290 



NA TURE 



[January 25, 190 



distribution of co-ordinates and velocities of the other 

 molecules ; or " Condition B," that the chance of a given 

 molecule having at any instant assigned velocities is not 

 independent of the positions and velocities of all the 

 other molecules at the instant. Condition A readily 

 leads to the Boltzmann-Maxwell distribution, but 

 Burbury finds that the assumption of Condition B (which 

 is, of course, of wider application than Condition A) leads 

 to a new law of distribution, according to which the 

 chance of a system of molecules having their velocity 

 components within the limits of the multiple differential 

 of these components is 



where 



Qe-^'^duydv-^dw-^ 



dtt,idvndw,„ 



Q = 2/«(«^2 ^ ^,2 ^ ^i) + ■Z^h,.,{ll,.tl, + VrV, + Wr'cV^). 



The b coefficients are functions of the distance between 

 the molecules, which become inappreciable except when 

 this distance is very small. When the b coefficients are 

 negative, their meaning is that two near molecules are 

 more likely to be moving in the same than in opposite 

 directions, and the motions of the molecules are then 

 said to be correlated; while in the opposite case of br» 

 positive the motions are said to be contrarelated. It 

 should be observed that iirU>-\-VrV,-\-'Wr'iv, is equal to 

 qrq, cos e where q,q^ are the speeds, e the angle between 

 their directions. 



The view that the ultimate distribution differs from 

 the Boltzmann-Maxwell distribution being at variance 

 with the results of " Boltzmann's Minimum Theorem," 

 Burbury carefully examines the proof given by Boltz- 

 mann, and concludes that " what the H theorem proves 

 then is this, that the distribution of velocities expressed 

 by the equation Fy"' = F/is the only distribution which 

 can be permanent consistent with the existence, and the 

 continued existence of Condition A or its equivalent." 

 In the motion obtained by reversing the velocities Con- 

 dition A is not satisfied. Burbury considers that in this 

 proof Boltzmann's assumption that the motion is " mole- 

 cular ungeordnet " is equivalent to "Condition A." He 

 remarks : — 



" Let us endeavour to construct synthetically a system 

 which shall without doubt be molecular ungeordnet. The 

 molecules being distinguished by numbers, I ask (say) 

 Dr. Watson to assign velocities to them according to 

 any law he pleases. Then I, in complete ignorance of 

 those assigned velocities, scatter the molecules at hap- 

 hazard through space, and they shall start from the 

 positions which I so give them with the velocities so 

 assigned them by Dr. Watson. That is prima facie a 

 molecular ungeordnet system ; in fact, it is as near an 

 approach to chaos as is possible in an imperfect world." 



Burbury next proves that if the intermolecular forces, 

 are finite. Condition A cannot exist, and tiu' + vv' + w7i/ 

 has an average finite value, a function of r which is posi- 

 tive if the forces are repulsive. This proof involves the 

 assumption that uu' is zero in the absence of intermole- 

 cular forces, and we are told : 



" Strictly, n the number of molecules in the system 

 being finite and the centre of inertia at rest, it must be 

 negative, but it may be neglected when n is great." 



This is rather a difficult assumption to accept without 

 further explanation. The proof that " correlation " must 

 exist when the molecules are equal elastic spheres is 

 NO. 1578, VOL. 61.] 



much more laborious. In the chapter on "Generalii 



il ./-..U- ...-i! .^! )1 -x^ !_ _1 .1 X ii •»«• '.?! 



theory of the stationary motion," it is shown that "Max- 



well's law of partition of energy " does not necessarily i 

 hold except when Condition A is satisfied. This is as it J 

 should be ; otherwise the heat given to a polyatomic gas 1 

 would be divided equally between all the atoms of all \ 

 the molecules, instead of being divided, as Boltzmann | 

 teaches us, mainly between the translatory and rotatory 

 motions of the molecules, which are the only motions to i 

 which Condition A is applicable. j 



Under the title " On molecules as carriers," we have a 1 

 short account of Boltzmann's simple method of treating ' 

 diffusion and allied phenomena, based on the latter's ] 

 " Vorlesungen liber Gastheorie." We hope that the \ 

 general mathematical reasoning on which Burbury's ; 

 theory of correlation rests is not to be gauged by his j 

 method of investigating the mean free path on p. 115, in i 

 which he says: "Let i -7r^-NX/a) = 0(X) = ^," and a few i 

 lines later infers that <|) = ^-'^'^ where /& = 7rt-N/ci), and M \ 

 is finite. i 



The chapter on " Thermodynamical relations" well • 

 brings out the fact that while Burbury's new distribution, ; 

 like the conventional one, fulfills the condition that dQ [ 

 has an integrating divisor, the usual symbol for which (in j 

 this country) is the first letter of the word " Tempera- { 

 ture," but little progress has so far been made in ex- ,: 

 plaining the fundamental properties of temperature by ] 

 molecular motions. The properties of irreversible ' 

 thermodynamics are nowhere more manifest than in the ' 

 friction, heat conduction, and imperfect elasticity of solid ■ 

 bodies whose molecules are not only correlated, but ap- 

 pear inseparably interlocked. Yet hardly any headway has '■ 

 been made in getting the equation of energy-equilibrium ] 

 between two bodies into a form analogous to that ex- > 

 pressing equality of temperature, except under highly i 

 specialised assumptions as to the law of distribution of I 

 energy, which prevent the conclusions from being applied \ 

 to any but attenuated gases. Every attempt to advance 'i 

 in the desired direction has hitherto led to hopeless \ 

 mathematical difficulties. ^ 



A discussion on the merits of Burbury's new method of \ 

 analysis would be out of place in the present review. I 

 His theory represents the outcome of much thinking, and I 

 is not to be disposed of hastily. It boldly faces the ques- 

 tion of correlation, and thus brings us one step nearer 

 towards explaining the properties of dense assemblages 

 of molecules. It has the remarkable property that the 

 character of the motion changes completely when the 

 expression Q ceases to be essentially positive, by the 

 vanishing of the determinant of the coefficients of Q or 

 of one of its leading minors ; and we know that the 

 state of a gas also suddenly changes by liquefaction. 

 Seeing, however, that it is necessary to regard actual 

 molecules, not as spheres or material points, but rather 

 as non-spherical rigid bodies, it still remains for Burbury 

 to tackle the far more difficult question of the distribution 

 of translatory and rotatory motions of unsymmetrical or 

 axially symmetrical molecules when correlation exists. 

 And we have a kind of vague feeling that probability con- 

 siderations and finite molecular forces which are functions 

 of the distances and positions of the molecules are 

 bringing us not much nearer the desired goal of explain- 

 ing temperature. Indeed^ the question of deducing the 



