REPRESENTATION BY ZETA FUNCTION 313 



phase system (14) of Fig. 8, we now find that in the three-phase 

 system (17) the reaction 



L{z) + solid X :^ L(u) (18) 



can occur. On addition of heat L(z) passes into L(u) with 

 solution of sohd X, whilst on removal of heat L{u) breaks up 

 into L{z) and solid X. If in Fig. 12 we represent the Hquids z 

 and u by the points z and u, then the systems discussed above 

 are all represented by the points of the portion zu2' of the 

 line 2.2'. 



(iii) T(X) > T{s) > T. The point (X) must now be situated 

 below the point s. Although the f-curve has now a somewhat 

 different form and is also situated higher than in Fig. 11, 

 nevertheless we may imagine it as represented in this figure, 

 and call the latter now Fig. 11a. We suppose the point {X) 

 to be at q'. Imagine a line through q' touching the f -curve in a 

 point h' between W and z'. It is then clear that of all conceiv- 

 able f-points of Fig. 11a only those of the part W'h' of the 

 f-curve and those of the tangent h'q' represent stable states. 

 From this follows for Fig. 11a: all liquids of Wh are stable, 

 whilst all other liquids, i.e., those of hX, pass into the system 



LQi) + solid X (19) 



with separation of solid X. If in Fig. 11 we imagine z' and u' 

 substituted by m' and n', we see that the system 



L{m) + L{n) (20) 



also exists, but only in a metastable state. When the stable 

 state is attained, these two liquids disappear, with formation 

 of the system (19). In Fig. 12 the liquids h, m and n, are 

 represented by points of the line 3.3'. 



When we raise the temperature, the f-curve not only shifts 

 downwards but also changes its form. As the points of contact 

 a' and h' in Fig. 5 are moved with respect to one another the 

 liquids a and h also change their composition. When a' and h' 

 coincide in a point c' at a definite temperature T{c), the liquids 

 become identical in composition. We call c a critical liquid and 



