190 
for an isothermic change in the outer bounding layers where we 
may suppose no sugar to be present. 
Let us further assume that in the homogeneous diluted solution 
the quantity uM for the water has another form but always the 
same value as for the outer layer that consists of pure water (or 
in the vapour phase without sugar, that is in coexistence with the 
solution). This uM in the homogeneous solution is a function of 
x, and p,; 
(5 E) MRT (Ge: ) (55) (5) *) 
=== = ai - and =U 4) a5 5 
da, A 1—2, da,* Jr dp, J x, da Pi 
when we increase the concentration of the sugar solution by de, 
while the pressure p, remains constant, uJ/ in the solution changes 
by — MRTdz,, and in the outmost sugarless layer near the wall by 
vdp,. From this it follows vdp, — — MRTdz,. When we admit 
that osmotic pressure appears this will have the value 
MRT de, 
v 
dn 
Here it may be remarked, that by admitting the osmotic pressure, 
the pressure will in all directions increase by the amount dp,. In 
the outer bounding layer the pressure p, thus gets its original value 
again. The total change of p, because of the two changes of state 
is therefore zero. 
The same is therefore the case with uM in the outer bounding 
layer as duM=vdp,. Also for the total change of wJ/ in the homo- 
geneous solution, so that 
duM duM 
(5 ) aa (5 jan =0, 
da, Jp, dp, Ja 
where Ap, = Ap,. By means of this relation Honpius Bor.prnen derived 
the formula of the osmotic pressure from thermodynamic considerations. 
The decrease of pressure in the layer at the solid wall may be 
compared with the decrease of vapour pressure. When the solved 
substance occurs neither in the vapour phase nor in the outmost 
layer at the solid wall, there will always be a decrease of vapour pressure 
and of the pressure at the wall in the direction of this wall according 
to the simple laws for very diluted solutions. To a definite solved 
substance in a definite solvent a wall will be semipermeable, when 
the pores in this wall are so narrow that only the solvent substance 
can enterinto them and not the solved substance. Itis evident that changes 
of temperature and pressure can also have influence on the semipermeabi- 
1) See Dr. G. Honprus Boupinau. Thesis. Amsterdam 1893. 
