1244 . 
It should be namely borne in mind that: 
First of all all the three W’s become smaller already on account 
of this that in (2) the Ni must be taken over a number of molecules 
S, which decreases in direct ratio with cs. 
Secondly, however, IV" decreases besides on account of this that 
the forces Xa, Y;", Z|’ which a certain molecule S experiences 
from all the other molecules S, decreases at the same time with the 
number of the latter to zero, likewise WW", because the dijerence 
of the concentrations of the molecules W on the two sides of &, 
—— 
MI 
which determines vw X", y Y", zZ", decreases to zero at the same 
time with c,. For W', which arises from the collisions of the molecules 
S with &, there does not exist an analogous second reason to approach 
zero. 
If therefore in the case of diluted solutions we contine ourselves 
in equation (A) to terms of the first order in cs, we have: 
AE WILOO. ien ede cp 
One can now easily convince oneself that this expresses that the 
dissolved molecules S exert on 2 the same pressure as when they 
were only enclosed in £2 and that as an ideal gas. W' can namely 
be calculated from the pressure P exerted by 2 on the sugar mole- 
cules, and becomes: 
pa EB IO a 
Further : 
RLS BRT Ae he Ge ee 
when «7 is the mean kinetic energy per degree of freedom. 
If we take particularly one gramme molecule of sugar, i.e. 7 
equal to the Avogadro value N, and put 
ND aed Be deel BAe, egies eee 
(A’) passes into: 
PY = nia ce ette en 
Van ’r Horr’s equation for the osmotic pressure of a dilute solution. 
The deviations from equation .(6) for solutions which are no 
longer exceedingly diluted, have been repeatedly treated thermodyna- 
mically.*) O. Sturn has tried to give a purely kinetic treatment in 
analogy with the kinetic theory of non-ideal gases. *) Compare also 
1) Comp. the perfectly analogous calculation for ideal gases L. Botrzmann. 
Gastheorie Il, p. 143, § 50. 
2) Van Laar: Z. f. phys. Ch. 15 (1894) 457; “6 Vorträge" (1906); vaN DER 
Waats and Kouystamm, Lehrbuch d. Thermodynamik. 
5) loc.cit. 
