( 705 ) 
4 Al 
there are three plaitpoints between the temperature of A, viz. 7, 
and that of P4, unless /, should lie higher than A, in which case 
Pq would take the place of 7. The curve 7, = f(z) is also 
inserted in the figure. It will have to intersect the plaitpoint curve 
at «<1, and that twice. The first point has not been indicated by 
a special mark, but the second point of intersection is supposed to 
be in the neighbouchood of B. If we draw a p‚r-section of the 
surface of saturation, and add to it a line indicating the pressure 
at which there would be coexistence if the mixture behaved as an 
homogeneous substance, the extreme point of this line would lie at 
the same value of w as that of the plaitpoint, at the value of 7’ of 
the second point of intersection just mentioned. 
For higher value of 7’ we have then again the rule that for a 
given mixture 7’, > 7), which is generally considered as the normal 
case. This being really the case for v very small, and « nearly 1, 
when there is intersection of the curves 7). = f (2) and 7.= gp (2), 
this will have to take place twice. For the points Q, and Q, the 
plaitpoint lies on the binodal line, and between the temperatures 
Q, and Q, there is three-phase-pressure. The concentration of the 
three coexisting phases is indicated by the dotted line Q',Q,Q,Q.. 
We might call the part QQ, of this line the vapour branch. The 
vapour branch presents a particularity in the drawing which has 
escaped attention so far, viz. that it can contain a point in which 
w has a minimum value. I have not drawn this particularity in the 
vapour branch of fig. 39, because it is less probable there. This 
applying to a circumstance which has not been noticed as yet, and 
which is yet not devoid of importance, a digression to show the 
possibility of the existence of such a point with minimum value of 
x, may be useful. The more so, because in the discussion properties 
will be mentioned the knowledge of which is necessary if we want 
to understand the full meaning of different particularities occurring 
for the three-phase-pressure. 
Let us call the concentration of the point representing the vapour 
phase, wz,, and let w, and w, denote the concentrations of the liquid 
phase — and let us put 2,< #,<2,. Now the following equations 
hold: 
1 
aS 
Va, dp — (z, Tac ae) B 3 Yar dT 
5 P 
and 
* 
vn dp = (2, — 2,) i ts +, dT. 
ay ‘eg 
