REPRESENTATION BY ZETA FUNCTION 



297 



vapors W and X and a' that of the binary vapor a. When 

 the points of WX represent homogeneous mLxed crystals, then 

 W'a'X' is the ^-curve of these mixed crystals, whilst W and X' 

 are the respective ^-points of the pure solid substances W and X 

 and a' that of the mixed crystalline phase a. 



3. We now take two phases A and B with the compositions 

 Xi mols X + (1 — Xi) mols W, X2 mols X -\- {\ — x^) mols W. 

 If we bring together mi units of A and nii units of B, and if we 

 suppose that they continue to exist unchanged beside one 

 another, then we have a system or phase complex 



miA + ?W2-B, 



(1) 



which may be stable or not. Let its total composition be 

 represented by x mols X + (1 — x) mols W. Since this system 

 contains in toto (mi + m2) mols and contains mia;i + 711.2X2 mols 

 X, we have 



X = 



mjXi + 702X2 

 mi + W2 



From this follows 



7ni{x — x^ = 7n2{x2 — x). 



(2) 



If we imagine the phases A and B and the system represented 

 in Fig. 2 by the points a, h and s, then we have Xx = Wa, 



