OF ARTS AND SCIENCES. 423 



The consideration of this case may be simplified by a method analo- 

 gous to that employed in thermodynamics. 



In the figure below, let abscissae represent areas of the surface, and 

 ordinates represent tension per unit-length. Any transformation due 

 to changes in the area and superficial tension of the surface may be 

 represented by a line on the diagram. The work done during the 

 transformation " a 6 " is equal to the area a a' b' b. The area of any 

 closed curve gives the work done during the cyclical process repre- 

 sented by the curve. Since the superficial tension is a function of the 

 difference of potential across the surface, the work will be a function 

 of the difference of potential. 



By keeping the liquids on each side of the surface in contact with 

 electrified bodies the difference of potential can be made to vary as we 

 please. The deformation of the sui'face, due to any force, may be 

 made to take place at constant, or at variable potential. 



A special form of cyclical process may be arranged such that the 

 transformations take place only in two ways. In one way the liquids 

 are kept in contact with conductors of infinite capacity and constant 

 potential ; in the other way they are insulated. The line representing 

 a transformation according to the first way is parallel to S, and 

 electrical energy must either leave or enter the liquids. For in 

 order to keep the difference of potential constant, when it tends to 

 increase, electrical energy must leave the surface of contact of the 

 li(juids ; and when the difference of potential tends to diminish electri- 

 cal energy must be furnished to the surface. 



As in thermodynamics any cycle can be considered to be made up 



of isothermal and isentropic lines, 

 so in the present case any cycle 

 may be considered to be made up 

 of lines of constant potential, and 

 lines of variable potential. 



Let the cycle in the figure be 

 composed of two lines of constant 

 potential, and two lines of variable 

 potential. 

 Along the line ab work is done in increasing the area of the sur- 

 face. By III. of Lippmann's results, the difference of potential tends 

 to increase, and k tends to increase. To keep the difference oi 

 potential constant electrical energy, ^j, must leave the liquids. 



Along the line be work is done upon the surface ; and the difference 

 of potential and k are increased. No energy of any kind is allowed to 



