in the Kinetic Theory of Gases. 88 



hold good for any values whatever of A., A, and S ; conse- 

 quently also when A. = 0, and only A and 8 differ from zero 7 

 and even if A = A = 0, and only 8 differs from zero, which 

 amounts to the assumption that neither the molecules of the 

 first kind nor those of the second kind enter into collisions 

 amongst themselves, but only the molecules of the first kind 

 enter into collision with those of the second kind. It is quite 

 unintelligible to me how Prof. Tait can represent* the matter 

 as if this latter assumption were a fundamental assumption, 

 which I had excluded from my investigations, so that my 

 results would only hold good under this latter assumption. 



If the molecule-diameter is very much less for the one kind 

 of gas than for the other, so that, for example, A. is nearly zero 

 and A nearly equal to 28, we have the case considered by 

 Prof. Tait in the passage quoted, that the molecules of the 

 first kind of gas enter into collision amongst themselves very 

 seldom, but, on the contrary, very frequently with those of 

 the other kind. It follows at once from the above formula, 

 that then also the molecules of the first kind of gas are brought 

 into the special condition only by collision with those of the 

 other kind of gas, and the mean kinetic energy of a molecule 

 must be the same for both gases, and moreover very quickly, 

 if only the impacts of molecules of the first kind with those of 

 the second kind occur very frequently f. This case is the 

 clearest example that the special condition and Avogadro's 

 law may both hold under circumstances which Prof. Tait 

 expressly excludes from their action. 



Also the second just- mentioned paper of Prof. Tait contains 

 not the least proof that in this simplest case Avogadro's law 

 ceases to hold or does not hold under the special condition of 

 one of the gases, or that in any other respect the objection con- 

 tained in the quotation given above is justified. For, from the 

 circumstance that in this case Prof. Tait's proof of Avogadro's 

 law is no longer applicable, it does not obviously follow that 

 the law itself ceases to hold good. Prof. Tali's second paper 

 contains, on the contrary, simply general statements, supported 

 by English and Greek quotations, that my assumptions are not 

 allowable. But how, if these assumptions are not allowable, 

 can I be reproached with having ignored them in my former 



* Phil. Trans. Edinb. vol. xxxiii. part ii. p. 251 (1887) ; in abstract, 

 Phil. Mag. [5] vol. xadii. pp. 141 & 483. 



t Only if the molecules of a certain kind enter into collision both with 

 each other and with the rest only very seldom, then, as a matter of course, 

 the special condition will also be reached by these very late. But not to 

 have mentioned this cannot be made a reproach either to me or any one 

 of my commentators, since there was not the least occasion to do so. 



G2 



