620 RICE ART. L 



and therefore 



+ U'7^ + e^"^ +s— 5M2 + etc. = 0. 



\ dfX2 dfJL2 dH2/ 



(This is the equation [546] on page 251, generahzed to deal with 

 the variation of several potentials and not merely of one.) 

 There are several points about this equation which require 

 careful consideration before we proceed, for they reveal the 

 nature of the assumptions implied. First, it is clearly assumed 

 that in the varied state the potentials of any component are still 

 equal in the two masses, and also equal to the varied potential 

 of that component at the surface; for example, the first com- 

 ponent has the potential /xi + 8ni everywhere. Thus we are 

 assuming that the varied state is one which does "not violate 

 the conditions of equilibrium relating to temperature and 

 potentials." Second, since the equation is meaningless unless 

 dji'/dni, dji'/dni, 9ri/a;Lti . . . have definite values, we are 

 assuming that 7/ = dv'/dni, 7/' = dv"/diJLi, Ti = —da/dni 

 and so on, and that dji/dfjLi, etc., are obtained from these by 

 further differentiations. So it is implied that the fundamental 

 equations are valid. The equation is not quite in the form of 

 [546]; to make it so we should have to write the first three 

 terms in the form 



(T;-7'; + r:|,)a.'. 



But this implies that s is a function of v'; otherwise ds/dv' has 

 no meaning. This, however, is taken care of by the necessary 

 condition of stable equilibrium that the surface of tension has 

 the minimum area for given values of the volumes v' and v" 

 separated by it. This minimum-area condition is not sufficient 

 for stable equilibrium, but it is necessary, and therefore in 

 discussing the stability of a state of equilibrium there would be 

 no necessity to proceed further if we knew that it was not satis- 

 fied. This condition therefore gives a unique value to s for a 



