( «2 ) 



closed for smaller value of x than thai of (he splitting point. If, 



however, the region extends far to the right, llien also (he right part 



. <<P . . dv 



of — =0 can again contain a closed part of v — x — = 0, with a 



i/r d,Vp 



top at a certain value of x. and the open side at .e = l. Also for 



regions lying entirely on the right side it remains of force that 



dv <l r dp 



v — x - = lies within — =0; so that it — = no longer 



</./•,, dv dv 



dv 

 extends over the entire width, v — x — cannot extend any longer 



dx p 



over the entire width either. 



If also in such middle region, and al the same time in a right 



dv 

 region we examine the course of the locus r — x — , where the 



potential lines are directed horizontally, we see when consulting 

 figs. 5 and (i that the locus mentioned remains restricted to smaller 



volumes than those of the line — = so Ion» as the curve 



dx B 



— =0 does not exist, or il it does, for all points outside this curve. 



dx* ' 



dp . ./hi- 



lt -— = cuts the curve — = 0, the locus mentioned passes 



d> . dv 



through these points <>| intersection. A\ ilhin - = 0llie liner — x — 



ill'' i/r 



dp 



lies at larger volumes than those of — =0. But then no intersection 



</,r,, 



dv dv 



of /• — x — = and v — ./- = inter se is to be expected. Hence 



dx g dx p 



there is no question of a loop-potential line. The result would have 



been perfectly different, if we had also examined the course of M s p a . 



lint this may be considered superfluous, now that we know the 



course of the (/-lines, so of M ., f(, — M i ,»(, and of M 1 fi x . This by no 



means exhausts the properties of the course of the potential lines, 



but as we are not going to avail ourselves of this third group of 



lines for the determination of the binodal line, I think that it will 



suffice to mention the above properties. 



For the determination of the course of the binodal line we shall 

 make use of the equation of p. 57, viz.. : 



<l M x f<j = r dp — x (/</. 



But first some preliminary remarks. Among all the lines to be discussed 

 in a theory of mixtures the isobars and the binodal lines are to be 



