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In a former paper (to be referred to here as Part I) which appeared in the ‘Proceedings of the Royal Society,’* I found an exact relation between vapour-pressures and osmotic pressure in the usual case in which the solute may be taken as involatile. The case now to be considered is the more general one in which both solvent and solute are volatile. The concentration and temperature in the main part of the paper are taken as constant; and the only restriction upon them is that the solutions and solvent must be capable of existing in the liquid form. The notation employed is the same as in Part I, any additional symbols being specially defined when they occur. 1. I shall make use of the general theorem, proved in Part I, that when a solution is in osmotic equilibrium with the pure solvent, the vapour-pressure of the solution is equal to the vapour-pressure of the pure solvent, each measured for the actual hydrostatic pressure of the fluid to which it refers; that is, with the former notation :πp =π 0 p 0 . This was shown to be true whether the solute is volatile or not.

On the osmotic pressure of compressible solutions of any degree of concentration. Part II.— Cases in which both solvent and solute are volatile