J. W. Gibbs — Equilibrium of Heterogeneons Substances. 501 



Modification of the conditions of equilibrium by ei,ectro- 

 MOTivE force. — Theory of a perfect electro-chemical 



APPARATUS. 



We know by experience that in certain fluids (electrolytic con- 

 ductors) there is a connection between the fluxes of the component 

 substances and that of electricity. The qnantitative relation between 

 these fluxes may be expressed by an equation of the form 



Be = ■ H ^ + etc. _ ^ _ etc., (682) 



where Be, Bm^, etc. denote the infinitesimal quantities of electricity 

 and of the components of the fluid which pass simultaneously through 

 any same surface, w'hich may be either at rest or in motion, and 

 a^, o'h, etc., ag, a^,, etc. denote positive constants. We may evidently 

 regard Dm^, Bn\, etc., Bm^, Brn^, etc., as independent of one 

 another. For, if they were not so, one or more could be expressed 

 in terms of the others, and we could reduce the equation to a shorter 

 form in which all the terms of this kind would be independent. 



Since the motion of' the fluid as a whole will not involve any elec- 

 trical current, the densities of the components specified by the suf- 

 fixes must satisfy the relation 



i^+ZL + etc. = ^+^ + etc. (683) 



These densities, therefore, are not independently variable, like the 

 densities of the components which we have employed in other cases. 



We may account for the relation (682) by supposing that electric- 

 ity (positive or negative) is inseparably attached to the diflferent 

 kinds of molecules, so long as thev remain in the interior of the fluid, 

 in such a way that the quantities a^, a'5, etc. of the substances speci- 

 fied are each charged with a unit of positive electricity, and the quan- 

 tities o'g, ft'h, etc. of the substances specified by these suflixes are each 

 charged with a unit of negative electricity. The relation (683) is 

 accounted for by the fact that the constants a^, o'g, etc. are so small 

 that the electrical charge of any sensible portion of the fluid varying 

 sensibly from the law expressed in (683) would be enormously great, 

 so that the formation of such a mass would be resisted by a very 

 great force. 



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 equa- 



