( 731 ) 



d'tp (dp\ 



But the occurrence of the curve = 1 — 1 = is not always pos- 



dxdv \dxj v 



sible, as we already showed in the discussion of the shape of the 



isobars. If we consult fig. 1 (These Proc. IX p. 630) it appears 



fdp\ 



that the curve — J = does not exist throughout the whole width 



of the diagram of isobars. 



With mixtures for which the course of the isobars is, as is the case in 



the left side of the figure, the line ( — I = does not exist at all. 



\dxj v 



Only with mixtures for which the course of the isobars is represented 

 by the middle part of fig. J it exists and if the asymptote is found, 

 it can occur with all kinds of volumes. Also with mixtures for which 

 the course of the isobars is represented by the right part of fig. 1, 

 it exists, but then only at very small volumes, and it possesses only 

 the branch which approaches the line v = b asymptotically. 



Let us now consider a mixture such that the curve [ — 1 = is 



\dxj v 



really present at such a temperature that also the curve = 



dx* 



exists ; then we have still to distinguish between two cases, i. e. 

 1. when the two loci mentioned do not intersect, and 2. when they 



do intersect. If they do not intersect, and the curve ( — ) = lies 



on the right of = 0, then the «7-line, after having had its maxi- 



a.s a 



mum and minimum volume, will intersect the line ( — ) = 0, in 



\dxj u 



that point of intersection will have a tangent // v-axis; it will 

 further run back to smaller volume, just as this is the case with one 

 of the i^-lines drawn in fig. 2. This may e.g. occur for mixtures cor- 

 responding to the left region of the diagram of isobars, when this 

 region is so wide that also the asymptote and a further part of the 



fdp\ 

 curve I — I = is found. If with non-intersection the relative position 



d*ty A/»\ 



of the two curves — - = and — — are reversed, this can 

 dx* \dxj v 



probably not occur but for mixtures which correspond to a region 



of the diagram of isobars which has been chosen far on the 



right side. The course of the <7-lines which then pass through 



d*ip 

 the curve — — = 0, is represented in fig. 5. But when the two 



dx 



50 



Proceedings Royal Acad. Amsterdam. Vol. IX. 



