tions, it is clear that he regarded osmosis as a chemical or thermodynamic phenomenon. Let us see how his mathematical theory agrees with the facts of recent investigations. The mathematician Cayley thought double-entry bookkeeping an example of a perfect science, because its theory and practise are in complete agreement, so that the detection of sources of error becomes simply a matter of expert skill. For similar reasons one of the principal aims of modern physical chemistry has been to arrive at an adequate theory of solutions as a guide in chemical and biological research. Such a theory has been proposed by van't Hoff, who, starting from Pfeffer's measurements of osmotic pressure, bases his argument upon the widely known equation which asserts that osmotic pressure in very dilute solutions obeys the laws of Boyle, Gay Lussac and Avogadro with the same physical constants that obtain in mixtures of dilute or ideal gases.[1] Pushing this analogy with gases farther, van't Hoff implicitly denied that there is any specific attraction between the solvent and solute (dissolved substance) or that the alleged semi-permeable membrane plays any active part in osmosis, holding that "osmotic pressure," like the pressure exerted by rarefied gases, is a real initial pressure caused by a bombardment of the membrane by the dissolved molecules. Now van't Hoff's equation, which Gibbs anticipated for dilute solutions of gases in liquids, and of which van't Hoff, Lord Rayleigh[2] and Gibbs[3] have each given rigorous thermodynamic proofs, was found to be true to the laboratory measurements for extremely diluted solutions of sugar and other substances, but (as Lord Kelvin said ten years ago) "wildly far from the truth" for solutions of acids, bases and salts.[4] Arrhenius, in his theory of electrolytic dissociation,[5] has explained these discrepancies as "harmonies not understood," due to free dissociation of ions in water and to increase of molecular conductivity with dilution; but Lord Kelvin's objection has still some force to this day. Two schools of chemists have thus arisen, one of which seeks to approximate the laboratory facts about solutions to van't Hoff's dynamic analogy with the gas laws, the other holding that osmosis is bound up with an ascertained selective action of the semi-permeable membrane, osmosis and solution being both due to "chemical affinity." Most prominent among those who have opposed the view that real solutions behave like ideal gases, are Louis Kahlenberg and J. J. van Laar. The special service of Kahlenberg has been to discredit the molecular or dynamic analogy between gases and liquids and to emphasize the point made by Fitzgerald in
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