density were drawn the ting fluid , the force necessary to hold it in its straight would be supplied by the fluid pressure .
The cylinder would therefore move the fluid in the direction the string pulling it .
* Since the above was written Mr. oudman 1 results .
They appeared in ' Roy .
Soc. Proc , vol. 92 , pp. 408-424 .
Mr. G. I. Taylor .
Motion of Solids in These conclusions have been tested and completely verified by means of experiments made by the author in the Cavendish Laboratory .
with water in a rotating tank .
a Tank of A glass tank full of water was mounted so that it could be rotated about a vertical axis at various speeds by means of an electric motor .
The speeds varied from 2 to 6 seconds per revolution .
Two bodies were prepared , one and the other sphelical .
The former consisted of a piece of thinwalled brass tube about 6 in .
iu .
stopped at the end with waxed cork , while the other was a spherical glass bulb .
They were weighted until they would fall very slowly water , and the positions of the were adjusted till they would stay almost at rest in any position in .
the water .
The centres ravity of the bodies were then coincident with the centres of ravity of the water displaced by them .
A sinlple mechanism was next devised to tow them through the tank from one end to the other .
It consisted of a wood pulley about 4 inches in diameter , mounted on a vertical spindle lich was driven into a wood bridge , fixed to the tank over the middle of it .
This spindle coincided with the axis of ation of the tank .
Cotton was then wound round the pulley , passed through some small rings screwed into a board fixed to one end of the tank , and led horizontally along the tank to the cylinder or sphere , which was fixed at the other end .
The body was held in a holder while the tank and water were being brought to a state of uniform rotation .
A device was arranged so that the holder could release the body and at the same moment the wood pulley on which the cotton was woumd could be fixed in space .
As the tank was then rotating round the pulley the cotton wound up round it , and pulled the bodies along the middle of the tank from one end to the other .
Result.\mdash ; It was found that the cylinder through the middle of the tank .
Even when the tank was very rapidly the cylinder always passed over the central line .
The sphere , however , was violently deviated to the left ( the tank was rotating clockwise ) .
When the tank was rotated quite slowly , about once in 6 seconds , the sphere would not quite touch the side , though it ' came up to the stop at the other end from a direction less than away from the central line .
When the tank rotated more rapidly the complete path could never be seen , because the sphere always hit the side of the tank before it had gone more than a few inches in the direction along which the cotton was trying to pull it .
After striking the side of the tank the sphere would follow the side along , touching all the time , Fluids when the Flow is not till it to a position close to the other end where the string was pulling in a direction making an angle of about with the side of the tank .
It would leave the side and approach the point towards which the cotton was pulling it along a curved path .
The accuracy with which the experiments just described verify the hydrodynamical theory of rotating fluids is at first sight ulost .
Besides the fact that there is apparently no case in which experiments made with real solids moving in real fluids agree with the predictions of hydronamics , it is known that the stream lines of a real fluid round a circular cylinder in particular bear no resem'ulance to the stream lines used in the ordinary hydrodynamical theory .
It will be noticed , however , that in order that there may be agreement between theory and experiment in the articulal .
respect to whicn attention has been drawn .
it is that the actual flow pattern shall be the same as the flow pattern contemplated in the ordinary hydrodynamical theory .
All that is necessary is that the flow pattern in the case of the cylinder shall be two-dimensional , while that in the the sphere shall be three-dimensional .
, nents 'n ; ith Vorte , 'Rings The theory explained on p. 1051eads to the conclusion that if a homogeneous solid , which is not cylindrical , be projected in a fluid of the same derlsity as itself it will be deviated , to the left if the rotation is clockwise , and to the right if the rotation is anti-clockwise , of the path it would pursue through the fluid if the whole system not rotating .
vortex ring affects the fluid round it in much the same way as a solid of the same dimensions as the cyclic portion of the flow system .
If it is projected through a fluid at rest it travels along a straight line .
We should expect , therefore , that if a vortex ring were projected through a rotating fluid it would follow a curved path relative to ) fluid , to the left the fluid were rotating clockwise .
This conclusion was tested experimentally and found to be correct .
small vortex box with a rubber top and a circular hole in the side was made .
This was filled with a solution of fluorescein and placed in one end of the tank , which was filled with water and held fixed .
On striking the rubbel lightly a vortex ring was produced which travelled straight down tlJe tank and struck the middle of the opposite end .
The same experiment was repeated when the tank and vortex box were rotating .
On tapping the box , rings started out in the same direction as before , but were deflected in a curved path , so that they hit the side of the end of the tank .
By the box quite htly and rotating the Mr. G. I. Taylor .
Motion of Solids tank fail .
lie rapidly the rings could be made to turn in such small circles that they came round and struck the vortex box again without the side of the tank on the way .
They would , in fact , turn in a circle whose diameter was only about four times the diameter of the rings .
It was ) ointed out by Dr. F. W. Aston , to whom the writer was showing this experiment , that the rings appeared to remain parallel to a plane fixed in space , while the rest of the fluid rotated .
He suggested that the yyroscopic action prevented the ring from being deviated this plane , and that in order that the ring might move relative to the fluid in a direction perpendicular to its plane it would have to move through the fluied along a curved path .
Jlolion of a which has a Jfotion at Infinity but does not Vecessarily Ras Whole .
The results in the rest of this paper have no immediate practical interest .
The author entered on the ation with a view to an idea of how the instability which is known to exist in a uniformly laminar flow would be likely to manifest itself , and to find out the characteristics of the motion of solids in fluids , which have been discussed in the first part of this paper , have any counterpart in the case of solids moving a fluid whose undisturbed motion is a uniform laminar flow .
The problem of the motion of a circular cylinder in a rotationally fluid divides itself naturally into two parts , that of finding the stream function for a boive motion of the cyiinder , and that of .
the force which the pressure associated with that stream function exerts on the cylinder .
The stream function for a certain type of rotational flow in which the vorticity is uniform will now be found .
Let be the polar co-ordinates of a poin referred to axes through the centre of the cylinder , and let be the co-ordinates of the centre of the cylinder referred to fixed axes , so that the equation represents a line parallel to the axis of , at a distance / from it .
Consider the stream function .
( 7 ) It satisfies the equation everywhere .
If , therefore , constants , etc. , be so chosen that the boundary condition ( S ) satisfied where being the radius of the cylinder , then is the Fluids ?
) the Flow is not stream function which represents the lnotion of a fluid which , if the cylinder were , would be moving in accordance with the velocities iven by the stream function . .
( 9 ) Now ( 8 ) must be satisQed for all values of ; hence we may equate coefficients of , and , separately to zero .
In this way the following relations between the constants are determined:\mdash ; ( 10 ) It will be noticed that , the stream metion of the fluid before the introduction the cylinder , is expressed in terms of co-ordinates referred to moving axes .
In order to find the motion of a cylinder in a fluid whose undisturbed motion before the introduction of the cylinder is known with reference to fixed axes , we must transform ( 9 ) so as to give in terms of co-ordinates and referred to the fixed axes used to fix the position of the cylinder .
The transformation is performed by then becomes .
( 11 ) If the motion of the fluid before the introduction of the cylinder be iven by the function where are given constants , we find , by coefficients of in ( 11 ) and ( 12 ) , the relations d in terms of and ?
, Solving ( 10 ) and ( 13 ) we obtain the following values of , 1 ) , ( 14 ) Mr. G. I. Taylor .
of Solids in Hence the stream function is obtained for the motion of a cylinder in a fluid whose undisturbed motion may be expressed by a stream function of the .
The two particular cases which are of the greatest interest are those of uniform rotation , for which , and uniformly laminar flow , for which the rate of shear .
Before , these cases , however , it is necessaiy to find an expression in terms of the force on the cylinder .
In tTeneral there does not appear to be a pressure like 's for the case of irrotational motion , or the expression given in equation ( 4 ) for pressure in a rotating fluid .
It is necessary to back to equations of motion of the fluid .
If the rate of in pressure along a direction which makes an with the axis of represented the symbol representing an element of in the direction , then the equation of motion is , where represents the component of velocity of the in the direction Its value may be found in terms of by the equation .
( 15 ) may be written where esents , as before , the rate of in at a point fixed in space .
If are the changes in the co-ordinates of a fixed point in time , ( 17 ) represents the rate of in at a point fixed relative to the axes .
The value of may ) obtained by the expression ( 15 ) with respect to time , which occurs in all terms which contain / 20 , or The values of and may be found by resolving the velocity of , the centre of the cylinder , along and perpendicular to Tlaus ; substituting in ( 17 ) , Fluids when the Flow is not substituting this in ( 16 ) , Now represents the component , normal to the surface , of the relative velocity of the fluid and the cylinder .
It must therefore vanish .
Hence and substituting for irom ( 10 ) , If be put equal to , we obtain the variation in pressure round the cylinder in the form .
( 18 ) If and represent the components of the resultant force acting on the cylinder due to pressure , These may be integrated by parts .
then becomes and ( 19 ) By substituting the value obtained for in ( 18 ) we can find the force exerted by fluid pressure when the , cylinder has any motion for which a stream function can be found .
This method will be applied to two particular cases : In Case ( 1 ) the general motion of the fluid is one of uniform rotation .
This problem been solved already in the first part of this paper , but it seems worth while to verify the calculation .
In Case ( 2 ) the general motion of the fluid is one of uniform shearing .
Case l.\mdash ; The stream function of the general motion of the fluid is Mr. G. I. Taylor .
Motion of Solids in .
Ill this case , then , and stream function of the lnotion round the cylinder is Substituting in ( 18 ) the value be found , and substituting this value in ( 19 ) it be found that , If these expressions be transformed by the transformation , so that , are the polar co-ordinates of a point referred to axes which rotate with the fluid , it will be found that the forces , may be resolved into components along , and perpendicular to it where This agrees with the results obtained on p. 104 , for the force whose components are and may be regarded as being made up in the following way : ( 1 ) a force acceleration of the cylinder relative to the rotating axes ) ; ( 2 ) a force acting towards the centre of rotation ; and ( 3 ) a force velocity of the cylinder relative to the rotating axes ) acting at right angles to the direction of relative motion .
These are evidently the same as the three forces discussed on p. 104 .
2.\mdash ; The general motion of the fluid is one of uniform .
The fluid moves parallel to the axis of with velocity , which increases at a uniform rate as increases .
In this case , which be written this with ( 12 ) it appears that and , while .
Hence from ( 7 ) and ( 14 ) Hence differentiating and putting Fluids when the Flow is not Hence from ( 18 ) Hence from ( 19 ) .
( 20 ) This result will now be applied to find the motion of a cylinder of the same density as the fluid when it is projected from the origin with velocity whose components are and The equations of motion of the cylinder are 01 The first of these may be integrated in the form constant .
That is to say , the component parallel to the axis of of the relative velocity of the cylinder and the fluid is constant and equal to U. The acceleration of the cylinder in the direction of the axis of ' is constant and equal to .
If , that is to say , if the cylinder is shot off in a direction perpendicular to the direction of shear , then the component of velocity parallel to the axis of is constant , and the fluid pressure is just sufficient to give the cylinder the acceleration , which is necessary in order that the velocity of the cylinder relative to the fluid round it may remain constant .
This property of uniformly fluids appears to be analogous to a certain extent to the property of rotating fluids discussed on p. 105 .
|
rspa_1917_0008 | 0950-1207 | On waves in an elastic plate. | 114 | 128 | 1,917 | 93 | Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character | Horace Lamb, F. R. S. | article | 6.0.4 | http://dx.doi.org/10.1098/rspa.1917.0008 | en | rspa | 1,910 | 1,900 | 1,900 | 15 | 164 | 3,477 | http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1917_0008 | 10.1098/rspa.1917.0008 | null | null | null | Fluid Dynamics | 48.388808 | Tables | 29.623776 | Fluid Dynamics | [
47.33682632446289,
-41.389129638671875
] | ]\gt ; in By HoPACE LAMB , F.R.S. ( Received July 10 , 1916 .
The theory of waves in an infinitely cylindrical rod was discussed by ochhammer in 1876 in a well-known paper .
* The somewhat simpler problem of two-dimensional waves in a solid bounded by parallel planes was considered by Lord ) and by the present writerI in 1889 .
The lnain ob.iect in these various investigations was to verify , or to ascertain small corrections to , the ordinary theory of the vibrations of thin rods or plates , and the wave-length was assumed in the end to be great in comparison with the thickness .
It occurred to me some time ago that a further examination of the twodimensional problem was desirable for more than one reason .
In the first lace , the number of cases in which the various types of vibration of a solid , none of whose dimensions is regarded as small , been studied is so icted that any addition to it would have some degree of interest , if merely as a contribution to elastic theory .
Again , modern seismology has various questions relating to waves and vibrations in an elastic stratum imagined as resting on matter of a different elasticity and density .
S questions naturally present great mathematical difficulties , and it seemed unpromising to attempt any further discussion of them unless the comparatively simple problem which forms the subject of this paper should be found to admit of a practical solution .
In itself it has , of course , no bearing on the questions referred to .
Even in this case , however , the period-equation is at first sight rather intractable , and it is only recently that a method of dealing with it ( now pretty obvious ) has suggested itself .
The result is to , I think , a fairly complete view of the more important modes of vibration of an infinite plate , together with indications as to the character of the higher modes , which are of less interest .
I may add that the numerical work has been ooreatly simplified by the help of the very full and conyenient Tables of hyperbolic circular functions issued by the Smithsonian Institution 'Crelle , ' vol. 81 , p. 324 ; see also Love , ' Elasticity , ' 1906 .
p. 275 .
Proc. Lond. Math. Soc vol. 20 , p. 225 ; 'Scientific Papers , ' vo1 .
.3 , ' Proc. Lond. Math. Soc vol. 21 , p. 85 .
S Love , ' Some Problems of Geodynamics , ' 1911 , Chap. XI .
'Hyperbolic Functions , ' Washington , 1909 .
I have to thank Mr. J. E. Jones for kindly verifying and , where necessary , correcting my calculations .
On in an Elastic 1 .
The motion is supposed to take place in two dimensions the ) being taken in the medial plane , and the axis of to this .
thickn of the plate is denoted by .
The stress-strain equations are , in the usual notation , , ( 1 ) It is known that the solution of the equations of motion is of type , ( 2 ) the functions subject to the equations where We now assume a time-factor ( omitted in the sequel ) , and write , ( 4 ) so that We further assume , for the present purpose , periodicity with pecC to is most conveniently done by means of a factor , the ) being accordingly .
( 6 ) Writing , ( 7 ) we have ) .
( 8 ) The equations ( 1 ) now ( 9 ) 2 .
When the motion is symmetrical with respect to the plane assume , in accordance with ( 8 ) , .
( 10 ) This gives , for the stresses on the faces .
( 11 ) VO L. XCIII .
Prof. H. Lamb .
these to zero , and eliminating the ratio , we have periodequation* In the most important type of long waves , , are all small , and the limiting form of the equation is whence in virtue of ( 4 ) .
Hence if be the wave-velocity This is in agreement with the ordinary theory , where the thickness is treated as infinitely small and the influence of lateral inertia is neglected .
For waves which are very short , on the other hand , as compared with the thickness , the quantities are , and the equation tends to the form .
( 16 ) This is easily recognised as the equation to determine the period of " " aylei waves\ldquo ; on the surface of an elastic solid .
It is known that the substance be incompressible the wave-velocity is whilst on Poisson 's hypothesis of .
( 18 ) These results will , in fact , present themselves latel . .
In virtue of the relations ( 4 ) , ( 7 ) , the equation ( 12 ) may be regarded as an equation to find when is given , i.e. to determine the periods of the various modes corresponding to any iven wave-length ; but from this point of view it is difficult to handle .
It is easier to determine the values of corresponding to given values of the ratio .
This is equivalent to finding the corresponding to a given wave-velocity .
Putting , in fact , , we find from ( 7 ) , ' ( 19 ) and therefore , ( 20 ) so that depends upon only .
An equivalent equation is given by Rayleigh .
Rayleigh , 'Proc .
Lond. Math. Soc vol. 17 , p. 3 ( 1887 ) ; 'Scientific Papers , ' vol. 2 , 1 ) .
441 .
On Waves in Elastic 4 .
For simplicity we will suppose in the first instance that the substance is incompressible , so that .
Putting the equation ( 12 ) becomes ( 22 ) whilst .
( 23 ) It is evident that real values of ?
must be less than unity .
Moreover we have , ( 24 ) which latter expression is easily seen to be positive so long as .
Hence as increases from , the first member of ( 22 ) increases from to its asymptotic value unity .
There is therefore one and only one value of corresponding to any assigned value of which makes the second member of ( 22 ) less than unity .
And since the right-hand member of ( 22 ) is less than unity for only so long as , which is the positive root of the second factor in ( 25 ) .
The admissible real values of therefore range from to .
The former of these makes , and gives to the value .
The values of corresponding to a series of values of between the above limits , together with the corresponding values of the ratio of wave-length to thickness , and the corresponding wave-velocities , are iven in Table I ( p. 118 ) .
So far has been taken to be real , or .
In the opposite case we may write , ( 26 ) and assume ) The period-equation is then found to be , ( 28 ) being still supposed to be real .
In the case of incompressibility , writing ur have whilst .
( 31 ) Prof. H. Lamb .
If as increases from we take vays the lowest root of ( 30 ) , we obtain series of values of continuous with the roots of ( 22 ) and down to zero , when .
This latter value makes , in agreement with the general formula for long waves .
Numerical results for a of values from to included in Table I. Table I.\mdash ; Symmetrical [ Ths unit of The relation between wave-length and wave-velocity for the whole of nlodes investigated in this and in the preceding section is shown by the Gllrve A on the opposite page .
The unit of the horizontal scale is ; Lhat of the vertical scale is . .
On the present hypothesis of incompressibility there is a displacement nction .
to the stream-function of hydrodynamics , viz. , we I .
( 32 ) Waves in an Elastic Plate .
The lines const .
give the directions in which particles oscillate , whilst if they are drawn for small equidistant values of the constant their greater 01 less degree of closeness indicates the relative amplitudes .
In the case of standing waves the system of lines retains its position in space ; in the case of a progressive wave-train it must be ined to with the waves .
If be real we find , omitting a constant factor , sinh .
( 33 ) In the opposite case we may write .
( 34 ) I have thought it worth while to make diagrams illustrating the configuration of the lines of displacement in the class of 1nodes of vibration which have so far been obtained .
The case of the Rayleigh waves , corresponding to , is , of course , of independent interest .
In the present problem their wave-length is nitely short ; but if we transfer the origin to the surface , and then make , we get , omitting a numerical factor , where .
On this scale the wave-length may have any value .
The diagram ( fig. 2 ) shows the great difference in the character of the motion , and the slow diminution of amplitude with increasing depth , as compared with the ' surface waves\ldquo ; of hydrodynamics .
* It follows , in fact , * Lamb , ' ' 4th ed. , art .
228 .
Prof. H. Lamb .
from ( 35 ) that the ratio of the vertical amplitude to that at the surface ( in the same vertical ) at depths of , 12 , wave-length , is 130 , respectively , whereas in the hydrodynamical probleln the corresponding In the case of , the displacement function is given by ( 34 ) .
I have chosen for illustration , as giving a wave-length neither too reat nor too small , the case of , which makes and , accordingly , .
( 36 ) The result is shown in fig. 3 , which , like the former , covers half a wave-length .
The diagram may be taken to illustrate also , in a general On Waves in Elastic Plate .
way , the most important type of longitudinal vibrations in a cylindrical rod .
6 .
The modes of vibration so far obtained include all the more interesting types , from the physical point of view , of the symmetrical class ; but there are , of course , an infinity of others .
These correspond to the higher roots of the equation ( 30 ) .
Thus when ?
we easily find the approximate solutions .
( 37 ) For ( 38 ) For ; ( 39 ) and so on .
In these modes the plane is mapped out into rectangular compartments whose boundaries are lines of displacement .
This may be illustrated by the case of , when the internal compartments are squares .
This happens to be particularly simple nwthematically .
The formula ( 34 ) for is indeterminate , but is easily evaluated .
It is found from ( 30 ) that for small concomitant variations of and about we have This leads to ( 40 ) with ( 41 ) where is an .
The configuration is shownl in for the case Prof. H. Lamb .
; but it is to be observed that the dotted lines in the diagram all represent nes which are free from stress , and that consequently any combination of them may be taken to represent free boundaries .
This particular solution is , moreover , independent of the hypothesis of incompressibility .
* The surfaceconditions ( 11 ) are , in fact , satisfied by , ( 42 ) which lead again to ( 40 ) and ( 41 ) .
is increased the compartments referred to become more elongated .
For large values of , and consequently small values of or , we in the limit is integral .
It is otherwise evident that the surface conditions are satisfied by , ( 43 ) whence .
( 44 ) vibration now consists of a shearing motion parallel to , with nodal planes symmetrically situated on opposite sides of .
The frequency is given by .
( 45 ) 7 .
When the motion is anti-symmetrical with respect to the plane we A , ( 46 ) are defined as before by ( 7 ) .
This gives for the stresses at the ( 47 ) These surfaces being free , we deduce .
( 48 ) noticed long ago by as a possible nlode of transverse vibration ( uniform throughout the length ) in a bar of square section , 'Theorie mathematique de ' 2nd ed. , p. 170 .
There an analogous solution in the case of the symmetrical vibrations of a cyd.ical .
The surface-conditi.ons given on p. 277 of Love 's 'Elasticity ' ( equation ( o4 ) ) are satistied ) In the notation of this paper the latter two conditions would be written .
Ray On Waves in an Elastic Plate .
When the waves are infinitely short this reduces to the form ( 16 ) appropriate to Rayleigh waves .
In the case of long flexural waves are small .
Writing , we find , ( 49 ) on the supposition that small , which is seen to be verified .
This makes , ( 50 ) in agreement with the ordinary approximate heory .
It may be pointed out in this connection that Fourier 's well-known calculation*of the effect of an arbitrary initial disturbance in an infinitely long bar is physically defective , in that it rests on the assumption that the formula analogous to ( 50 ) is valid for all wave-lengths .
As a result , it makes the effect of a localised disturbance instantaneously at all distances , whereas there is a physical limit , , to the rate of propagntion .
8 .
For the purpose of a further examination we assume the substance of the plate to be incompressible , so that , and write equatiolt ( 48 ) becomes where -velocity is given by ( 23 ) .
Since must be less than unity , whilst the second member of ( 51 ) exceeds 1 if , it appears that for real solutions we are restricted to values of ?
between and 1 .
A series of values of corresponding to of within this range is given on the next page .
The displacement-function is foumd to be The forms of the lines const .
for the case of are shown in fig. 5 , for a range of half a wave-length .
arded as to a stauding vibration , they indicate a rotation of the matter in the bourhood of the nodes , about these points .
* See Todhunter , 'History of the Theory of Elasticity , ' , p. 112 ; Rayleigh , Theory of Sound , ' vol. 1 , art .
192 .
Prof. H. Table II.\mdash ; Asymmetrical Type .
[ The unit of is ] small values cf If the value of V is given by equation ( 50 ) .
FIG. So far it has been supposed that , and consequently that is real .
In the opposite case we assume in place of ( 46 ) , ( 5.3 ) and the period-equation is , ( 54 ) where is defined by In the case of incompressibility this becomes where .
As the preceding investigation ( summarised iu Table ) evidently coyel'S all the modes in which has the same throughout the thickness , the additional modes to which this equation relates may be dismissed -ith the remark that they are fous to those referred On Waves in an Ptate .
to in S6 above .
The particular case is illustrated by if we imagine the lowest horizontal dotted line to form the lower boundary .
Infl uence of Comprcssibility .
9 .
the hypothesis of incompressibility has been adopted for simplicity , the numerical calculations , so far as the more important modes are concerned , are not much more complicated if we abandon this restriction .
It will be sufficient to consider the case of the symmetrical types .
We have from .
( 4 ) and ( 7 ) .
( 56 ) Hence if we write the equation ( 12 ) takes the form The relation of to the wave-length is iven by whilst the wave-velocity is given by ( 20 ) .
For numerical illustration , we may adopt Poisson 's hypothesis as to the relation between the elastic constants .
Putting , then , , we have , ( 60 ) .
( 61 ) Real values of must lie between and , this the positive root of the equation ( 62 ) obtained by equating the second member of ( 60 ) to unity .
The wavevelocity corresponding to this latter value is , ( 63 ) in accordance with the theory of Rayleigh waves , the wave-length being now infinitely small compared with the thickness .
Prof. H. Lamb .
When is imaginary , we have , ( 64 ) The more important modes coming under these formulae are determined by the lowest root of ( 64 ) for values of ranging from to , this latter number corresponding to an infinitesimal value of .
to waves of infinite length .
Numerical results are given in Table III , and the relation between wave-length and wave-velocity is shown by the curve in fig. 1 ( p. 119 ) .
The unit of the vertical scale is as before .
Table III.\mdash ; Symmetr [ The unit of As increases from , the modes corresponding to the higher roots of ( 64 ) have at first the same general character as in the case of incompressibility On lWaves in Elastic ( S6 ) .
When , we have the division into square compartments , to which fig. 4 refers .
When is infinite , whilst is finite , we have .
( 66 ) A reference to ( 11 ) shows , in fact , that , independently of any special relation between the elastic constants , the conditions are satisfied by and .
( 67 ) This leads to ( 68 ) There is here a transition to the case where , as well as , is Writing , ( 69 ) and assuming ( for the case of symmetry ) the period-equation is found to be Since we find , writing .
( 74 ) Also .
On Poisson 's hypothesis these become The value of may range downwards from to On Waves Elastic Plate .
A minute examination of these modes would be laborious , and old hardly repay the trouble .
In the extreme case where , the equation ( 76 ) is satisfied by either a zero value of , or an.infinite value of .
The former alternative gives the shearing motions parallel to already referred to at the end of S 6 ( equations ( 43 ) and ( 44 ) ) .
The other alternative gives a vibration at right an to 7 It is , in fact , obvious from ( 11 ) that the conditions are satisfied by , ( 78 ) whence , ( 79 ) .
( 80 ) When slightly exceeds , we have modes of vibration resembling the above types , except for a gradual change of phase in the direction of The corresponding values of , as given by ( 77 ) , are very great , but it is to be remarked that the notion of " " wave-velocity\ldquo ; is in reality hardly applicable ( except in a purely geometrical or kinematical sense ) to cases of this kind , and that results to modes lying outside the limits of the numerical Tables are more appropriately expressed in terms of frequency .
* As already remarked , there is a physical hmit to the speed of propagation of an initially local disturbance .
( ' Hydrodynamics , ' art .
261 , where a similar point arises .
|
rspa_1917_0009 | 0950-1207 | Magnetic induction and its reversal in spherical Iron shells. | 129 | 148 | 1,917 | 93 | Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character | J. W. Nicholson, M. A., D. Sc.|Ernest Wilson, M. Inst. C. E., M. Inst. E. E.|Prof. J. A. Fleming, F. R. S. | article | 6.0.4 | http://dx.doi.org/10.1098/rspa.1917.0009 | en | rspa | 1,910 | 1,900 | 1,900 | 16 | 294 | 7,795 | http://corpora.clarin-d.uni-saarland.de/surprisal/6.0.3/?id=rspa_1917_0009 | 10.1098/rspa.1917.0009 | null | null | null | Electricity | 45.048266 | Fluid Dynamics | 26.365286 | Electricity | [
31.5678653717041,
-63.05372619628906
] | ]\gt ; Magnetic Induction and its Reversat in Sphericat Iron Shells .
* By J. W. NICHOLSON , M.A. , D.Sc .
, Professor of Mathematics in the University of London ; ERNEST WILSON , M.Inst .
C.E. , M.Inst .
E.E. , Siemens Professor of Electrical , in the University of London , King 's College .
( Communicated by Prof. J. A. Fleming , F.R.S. Received November 30 , 1916 .
) In a previous communication to the Society , an account was given of am investigation of the magnetic of a large space , by the use of a series of spherical iron shells .
The basis of this investigation , which is still in progress , is strictly quantitative , and the work has been retarded , to a great extent , by the fact that several processes adopted commonly by various investigators of magnetic phenomena have never been examined accurately on the theoretical side , and in several cases even on the experimental side , to an order of precision which is sufficient for delicate measurements .
One of the main objects ultimately in view , in the work described already , is the production , hout the volume of a large iron specimen , of a magnetic field so small , in comparison with that of the earth , for example , as to render possible some accurate conclusions regarding the behaviour of iron under indefinitely small magnetic forces .
This behaviour is at present a matter of doubt , and it remains to be shown that he indications of its real nature , obtained in earlier papers by one of us , continue to point in the same direction when the force is decreased below any values which have been employed hitherto .
In the experiments described in the former paper , field so low as C.G.S. unit was obtained in a spherical space of radius cm .
by the use of four concentric shells .
It was accompanied , however , by a leakage field of C.G.S. unit , and the shells still showed some traces of permanent polarisation after continued treatment with many reversals of a slowly decreasing current .
This method of demagnetisation is used extensively , and in its application coils have sometimes been wound somewhat loosely on the iron to be demagnetised , and the constant field given by Maxwell 's formula for a spherical internal space surrounded by a very closely wound coil assumed to exist .
But if a thin shell is wound in this manner , although the more internal parts may be subject to this field , the results must be widely different in the outer material of the shell .
Further experimental work on * We wish again to acknowledge a grant for the purpose of researches on shielding , which was voted to us by the Council of the Society out of the Gore Fund .
'Roy .
Soc. Proc , vol. 92 , p. 629 ( 1916 ) .
Profs .
J. W. Nicholson and E. Wilson .
Magnetic the improvement of magnetic shielding beyond the order obtained already\mdash ; in fact by such methods as the employment of a very small netising current to remove , in the internal space , the small part of the earth 's field which may remain after the operation of the shielding effect of a set of shells \mdash ; requires a precise knowledge of the value of magnetic induction in a shell , or one member of a set of shells , wound by a spherical helical coil .
the condition of indefinitely close packing is found to be essential to the success of Maxwell 's formula , which\mdash ; but only from this particular point of view\mdash ; does not appear , either from an a priori theoretical consideration , or from the experimental results described in the present paper , to have the large of validity which has been assumed for it hitherto by practical workers on magnetic phenomena .
It is noteworthy that Maxwell himself did not claim any validity for his expression of the force inside a spherical helix when that helix was not in fact in the ideal state of close winding .
The use of such a helix for the purpose of demagnetisation of a hollow shell\mdash ; where importance attaches more to the material of the shell than to the air space within\mdash ; was not adopted at that time , and the practical problem had given no indication of its ultimate importance .
Evidently the spacing of the helix constituting an ordinary cylindrically wound solenoid , if small in comparison with the radius of the cylinder , would not seriously disturb the uniform distribution of magnetic induction in a thin iron bar placed along its axis , but at the outer surface of a thick bar filling the helix the distribution would be widely different .
We may argue from this by analogy to the spherically wound thin iron shells whose thickness is of the same order as the space between consecutive turns of the coil .
Apart from the case of a closely wound coil on a shell of non-magnetisable .
material , Maxwell did not consider the problem of the spherical helix in further detail .
No subsequent writer has taken up the question , and it has been necessary to include in this paper some preliminary theoretical discussion of the problems whose experimental investigation has been required .
The calculations relate to the ideal case of indefinitely close winding\mdash ; no simple mathematical treatment of a more practical case has yet been found\mdash ; and the results are compared with those found for the actual coils which were , described in the earlier paper .
An estimate of the effect of spacing in the helix is thus obtained , and the calculations are of importance in themselves , as indicating some quantitative relations , inherent in problems of this nature , which it would be difficult to obtain by general reasoning .
The distribution of magnetic induction in a set of shells , all of which may possess magnetisimg helices internally and externally , follows certain very curious laws .
Induction and its Reversal Iron Shells .
Into the experimental problem of reversal of the magnetic induction of a shell , two main factors en.ter .
The first the nature of the magnetising coil and the necessary current it must contain .
As stated already , the investigation of this problem is one of the main objects of the present paper .
But in addition , demagnetisation of a mass of iron is much retarded by eddy currents set up in the iron by any change applied to the magnetising forces .
These currents , while flowing , shield the inner shells , in the case of a set , from the effect of the changed field , and if the reversals of current in coils are made too quickly , the process is very inefficient as a demagnetising agency , for , in the time occupied by two reversals , the effect does not penetrate to the inner part of the iron .
The latter part of the paper contains a further contribution to the study of this phenomenon , as it is necessary to obtain some estimate of the time required between reversals , for small .
values of the magnetic induction .
Previous work on eddy current phenomena has been almost completely restricted to cases in which the average magnetic indu ction is of a much higher order of magnitude than in the present experiments .
Before proceeding to a description of the experimental work , it is desirable to give some .
account of the solution of the theoretical problems which are involved , and which have not hitherto received attention .
The analysis required throughout , however , is a fairly simple extension of a well-known method of treating a set of shells without magnetising coils , and for this reason the work is set out somewhat briefly , and , in certain of the cases , only the final results are quoted when there is no novelty in the mode of treatment or when the complete ation is somewhat long , and only interesting from the point of view of its fiual results .
No attem is made to deal with other than the ideal cases in which the magnetising heliees are wound extremely closely .
In this manner , two simple surface conditions become applicable at every coil\mdash ; the continuity of normal magnetic force , and a discontinuity of a prescribed amount in the magnetic potential\mdash ; as shown in the following section .
But the of magnetic induction in the actual set of shells similar , in a general manner , to that calculated for these ideal cases , whose consideration has , in fact , served to direct the experimental work into the most fruitful channels .
The Spherically ing Coil .
The fact that a coil wound closely over a sphere of unit permeabihty , with all its turns perpendicular to the same diameter , produces a uniform internal field is well known .
* For a diameter , with turns each carrying a current * Maxwell 's ' Electricity and Magnetism , ' vol. 2 , para .
676 ( ed. 1873 ) .
VOL xcm.\mdash ; A. Profs .
J. W. Nicholson and E. Wilson .
Magnetic the strength of the field is parallel to the diameter .
Maxwell quotes also the formula for the magnetic potential outside such a region in the same circumstances , as the result of a investigation into the theory of current sheets .
It can , however , be obtained at once by direct integration and , as the need for such a proof appears to be marked , the investigation follows .
If OA is the diameter , and there are turns per unit length of diameter , the number in any section of centre X is , each carrying a current FIG. 1 .
where .
The solid angle subtended at by these currents ia , where is the angle in the figure , and , for a radius of the sphere , the netic potential of the whole system at is in where , if OP and thus rrino : The integral may be evaluated eadily to which may be generalised at once after the usual manner of potential theory to at an external point referred to the centre and diameter .
The external effect is therefore that of a simple magnetic doublet of moment , situated at the centre of the sphere .
The normal magnetic intensity on the surface of the sphere is with , or , and is continuous with that derived from the In.duetion its Reversal in Spherical Iron Shells .
internal potential .
The potential itself , on the other hand , is discontinuous at , for ( inSin)cos a so that the amount of the discontinuity is .
These constitute the two surface conditions mentioned already as applicable at the surface of the coil , and they admit of an instructive comparison.with the corresponding conditions for a spherical shell magnetised normally at every point\mdash ; the discontinuity of potential is in this case , where is the strength of the shell .
We may now consider a spherical helix wound closely on a shell of non-magnetic material , enclosing a concentric shell , of inner and outer radii and , and of permeability .
The radius of the coil is , and it is wound with turns per unit length of diameter , each carrying a current .
With the origin at the centre , and the diameter perpendicular to the windings as initial line of polar co-ordinates , the field in the hollow of the inner shell may be defined by a potential , whereas in the magnetic material of the inner shell the potential is of the form Capital letters denote constants as usual .
Between this shell and the coil , and outside the coil , the potentials are respectively The usual conditions are fulfilled at the two surfaces of the shell of permeability , thus These four equations may be supplemented by the conditions at the coil , where .
These are and Accordingly whence from the solution of the six equations .
These values are , as might be expected , independent of the radius of the magnetising coil , which remains Profs .
J. W. Nicholson and E. Wilson .
gnetic equivalent , in its effect on an inside iron shell , to a uniform magnetic field external to the shell .
The most convenient magnitude for measurement in such a thin shell is the maximum transverse induction ( transverse to the radius vector at when the use of an exploring coil is adopted , as in succeeding experiments .
Now , the magnetic potential in the material is and the transverse magnetic induction is or It is greatest in the plane , and the average value in that plane , denoted subsequently by , is For a thin shell , the variation across the section , or any other section , is so small that may be used for , so that , quoting the values of and , we obtain If , where , in the subsequent experiments , is about to a good approximation .
It is , perhaps , desirable at this point to lay some emphasis on the smallness of the values of .
produced in a single shell by the demagnetising currents adopted in the experiments ibed in the for.mer paper .
For , , and , a current of 1 ampere , or C.G.S. unit\mdash ; which was the order of the magnitude of the current used\mdash ; only produces an average magnetic induction , in a single shell , of amount C.G.S. units , at .
The actual value will be even smaller , on account of the loose winding of the coil , which corresponds to Consider now a magnetising coil , of radius , wound internally to the shell of radii and , perhaps on a shell of non-magnetic material in the interior .
The fields in the various regions are represented very simply .
In the space internal to the coil the field is uniform , whereas between the coil and shell , and in the material of the shell , it can in each case be represented by the superposition of a uniform field and that of a central magnetic doublet of suitable moment .
Outside the shell , being finite at infinity , it is the field of a central magnetic doublet only .
There is no necessity to record the Induction .
and its Reversal in lron Shells .
analysis , which follows the same lines as before .
The final magnetic potential in the material of the shell is found to be where The average value of , obtained as before , is , or , to a close approximation for a thin shell , directly proportional to the cube of the radius of the coil .
If the coil is effectively wound on the inner surface of the thin shell of magnetic material , we may put , and comparison with the previous case indicates an interesting theorem:\mdash ; The maximum transverse magnetic inductions obtained by winding a thin iron shell ( 1 ) internally , and ( 2 ) externally , with the same coil calrying the same current are in the ratio 1 No conclusion , however , can be drawn from this result as legards the relative maxima induced simultaneously in two thin shells of nearly equal radii with a coil wound in the small air space between them .
Their mutual effect is then of great importance and is considered in the next section .
Two Concentric Shells enclosing a Magnetising Coil .
The of the arrangement is somewhat long , but it follows the previous lines so closely that we only present a bare summary .
Let and be the two radii of the inner and outer shells , each of permeabihty , and let be the radius of the coil situated between them , so that are in ascending order of magnitude .
Between and and and , and and , two constants are in each case required to define the magnetic potential when a current is passed through the coil .
When the field is uniform , and beyond it is that of a central magnetic doublet .
Each of these two regions requires one constant , so that , for a complete specification of the magnetic distribution produced by the current , 10 constants must be determined .
The usual conditions at the four surfaces of the shells lead to eight equations , and two other equations are derived from the continuity of normal force , and the discontinuity of potential , , at the ooil .
The equations are as usual linear , and their Anal solution is expressed most conveniently as follows:\mdash ; Profs .
J. W. Nicholson and E. Wilson .
Magnetic If both being positive , the transverse magnetic induction at is , at the inner surface of the inner shell , and at the outer surface of the outer shell , These may be taken as the average values across the sections of maximum , in the case of the shells to which our experiments relate , with an error of not more than about 3 per cent. In the special cases , whence and , whence , one shell is abolished , and the two previous solutions for a single shell are obtained .
This solution is exact when the coil is wound indefinitely closely .
It is of interest to calculate the numerical values in one special case for future comparison , and for this purpose we select the two largest shells used in the experiments , and referred to in the former paper as Nos. 3 and 4 .
Their permeabilities were practically identical , and .
The radii of the inner ( No. 3 ) were and cm .
, and of the outer ( No. 4 ) and Let the coil be wound on the inner so that cm .
, then whence and therefore , when excited by a current in turns per unit diameter of a coil wound on the inner shell , .
in the outer should be in on reduction , and in the inner , in , their ratio being innel. .
The mutual action of the shells has thus changed the ratio from 1 : 2 to 3 : 4 .
The maxima are therefore more nearly equal than might have been anticipated , and , in the earlier experiments , a current used to demagnetise any one shell must have been almost equally effective in the case of the shell on the other side of the air Induction and its Reversal in Spherical on Shells .
space containing the coil .
Moreover , in the absence of the outer shell , the value of .
produced in the inner may be shown to be in , so that its value is increased in the inner shell , by the presence of the outer , in the ratio .
Thsse results may be summarised as follows for this pair of shells : If a coil wound round the inner , in the absence of the outer , produces a value of .
equal to unity , then ( 1 ) if the inner is removed , and the outer placed round the coil , .
in the outer is , and ( 2 ) if both are present simultaneously , .
in the inner is about , and in the outer is .
We can deduce that in the demagnetisation of the entire set of shells in the original experiments , the application of currents of alternate signs simultaneously in all the coils must be at least six times as effective , for the second and third internal shells , as the successive application of these currents\mdash ; a result which could hardly have been foreseen from general principles .
Certain minor features in the curves then obtained can be interpreted on this basis .
These ratios necessarily become larger in the experiments described below , when all four shells are present simultaneously , and the current is passed through the coil on No. 3 .
But we do not include a detailed ] ation of this case , which would be tedious .
A discussion of one or two particular problems can be obtained somewhat simply , and , by comparison with experiment , will enable a determination to be made of the effect to which the theory may be vitiated by loose winding of the coils .
We shall accordingly consider only special problem to which the more interesting experiments relate .
Magnetising applied to the Outcrrnost of a Set of Four Shells .
The most important with reference to the testing of the theory in its ultimate application to the further shielding of the internal hollow of a set of four shells by the use of a magnetising current\mdash ; is perhaps that in which the current is applied to a coil wound round the outer shell , whose value of .
is tested by an exploring coil , as described later .
The necessary calculation for this case is greatly facilitated by the use of the recurrence formulae developed in the earlier paper , * whose notation will be adopted without further description .
The constant field in the hollow being , calculation gives the following successive values of the functions and there described .
The mean radii of the four shells and air space form the sequence , , cm .
, 'Roy .
Soc. Proc , vol. 92 , p. 635 ( 1916 ) .
Profs .
J. W. Nicholson and E. Wikon .
Magnetic and the permeabilities , from inner to outer , are , 163 , 148 , where fairly large error in the first , and a smaller error in the second , are of no importance .
We then find , the recurrence formula without a rougher approximation than 1 per cent. , It is desirable that these intermediate functions should be placed on record for reference in future work on magnetic shielding , which is now in progress with these specimens of iron .
Again , and finally relating to the air space just inside the } shell , on which the coil is wound .
If the potential in the fourth shell is and its inner and outer radii are and , accordingly , giving the ratio of A to , where is its permeability .
Application of the conditions at and at the coil shows , moreover , that so that A and may be obtained .
Thus in the outer shell , with If the current is in amperes , division by 10 is necessary in order to obtain the value in C.G.S. units .
If , or half a turn per centimetre of diameter , were a sufficiently Induction and its in Iron Shells .
close winding to render the formula exact , a current of 1 ampere should give the experimental value C.G.S. units for the outer shell when examined by an exploring coil .
Returning to the recurrence formulae , we notice that This result enables us to correct the previous formula , applicable to a coil wound between the third and fourth shells , for the presence of the other two shells in the interior .
For , in that formula , the function remains unaltered and the only effect of the two inner shells is to alter , which becomes instead of its original value in the former calculation , which was The rest of the formula is as before , and refer to the third shell .
The numerical value of in the present case is found .
to be corresponding to , and thus and , finally , for a coil carrying a current , wound round the third of a set of four shells of the present constants , .
in the outer is given by in , or in , if the current is in amperes .
For , the value per ampere of current is C.G.S. units .
A comparison with a direct experiment is made later .
In the meantime , it is instructive to notice that , in the absence of the two inner shells , .
for the fourth shell when the third is wound was calculated previously as 558 in .
The inner : shells have raised its value in the ratio 13 : much smaller mutual effect is involved , as might be expected , owing to the shielding influence of the third shell .
Experimental Determination of .
by an Exploring Coil .
The four shells remained , throughout the experiments , set up concentrically , each being wound with a magnetising coil , and the axis of all the coils was the diameter coinciding with the direction of the earth 's field .
The value of was in each case , the number of turns wound on the shells being respectively 34 , 38 , 42 , and 46 .
The various dimensions have been specified already , and the shells are formed from high permeability magnet steel .
Since the previous experiments were made , the butting surfaces of all the shells have been machined in such a manner that each of the two halves of any Profs .
J. W. Nicholson and E. Wilson .
gnetic ; original shell penetrates the other .
Preliminary tests , not described in this paper , have indicated that the originally present on account of this lack of machining has almost entirely disappeared , so that the theoretical formulae are strictly applicable if the coils are sufficiently closely wound .
The four concentric shells were placed with their junction planes at right angles to the direction of the earth 's magnetic field , and therefore parallel to the plane of any winding of a coil .
The exploring coil lay .
a plane parallel also to these junction planes , and distant about 7 cm .
from the junction plane of the fourth shell .
It surrounded the iron of the outermost shell , referred to .
as No. 4 , and consisted of one complete turn of insulated copper wire touching the outside of the shell , and one complete turn touching also the inside .
The ends of the inside turn were brought out of the shell through a small hole in the junction plane , by bending the two ends , which are now stranded at right angles to the plane of the coil and then threading them through the hole .
The inside and outside turns were then placed in series so that the coil completely surrounded the iron once .
The section of the effective part of the coil is thus a plane annulus whose radii are practically those of the outermost shell , and the coil is cut , in view of its parallelism to the magnetising coils , by the transverse magnetic induction at in the outer shell , over the whole area of section of that shell .
normal induction across the coil is thus the product of the sectional area , where and are the radii cm .
, of the outer shell , and the average value of .
for the outer shell as calculated already .
More strictly , this product .
should be multiplied by a magnitude of the order cos10o , on account of the small displacement 7 cm .
of the plane of the exploring coil from the diametral plane .
But this would only make a change not exceeding 2 per cent. The exact position of the exploring coil was so chosen that , while iving B with this degree of accuracy on one ground , it should at the same time be so far removed from the junction that the effect of any small air space should be negligible .
For although the two hemispheres constituting the whole shell were dovetailed together , the degree of fit was not sufficient to ensure perfect contact throughout .
A very small air space does in fact still exist , and we may therefore assume that the observed netic induction might on this account be slightly smaller than the calculated value even in the ideal state of packing of the magnetising coils .
The resistance of the exploring coil was quite egligible in comparison with that of the ballistic alvanometer .
This instrument , which was of the d'Arsonval type , had a resistance of 467 ohms at C. ; to this additional resistance was added in order to obtain the sensibility necessary to ensure Induaet and its Reversal in Iron Shells .
141 that the defleotion was not of a nitude capable of serious error on account of permanent set in the suspending fibre .
Let be the resistance of the circuit of galvanometer , exploring coil , and extra resistance when this was used , and the periodic time of the swinging coil of the instrument , in which a steady current of amperes produces a deflection .
Let be the ratio of two successive deflections of the galvanometer coil when on open circuit .
Then if is the number of turns in the exploring coil , A the area of cross-section of the iron in the plane of the coil , in square centimetres , and the mean of the first and second deflections obtained by reversal of the current in \amp ; e magnetising coil , we can the formula : The following values of the constants were obtained as the result of a calibration of the instrument and shell:\mdash ; sec. sq .
cm .
with .
Throughout the experiments , double de{lections were observed on a scale having mm. divisions at a distance of 1340 mm. from the mirror .
The decrement factor was used so long as it did not exceed But the resistance of the exploring coil is so small in comparison with that of the galvanometer that , when no extra resistance is inserted in the circuit , the galvanometer is short-circuited when used for deflections produced by reversal of current in a magnetising coil .
Under these circumstances the decrement is very much greater , and the spot of light , after the first throw , returns to zero and gives a relatively small deflection on the other side .
The ordinary treatment of damping is not.then applicable .
But we notice that failure to correct for a damping factor only introduces an error of about 3 per oent .
, and this occurs in practice in our experiments when a resistance of 10,000 ohms is added .
The interpretation of readings with smaller resistances added can be found by a preliminary expel.iment , which was made as follows:\mdash ; The third magnetising coil , wound between the two outermost shells , was used and a current of amperes passed through it .
Deflections were observed with varied additional resistances in the circuit of the exploring coil .
Reversal of current in the magnetising coil in every case produces the same value of .
in the fourth shell , and therefore the same induced electromotive force in the exploring circuit .
The product of deflection and total resistance should therefore be the same in every case , if the damping factors * See , e.g. , ' Phil. Trams , vol. 180 , p. 446 1889 ) .
Profs .
J. W. Nicholson and E. Wilson .
Magnetic are identical .
This product may be taken as correct with 10,000 ohms added 3 to the resistance of the galvanometer , and thence the true deflection , in the absence of damping , calculated in the other cases .
The interpretation of a reading with any added resistance may then be obtained by interpolation .
This method has the advantage of assuming no theory of the abnormal damping .
The results are shown in the annexed Table:\mdash ; Table I. Variation of Damping with Resistance .
If is multiplied by the value in the last column , we get a practical determination of the decrement factor , independently of any theory , and valid even for the enormous factor which occurs with no added resistance .
Interpolation is not in fact necessary , for all the experiments later are performed with added resistances of , 1000 , or ohms .
In the experiments of the earlier paper , large resistances were always used , so that no discussion of abnormal damping was then necessary .
Thus any first swing with , 1000 , 10,000 ohms added resistance must be multiplied by the factors , or respectively , in order to obtain the undamped reading .
We do not attempt to discuss any theory as to the origin of these values , for it constitutes an independent problem of some difficulty , and is not strictly relevant to the present paper .
Experimental ResuTts .
The values of .
have been determined in the following cases:\mdash ; The four shells were set up as described , and the readings taken in correspondence with various currents in the magnetising coil on the third shell , the exploring coil on the fourth shell .
( b ) Similar readings were taken when the system was excited instead by the magnetising coil on the fourth shell .
The values of .
were obtained in accordance with the discussion in the preceding section , and are shown in the subjoined Tables II and III .
its Reversat Iron Shells .
Table II.\mdash ; Magnetising Coil on the Third Shell .
Table III.\mdash ; Magnetising Coil on Fourth Shell .
Discussion .
The graphs shown in fig. 2 indicate also the results of these experiments .
For small values of the currents , they are very closely represented by straight lines , as would be expected .
The effect of the curve of magnetisation then comes into play , so that , although , on account of loose winding of the coil , the values of ./ current are initially smaller than predicted on theoretical grounds , they ultimately become larger than those calculated on the assumption of constant permeabilities of the shells , and the graphs beoome more parabolic .
The calculations of an earlier section indicate that , if the permeabilities were constant , current should be equal to when the third magnetising coil is used , and 74 when the current is passed through the fourth .
For the smaller values of the current , the values of .
may be expected , iu view of the curve of magnetisation , to follow the empirical law , where is the current , at least roughly , although the constant would have no simple physical meaning on account of the different magnetising forces on the various shells which shield one another .
For currents to , the average value of A is , neglecting the reading ' .
2 .
4 .
6 .
8 account of initial slope of the magnetisation curve .
We may take as the true value of A very closely , when ampere .
The first four readings may be fitted into the formula , with errors in of magnitudes .
The later values require an extra term in the empirical formula , but for the currents of this order , only a very small experimental error not exceeding about 3 per cent. is indicated .
Small magnetic inductions can thus be measured with extreme accuracy by this method of the exploring coil .
The limiting value of the ratio with the present magnetising coil is evidently about instead of , showing that Maxwell 's formula involves a considerable error when applied to a coil even so closely wound as the present one , when the iron of the core is near the coil .
At the same time , the data are ow available for future use of these coils , and the need for a theoretical investigation of a loosely wound coil , which has been prominent for some time , without any solution , is removed .
The Table for the coil on the fourth shell exhibits tInduction aShellsfor nurtherl 4 remarks .
Perhaps one of the most interesting problems opened up by the present investigation is an enquiry into the limit to which demagnetisation of a shell can be carried .
It would be necessary , for certain types of previous magnetio history of the iron , to apply reversals of a continually diminishing force , which began with a value corresponding to maximum permeability , as shown on the ( BH ) curve of the material .
This would be difficult , on account of the necessary magnitude of the current for an arrangement of shells such as the present , which , however , as shown in the earlier paper , that of maximum shielding for a large space .
Since effective demagnetisation , or , at least , the production of uniformity in the internal field of the central hollow , is a necessary preliminary to the removal of that residual field by the application of currents , the problem is of some importance But at this point it is sufficient to indicate the necessity for a determination of what constitutes " " effective netisation Induced Currents .
The reversal of magnetisation within undivided iron magnet cores has been studied to a great extent on its experimental side , and it is known that the induced currents in the iron continue for a considerable time , and tend to maintain.the magnetisation in its condition preceding the reversal .
When a ballistic galvanometer is used in combination with an exploring coil wound on such magnets , the deflections of the instrument do not give the complete change of magnetic induction ; the effect is similar to the damping caused by connecting a resistance across the terminals of the instrument .
A continued current in one direction , caused by the slow change of magnetisation , gives rise to a first deflection considerably greater than the second\mdash ; in the opposite direction\mdash ; and the third deflection may exceed the second .
So far as are aware , the lowest forces at which the delay caused by induced currents in large masses has been examined , are and in C.G.S. units .
In the first case the magnet was of wrought iron of diameter cm .
( 4 inches ) , and in the second , of dynamo magnet steel of diameter cm .
( 12 inches ) .
Changes at the centre of the core were observed 46 seconds after reversal in the former case and 400 seconds in the latter .
The experiments showed , moreover , that , with small forces of this order of Phil. Trans.\ldquo ; Journ IProc .
Profs .
J. W. Nicholson and E. Wilson .
Magnetic magnitude , there is but a single maximum rate of change of the magnetic induction , which occurs at a comparatively early stage .
But the values of the magnetic induction corresponding to these forces were of the orders 7000 and 5000 C.G.S. .
In the experiments of present communication , the netic induction in the outermost shell is only C.G.S. units when a current of 7 amperes is used in its magnetisin coil .
Corresponding to a current of amperes in the coil wound on the third shell , the maximum transverse induction in the urth or outermost shell is 272 C.G.S. units .
These currents have not as yet been greatly exceeded in our experiments on demagnetisation .
It is interesting , and of some importance , to enquire whether the delay caused by the reversal of such small inductions is sufficiently great to affect the decrement , as ordinarily obtained , of the readings of a galvanometer whose periodic time is 8 seconds .
Some nents have been made in order to test this point .
A list of deflections due to a reversal of a current in the third coil , and its corresponding effect on an exploriIlg coil wound on the fourth shell , has been used already for another purpose .
The same arrangement , with a current of amperes reversed , and various additional resistances inserted in the galvanometer circuit , was used also in determining the ratio of first to second deflection corresponding to each resistance .
The exploring coil was then cut out of the galyanometer circuit , and deflections were observed corresponding to the same resistances as before , ranging to 10,000 ohms , when the coil of the galvanometer was initially set in motion by a primary cell of low voltage woYking through a very high resistance , the battery circuit being open while the readings were taken .
The ratios of first to second deflection were again calculated , and the comparison is made in Table Table When the additional resistance was zero , or in short circuit , the second deflection was so small as to render the ratio very uncertain .
But the ratios Induction and its Reversal in Spherical Iron Shells .
147 corresponding to other resistances are in such close agreement that the delay in the change due to eddy currents must be effectively negligible .
This result is of some importance , for it might have been inferred from the earlier experiments that a considerable delay was possible in a shell of thickness 2 .
The argument would be applied as follows:\mdash ; In the distribution of induced currents in its mass a plate is comparable with a wire whose diameter is twice the thickness of the plate ( loc. cit The time required to effect a complete reversal of any value of the magnetic induction in one of our shells should be of the same order as in a cylinder of diameter 4 cm .
In two cylinders of different diameters , .
each subjected to the reversal of the same magnetic force , similar magnetic events will happen , but at times proportional to the squares of the diameters .
Comparing therefore a solid shell of thickness 2 cm .
with the solid magnet of diameter 10 cm .
, mentioned in the earlier experiments , the delay in the shell would be of order 46 seconds .
Comparison with the magnet of diameter 30 cm .
gives 400 seconds .
It is evident that if the induced currents are to disappear when the magnetic induction is of the order 6000 , a considerable time must elapse between successive reversals of the magnetising force in this process of demagnetisation by reversal and diminution .
But the present experiments show that for magnetic inductions not exceeding 300 C.G.S. units this necessary time interval is greatly reduced , for the delay due to induced currents is negligible comparison with such a time as 8 seconds , the periodic time of the ballistic galvanometer employed .
This has important implications in connection with work at frequencies .
Summary .
( 1 ) The paper contains a solution of certain problems which arise in the production of an effective magnetic shield for large spaces .
These relate mainly to the effective demagnetisation of the shells of which the shield is constituted .
( 2 ) Theoretical solutions of problems relating to the effects of indefinitely closely wound coils on various shells of such a shield are given , and compared with the experimental values for an actual .
coil , as determined by an exploring coil and ballistic galvanometer .
( 3 ) The experiments supply an estimate of the deviations of Maxwell. 's formula , for the field inside a spherically wound helical from the true values , when the spacing in the iS of importance . .
XCIIL\mdash ; L Lord Rayleigh .
( 4 ) A study of the necessary interval between current reversals in the process of netisation has been made , and it is shown that the delay in reversal of magnetic phenomena in considerable masses of iron , due to eddy currents , is extremely small when the magnetic inductions are less than 300 C.G.S. units .
On the of Revotving Fluids .
By RAYLEIGH , O.M. , F.R.S. ( Received December 8 , 1916 .
) So much of depends ultimately upon the dynamics of revolving fluid that it is desirable to formulate as clearly as possible such simple conclusions as are within our reach , in the hope that they may assist our meant when an exact analysis seems impracticable .
An important contribution to this subject is that recently published by Dr. Aitken .
* It formed the starting point of part of the investigation which follows , but I perhaps to add that I do not share Dr. Aitken 's views in all respects .
His paper should be studied by all interested in these questions .
As regards the present contribution to the theory it may be well to premise that the limitation to symmetry round an axis is imposed throughout .
The motion of an inviscid fluid is governed by equations of which the first expressed by rectangular co-ordinates may be written , ( 1 ) where , ( 2 ) and is the potential of extraneous forces .
In ( 2 ) the density is either a constant , as for an incompressible fluid , or at any rate a known function of the pressure .
Referred to cylindrical co-ordinates , with velocities , reckoned respectively in the directions of increasing , these equations , ( 3 ) " " The Dynamics of Cyclones and Anticyclones.\mdash ; Part 3 'Roy .
Soc. Edin .
Proc. , vol. 36 , p. 174 ( 1916 ) .
Compare Basset 's ' Hydrodynamics , ' S19 .
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