( 650 ) 



cannot be made to harmonize with the v, .r-figures plotted by the 

 former ; for in these threefold intersection of the binodal with the 

 rim does really occur before the detachment takes place (Compare 

 in fig. 6 of the said paper by Smits the line fed with f .c^e.e,' c ,'/,'; 

 between this a v, #-line must necessarily be found intersecting the 

 rim in three points). Now that attention has once been drawn to 

 these unstable and metastable equilibria, it seems desirable to remove 

 these discrepancies. 



For this purpose the best thing is to start from the v, ^--figure. 

 The general equation of coexistence of phases in the variables v, x 

 and T becomes in this case, if we now consider phase 2 as 

 solid phase, 1 as fluid phase 1 ): 



so that we get for constant temperature: 



civ " d»* d> ' 



^— > s — v f ) + r3-('^— V) 

 du OüOa' 



Iu what follows we shall denote the numerator and the denomi- 

 nator of this fraction by N and D. The geometrical meaning of 

 D has already been given by van der Waals in his first paper 

 on these subjects 2 ): the locus D = is the locus of the points of 

 contact on the tangents drawn from the point for the solid substance 

 to the isobars. It is easily shown that the locus N=0 is the locus 



dtp 

 obtained by putting the ^-lines i.e. the lines ^— = C in this instead 



of the />lines. So a double point or an isolated point, as they are 

 assumed by Smits, can only occur where, the loci A r = and D = 

 intersect. As in such a point, as appears from the geometric meaning, 

 the p- and the (/-lines have the same tangent, and accordingly touch, 

 such a point must also lie on the spinodal line 3 ). In perfect agreement 



