200 Prof. R. Clausius on the Theorem of the Mean Erg ah 

 or also, according to (29), by 



-© 



SR. 



(113a) 



from which it is evident that y is a small constant quantity. 

 The equations will then read : — 



U = 



logU=log(V-e) 



(114) 



(n-1) 



V-, 



This equation for U gives forthwith also those for E and U— T; 

 and in like manner, taking into consideration (97), in which Nra 

 is also to be put =1, we can derive from the equation for logU 

 those for log (£ and log 3, viz. 



E = T ( 1 + V^ e T^) ) 



io g e=iog[(v-€T)i]-|(»-i; 

 u-t=-t(i-^t-;), 



lo g 3=log^-|(„-l)^- 



1 



(U5) 



(116) 



Consequently the six quantities to be determined are repre- 

 sented in a simple manner as functions of T and V; and it is 

 easy to convince one's self that these functions give the mutually 

 accordant differential coefficients 



dJJ 



<LE 



dlogU dlog(S 



<4(U-T) s 

 dlogS 3 



At the same time it may be again mentioned that the equa- 

 tions of this last section are only to be applied to the molecular 

 motions of gases when we neglect the attraction of the molecules 

 . — which of course alters the value of the ergal, and may even 



affect its sign. 



