REPRESENTATION BY ZETA FUNCTION 315 



tangents z'(X) and u'{X) we may also draw a third tangent 

 e'(X). Consequently, besides the liquids z and u there exists 

 also a third liquid e which is saturated with respect to X. So 

 in Fig. 12 there is possible, between z and u, a liquid e saturated 

 with respect to X which is not stable (as appears from Fig. 11). 

 We now take a temperature somewhat higher than T(s), so that 

 (X) in Fig. 11 is situated a little above s. We may now draw 

 three tangents through (X), which we shall call zi{X), ei(X) 

 and Ui{X). Then point Zi is situated a little to the right of 

 z', ex a little to the left of e' and w/ a little to the right of u' . 

 Of the three liquids saturated with respect to X, which we call 

 2i, ei and U\, now only Wi is stable, as appears from Fig. 11. In 

 Fig. 12 we represent them by the points 2i, ei and d (i.e., d = u-). 

 If we raise the temperature still higher, then, as follows from 

 Fig. 11, the pomts z^ and ex of Fig. 12 coincide finally in a point 

 g. In a corresponding manner we may prove that in Fig. 12 

 there exists also the metastable-unstable branch eku. From 

 this it appears that the saturation curve of X is a continuous 

 curve with a maximum and a minimum temperature. Only 

 the parts hz and uT{X) which lie outside the heterogeneous 

 two-Hquid field represent stable liquids. The other liquids are 

 metastable (viz., zg and ku) or unstable (viz., gh). 



IV. Binary Systems in Which Besides Liquids Only the Solid 

 Components W and X and a Solid Compound May Occur. 



n. When W and X form a compound fl", we may imagine 

 the systems : 



solid W + solid X, (21) 



solid W + solid R, solid X + sohd H, (22) 



solid W + solid X + solid H, (23) 



when we leave liquid phases out of account. The compound 

 and its f-point are represented by B. and (//) in Figs. 13, 14, 

 and 16. If in Fig. 14 we imagine the curves omitted and 

 consider only the f-points (W), (//) and (X), together with 

 their conjugation lines, we may distinguish three cases. 



