J. W. Gihhs — Equilibrium of Heterogeneous Substances. 503 



ment of tlie intrinsic energy of tlie ponderable matter, and the third 

 the increment of the euerg}' due to gravitation.* But by (682) 



8tn^ =z a^ Se 

 It is therefoi'e necessary for equilibrium that 



V" - F' + a^ (/.//' - //.' - T" + F') = 0. (684) 



To extend this relation to all the electrodes we may write 



V' + «'a (/'.' - r') = V" + a, (//." - T") 



= F'" + a, (//,'" — F'") ■— etc. (685) 

 For each of the other cations (specified by ^ etc.) there will be a sim- 

 ilar condition, and for each of tlie anions a condition of the form 



V - a^ (/.; - F') = V" - «', iM," - r") 



— V'" — o'g (/V" - i^'") = etc. (686) 

 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 



V" - V =:a^ {mJ - /^a"), (687) 



and for any anion 



V" -V' = a^ (/.," - /V), (688) 



where T"" — V denotes the electromotive force of the combination. 

 That is: — 



Whe7i 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 potenticd for any ion or apparent ion at the su,rfaces 

 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. 



IjCt us apply this principle to different cases. 



(I.) If the ion is an independently variable component of an elec- 

 trode, or by itself constitutes an electrode, the potential for the ion 

 (in any case of equilibrium which does not depend upon passive resist- 

 ances to change) will have the same value within the electrode as on 

 its surface, and will be determined by the composition of the elec- 

 trode 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 



* It is here supposed that the gravitational potential may be regarded as constant 

 for each electrode. When this is not the case, the expression maj" be applied to small 

 parts of the electrodes taken separately. 



Trans. Conn. Acad., Yol. III. 64 June, 18t8. 



