Page:Scientific Papers of Josiah Willard Gibbs.djvu/448

412 But we cannot get anything by differentiating an inequality, and it does not appear à priori which side of (10) is the greater when the condition of reversibility is not satisfied. The term $$\frac{\text{Q}}{t}$$ in (11) is certainly not greater than $$\eta '' - \eta '$$, for which it was substituted. But this 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,

.