720 



pliase L and a coiistant (f.i. soliti) phase F. The composition of L 



may be .e, y, z and 1 — x — y — z expressed in the components, the 



composition of F: a, b, c and 1 — a — h — c. 



When we deduce in some way tlie condition of equilibrium for 



tliis system F -\- L, then we find: 



dS dC dC 



S-(^-«)--(y-6)--(^-c)- = g, ... (8) 

 o.v Oy dz 



wherein y represents the therraodynamieal potential of L and ^, 

 that of F. 



We now express the composition of L and F in the composants 

 M, N, P and Q. Let be the composition of L. m, n, p and 

 1 — m — n — p; that of F: «, /*, y and 1 — « — ?—•/■ In a similar way 

 as we may deduce (3) we then find : 



dS dS dg 



Oni an Op 



Let us take two variable phases L and Zj (f.i. two liquids or 

 vapour -|- liquid or mixed crystals -\- liquid etc.). We express the 

 composition of those phases with the aid of the components viz. 

 .(■ y z and ,ï, y, 2,, with the aid of the com[)osants viz. m n p and 

 7/i, ?i, pi. In the first case we find as conditions tor equilibrium: 



ds as as ^ ds. dg, ds, 



S — «3 y~ 2 — = ?, — «, r y 



z. 



dx ' dy dz dx^ dv, dz^ 



dS^dg. ^^^1 ^i^^' 



d.i; </«, dy dy, dz d«, 

 When expressed in the composants, we find: 



a? d§ as ^ as, a?' ag, 



g — m ^ n ^ p — = g, — m, n, ^ p, — 



dm On Op Om^ on^ Op^ 



(5) 



(6) 



d£_dg^ ag_dg, is^ag, 



dm dm^ dn dn^ dp d/), 



Generally we may say that the equations for equilibrium have a 

 same form, independent on the fact whether they are expressed in 

 components or in composants. 



We now shall consider more in detail the relatione between 

 components and composants. For this we take again the composants 

 MNP and Q. We represent, expressed in components, the com- 

 position : 



of M by a, ^, y, and 1— «,—/*,— y, 

 „ JSr „ «, f?, y, „ 1— «,— ^,— y, 

 >. P „ ft, (3, y, „ 1— «,— p(,— y, 



.. Q „ «. ?, y. ,. 1— «,— /*4— y. 



