JO SI AH WILLARD GIBBS 559 



tions, it is clear that he regarded osmosis as a chemical or thermo- 

 djTiamic 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 chem- 

 istry 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.^^ 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 Eayleigh^^ and Gibbs^^ have each given rigorous 

 thermodynamic proofs, was found to be true to the laboratory measure- 

 ments 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.®" Arrhenius, in his theory of elec- 

 trolytic dissociation,®^ has explained these discrepancies as " harmonies 

 not understood," due to free dissociation of ions in water and to in- 

 crease 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 Kahlen- 

 berg has been to discredit the molecular or dynamic analogy between 

 gases and liquids and to emphasize the point made by Fitzgerald in 



"Van't Hoff, Ztschr. f. pMjs. Chem., 1887, I., 481. 



^Nature, London, 1896-7, LV., 253. 



^'Ibid., 461. 



'"Ibid., 273. 



'^Ztschr. f. phys. Chem., 1887, I., 631. 



