( 848 ) 



are conceivable in which the spinodal line could intersect the line 



d*b 



v = b twice, but that if — has positive value, as is really to be 



dx* 



expected, intersection will never take place. But if we acknowledge 



again that the knowledge of the equation of state is insufficient for 



very small volumes it follows that we had better not pronounce the 



solution of this question too decisively. 



If the spinodal line is closed on the side of the small volumes, 



then a realisable plaitpoint will be found there, while there must 



be a hidden plaitpoint in the neighbourhood of the points 2 



d*q 



and 3. It the temperature is raised, the line = 0, as it now 



dx* 



also intersects the line = 0, can contract to above — = 0, 



dxdv dv 7 



d 3 q 

 before disappearing. If it has sufficiently ascended above — - = 0, 



the spinodal line will get a point where it splits x ) up, at which 2 



new plaitpoints (homogeneous ones) are formed. So at this splitting 



d'v d'v 



point — = and - = 0. This furnishes an indication as to the 

 t/.rV dx' q 



place where this splitting point will lie. That the (/-line below 

 = must have a point of inflection, has been shown before 



</.r</r 



(p. 736), where we derived a series of points of inflection of the 

 (/-lines passing through the point in which ■— = has the greatest 



volume. We have also previously (p. 628) derived a series of points 



dp 

 of inflection of the valines starting from the point where — — =0 



dx 



dp dp 



and — = intersect, and passing through the point where - = 



dv dx 



has the minimum volume. From this we conclude that the double 



dp 

 dx 



dp . 



plaitpoint can only occur when the line — = is intersected by 



d*ip 



= pretty far to the left of the point with minimum volume, 



dx 1 



dp 

 and so not far to the right of the asymptote of the line — = 0. 



] ) This splitting point I had already in view in my Theorie Moleculaire (Gont. II 

 p. 42 and 43) where I indicate the temperature at which the detached plait (longi- 

 tudinal plait) leaves the v,a>diagram, when it has not contracted to a single point. 



