FOUNDATIONS OF THE KINETIC THEORY OF GASES. 257 



necessarily differ, at least slightly, from those obtained by any other inves- 

 tigator. 



By § 11 we see at once that 



/ vv r 1 / £ v av 



1 r 4x'- +i e-**dx 



(vv 1 /3+v 1 3 /v)dv 1 





s^-, suppose. 



The finding of C r is of course a matter of quadratures, as in the Appendix 

 to the First Part of this paper, where the values calculated are, in this notation, 

 d and C ; and Mr Clark has again kindly assisted me by computing the 

 values of C x , C 3 , C 5 , which are those required when we are dealing with 

 Viscosity and with Heat-Conduction in a single gas. The value of C 2 has also 

 been found, with a view to the study of the general expression for C r . These 

 will be given in an Appendix to the present paper. 



34. When we come to deal with Diffusion, except in the special case of 

 equality of density in the gases, this numerical part of the work becomes 

 extremely serious, even when the assumption of a " steady " state is permissible. 

 As will be seen in § 28 of my first paper, we should have in general to deal 

 with tables of double entry, for the expressions to be tabulated are of the 

 form — 



/■» *r _j /*» 4s r+4 r* 3 <fa 



For the second gas the corresponding quantity will be written as 2 € r . Here 



Ws + sA 2 . 



IV2T) ' 



and 



nh. 



so that they are numerical quantities, of which the first depends on the relative 

 masses of particles of the two gases, while the second involves, in addition, not 

 only their relative size but also their relative number. It is this last condition 

 which introduces the real difficulty of the question, for we have to express the 



