( 451) 
increasing value of p starting from — for p= 0. In fig. (1) this is 
represented by the lowest part of the branch aed. As for coexisting 
phases of a simple substance the value of £ per unity of weight 
(the thermodynamic potential) must have the same value, the vapour 
branch and the liquid branch have a point in common. In fig. (1) 
this point is e. The further course of the liquid branch may be 
easily derived from df—=vdp. For the experiment we only want 
to know the branches ae and ed. But the place of e is only found 
as double point of the intersecting branches of the complete curve. 
By applying the principle of continuity we find: 
1st. the continuation of the vapour branch, rising till the pressure 
has become equal to the maximum pressure of the isothermal; 
24, the unstable branch, for which the pressure decreases to the 
value of the minimum pressure of the isothermal ; 
3rd, the beginning of the liquid branch (the portion ce). 
The direction of the curve at any point is determined by the 
value of the volume. That the point 6 is a cusp follows from the 
fact that immediately before and immediately after that point the 
direction of the tangent is given by the same value of v. But 
ee 
dp? dp 
after the point 6. On the unstable branch this quantity is positive, 
on the other parts of the curve negative. What applies to b, is also 
of force for c. 
When the pressure lies between the two limits mentioned, which 
I shall indicate by pw and pm (maximum pressure and minimum 
pressure of the isothermal), the value of ¢ is trivalent. If p is smaller 
than the pressure of the double point, the vapour branch is the 
lowest, and if on the contrary p is greater, then the liquid branch 
is below. For a simple substance the pressure of the double point 
is the pressure of coexistence (maximum pressure). 
To conclude to this form of the ¢-curve, the real form of the 
isothermal need not be known. The principle of continuity suffices. 
has opposite sign immediately before and- immediately 
We conclude to the same shape of the ¢-curve for a homogeneous 
mixture. It is true that in the equation of state given by me, the 
values of a and b are dependent on the nature and the concentration 
of the components; but the shape of the equation of state, for which 
