530 RICE ART. L 



makes 



dCi dC2 



equal to zero, to be coincident with the surface of tension. The 

 proof that such a position can be found and the reasons for 

 choosing it are expounded at length. In view of the fact that 

 Gibbs takes S to be composed of parts which are approximately- 

 plane and which are supposed in the course of the proof to be 

 deformed into spherical forms of small curvature, we may as 

 well introduce that simplification into the argument at once 

 and assume that Ci = c^ so that Ci = C2, and we have then to 

 show that we can locate s in such a way that 



To-"' 



where c is the common value of Ci and C2. 



Let CDEF in Fig. 4 represent the portion of the region of dis- 

 continuity, and suppose AB represents an arbitrarily assigned 

 position of s so that EA = FB = x. We shall represent the 

 thickness of the film EC by f . We now suppose that a deforma- 

 tion to a spherical form indicated by the diagram with accented 

 letters is produced. This means that c varies from zero to 

 1/R, where R is the radius of the sphere of which A'B' is a por- 

 tion; i.e., 8c = 1/R. We also suppose that s does not vary in 

 magnitude; i.e., that the area of the spherical cap indicated by 

 A'B' is equal to the area of the plane portion indicated by AB; 

 nor is there to be any variation of the other variables rj^, mi^, 

 tUi^, etc. Hence, by [493], 



C 



5e« = 2C8c = 2 ^• 



But the only possible reason for which e^ will vary under these 

 circumstances is the fact that the volume of the element of film 

 indicated by C'D'E'F' is different from that of the element 

 CDEF. In short one must remember that a, though called a 

 surface energy, is strictly an energy located in the film with a 



