( 123 ) 



Physics. — "Contribution to the tlieory of binary mixtures'' V. 

 Bv Prof. J. D. van der Waals. 



Continued. Sec p. 74. 



Up to now we have assumed in the determination of the binodal 



line that the second component, for which the quantity h is larger 



than for the first component, lias a lower critical temperature, so 



that we suppose ( r J\^<^{7\\. In the opposite case, so (Tk)^^>{2\) i , 



we meet with some new complications, which we shall shortly 



discuss. So we choose now a region from the general p-figure, 



fdp\ 

 which lies more to the right, and in which the line — —0 i g 



\dasj» 



found. Fig. 14 of These Proceedings April 26, 1907 may be ser- 

 viceable for this discussion. In this figure the points 1, 2, 3, 4, 5 

 and 6 are points of the spinodal line. If we had inserted the spinodal 

 line itself in the figure, this curve would have an ordinary shape 

 on the vapour side, remaining all the lime at larger volumes than 



those of the line [ — 1=0. But on the liquid side the normal course 

 \dv) x 



of the spinodal line has heen strongly modified by the presence of 

 the 



— = of the first component, proceeds then to smaller volumes. 



ilr 



till the presence of = forces it back to very small volumes, 



da? 



and is the cause that the distance between the spinodal line and the 



dp <&■$> 



line — =0 is abnormally enlarged. In the points where = and 



dv ax* 



= intersect, the spinodal curve touches the curve = 0. 



d.v dv da:* 



Two plaitpoints occur, viz. the realisable plaitpoint at very small 



volume, and the hidden plaitpoint in the neighbourhood of the points 



2 and 3. This hidden plaitpoint lies in this case on the left-hand 



side in accordance with the shape of the y-lines. In fig. 17 this 



hidden plaitpoint lies on the right-hand side, and the shape of the 



dp 



(/-lines in the region where - is positive, is such that there is a 

 dv 



(/-line which may be drawn tangent to the spinodal curve, the 



hidden plaitpoint being the point of contact. In tig. 17 the (/-lines 



8 



Proceedings Royal Acad. Amsterdam. Vol. X. 



the line — = 0. On the left-hand side it begins in the point 

 da? 



