1896-97. ] 
Lord Kelvin on Osmotic Pressure . 
323 
On Osmotic Pressure against an Ideal Semi-permeable 
Membrane. By The Right Hon. Lord Kelvin, LL.D., 
D.C.L., F.R.S. 
(Read January 18, 1897.) 
To approach the subject of osmotic pressure against an ideal 
impermeable membrane, consider first a vessel filled with any 
particular fluid divided into two parts, A and B, by an ideal 
surface, MM. Let a certain number of individual molecules 
of the fluid in A, any one of which we shall call I) (the dissolved 
substance), he endowed with the property that they cannot 
cross the surface MM (the semi-permeable membrane) ; but let 
them continue to be in other respects exactly similar to every 
other molecule of the fluid in A and to all the molecules of the 
fluid in B, any one of which we shall call S (the solvent), each of 
which can freely cross the membrane. Suppose now the contain- 
ing vessel and the dividing membrane all perfectly rigid.* Let 
the apparatus be left to itself for so long time that no further 
change is perceptible in the progress towards final equilibrium of 
temperature and pressure. The pressures in A and B will be 
exactly the same as they would be with the same densities of the 
fluid if MM were perfectly impermeable, and all the molecules of 
the fluid were homogeneous in all qualities ; and MM will be 
pressed on one side only, the side next A, with a force equal to the 
excess of the pressure in A above the pressure in B, and due solely 
to the impacts of D molecules striking it and rebounding from it. 
If now, for a moment, we suppose the fluid to be “ perfect gas,” 
we should find the pressure on MM to be equal to that which 
would be produced by the D molecules if they were alone in the 
space A ; and this is, in fact, approximately what the osmotic 
pressure would be with two ordinary gases at moderate pressures, 
one of which is confined to the space A by a membrane freely per- 
meable by the other. On this supposition the number of the S 
* In the drawing, the vessel is represented by a cylinder closed at each end 
by a piston to facilitate the consideration of what will happen if, instead of 
supposing it rigid, any arbitrary condition as to the pressures on the two sides 
of the membrane be imposed. 
