Pfeffer's measurements, with solutions of 1 g. of sugar in 100 c.c. of water (the volume of the solution is 100.6 c.c.), were shown to prove, that the observed osmotic pressures agreed excellently with the gas pressures, calculated for the equimolar weight of hydrogen, in the same volume and at the same temperature: Osmotic Pressure Temperature. ────────────────────────── Found. Calculated.[20] Atmosphere. Atmosphere. 6.8 0.664 0.665 13.7 0.691 0.681 14.2 0.671 0.682 15.5 0.684 0.686 22 0.721 0.701 32 0.716 0.725 36 0.746 0.735 Morse's more recent and more exact results show, that the osmotic pressure of solutions of cane sugar and of glucose (corrected for the volume occupied by the sugar, see footnote, p. 15) agrees within 6% with the values demanded by van 't Hoff's theory, being about 6% larger for concentrations ranging from 0.1 to 1.0 molar. The difference of 6% is noteworthy and is probably due to secondary causes, but suggests extended investigation of its source. «Indirect Determinations of Osmotic Pressure.»—The experimental results given have been obtained by direct measurements of osmotic pressures with the aid of semipermeable membranes. [p017] Perfect membranes are very difficult to prepare, and membranes of this kind can be used only with a few solutes. Nature offers us, however, forms of semipermeable "walls" between solutions and pure solvents, which in many instances are perfect. The atmosphere, above a volatile pure solvent and a solution of a nonvolatile substance in that solvent, when both liquids are placed side by side in a closed space, would serve as a semipermeable wall: the solvent vaporizes and may pass freely from solvent to solution and ‹vice versa›, but the solute, in the case under consideration, is nonvolatile and therefore cannot pass through the atmosphere. The vapor pressure of a pure solvent being always found to be higher than that of a solution in this solvent, at the same temperature, the solvent would pass in such a closed space as vapor ‹from the pure solvent› and would ‹condense› in the solution; it thereby dilutes the solution and the solute, and the solvent in the solution, expand, exactly as in the absorption of a solvent by a solution through a semipermeable membrane. Again, the vapor pressure of a solution being lower than that of the pure solvent, the solution (of a nonvolatile solute) must be heated higher than the pure solvent, to bring both to the boiling-point; that is, there is an ‹elevation of the boiling-point›, when a nonvolatile solute is dissolved in a solvent. The solute being nonvolatile, only the solvent passes off in the process of boiling, the solute becomes ‹more concentrated›, and, according to van 't Hoff's extension of