﻿388 Mr. Gr. H. Livens on the Law of 



a maximum when each E/ is equal to the corresponding E r , 

 subject to the sum being equal to E. The analytical 

 condition for this is, in the usual way, that all the E/'s are 

 given by the system of equations 



as as 



combined with the equation 



E/ + E 2 '-h =E. 



If now we proceed on the basis suggested above and put 





W r =V^> 



we find that 



S=2£logW r 





=2« kho-Y 



so that 







^8 u r k'dVy 



Now suppose that the first part of the system is a perfect 

 gas. Its energy will be then simply the kinetic energy 



the sum 2 here extending to say m x terms, all representing 

 identical types of coordinates. In this case V 3 is the volume 

 of the generalized space in which X lef lies between E t — J^ 

 and E x + Jei, which is known to be of the form 



V,=0 1 E 1 *-'- 1 ^ 



wherein G 1 is a definite constant. Thus 



which since m x is very large is practically the same as 



1 avi_ m 1 



so that 



a S a-Jzm 



But if denote the absolute temperature of the system in 

 the steady state and R the usual absolute constant of gas 



