Dynamical Theory of Heat and Light. (9 



well's 1860 proof has always seemed to me quite inconclusive, 

 .and many times I urged my colleague, Professor Tait, to 

 enter on the subject. This he did, and in 1886 he com- 

 municated to the Royal Society of Edinburgh a paper * on 

 the foundations of the kinetic theory of gases, which con- 

 tained a critical examination of Maxwell's 1860 paper, highly 

 appreciative of the great originality and splendid value, for 

 the kinetic theory of gases, of the ideas and principles set 

 forth in it ; but showing that the demonstration of the 

 theorem of the partition of energy in a mixed assemblage of 

 particles of different masses was inconclusive, and success- 

 fully substituting for it a conclusive demonstration. 



§ 15. Waterston, Maxwell, and Tait, all assume that the 

 particles of the two systems are thoroughly mixed (Tait, 

 § 18), and their theorem is of fundamental importance in 

 respect to the specific heats of mixed gases. But they do 

 not, in any of the papers already referred to, give any 

 indication of a proof of the corresponding theorem, regarding 

 the partition of energy between two sets of equal particles 

 separated by a membrane impermeable to the molecules, 

 while permitting forces to act across it between the mole- 

 cules on its two sides f, which is the simplest illustration of 

 the molecular dynamics of Avogadro's law. It seems to me, 

 however, that Tait's demonstration of the AVaterston-Maxwell 

 law may possibly be shown to virtually include, not only this 

 vitally important subject, but also the very interesting, 

 though comparatively unimportant, ease of an assemblage of 

 particles of equal masses with a single particle of different 

 mass moving about among them. 



§ 16. In §§12, 14, 15, " particle " has been taken to mean 

 what is commonly, not correctly, called an elastic sphere, but 

 what is in reality a Boscovich atom acting on other atoms in 

 lines exactly through its centre of inertia (so that no rotation 

 is in any cnsc produced by collisions), with, as law of action 

 between two atoms, no force at distance greater tJian the sum 

 .of their radii, infinite force at exactly this distance. None of 

 the demonstrations, unsuccessful or successful, to which I 

 have referred would be essentially altered if, instead of this 

 last condition, we substitute a repulsion increasing with 



* Phil. Trans. R.S.E., "On the Foundations of the Kinetic Theory of 

 Oases," May 14 and December 6, 1886, and January 7, 1887. (Abstract 

 in Phil. Mag. April 1886 and Feb. 1887.) 



t A very interesting statement is given by Maxwell regarding this 

 subject in his latest paper regarding the Boltzmann-Maxwell doctrine. 

 4< On Boltzmann's Theorem on the Average Distribution of Energy in a 

 System of Material Points," Cainb. Phil. Trans., May 6, 1878; Collected 

 Works, vol. ii. pp. 713-741. 



