THERMODYNAMIC AL SYSTEM OF GIBBS 165 



. . .nin are in general different in the two phases. Or, if for 

 convenience we compare equal volumes of the two phases (which 

 involves no loss of generahty), the quantities 77, mi, nh, . . . nin 

 will in general have different values in two coexistent phases. 

 Applying tliis to coexistent phases indefinitely near to a critical 

 phase, ... if the values of n of the quantities t, p, /xi, mz, • • • Mn are 

 regarded as constant (as well as v),* the variations of either of 

 the others wUl be infinitely small compared with the variations 

 of the quantities 77, mi, m^, . . . w„. This condition, which we 

 may write in the form 



= 0, (242) [200] 



Mn-I 



characterizes . . . the limits which divide stable from unstable 

 phases with respect to continuous changes." 



Critical phases are also at the limit which divides stable 

 from unstable phases in respect to discontinuous changes. 

 Thus, in Figure 8, phases represented by points inside the curve 

 ACB are unstable with regard to the formation of the co- 

 existent phases, represented by points on this curve. The co- 

 existent phases thus He on the limit which separates stable from 

 unstable phases in respect to discontinuous changes, and the 

 same must be true of the critical phase. 



The series of phases determined by giving t and p the constant 

 values which they have in the coexistent phases N and P 

 (Fig. 8) consists of unstable phases in the part NP between the 

 coexistent phases, but in the parts MN and PQ, beyond these 

 phases, it consists of stable phases. But when t and p are 

 given the constant values determined by the critical phase C, 

 the whole series of phases XY (obtained by varying the com- 

 position) is stable. Thus, in general, "if a critical phase is 

 varied in such a manner that n of the quantities t, p, m, fj.2, 

 . . .(Xn remain constant, it will remain stable in respect both to 



* Since two coexistent phases are only capable of n independent 

 variations, this condition ensures that the variation considered cor- 

 responds to the change from one coexistent state to the other, which is 

 infinitely close to it. 



