424 PROCEEDINGS OF THE AMERICAN ACADEMY 



enter or leave the liquids. Along the line c d the surface contracts 

 and does work at the constant increased difference of potential. The 

 tendency of the difference of potential along c d'l?, to diminish, and to 

 keep it constant electrical energy, E.^, must enter the liquids. 



Along da the surface contracts and the difference of potential and 

 superficial tension diminish to their original values. 



The liquids, after this process, are in every respect in their primitive 

 condition ; and the difference of potential across the surface being the 

 same, the total quantity of electricity upon the surface must be the 

 same as at the beginning of the process- 

 It is obvious from Lippmann's results that the cycle is also com- 

 pletely reversible. Since during the cycle there is a gain of work 

 abed, the electrical energy which enters the liquids must be greater 

 than that which leaves them, and we have 



abcd= M^ — Bj^. 



As the liquids are conductors, the only place at which a difference of 

 potential exists, in the whole body, is at the surface of separation. 

 The quantities of electricity entering and leaving the body, do so at 

 this difference of potential. 



Let Pj and P^ represent the differences of potential for the lines a b 

 and c d respectively. 



-^ is proportional to the quantity of electricity ^j which leaves the 



liquids along a b. 



E 



-=^ is proportional to the quantity Q^ which enters the liquids along 



-' 2 

 cd. 



Since the total quantity of electricity upon the surface is the same 



at the end of the process as at the beginning, 



n p ^' 



As any cycle may be decomposed into special cycles like the one that 

 has been considered, we have for the most general case, 



fdEz=W=—fkdS, V. 



f'^=0=fdm. VI. 



