(126 ) 
MRT/v. Carrying out the integration we get MRT log y/vc,, for 
which we may also write MRT log pe/p,. We get then: 
Vey 
[pe + porto = | pdv + po vo — Pe re, + MRT + MRT I p/p; 
Vo Uo 
§ 5. Let us consider the first three terms. The first is represented 
in the figure by the area C+ D, the second by A + B, the third 
by B-+ D. The three terms together are therefore A + C. If now 
as we assumed, the vapour is very dilute, and therefore the tempe- 
rature far from the critical, hence also the isotherm very steep when 
cutting the line of coexistence liquid-vapour (or strictly speaking: at 
the pressure p,, which however is very near the line of coexistence 
on the liquid side), then we may neglect C by the side of A, and 
we are the more justified in this as the pressure p, is higher, so the 
mixture in question more concentrated. For C= {plo— D. If we 
Uo 
introduce 
and integrate, we get: 
a a MRT a 
MRT 1 (v,,— 6) +-—— MRT 1 (v,—b) = ( :) (ve, = Vo) 
n 
cr Vo Vod Va 
A MRT a MIT 
—— )%— |t 
vo=b Vo ve, —b Va 
If we arrive at very high pressures, », — h approaches zero and 
numerator and denominator become both infinite, but the denominator 
of a higher order than the numerator. It is already apparent from 
the form of the isotherm which becomes steeper and steeper, that 
when neglecting C by the side of A we make proportionally a smaller 
mistake the higher p, is. And that the neglect is allowed for small 
osmotic pressures is selfevident. We may therefore put for the three 
terms discussed in this §: 
A = (po — pe) Vo. 
7 
‘(9p zie 
$ 6. It remains to calculate the term { (2) ae This integral 
v 
