(2) 
For a binary system this relation is simplified to: 
06 
v., dp = («#,—2,) aa dx, 
al 
We know from the properties of a binary system, that we have 
then a curve p=—/(x,) and a curve p= f(r,), and that the branch 
representing liquid phases is always found higher than the one repre- 
senting vapour phases. Both curves start at the point representing the 
vapour-tension of the first component, and finish at the corresponding 
point for the second component. This however is only true if the 
temperature is lower than 7, of that component. If 7 > (7;,,), then 
the two curves are joined fluently so that they form a single one. 
For a ternary system we have to deal with two surfaces p = f (#,,/,) 
and p= f (w,,y,) instead of the curves p= f (w‚) and p — f(«,). We 
will use as a rule the index 1 for a liquid phasis, the index 2 for 
a vapour phasis. These surfaces cover the rectangular triangle OXY, 
and above the angles of this triangle they have points: in common. 
The common ordinates represent the maximum tensions of the three 
components. This hoids good, if the temperature is lower than 7, 
of each of the components. In some cases these sheets may have still 
another point in common, just as is the case with the two branches 
for a binary mixture if a maximum pressure occurs. But for the 
present we will disregard the existence of such a maximum pressure. 
If T< 7. of one of the components then the two sheets of the 
p-surface do not cover any longer the whole rectangular triangle, but 
they have joined fluently to one surface. 
In the above equation II the properties of these two sheets of the 
p-surface are expressed in the form of a differential equation ; — we 
will now proceed to deduce the principal properties from this equation. 
Even for the pressure-curves of a binary mixture the number of these 
properties is already considerable. For a ternary system they will of 
course be still much more numerous, and even properties occur which 
have no analogon for a binary system. But many of the properties 
of the pressure-curves of a binary mixture may directly be extended 
to the corresponding ones for the pressure surfaces of a ternary 
mixture. Such properties need hardly be treated here, as we sup- 
pose the properties of a binary mixture to be known. Accordingly 
I will limit myself in the main to treating those properties that are 
proper to ternary systems but not to binary systems. The study of 
the ternary systems however has induced me, to give a more detailed 
discussion of some equations, given in Cont. II for a binary mixture, 
from a more general point of view. And in some cases this detailed 
