616 RICE 



ART. L 



with a very large external mass which contains all the compo- 

 nent substances at suitable temperature and potentials; this is 

 also enclosed in an external rigid envelop and bounded inter- 

 nally by the envelop enclosing the system. A movement of 

 the surface of discontinuity in the system entails in general a 

 change in the volumes of the homogeneous masses of the system. 

 This does not involve any change in the potentials of the 

 various components in them or in the surface (in so far as they 

 are components in the surface) ; for the amounts of components 

 withdrawn from or passed into these masses are passed into or 

 withdrawn from the external mass, and that is so large that the 

 amounts are relatively too small to affect the potentials in it. 

 For the two masses we have equations such as these : 



Ae' = t At)' - p' Av' + fjiiAmi + . . . , 

 Ae" = t At?" - p"Av" + yuAmi" + ..., 



and an equation 



Ae'" = t At?'" + fnAmi" + ... 



for the external mass, since its volume does not change. For 

 the surface 



A^ = t Aijs -\- (tAs + MiAmi-s + . . . 



The variations may be finite* since t, ni, ^2, ... remain constant; 

 p' and p" are not necessarily equal since we are not assuming 

 the surface to be plane, but since each of them is a definite 

 function of t, /xi, 1J.2, . . ., each remains constant. Now if 



Ae' + Ae" + Ae"' + Ae-^ > 



the complete system is stable as regards the movement of the 

 surface. Since the total entropy and masses are constant we 

 can state that if 



aAs - p'Av' - p"Av" > 



* Finite, that is, with reference to the system; they are small com- 

 pared to the external mass. 



