me on account of the predilection which it shows for purely kinetic 
considerations. The reasons why | do not share this predilection in 
this case, will appear from another communication, occurring in 
these Proceedings; here L shall confine myself to the thermodynamic 
method, and specially to the form given by VAN pur Waars. 
§ 2. In § 18 of his Théorie Moléculaire Vay per Waars treats the 
ease, that of a binary mixture the first component can expand through 
a given space, whereas the other is confined to a part of that space. 
He demoristrates that for equilibrium a difference in pressure between 
the parts of the space is required which for dilute solutions has the 
value indicated by the law of Van r Horr. In this a thesis is used, 
which is very plausible (and which moreover may be proved in the 
same way as the condition for equilibrium in the general case) 
that namely equilibrium is established when the thermodynamic 
potential of the first component is the same in the two parts of 
the space. I shall here apply this condition to a binary mixture 
of arbitrary components and arbitrary concentration, the vapour 
of which follows the gas-laws, and which is in equilibrium with 
one of the components in pure condition under the pressure of its 
own vapour through a semipermeable wall. How such an equili- 
brium might be reached in reality in a special case, and whether 
this would be possible, need not be discussed. 
§ 3. We assume that there are (1—v) molecules passing through 
the membrane and x non passing molecules, then the thermodynamic 
potential of the first substance in the mixture is 
‘Ow ‘Ow 
WE fp, ap) 0 el. =d Gal == 
7 7 
7 . 0 
= | payer MRT a), | Ge) dv + F(T) 
sf EIT 
v 
in which the integrations must be extended from a volume y so 
large that all the laws of ideal gases apply there, to the volume in 
question, F(T) being a function of the temperature, which occurs 
here only as an additive constant. In order to be able to carry out the 
integrations, we require — as mentioned above — an equation of 
state p = (Oe): 
For this purpose I shall adopt Var per Waars’ equation with 
constant 4; though in this way we certainly do not get strietly 
accurate results, yet we shall be able to decide about the quantities 
which must occur in the formula. 
§ 4. If in fig. 1 the isotherm of the mixture is indicated and 
