Gai) 
state the value which it has in the double-point, though the pressure 
exceeds that of the double-point. This approximation comes to the 
same as to say that we neglect the volume of the liquid compared 
with that of the vapour; and also this approximation is of no signi- 
fication if the gases are very rare. But the chief reason, for which 
we have to consider these equations (4) and (5) only as approximations 
is that we make use of the following relation for the pressure of the 
double-point : 
if we suppose in this equation f for all substances and so also for 
all mixtures to be the same and independent of the temperature. 
Therefore if we set: 
1 dp’ 
pda,’ 
! 
We = 
we assume a relation, which is incontestable in all those cases, in 
which the vapour-phasis may be considered as a perfect gas. But if 
we do more and if we assume a peculiar property of the equation 
of state, as that one assumed in the formula for the pressure p' of 
the double-point, the decision of the question, whether the equations 
(5) and (6) are contestable or not depends upon the question whether 
the relation used is accurate. Therefore in applying the equations (5) 
and (6) it is not our aim to obtain numerically perfectly reliable 
results, but only to get an idea of the course of the coexistence pressure 
for different mixtures which is in the main reliable, and which makes 
us understand the phenomena. 
According to these considerations, knowledge of the pressure of 
the double-points is required for the determination of the shape of 
the surface of saturation. If we introduce this pressure also into the 
graphical representation, we add a third surface to the two surfaces, 
liquid sheet and vapour sheet. The third sheet is found between the 
first and the second one, and the only points which it has in common 
with them are those above the angles of the rightangled triangle. In 
the case, that points of maximum pressure occur, in which points 
the liquid sheet and the vapour sheet touch each other, this third 
sheet also will touch both of them. If we cut these three sheets by 
a plane p=, we get three sections and the projections of these 
sections are the curves, which we have already mentioned in (a) 
p. 3 as curves of equal pressure; to these however is added the 
curve of equal coincidence pressure. After this expatiation on the 
signification of the quantities occurring in formula II, p. 3, we 
