REPRESENTATION BY ZETA FUNCTION 307 



complexes) are stable in each of these five cases. We shall 

 represent them in Fig. 10, in which temperature has been taken 

 as the ordinate (isobaric T-x diagram). The points T(W) 

 and T(X) in this figure represent the respective melting-points 

 of the substances W and X. 



(i) T > T{X) > T{W) > T(e) (Fig. 4). We have already 

 seen that in this case the stable states for W and X are the 

 liquid state, and that all liquids are stable. We represent these 

 liquids in Fig. 10 by the points of a line 1.1' situated above T{X). 



(ii) T{X) > T > T{W) > Tie) (Fig. 6). Every straight 

 line uniting an arbitrary point z' of the f-curve with the point 

 (X) is the f-line of a system 



L{z) + solid X, (10) 



consisting of the two phases, liquid z and solid X. If we take, 

 for example, the line a'{X), then every point of this line (e.g., 

 h", c", etc.) represents the f-point of a system, L{a) + solid X. 

 Similarly every point of the fine c'{X) represents the f -point of a 

 system L{c) -f solid X. So we may imagine an infinite number of 

 lines z'iX), of which in Fig. 6 only a'{X), c'{X) and d'{X) have 

 been drawn. Of all these conceivable lines, the line c'{X), 

 touching the f -curve in c', plays a great part. It is clear from 

 the diagram that the f-points of all phase-complexes whose 

 compositions lie between W and c lie above the corresponding 

 points of the f-curve (f-points of the hquids of corresponding 

 composition), whilst the f-points of all hquids whose composi- 

 tions lie between c and X lie above the corresponding ^-points of 

 the phase-complex L{c) + solid X. Hence of all conceivable 

 f-points of Fig. 6 only those of the part W'a'h'c' of the ^-curve 

 and those of the tangent c'{X) represent stable states. Thus of 

 all conceivable systems of the type (10) only the system 



L{c) + solid X (11) 



is stable. Thus L(c) represents the liquid saturated with respect 

 to solid X and therefore in equilibrium with it. All liquids 

 between c and X are supersaturated and tend to pass into (11) 

 with separation of solid X, whilst all liquids between W and c 



