THERMODYNAMIC AL SYSTEM OF GIBBS 

 Therefore, by (43), 



/ dnn-i \ 

 \dmn-ijt. 



p. Ml. • • • Mn-i> 



where C/„_i is the determinant 

 d^^ d^^ 



Un-l 

 UnJ 



d^^ 



171 



(257) 



drrii dnh, 



dH 

 dm^ 



dmn-\ dmi dm„_i dmz 



dm-^ 



dH 

 dm-2 dm I 



dH 



drrii dm„_i 

 dnii dtrin-i 



dml^i 



, (258) [206] 



and Un-2, etc. are the minors obtaiaed by erasing successively 

 the last column and the corresponding row. A phase for 

 which all these determinants have positive values is therefore 

 stable. 



When there are three components and dmz = 0, these con- 

 ditions become 



d^ ^ 

 drrii^ dnii^ 



\dmi dw2/ 



>0, 



dn_ 

 dmi' 



>0, 



dn_ 

 dmi^ 



> 0. 



(259) 



If, instead of making wis constant, we use as the variables ex- 

 pressing the composition x = Wi/(wi -{- m^ -{- mz) and y = 

 m^/imi + m2 + ms), these conditions maybe obtained in the form 



dx^ 



dy' 



\dx dyj 



>0, 



d^ 

 dx' 



>0, 



d^ 

 dy' 



> 0. (260) 



Thus if a f-surface is constructed for homogeneous phases 

 having the same temperature and pressure, with coordinates 

 X, y, f, the condition of stability of any phase is that the f- 

 surface for adjacent phases shall be above the tangent plane, 

 taken at the point representing the phase in question, every- 

 where except at the single point of contact. 



