the Kinetic Theory of Gases. 175 



used as a basis for further argument. In quoting my remarks 

 on this point Prof. Boltzmann very significantly puts an "&c." 

 in place of the following words : — " it is specially to be noted 

 that this is a question of effective diameters only and not of 

 masses : — so that those particles which are virtually free from 

 the self-regulating power of mutual collisions, and therefore 

 form a disturbing element, may be much more massive than 

 the others." It was of this preliminary matter, of course, 

 that I spoke when I wrote the following sentence, which 

 seems to have annoyed Prof. Boltzmann : — 



" I have not yet seen any attempt to prove that two sets of 

 particles, which have no internal collisions, will by their mu- 

 tual collisions tend to the state assumed by Prof. Boltzmann." 

 I think it probable that Prof. Boltzmann has not fully 

 apprehended the meaning of the word " assumed " in this 

 sentence. Otherwise I cannot understand why he is annoyed 

 because I took his proof for granted. 



In taking leave, for the time, of this special question, I 

 need scarcely do more, and I cannot do less, than reaffirm the 

 assertion just quoted: —while adding the remark that this is 

 very far from being my sole objection to Prof. Boltzmann's 

 very general Theorem. In fact Professors Burnside* and 

 J. J. Thomson t have quite recently advanced other serious 

 objections. Prof. Boltzmamr's Theorem, in a word, is not 

 yet demonstrated. 



Third. As to the questions of viscosity and heat-conduction; 

 my investigations were expressly made on the assumption that 

 change of permeability, due to motion, was negligible. When 

 I found that I had obtained in a very simple way certain 

 characteristic results of Clerk-Maxwell and of Clausius respec- 

 tively, I was satisfied with the approximation I had made. 

 Prof. Boltzmann does not allude to the fact that my investi- 

 gation was distinctly stated to be an approximate one only, 

 and that the additional consideration he now adduces had 

 been before me and had been rejected (rightly or wrongly) 

 for reasons given. I said : — 



" Strictly speaking, the exponent should have had an addi- 

 tional term See the remarks in § 39 below." 



And, in the § 39 thus pointedly referred to, one of the 

 remarks in question is : — 



" We neglect, however, as insensible the difference between 

 the absorption due to slowly moving layers and that due to 

 the same when stationary." 



And, in fact, the result which I gave for the viscosity (and 



* Trans. Roy. Soc. Edin. 1887. f PM1. Trans. 1887. 



