ART. D 



Pn = 



drriidv 



dV 



dm-^ 



dV 



dmidnin-i 



d^ 



dm„-idv dmn-idrrii 



dml_i 



, (254) 



and the determinants F„_i, etc. are obtained by erasing suc- 

 cessively the last row and the corresponding column in (254), 

 By (231), dp/dv or ( — d^^p/dv"^) cannot be positive for a stable 

 phase, therefore none of the determinants derived from (254) 

 can be positive. If they are all negative the phase is necessarily 

 stable. For two components, when dntz = 0, these conditions 

 become 



d^ ^ 

 dv^ dm^ 



\dvdmi) ' 





dmi^ 



>0, (255) 



the last of which is a consequence of the other two. Thus, if 

 we construct a surface, the points of which have as coordinates 

 the values of Vi, Wi, ^ for homogeneous phases having the same 

 temperature and a constant value of W2, the condition of 

 stability of any phase is that the surface shall be above the 

 tangent plane taken at the point representing this phase, for 

 all adjacent phases. 



Lastly, if t, p, mi, m-i, . . .nin are taken as the independent 

 variables, and dt = 0, dp = 0, and dw„ = 0, we have 



dm = 



dfxz = 



dni 

 drrii 



djxj 

 dnii 



drrii + 



dmi + 



dni 

 drrii 



dn2 

 dnii 



drrii 



drrio 



+ 



+ 



dm n-i 



djii 

 dnin-i 



drrin- 



drn„-i, 



} (256) 



dfXn-\ = J... drrii + j drrii 



drui 



drrii 



dfln-l , 



+ drrin-i. 



dmn-i 



