1 
) 
nO 
$ 6. Now we apply the reasoning of the preceding paragraph to 
the collisions of the dissolved substance on a wall defined as under 
3. We assume the solution to be so diluted, that the volume of the 
molecules of the dissolved substance may be neglected compared 
with the whole volume. For simplicity — though it is not essential 
to the proof — we assume now also that the molecules are spheres. 
Then here too the available space must again be put equal to r— 2; 
but the part of the plane of impact, accessible to collisions, is now 
different. For as the molecules of the solvent pass through the 
wall, their centres may now just as well be on the other side of 
the plane of impact. We have therefore not to integrate with respect 
to A from O to */, 6, but from —*/, oto + '/, 6, which evidently 
vields the double value. The pressure on the wall becomes therefore 
proportional to 
heal ——?) 
v—2b v 
so that the influence of the molecules of the solvent vanishes and 
vaN Cr Horr’s formula is proved for the quantity defined by us. 
§ 7. That this quantity has further always the same value as 
the quantity which may be measured experimentally, is proved as 
follows. Let us think the action of the membrane in such a way 
that it suffers the molecules of the solvent to pass through freely, 
but repels those of the dissolved substance perfectly elastically. 
Something similar would take place when the membrane worked 
as a ‘molecule sieve”, i.e. when the pores were such as to allow 
the molecules of the solvent (thought smaller) to pass, the others 
not. According to the definition the latter will then exert a 
pressure on the membrane equal to our osmotic pressure. The other 
molecules passing through the wall unmolested, there is no mutual 
action with the wall, and so they co not exert any force on it. 
1) If one should object to the train of reasoning followed here, one can find in 
Boiraann’s “Gastheorie” a proof for this formula which intrinsically agrees per- 
fectly with that given in this paper, but will appear stricter to some. There one 
will also find the above given integration carried out. 
*) It is clear that we shall get the same result, when we do not take 20, 
but f (b/v.) for the voiume of the distance spheres. For as the place of the plane 
of impact wilh respect to the molecules of the solvent is quite arbitrary in our 
present case, the part of the plane of impact, which lies within the distance spheres 
will stand to the whole area in the same proportion as the volume of the distance 
spheres to the whole volume, 
