To state precisely the other relations, we must admit, in addition, the experimental laws discovered by Pfeffer.

But without any hypothesis it becomes possible to demonstrate the laws of Raoult on the lowering of the vapour-tension and of the freezing point of solutions, and also the ratio which connects the heat of fusion with this decrease.
These considerable results can evidently be invoked as _a posteriori_ proofs of the exactitude of the experimental laws of osmosis.

They are not, however, the only ones that Professor Van t' Hoff has obtained by the same method.

This illustrious scholar was thus able to find anew Guldberg and Waage's law on chemical equilibrium at a constant temperature, and to show how the position of the equilibrium changes when the temperature happens to change.
If now we state, in conformity with the laws of Pfeffer, that the product of the osmotic pressure by the volume of the solution is equal to the absolute temperature multiplied by a coefficient, and then look for the numerical figure of this latter in a solution of sugar, for instance, we find that this value is the same as that of the analogous coefficient of the characteristic equation of a perfect gas.

There is in this a coincidence which has also been utilized in the preceding thermodynamic calculations.