690 RICE ART. L 



By cross-differentiation 



dV ds ^ dVds dVds 



dsdV 



Therefore 



aa _ dQ 

 dV ~ ~ ds 



This is the result which Lippmann appHed to the cathode 

 mercury surface of his electrometer. In the usual form of the 

 experiment a steady current is established in a potentiometer 

 wire, the positive end of which is attached to the large mercury 

 surface of the electrometer; a wire from the mercury in the 

 capillary tube goes to the travelling contact maker on the 

 potentiometer. As the contact slides away from the positive 

 end towards the negative, so that the potential V of the mercury 

 cathode above the electrolyte is lowered, it is observed that a at 

 first increases and then, passing a maximum, decreases until a 

 state of affairs is reached at which the polarization of the 

 cathode is unable to prevent a flow of current under the external 

 E.M.F. and equilibrium ceases to be possible. If E represents 

 this applied E.M.F., i.e., the P.D. between the positive end of 

 the potentiometer wire and the contact in any state of equilib- 

 rium, then V = Vq — E, where Va is the excess of potential of 

 the mercury above that of the electrolyte in the "natural state" 

 (i.e., when the applied E.M.F. is zero) ; and if E„i is the value of 

 this apphed E.M.F. in the state of maximum surface tension, 

 then Vm = Vo — Em, where 7™ is the P.D. between mercury and 

 electrolyte in this state. Since initially da/dE is positive, 

 da/dV is negative and so dQ/ds is positive. Now dQ/ds 

 measures the increase of charge required for unit increase in the 

 area of surface, the potential being kept constant; in other 

 words the charge per unit area; it is also in general a function of 

 s, V, t, just as Q is, and we write it q{s, V, t). Thus initially 



