721 



In Older to express the coniposition of a pliase 



F=xX + yY+zZ+(l^^~y-z)U. . . . (7) 



in tlie four composants, we put; 



F=mM+nN+pP4-{l-in-7i—p)Q ... (8) 



so thai Q is the fundamental composant. As (7) and (8) represent 

 the same phase F, it follows: 



m (m, — «J + n (it, — «J + p (u, — a J = .^• — a, j 



'" (Yi — y^) + « (Vi — y,) f p (y, — y J = « — y, ' 



so that ni 71 and /> are defined. 



In order to define, however, 7?i ?t and p from (9) the determinant, 

 formed by the coefficients of m ti and p maj not be zero. Conse- 

 quently' in general we have the following: 



in a system of ii components we may choose n arbitrary phases^ 

 like composants, notwithstanding their determinant is not zero. 



For a ternary system this means: we may choose three arbitrary 

 phases as composants notwithstanding those are not situated on a 

 straight line. In a cpiaternary system we may take 4 arbitrary phases 

 as composants notwithstanding those are not situated in a flat plane. 



When we represent the composition of a phase F as in (8) with 

 the aid of composants, then we may consider the thermodynamical 

 potential C of this phase also as a function of m n and p. Hence 

 it follows : 



dm diP dm by dm dz dm 



and still 2 similar relations, which we obtain by substituting in (10) 

 m by 11 and p. With the aid of (9) we now find : 



dg dg dg dg 



— = («,-«,) V- + (/3,-ff.)T- + (y,-y,)^ 



dm oz oy Oz 



dg dg dg dg 



d-n=(— '^d;. + ('^'-'^'^d,+^^'-^^^)d; • • (^^) 



dg , dg ^ dg dg \ 



J- =(«.—«4)^ + (/J.— ffJr- + (y.-yj^ 



dp Ox oy Ox I 



From those equations it follows also, with the aid of (9) 



dg dg 



(y-(*,)^ + (^-y.)^ • (12) 



Oy oz 



