( 135 ) 
If the gas phases are very rarified the latter equation may be sim- 
plified to: 
1 dp a Pee hi 
p OP y,(1—y,) 
which form is identical with that which applies if a second component 
is added to a simple substance, and from which accordingly the 
quantity «’, has disappeared. This identity of the form of the equation 
does, however, not justify the conclusion that also the shape of the 
curve p= Ff (yz) will be identical. The same form of the equation 
applies also to a binary system, and yet it includes the great variety 
of curves which the pressure as a function of the composition of the 
vapour can present. All those differences in shape are to be ascribed 
to the different ways in which y, and y, depend upon each other. 
In the same way every plane section of the vapour sheet for a 
ternary system by a plane, normal to the plane of the triangle and 
passing through the summit, will be represented by this equation, 
though these sections may present an infinite variety of forms, which 
again may differ from those of a binary system. Yet we may make 
use of this equation and deduce some general properties from it. 
So e.g. will be zero if on the chosen section a point 7, 7, 
dy, ; 
occurs for which 
YY =O. 
If the succession of the values of the pressures is p, << p,< p, 
this can never occur. In this discussion, however, we will think the 
succession to be changed according to the circumstances in order 
that we are not obliged to draw the section every time through 
another angle of the triangle. If the succession is p, << p, <p: & 
locus oeeurs indeed, for which y, = y, and this locus coincides with 
that for which the pressure of the vapour phases which oceur on the 
chosen section is maximum or minimum. We might have expected 
a priori that in general a maximum or minimum would be found 
on the section which passes through the angle for the component 
whose pressure lies between those of the other components, and 
which cuts the opposite side in a point with the same pressure. 
This maximum or minimum will, however, not have the same 
significance as that of a binary system. For in the case of a binary 
system the composition of the vapour is the same as that of the liquid 
phasis; for a ternary system only y, and y, are equal, but 2, and x, 
differ. In such a point the pressure of the liquid phasis is not 
equal to that of the vapour phasis as is the case with the 
maximum pressure of a binary system, — but the pressure of 
