from Faraday to J . J . Thomson. 377 



alterations may be performed independently, reversibly, and 

 isothermally, and that the state of the large electrode H, } is not 

 altered thereby. Let de denote the quantity of electricity which 

 passes through the cell from 5" to H, when the state of the 

 system is thus varied : then if E denote the available energy of 

 the system, and y the surface-tension at H, we have 



dE = ydS + Vde, 



y being measured by the work required to increase the surface 

 when no electricity flows through the circuit. 



In order that equilibrium may be re-established between the 

 electrode and the solution when the fall of potential at the 

 cathode is altered, it will be necessary not only that some 

 hydrogen cations should come out of the solution and be 

 deposited on the electrode, yielding up their charges, but also 

 that there should be changes in the clustering of the charged 

 ions of hydrogen, mercury, and sulphion in the layer of the 

 solution immediately adjacent to the electrode. Each of these 

 circumstances necessitates a flow of electricity in the outer 

 circuit : in the one case to neutralize the charges of the cations 

 deposited, and in the other case to increase the surface-density 

 of electric charge on the electrode, which forms the opposite 

 sheet of the quasi-condenser. Let Sf (V) denote the total 

 quantity of electricity which has thus flowed in the circuit 

 when the external electromotive force has attained the value V. 

 Then evidently 



so 



dE= {y+ Vf(V)\dS + VSf (V}dV. 



Since this expression must be an exact differential, we have 



so that - dy/d V is equal to that flux of electricity per unit of 

 new surface formed, which will maintain the surface in a 



