412 ELECTROCHEMICAL THERMODYNAMICS. 



But we cannot get anything by differentiating an inequality, and it 

 does not appear d priori which side of (10) is the greater when the 



condition of reversibility is not satisfied. The term -^ in (11) is 



u 



certainly not greater than rf f rf, for which it was substituted. But 

 tliis does not determine which side of (11) is the greater in case of 

 irreversibility. It is the same with Helmholtz's method of proof, 

 which is quite different from that here given, but indicates nothing 

 except so far as the condition of reversibility is fulfilled. (See 

 Sitzungsberidite Berl. Acad., 1882, pp. 24, 25.) 



I fear that it is a poor requital for the kind wish which you 

 expressed at Manchester, that I were present to explain and support 

 my position, for me to impose so long a letter upon you. Trusting, 

 however, in your forbearance, I remain, yours faithfully, 



J. WILLARD GIBBS. 



