284 



MOREY 



ART, G 



than the chemical potential of the stable coexisting set of 

 phases, which condition is represented by the inequality 



Vdjp — 'S.dt > midiii + niidni . . . + nindfXn. 



Similarly, the condition that the equilibrium 



P" + P'" + P^^ . . . + P" + i + P"+' 



is stable is that the missing phase P' is unstable. 



By solving the (n + 1) equations of the type of (1) [97], 

 referring to the (n + 1) coexisting phases of the equilibrium 

 in which P" is the missing phase, for dm, dixz, dm, and dt in 

 terms of djp, and substituting in the above inequahty, (the 

 quantities F, H, Wi, mz, . . . rUn referring to phase P") the 

 stability is found to depend upon the sign of the following ex- 

 pression : 



dp 



H" V" 

 H'" V'" 



jjIV ylV 



mi 

 mi 



II 



IV 



mi 

 m<i 

 mi 

 mi 



II 



IV 



mz 

 mz 

 mz 

 mz 



II 



III 



IV 



Jjn+l yn+1 fyi^n+l '^^n+l ^g^+l 

 JJn+2 yn+2 ^,"+2 f}i^^+^ 7^3"+^ 



mr, 

 mn 



II 



mn 

 m'7 



m 

 m 



n+l 



t 



n+2 



(A) 



H' 



m\ 

 m\ 

 mi 



IV 



m2 

 m2 

 m-i 



III 



IV 



mz 

 mz 

 mi 



IV 



Jjn+l ^n+l ^^n+1 ^^n+l 



H"+2 ,/j^n+2 rn2"+^ m3"+2 



mn 

 mn 

 mn 



IV 



m 

 mn 



n+l 



I 



n+2 



The equilibrium, P' + P"' + P^^ . . . + P"+i + P^+\ 

 will be stable if this expression is negative, and vice versa. 

 Also the univariant equilibrium, P" + P'" . . . + P"+i + P"+^ 

 in which P' is the missing phase, is stable when the expression 



