( 12? ) 



not equal to 0, but to q (.», — a?0 — J qdx. For the loop-y-line the 



l 



length ot the isobar along which jxdq must be taken, is equal to 0, 



and x t and ,i\ coincide. For a g'-line of lower degree x\ and x t differ. 

 In the above equation it is supposed that branch e is taken as starting 

 point, and that a course is followed necessary to reach branch c. 

 The point from which we start, lies on the closed circle of the q-\me 

 and in the stable region. We now follow indifferently either the 

 lowest branch of this circle or the highest, but dependent on the 

 pair of coexisting phases that is to be determined. Let us suppose 

 that we follow the lowest course, then we get to branch d, and 

 meet the point of intersection of the isobar which we must follow 

 to meet the other branch of the g-line in a point which has equal 



volume v a . As this isobar must pass through the line 





where maximum volume exists, the equality of the volumes v s is 

 possible 1 ), but the values of x which we have called x t and a?„ 

 are different, viz. x,<^x t . For ,?•, the value of q is the chosen one 

 and for x, the value of q is again the same. Between .r, and x\ 

 this value is variable. Now : 



cF\\> d"ty dv 



dx 1 dxdv dx„ 



[dx) p 



d"\p d> / d'tf> V 

 fdq\ dx % dv' \dxdv) 

 \dx)~ <Pip 



dv* 

 (see fig. 14) being positive, I — I -is positive outside the spino- 



dv i \dn 



dal line, and negative inside it. Along the p-line, starting from smaller 

 value of x, the value of q is, therefore, increasing, maximum on 

 the spinodal curve, then decreasing, minimum on the spinodal curve, 

 after which it increases continually, as represented in tig. 22. 



J ) The same observation holds for all points which are points of intersection 

 of different branches of the p-line in figs. 90 and 21. In such a point of inter- 

 section p and v are equal, and this could only occur when the phases denoted 



dp 

 by such a point of intersection lie on either side of the line — = 0. 



