502 ./ W. Gibbs — JEquilibriurn of Heterogeneous Substances. 



tions of the form (682), in Avhich tlie fluxes are expressed with refer- 

 ence to diff'erent sets of components. If the components chosen are 

 such as represent what we believe to be the actual molecular consti- 

 tution 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-cheynical equivalents. For our present pur- 

 pose, which has nothing to do Avith any theories of molecular consti- 

 tution, we may choose such a set of components as may be conven- 

 ient, 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 Avhich 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 wdiich 

 we have found without reference to electrical considerations, will 

 apply to an electrolytic fluid and its independently vai'iable compo- 

 nents. But we have still to seek the remaining conditions of equili- 

 brium, which relate to the possibility of electrolytic conduction. 



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

 surfaces of discontinviity (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 electric- 

 ity 6e accompanied by the quantity 6m^ 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 rep- 

 resented by the expression 



( Y" _ V') de + (///' - yw/) dm^ + {T'^ T") 6w,, 



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

 kind of metal connected with the two electrodes, T', T", the gravita- 

 tional potentials at the two electrodes, and ///, ///', the intrinsic 

 potentials for the substance specified. The first term represents the 

 incremen*) of the potential energy of electricity, the second the incre- 



