SURFACES OF DISCONTINUITY 689 



plausible; but there is no need to resort to this fallacious view of 

 the nature of surface energy. Actually there is at the surface 

 an amount of energy <tos due to ordinary molecular causes, where 

 (To is the surface tension with the surface uncharged and s the 

 area of surface, and in addition an amount of electrical poten- 

 tial energy ^QV where Q is the charge and V the potential of the 

 conductor. (Note that there is no hypothesis of a potential 

 discontinuity of amount V at the surface and a double layer of 

 charge.) Were the form of the conductor to change so as to 

 increase the surface by an amount 5s and heat to be supplied 

 reversibly so as to maintain the temperature constant, the 

 increase in the energy due to molecular causes is crods, but since 

 the same charge Q is on the surface its surface density will be 

 reduced and there will be a fall in electric potential energy, for 

 further separation of similarly charged particles always involves 

 decrease of potential energy. Hence the actual increase in 

 surface energy at constant temperature is less than aoSs which 

 means that the surface tension of the charged surface is less 

 than ffQ. The total surface energy is e,(s, V, t), a, function of 

 area, potential and temperature, and o-(s, V, t), the surface 

 tension, is defined in the usual way as dcg/ds. A change to a 

 new state of equilibrium with the variables at the values 

 s + 8s,V -\- 8V,t produces a change in the total energy given by 



dQ dQ 



a8s + V^8s + V-8V, 



where Q(s, V, t) is the electric charge on the surface. Hence 



des , ^dQ 



Ts=^^^'^' 



dV dV 



