Physics. — “A formula for the osmotic pressure in concentrated 
solutions whose vapour follows the gas-laws”’. By Dr. Pu. 
KoHNsTAMM. (Communicated by Prof. J. D. van prr Waats). 
§ 1. The formula for the osmotic pressure may be derived in two 
different ways: by a thermodynamic and by a kinetic method. When 
putting these two in opposition I mean by no means an absolute contrast, 
on the contrary I believe an opinion which I hope soon to treat 
more fully elsewhere — that without an equation of state based on 
kinetic considerations thermodynamics has nothing to start from 
and that therefore we can only oppose “purely kinetic” and “thermo- 
dynamie-kinetie”” considerations. 
Not numerous are those who have tried to find formulae for the 
osmotic pressure of more concentrated solutions by a thermodynamic 
method. Only Honpivs Bonpincu') and after him Van Laar ?) have 
pointed out that it appears from the theory of the thermodynamic 
potential that the concentration of the solution should not be taken 
into account in the form w, but as log (1—2) and that for further 
approximation a correction term of the form «c* must be applied, 
and lately the latter has again come forward to advocate with great 
zeal the validity of this result. 
More numerous are the attempts to determine the osmotic pressure 
in concentrated solutions by direct, molecular-theoretic methods; I 
may mention those of Brenig *), Noyes ©), BARMWATER *), WIND ®). 
This fact is surprising because Van “r Horr himself, though he 
has a definite conception of the nature of the osmotic pressure, has 
never dared to base his equations on it, but has clearly indicated 
as basis of his theory of the osmotic pressure the thermodynamic 
considerations, by means of which he derives the osmotic pressure 
from the gas-laws. And; it is the more surprising because all 
these attempts wish to follow the train of thought which led 
Van per Waats to his equation of state, though VAN per Waars 
himself has clearly shown, that in his opinion the osmotic pressure 
must not be sought in this way, but by the thermodynamic method, in 
connection with the equation of state given by him. That notwithstanding 
this so often the other way has been followed, seems noteworthy to 
1) Diss. Amsterdam 1893. 
8) Zsch. phys. Ch. 15, 466 (1894). 
8) Zsch. phys. Ch. 4, 444. 
4) Zsch. phys. Ch. 5, 53. 
5) Zsch. phys. Ch. 28, 115. 
6) Arch. Néerl. (2) 6, 714. 
