634 SUPPLEMENTARY. 



Let S be the surface of mercury in contact with acidulated water, 

 A the capillary tension of the liquid, and x the excess of potential 

 of the water over that of the mercury ; when, for any cause whatever, 

 the surface is increased by */S, the work of the capillary tension is 



Let us now suppose that a quantity of electricity dm, furnished 

 by an extraneous source, reaches the surface of the water ; there 

 will be an increase dx of the difference of potential, at the same 

 time as a dilatation dS of the surface. The quantities x and S are 

 then independent variables of the phenomenon. Since, other things 

 being equal, the mass dm is proportional to the surface, we may 

 write 



(10) dm = YSdx + XdS. 



The factor X represents the capacity of unit surface at constant 

 potential, and Y the electrical capacity of unit surface, the surface 

 being constant and the potential variable. The principle of the 

 conservation of electricity gives the condition 





On the other hand, the electrical work xdm, introduced into 

 the system, produces an increase of potential energy of the surface, 

 and an external work - AdS. If this operation be repeated several 

 times in opposite directions, so as to return to the initial state, and 

 that there has been neither gain nor loss of heat, the variation of 

 energy of the system will be null, which gives 



J 



that is to say, replacing dm by its value, 

 (12) 



I 



As this expression must be null for any closed circuit, we have 

 also 



