66 PROFESSOR TAIT ON THE 



are concerned, that the particles of a gas are all moving with equal speeds. 

 Of the Virial, which Clausius introduced in 1870, we shall have to speak 

 later. 



In the Philosophical Magazine for 1860 Clerk-Maxwell published his 

 papers on the " Collisions of Elastic Spheres," which had been read to the 

 British Association in the previous year. In this very remarkable investigation 

 we have the first attempts at a numerical determination of the length of the 

 mean free path. These are founded on the observed rate of diffusion of gases 

 into one another ; and on the viscosity of gases, which here first received a 

 physical explanation. The statistical method is allowed free play, and conse- 

 quently the law of distribution of speed among the impinging particles is 

 investigated, whether these be all of one kind or a mixture of two or more 

 kinds. One of his propositions (that relating to the ultimate partition of energy 

 among two groups of colliding spheres), which is certainly fundamental, is 

 proved in a manner open to very grave objections : — not only on account of the 

 singular and unexpected ease with which the proof is arrived at, but also on 

 account of the extraordinary rapidity with which (it seems to show) any forced 

 deviation from its conclusions will be repaired by the natural operation of the 

 collisions, especially if the mass of a particle be nearly the same in each 

 system. As this proposition, in the extended form given to it by Boltzmann 

 and others, seemed to render the kinetic theory incapable of explaining certain 

 well-known experimental facts, I was induced to devote some time to a careful 

 examination of Maxwell's proof (mainly because it appears to me to be the 

 only one which does not seem to evade rather than boldly encounter the real 

 difficulties of the question *), with the view of improving it, or of disproving 

 the theorem, as the case might be. Hence the present investigation, which has 

 incidentally branched off into a study of other but closely connected questions. 

 The variety of the traps and pit-falls which are met with even in the elements 

 of this subject, into some of which I have occasionally fallen, and into which I 

 think others also have fallen, is so great that I have purposely gone into 

 very minute detail in order that no step taken, however slight, might 

 have the chance of escaping criticism, or might have the appearance of an 

 attempt to gloss over a real difficulty. 



The greater part of the following investigation is concerned only with the 

 most elementary parts of the kinetic theory of gases, where the particles are 



* Compare another investigation, also by Clekk-Maxwell but based on Boltzmann's processes, 

 which is given in Nature, viii. 537 (Oct. 23, 1873). Some remarks on this will be made at the end of 

 the paper. Meanwhile it is sufficient to point out that this, like the (less elaborate) investigations of 

 Meteb and "Watson, merely attempts to show that a certain state, once attained, is permanent. It gives 

 no indication of the rate at which it would bo restored if disturbed. As will be seen later, I think that 

 thi.3 " rate " is an element of very great importance on account of the reasons for confidence (in the 

 general results of the investigation) which it so strikingly furnishes. 



