(542) 
a section parallel to the z-axis, the value of p is also maximum. 
The point P on the other hand, lying on the isothermal of the con- 
centration «p, represents a phasis for which the pressure on the 
isothermal is minimum, while p along a line parallel to the z-axis 
in P, is maximum. From this follows 1st that the isobar passing 
through P has a double point in the point P, and 2"¢ that the 
lines of equal pressure enclose the point Q, — and in such a way 
that as the pressure approaches that of Q, the closed curves get 
narrower, and keep also entirely within the limits of z — 0 and 
«== 1 and are completely enclosed in the zv diagram. 
The isobar through P had a shape which may be considered as 
transition form between the shapes for pressures which are greater, 
and pressures which are smaller than pp. For pressures which are 
greater the isobar consists of two separate branches, viz. Ist a 
closed curve round Q and 2rd a branch lying above P and which 
therefore, remaining on the liquid sheet, belongs to a volume 
smaller than that of P. In fig. 7 we can take for it e. g. the 
branch passing through C, which must show a maximum-volume 
on the dotted line. Then the closed curve of Q, belonging to the 
same isobar, is indicated by the curves passing through C’ and C”, 
For the isobar of P these two separate branches have drawn so 
near each other, that they have met in P. Accordingly this isobar 
has the following shape, indicated by 4APB'B'A"A'PB. The points 
B' and B" must be thought connected by a piece lying outside 
«==1 and in the same way the points A” and A’ by a piece 
outside «= 0. The lines of equal pressure for p < pp must fill up 
the space lying within APA’ and BPB and that below A’B". 
A similar curve, provided p >pz, begins below 4 on the curve 
«= 0, passes on to greater values of 7, has a tangent parallel to 
0 
the v-axis on the locus for which (5) =0, and then returns to 
VS ax 
smaller values of «. It is continued for vapour volumes greater 
than that of AB", and appears again between BPB' provided p be 
also greater than Py. The shape between BPB' is analogous to 
that of APA’. 
In order to find the mixture for which liquid and vapour con- 
centration is equal, we must determine on a line, parallel to the 
v-axis two points chosen on the same isobar, in such a way that 
Ja = dv=0, In the figure the points D' and D" have been 
% 
Vz 
