1896 - 97 .] 
Lord Kelvin on Osmotic Pressure. 
325 
due to the impacts of S molecules and I) molecules striking the 
other piston, P, and rebounding from it, and their attractions upon 
its molecules ; and as to the numbers per unit volume of the S 
molecules on the two sides of MM, except that they are not gener- 
ally equal. [ Addition , of date June 30, 1897. — In an interesting 
article published in Nature of March 18, Prof. Willard Gibbs has 
shown that in the present ideal case the difference of pressures on 
the two sides of the ideal semi-permeable membrane fulfils van’t 
Hoff’s law. But this is only because of the identity of character 
of the S and D molecules in all qualities except in respect to action 
on the ideal semi-permeable membrane : and the demonstration 
essentially fails when the law of variation of pressure and density, 
according to height, differs in two vertical tubes, one of them con- 
taining S molecules alone, and the other containing a mixture of 
S and D molecules.] 
Ho molecular theory can, for sugar or common salt or alcohol, 
dissolved in water, tell us what is the true osmotic pressure against 
a membrane permeable to water only, without taking into account 
laws quite unknown to us at present regarding the three sets of 
mutual attractions or repulsions: (1) between the molecules of the 
dissolved substance ; (2) between the molecules of water ; (3) be- 
tween the molecules of the dissolved substance and the molecules of 
water. Hence van’t Hoff’s well-known statement, applying to solu- 
tions, Avogadro’s law of gases, has manifestly no theoretical founda- 
tion at present ; even though for some solutions other than mineral 
salts dissolved in water, it may be found somewhat approximately 
true ; while for mineral salts dissolved in water it is wildly far 
from the truth. The subject is full of interest, which is increased, 
not diminished, by eliminating from it fallacious theoretical views. 
Careful consideration of how much we can really learn with cer- 
tainty from theory (of which one example is the relation between 
osmotic pressure and vapour pressure at any one temperature) is 
exceedingly valuable in guiding and assisting experimental efforts 
for the increase of knowledge. All chemists and physicists who 
occupy themselves with the “theory of solutions/’ may well take 
to heart warnings, and leading views, and principles, admirably 
put before them by Fitzgerald in his “ Helmholtz Memorial Lec- 
ture ” {Trans. Chem. Soc., 1896) of January 1896 (pp. 898-909). 
