( 750 ) 
aim at are the properties of solutions under the pressure of their 
saturated vapour: lowering of the freezing point and the vapour 
tension, rise of the boiling point and coefficient of division or more 
accurately (ef § 6 above) freezing point, boiling point, vapour tension 
of the mixture and the concentration of coexisting phases. And this 
does not only apply to physicists and chemists, who rarely if ever 
work with membranes, but also to biologists, to whom they are of 
the greatest importance. For differences in pressure of about ten 
atmospheres will probably hardly ever occur in biologic experiments 
and a fortiori not in the living organism either. The equilibrium 
between two solutions will therefore never be established by diffe- 
rence in pressure, but by the difference in concentration required 
to make the pressure equal. So we have not to deal here either 
with compressed solutions. *) 
For the calculation this implies that when making use of the 
thermodynamic potential we need extend the integration along the 
isotherm only to the pressure pe and the thermodynamic potential 
may then be determined with sufficient approximation from the 
well-kwown formula for the vapour pressure : 
log = a == 1) 
Pk ú 
thoneh it be with the factor 7 determined experimentally instead 
of the value 4 found theoretically. But if the osmotic pressure is 
used we can naturally not do without the integration up to p, 
(in the term | 2 ze) and it is exactly this part of the isotherm 
\. ec v 
which is known the least, where e. g. the variability of b is felt 
strongest, even the only term, on which it has influence when the 
just mentioned formula for the vapour pressure is used. Quite 
unnecessarily therefore the result is made less reliable by the intro- 
duction of the osmotie pressure. 
And supposed even that we had found the desired expression, 
of what use could it be to us? It is true that the quantities, which 
we really wish to know and which I mentioned before, are con- 
1) For this reason hardly anything would be lost when in the discussion of 
really osmotic questions it was made a rule to treat them without “osmotic pres- 
sure” and simply to introduce the concentrations on either side of the wall; whereas 
in this way there would be a great gain in lucidity of expression, witness the 
example cited by Mr. van Laar (lc. § 5). For the interpretation given there may 
be correct or incorrect, it can hardly be denied that the cited phrases may be 
easily misunderstood in the sense of the well-known question of Puris, which has 
so repeatedly been seriously discussed, how e.g. a Call, solution of no less than 
53 atms. osmotic pressure could be kept in a thin glass vessel without making it 
burst asunder! 
