of a Gas " in Mass." 39 



average, which is maintained in the same roughly approximate 

 manner as is the ' special state,' and can like it be assumed to 

 hold with sufficient accuracy to be made the basis of calculation. 

 The mere fact that a ' steady ' state, say of diffusion, can be 

 realized experimentally is a sufficient warrant for this assump- 

 tion ; and there seems to be no reason for supposing that the 

 irregularities of distribution of the translatory velocity among 

 the particles of a group should be more serious for the higher 

 than for the lower speeds, or vice versa. For each particle is 

 sometimes a quick, sometimes a slow, moving one: — and ex- 

 changes these states many thousand times per second. All 

 that is really required by considerations of this kind is allowed 

 for by our way of looking at the mean free paths for different 

 speeds." 



I confess I cannot see how objection can possibly be taken 

 to this assumption when the question is that of the Viscosity 

 of a pure gas ; though Mr. Burbury specially mentions Vis- 

 cosity among the subjects which he considers to be on this 

 account erroneously treated in my paper. And it would 

 require, I think, a most determined sceptic to entertain a 

 doubt of its lawfulness in the question of Thermal Conduction, 

 also in a pure gas. In the matter of Diffusion some doubts 

 may possibly occur to one looking at it for the first time ; and 

 it was on that account that I inserted in my paper the words 

 quoted above. To deny their validity would, I consider, be 

 tantamount to a wholesale repudiation of the statistical method 

 of treatment, which has done so much for questions of this 

 kind. Mr. Burbury departs from the statistical method in his 

 equation (1) by treating as a separate gas, icith its own pres- 

 sures and resistances, the class of particles of one gas which 

 have speeds from v to v + Sv : — thus ignoring the community 

 of interests which the mutual collisions secure for all the par- 

 ticles of a gas. It might be lawful, though perhaps not very 

 useful, to treat thus a part of one gas ; but it must be a part 

 which contains particles with all varieties of speed in their 

 proper proportions. 



But more. I think I have given a self-consistent, and 

 therefore accurate, solution of the problem of steady Diffusion 

 (at all events when the masses and the diameters of the 

 particles are the same in the two gases), basing my work 

 entirely on the assumption above. If Mr. Burbury can show 

 that solution to be erroneous, he may possibly make out 

 a presumptive case against the assumption on which it was 

 founded: — but not otherwise. 



