332 EQUILIBRIUM OF HETEROGENEOUS SUBSTANCES. 



It will be observed that the choice of the substances which we 

 regard as the components of the fluid is to some extent arbitrary, and 

 that the same physical relations may be expressed by different 

 equations of the form (682), in which the fluxes are expressed with 

 reference to different sets of components. If the components chosen 

 are such as represent what we believe to be the actual molecular 

 constitution of the fluid, those of which the fluxes appear in the 

 equation of the form (682) are called the ions, and the constants of 

 the equation are called their electro-chemical equivalents. For our 

 present purpose, which has nothing to do with any theories of mole- 

 cular constitution, we may choose such a set of components as may be 

 convenient, and call those ions, of which the fluxes appear in the 

 equation of the form (682), without farther limitation. 



Now, since the fluxes of the independently variable components of 

 an electrolytic fluid do not necessitate any electrical currents, all the 

 conditions of equilibrium which relate to the movements of these 

 components will be the same as if the fluid were incapable of the 

 electrolytic process. Therefore all the conditions of equilibrium which 

 we have found without reference to electrical considerations, will 

 apply to an electrolytic fluid and its independently variable com- 

 ponents. But we have still to seek the remaining conditions of 

 equilibrium, which relate to the possibility of electrolytic conduction. 



For simplicity, we shall suppose that the fluid is without internal 

 surfaces of discontinuity (and therefore homogeneous except so far as 

 it may be slightly affected by gravity), and that it meets metallic 

 conductors (electrodes) in different parts of its surface, being other- 

 wise bounded by non-conductors. The only electrical currents which 

 it is necessary to consider are those which enter the electrolyte at 

 one electrode and leave it at another. 



If all the conditions of equilibrium are fulfilled in a given state of 

 the system, except those which relate to changes involving a flux of 

 electricity, and we imagine the state of the system to be varied by 

 the passage from one electrode to another of the quantity of electricity 

 Se accompanied by the quantity m a of the component specified, 

 without any flux of the other components or any variation in the 

 total entropy, the total variation of energy in the system will be 

 represented by the expression 



in which V, V" denote the electrical potentials in pieces of the same 

 kind of metal connected with the two electrodes, Y', Y", the gravita- 

 tional potentials at the two electrodes, and ///, JUL & ", the intrinsic 

 potentials for the substance specified. The first term represents 

 the increment of the potential energy of electricity, the second the 



