(8) 
of Borre for rare vapours, but obtain utterly absurd results, if we 
neglect this deviation for liquids, in the same way we may neglect 
the difference in the degree of this deviation according to the different 
composition, if we are treating of a rare vapour phasis, but if we 
should disregard this difference in the case of a liquid phasis it would 
lead to absurdities. 
Let us now imagine for the different mixtures the pressure to be so 
far increased, that the double point in fig. 1, p. 450 is reached 
Experimentally this can of course not be performed without disturbing. 
the homogeinity, and without condensation of a part of the vapour 
phasis, which is compressed. But though what we imagine cannot 
be realised, yet we may put the question, what would happen with 
the quantity under consideration, if we according to the principle of 
continuity, should imagine the homogeneity to continue to exist. Then 
we find the value of w for the liquid phasis in that double point, and 
we may write the equation : 
' 
) 
} 
Mrt NDE EEn 
The pressure pin this equation is that one, which we have before 
alled coincidence-pressure. As has already been observed this state 
cannot be realised. Such a liquid, coexisting with such a vapour 
would be a state of equilibrium; but an unstable one, or one that 
is metastable. It is however possible by increasing the pressure still 
more to get in this way a homogeneous liquid which differs only 
slightly from the one under consideration and which in fact can be 
realised as a homogeneous phasis. It appears from fig. (1) that u for 
this more compressed liquid is somewhat greater than the value 
written down in the last equation. But again that surplus of the 
amount of uw may be neglected. For we have always: 
MRT du = vdp. 
But if we calculate the surplus of uw, v represents the liquid-volume. 
vdp 
MRT 
is a quantity without significance, if » is a volume ofa liquid. From 
this follows that the quantity which we have represented by w',, may 
be found approximately in differentiating the above equation (4) and 
therefore may be represented by : 
1 dp! 
Battie p' de, 
And unless the increase of the pressure should be excessive 
In the same way we have: 
