64 Mr. S. H. Burbury on the Second Law of Thermodynamics 



formed from M by altering the distance between each pair of 

 points in the ratio 6 : 1 — that is, 



If, then, u, Xi d?u fyx, . . • dz k be denoted in the altered volume 

 by accented letters, we shall have 



u' = log JjJ. . . e h *'dx\ dy\ . . . dz? k 



= log \6 ZK ~e h x'dx x dy x . . . dz k \ , 



since every linear element da t ,dy l} &c. is altered in the ratio 6 : 1. 

 In the last expression for u' } y^ is to be treated as a func- 

 tion of x x , y Xj . . . z K . Then 



t jjj . . . e^dx l dy x ...dz„) 

 = 3X log 0-h . i\lyh^^ 1 d 1/l ...d 2x 



!))••• <?**<My,...<fe* 



in which expression C JL denotes the mean for all configurations 



of the alteration of % consequent on v becoming v + Sv. 

 Collecting our results, w T e obtain 



Su^Sh+^Sv. x&h+X^-hp&». . (B) 



dh dv * v dv x 7 



IV. The system being in stationary motion must satisfy 

 Clausius's equation 



in which P is the force acting from without on the surface of 

 the vessel, and J 25)R?' ^ s ^ e niean virial of all the other 

 forces acting on the system — that is, of all the forces of which 

 the ergal is %. 



