176 Prof. R. Clausius on the Second Axiom 



coefficient ~ by the fraction -, the equation 



d{Bx) _ 1 m d(Bx) _ 







dt i d<f> 







Here we may exchange the differentiation 



ind the variation on 



the right-hand side, whereby we obtain 







d(Sx) 1 £ dx 







dt i d<p 







After this exchange, we again introduce on 



the right- 



hand side 



the differential coefficient according to t, putting 





dx dx dt . dx 



• 





d(f> dt d(j> dt 







Thereby we obtain 







d{hx) 1 cY . dsc\ 

 ~~df ~i V dt) 







1 / . £ dx dx 

 " i \ dt dt 



u\ 





dr dr 







=s * + ^ 81 ^ 



i. 





By employing this equation, equation (26) is changed into 

 d ^ dx ~ ^ d q x ^ , ^ dx/^dxdx^, A 



di tm dt Sx ^ m -dfi S3C+ ^ m WVdF + di Sl0 ^) 



As, in accordance with equation (25), the differential coefficient 

 here standing on the left-hand side is equal to 0, we hence obtain 



In like manner for the two other coordinates we can form the 

 following equations : — 



_ 2 ^=Zfs(g)\2,»(g)W. • (28*) 



When w,e add together these three equations, and at the same 

 time consider the equation 



(SH*)"+ (!)"-• 



