EQUILIBRIUM OF HETEROGENEOUS SUBSTANCES. 337 



I" 



constant condition while it is extended, is represented by in 



a a 



numerical value, and its direction, when F a ' is negative, is from the 

 mercury into the acid. 



We have so far supposed, in the main, that there are no passive 

 resistances to change, except such as vanish with the rapidity of the 

 processes which they resist. The actual condition of things with 

 respect to passive resistances appears to be nearly as follows. There 

 does not appear to be any passive resistance to the electrolytic process 

 by which an ion is transferred from one electrode to another, except 

 such as vanishes with the rapidity of the process. For, in any case 

 of equilibrium, the smallest variation of the externally applied electro- 

 motive force appears to be sufficient to cause a (temporary) electrolytic 

 current. But the case is not the same with respect to the molecular 

 changes by which the ion passes into new combinations or relations, 

 as when it enters into the mass of the electrodes, or separates itself 

 in mass, or is dissolved (no longer with the properties of an ion) -in 

 the electrolytic fluid. In virtue of the passive resistance to these 

 processes, the external electromotive force may often vary within wide 

 limits, without creating any current by which the ion is transferred 

 from one of the masses considered to the other. In other words, the 

 value of V V" may often differ greatly from that obtained from 

 (687) or (688) when we determine the values of the potentials for the 

 ion as in cases I, II, and III. We may, however, regard these equa- 

 tions as entirely valid, when the potentials for the ions are determined 

 at the surface of the electrodes with reference to the ion in the 

 condition in which it is brought there or taken away by an electrolytic 

 current, without any attendant irreversible processes. But in a 

 complete discussion of the properties of the surface of an electrode it 

 may be necessary to distinguish (both in respect to surface-densities 

 and to potentials) between the substance of the ion in this condition 

 and the same substance in other conditions into which it cannot pass 

 (directly) without irreversible processes. No such distinction, how- 

 ever, is necessary when the substance of the ion can pass at the 

 surface of the electrode by reversible processes from any one of the 

 conditions in which it appears to any other. 



The formulae (687), (688) afford as many equations as there are ions. 

 These, however, amount to only one independent equation additional 

 to those which relate to the independently variable components of the 

 electrolytic fluid. This appears from the consideration that a flux of 

 any cation may be combined with a flux of any anion in the same 

 direction so as to involve no electrical current, and that this may be 

 regarded as the flux of an independently variable component of the 



electrolytic fluid. 



G.I. Y 



