189 
Here is 
ay, 
uz, = pv — | pdv’' = pv — MRT log (v' — bo) — —. 
v' 
du M MRT ee 
ee ait 
de, Jp 1e, RE p 
and as we confine ourselves to very diluted solutions 
du M 
== RL 
de, p 
We find therefore the relation 
vA p= At M: 
The value of the thermodynamic potential of the solvent at the 
wall, where we take «= zero, may be represented by 
et + p,v—uM. 
For a change of the value of uM therefore we have the relation 
de —tdy + p,dv + vdp, = duM. 
When this explanation of the origin of the osmotic pressure is right 
then vdp, = duM. And asthe only change the state of the bounding 
layer in the immediate neighbourhood of the wall can undergo by an 
increase of the concentration of the homogeneous solution by dz, 
is a change in density, we must have for any such change 
de — tdy + p,dv = 0. 
But this consequence is in perfect correspondence with the ther- 
modynamic theory of capillarity. 
Let us consider an element of the outer layer and let us expand it, 
without changing its thickness, in the direction of the wall, so that 
v becomes v + dv. The external work done at the expense of the 
supplied heat is p,dv and not p,dv. The supplied heat is tdy, so 
that we have: 
tdyn =p, dv + de. 
In fact this equation is nothing but the well-known equation from 
the theory of capillarity : 
de = tdy — p, dv + ods, 
when we do not apply it to the layers as a whole, but to only 
one of the layers. 
As our conclusion is right, we may evidently also treat the 
problem in another way viz. by assuming that we have 
duM = vdp, 
