EQUILIBRIUM OF HETEROGENEOUS SUBSTANCES. 333 



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 



V"- F'+a a (yu a "-// a '- Y"+ Y') = 0. (684) 



To extend this relation to all the electrodes we may write 



F' + a^'- Y> F"+a.OC- Y") = F" + a a OC'- Y'") = etc. (685) 

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

 similar condition, and for each of the anions a condition of the form 

 V - a g (fjL e ' - Y') = F" - a g ( f i g f/ - Y") = V" - a g (,u g '" - Y"') = 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 =.(/!.' -//."), (687) 



and for any anion 



V"-V' = aM'-tt e '), (688) 



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 



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

 each electrode. When this is not the case the expression may be applied to small parts 

 of the electrodes taken separately. 



t If the electrolytic fluid dissolved the mercury as well as the zinc, equilibrium 

 could only subsist when the electromotive force is zero, and the composition of the 

 electrodes identical. For when the electrodes are formed of the two metals in 

 different proportions, that which has the greater potential for zinc will have the less 

 potential for mercury. (See equation (98).) This is inconsistent with equilibrium, 

 according to the principle mentioned above, if both metals can act as cations. 



