REPRESENTATION BY ZETA FUNCTION 



311 



tangents to the f-curve drawn from the points (W) and (X) of 

 Fig. 9 (and similar figures). 



14. When the sohd substance X can exist in the two modifi- 

 cations a and /?, we may suppose the f-point of soHd a in Fig. 6 

 represented by (X) and that of soHd /3 by ^', so that the modifica- 

 tion )8 is metastable with respect to a. If we draw a tangent 

 to the f-curve from 13', the point of contact, which is situated 

 somewhere between c' and X', represents the f-point of the 

 liquid saturated with respect to solid /?, whilst the liquid itself 

 lies somewhere between c and X. From this it follows that, 



fr 



1' 



w 



e 



Fig. 11 



u 



when a substance X exists in two or more modifications, the 

 most stable form has the smallest solubility. 



15. In Fig. 11, in which the f-curve has a part concave to the 

 composition axis, the point of intersection of the double tangent 

 z'u' with the line XX' has been represented by the point s. If 

 we take T = T{X), then (Z), i.e., the f-point of solid X, coin- 

 cides with X'. If we lower the temperature, then the point 

 {X) and the f-curve rise, whilst the latter also changes its form. 

 Since, however, X' rises more rapidly than (Z), the point {X) 

 comes to fall below X', and the lower the temperature the lower 



