i20 



NATURE 



January 31, 1895 



the Boltzmann-Maxwell dislribuiion, they will be so distributed 

 al acy subsequent instant. But in the absence of collisions or 

 encounters between the sysiem , thi< distribution will iiot be 

 unique. There exist o her distributions equally well satisfying 

 the condition of p rmanence. 



The case of I wo or more molecules of gas in the process of en- 

 ciunier can be deduced, a-^ shown in my Report ;i3°'> ''y taking 

 each "system "to rcpres-nt a pair ot molecules, there being 

 at every instant an indefinitely large number of such pairs 

 having difTerent coordinates and mo-nenla. It now seems 

 definiely settled that if the molecules are rigid bodies, the only 

 possible permanent distribution unaffected by encounters is the 

 BoltzmtnnMaxwell distribution combined with motions of pure 

 translation and pure n tntion of the mass of gas as a whole 

 {Report. §46). 



Many writers have limited their investigations to the case 

 where all the encounters are binary, and I see that Prof. Fitz- 

 gerald has emphasised this point in his recent letter. I do no' think 

 this is the right place to diaw the line. I can see no difficulty 

 in talcing account of encounters between three, four, or more 

 molecules, provided that such encounters are suHiciently nu- 

 mcrojs 10 have a law of distribution. Where the line mu-t lie 

 drawn is indicated in my Report. S 30(iii.l The molecules 

 which act on one another in any one encounter must form an 

 infinitesimal fraction of the whole mass ol gas, or the gas must 

 at any instant be divisible into an infinitely large number of 

 independent molecules and groups ui molecules, each molecule 

 or group thus constituting for the time being a free system by 

 itself. When the mo'ecules act nn each other at all dislarces, 

 orii is impossible to divide them intosmall independent gi cups, 

 the whole o' our theory breaks down. 



It IS this limitation which, to my mind, precludes our apply- 

 ing the Kinetic Theory in its present state, nol only to molecules 

 moving ai'Oiit in a continuous medium, such as the ether may be, 

 but also to -olids and, probably, lii|uid-. 



A good ileal of confusion has, I fear, a'i en with regard to 

 what 1 have called Maxwell's La* of Paitition of Kinetic 

 Energy, i.e. the statement that "if the kinetic energy of a 

 sjstem be expressed as a sum of squares, the mean values of these 

 squares are equal," from the fact ihat the term "■mean -mltic" 

 may be taken to represent "lime average for a single system " ; 

 and I fancy this may be the point Prof. Fitzgerald had in view 

 when he a-ked if the conclusions would not apply to the Earth 

 or a " finite number of particles moving about for an inde- 

 finitely long time." It cannot be too strongly emphasised that 

 this interpretation of mean values involves assumptions which 

 have hardly been sufficiently justified in any general class of 

 cases, and which have been repeatedly pioved to be invalid 

 in simple case; (Report, §S 9-12).' To give a simple (if not 

 quite analogous) illustration : suppose that on drawing counters 

 oat of a bag, we were to obtain on the average an equal number 

 of red, white, and green counters. We should not be justified 

 in inferring that if we kept a single counter sufficiently long 

 it would change colour and become in turn red, white, and 

 green. 



As an illustration of a case where the Bollzmann-Maxwell 

 Law is inapplica'ile, consider a sphere of density a moving in 

 a perfect liquid ol density p. The kinetic energies of the 

 sphere and liquid are in the ratio of o- : J p, as we know from 

 hydro<Iynamical considerations, and the same is true for any 

 number of spheres whose distances apart arc very large com- 

 pared with their r.idii. This is not a case where nn transference 

 of energy lakes place between the sphere and liquid, and it is 

 not therefore open to Prof. Fitzgerald's objection to the case I 

 previou.tly cited. Whenever the motion of the solid is varied, 

 energy n transferred to or from the liquid. 



If a iiif.eoii; ether will satisfy the requirements of physicists, 

 then the Bultzmann- Maxwell Law is uiidiubtcdiy applicable to 

 the elher. If not, the ether falls entirely beyond the scope of 

 our investigation. The Kinetic Theory is obviously a theory 

 framed to account for one class ol physical phenomena only, 

 viz. the thermal properties of gases. If any observed pheno- 

 mena are not deducililc from the results of the theory, it is to 

 my mind iufTicient to *how lhat this is because the funda- 

 menial assumption* of the theory are not satisfied, i.e. that the 

 phennncna in queslioD are not incomiilenl with the Kinetic 

 Th-o.y. G 11 liuvAs. 



Pelerhousr, Cambridge, January 16. 



• Se« al«n Natchr. January 10, p. 162. 



NO. I318, VOL. 51I 



Boltzmann's Minimum Function. 



I SAID in my first letter on this subject that the condition .\, 

 on which, or its equivalent, the proof is based, could not apply 

 to the reversed motion. As that assertion has been questioned, 

 may I confirm it thus? 



The initi.-<l distribution of R, the relative velocity, i.e. the 

 number of pairs of spheres for which it has given direction, is 

 arbiiriry — condition .\ is fulfilled. Then, as proved, whatever 

 the initial distribution, after collisions, the distribution of R is 

 uniform, i.e. all directions equally probable. Now reverse the 

 velocities. If condition .\ is fulfilled in the reversed motion, 

 then after the reversed collisions the distribution of R isuniforni. 

 It is equally certain that it must be the same as the initial dis- 

 tribution. 



If, therefore, condition A is fulfilled in the reverse motion 

 as well as in the direct, that can only be because the dis- 

 tribution of R was uniform to begin with. But that means that 



/f-T 

 H was minimum to begin with, and therefore ' = o through- 



dt 



out. 



Lioltzmann's theorem can be applied 10 both motions only on 

 condition ;hat it h is no effect in either. 



I New-square, Lincoln's Inn. S. H. BURiiURV. 



Electroscopes in Lecture. 



I Si;ppoSE teachers still use gold-leaf electroscopes for their 

 junior lectures ; certainly I have Tiund nothing else so dead- 

 beat, or so readily understood ; and by projecting with a lens a 

 shadow of the leaves on a square-foot translucent screen, the 

 movements are perfectly visiole to a l.irge audience by d.iy- 

 light. But the one objection 10 the instrument, when usei! f'>r 

 explaining the fundamental facts, say, of induction, is ih. 1 it 

 ini.!icates similaily positive and negative potentials. \'ester,iiiy, 

 however, my assistant, Mr. L. E. Robinson, ingeniously stood 

 the metal cased instrument on a cake of paraffin wax, and' 

 electrified its outside negatively. By this process the zero of ■ 

 deflection is changed ; the leaves stand apart for zero 

 potential, diverge m >re for positive, and collapse for ne^'itive. 

 A zero sh.adowpoinler and rough scale may be readily u^c.l ; 

 and I propose now to mount a projection electrost pc m i 

 suitable slightly charged Leydea jar, whose outer cnat can then 

 be treated as the usual earthed terminal of the instrument, 

 whose case is connected to or formed by the inner coat of the 

 jar. The insulated or variable terminal is conveniently arranged 

 as an insulated sphere or other shaped body on the lecture 

 table, not far from the small screen, attached by a long enough 

 thin wire to the leaves — of which it is perhaps best to have only 

 one movable. Oi.i\ kr J. LoDCi;. 



January 25. 



The Perseid Meteors. 



Your interesting rcference(NArURli, January 24, p. 30i)toUr. 

 Bredichin's investigation of the Perseid shower, induces mc to 



t ofiTcr one or two remarks on the subject. In the paragraph alluded 

 to, it is staled lhat the radiant was observed from July 22 to 

 September 12, 1893; but Ibis long duration cannot possibly refer 



I to the same system as that which furnislies the abuiulaiii maximum 

 on August 10. It is true there arc r.idiants in Peiseu^ in Sep- 

 tember, and the succeeding months of October, November, and 



j necembcr supply many others, but, after the end of ihe third 

 week in August, nothing is seen of Ihe real Perseids. I cannot 

 say exactly on how many nights the display continues active, but 

 it IS certainly vi-ible fruiii July 19 to August 18, and the diurnal 

 motion of the radiant is about 1° lo the E.N.E. 



There are really very few of the liue Perseids seen after 

 August 12, for ihe shower dies rapidly away after the maximum. 

 On August 15, 1893, during a walch of ihice hours, I saw only 

 oae Pels i I. On August 16, 1893. cluring a Nvatch of 4^ hours, 



I I noted only four Perseids. I mention these facts lo prove the 

 extreme leniiily of ih' stream at the middle of .\ugiisl. But 

 there arc ditVerenccs from vcar to \'ear. An observer watching 

 the heavens for a similar interval on the same dales in succeciU 

 ing years will gel a varied experience. Thus one year cannot 

 be regarded as Ihe criterion of^ all. 



Some years ago I recorded a few swift .slreak-lcaving melems 

 between August 19 and 24, from a railiant at 78° -(- 56" on the 

 northern borders of Auriga, and supposed they might be late 



