ON OUR KNOWLEDGE Ol-' THERMODYNAMICS. 81 



Statement of the Boltzmann- Maxwell Law. 



34. It is highly desirable that some definite understanding should be 

 agreed on as to what precisely constitutes the Boltzmann-Maxwell Law. 

 I would suggest therefore — 



(i) That the distribution of a large number of molecules or other 

 dynamical systems of the same or different kinds in which the co-ordinates 

 {q) and momenta (;;) of each system are so arranged that the number of 

 systems in the neighboui-hood of any given state is proportional to 



e-^'^dpi . . . djjjcji . . . dq„ . . . (26) 



h being the same for all the kinds of molecules or systems, be called The 

 Boltzmann-Maxwell Distribution. 



(ii) That the law which asserts the permanency of the Boltzmann- 

 Maxwell distribution in any particular case be called The Boltzmann- 

 Maxwell Law. 



(iii) That in future these names be not applied to any corollaries such 

 as that which asserts the equality of the average value of the squares 

 into which the kinetic energy can be split up. That corollary I have 

 called Maxioell's Law of Partition of Kinetic Energy. 



I trust that the adoption of these names will be of assistance in 

 securing that uniformity of nomenclature which is always so desirable 

 in all branches of science. 



Verification for Particular Cases. — Spheres and Circles. 



35. It is not necessary to consider in detail the law of distribution in 

 smooth colliding spheres whose centres of mass are at their centres of figure 

 or, what is the same thing, material particles which rebound when they 

 approach within a certain distance of one another. The truth of 

 Avogadro's law, according to which the mean translational kinetic energies 

 of the molecules of two mixed gases are equal, is now universally admitted. 

 Even Tait does not deny it, but contents himself with maintaining that 

 the law cannot be established without making certain assumptions, and 

 these assumptions are discussed at great length by Boltzmann,' who, 

 however, places more implicit confidence in Maxwell than is warranted 

 by Section T. of this Report. It seems to me that Tait's three assump- 

 tions,^ which are quoted in my first Report,^ actually require little beyond 

 the assumption that there is a law of permanent distribution. At any 

 rate, this is all that is necessary for showing that Avogadro's law is a 

 possible permanent law. The question as to how far the general law of 

 distribution is unique can be much better discussed in connection with 

 other applications (see § 45 below). 



36. The next cases are those of splieres in which the CM. is at a small 

 distance from the centre of figure, i.e., having a ' bias ' as in the game of 



' ' Ueber die zum theoretischen Beweise des Avogadro'schen Gesetzes beforder- 

 lichen Voraussetzungen,' Sitzbcr. der k. Wiener Aliad., xciv. (ii.), Oct. 1886. 



^ ' On the Foundations of the Kinetic Theory of Gases,' Trans. H.S.E., vol. xxxiil. 

 Parti. (1886), p. 77. 



' Cardiff Beport, 1891, § 41, p. 113. 

 1894. G 



