188 
wall cannot not be great enough. This part therefore contains only 
the outer layer of the passage layer. In this case the pressure p, 
close to the wall and in the direction of the wall will be the same 
everywhere both in the vessels and in the tube. Now when in the 
vessel on the left the concentration is increased by an amount Az,, 
then in every part of the left vessel as far as the narrowing of the 
tube, the pressure along the wall will have diminished by an amount 
Ap,; the equilibrium is destroyed, in the narrow part we now have 
a fall of pressure, which will cause a current of pure water through 
the narrow part from right to left. By preventing the solution in 
the left vessel from occupying a greater volume, the equilibrium 
will be established again by the displacement of some water. Owing 
to this the pressure in the left vessel will increase everywhere in 
all directions by the constant amount Ap,, so that the pressure 
along the wall in this vessel will again become p,, and the equili- 
brium will be established again. This increase of pressure Ap, is 
what is usually called the osmotic pressure, the over-pressure in the 
left vessel. Now when in the right vessel no sugar is present, so 
that in the left vessel there is already an osmotic pressure corre- 
sponding to the small concentration 2,, we may say, that the 
decrease of the pressure p, along the wall caused by an increase 
de, of tbe concentration is equal to the increase of the osmotie 
pressure due to the capillary action. 
7 
M 
From the experiment we know that Ap, = ———Aaz,, where Ap, 
v 
has been written for the osmotic pressure. When Ap, represents the 
MRT 
change of pressure along the wall, we may write —Ap, = Az. 
v 
In this last relation v is the volume of M, grams of pure solvent under 
if 
Se ee dv 
the pressure of the vessel. We may write for it: v'—2, (=) , where 
P 
/ 
v’ is the volume occupied by M, (1—.) grams of the first component 
and by M,a grams of the second under the same pressure. 
In the equation 
vA p, = — MRT Aa, 
the right hand side represents also the change of the thermodynamic 
potential, when the concentration increases by Aw,, while the pres- 
sure remains constant. The theory of vaN DER Waars namely gives 
for the value of this potential in the homogeneous solution 
a] dy, 
uM = MRT log(1—z«,) + us, — «, | — }. 
dz, Jp 
