Page:Scientific Papers of Josiah Willard Gibbs.djvu/369

Rh increment of the intrinsic energy of the ponderable matter, and the third the increment of the energy due to gravitation. But by (682) It is therefore necessary for equilibrium that  To extend this relation to all the electrodes we may write  For each of the other cations (specified by $_{\text{b}}$|undefined etc.) there will be a similar condition, and for each of the anions a condition of the form  When the effect of gravity may be neglected, and there are but two electrodes, as in a galvanic or electrolytic cell, we have for any cation  and for any anion  where $$V'' - V'$$ denotes the electromotive force of the combination. That is:— When all the conditions of equilibrium are fulfilled in a galvanic or electrolytic cell, the electromotive force is equal to the difference in the values of the potential for any ion or apparent ion at the surfaces of the electrodes multiplied by the electro-chemical equivalent of that ion, the greater potential of an anion being at the same electrode as the greater electrical potential, and the reverse being true of a cation.

Let us apply this principle to different cases. (I.) If the ion is an independently variable component of an electrode, or by itself constitutes an electrode, the potential for the ion (in any case of equilibrium which does not depend upon passive resistances to change) will have the same value within the electrode as on its surface, and will be determined by the composition of the electrode with its temperature and pressure. This might be illustrated by a cell with electrodes of mercury containing certain quantities of zinc in solution (or with one such electrode and the other of pure zinc) and an electrolytic fluid containing a salt of zinc, but not capable of dissolving the mercury. We may regard