JOSIAH WILLARD QIBBS 45 on Combustion." Where water is the impurity, thermodynamic change is supposed to be due to electrolysis: the moisture being the necessary third ingredient for producing a little Voltaic circuit and the electric shock precipitating chemical action as in catalysis. The phase rule, Bancroft reminds us, has taught us to look upon an abso- lutely pure substance, 100 per cent, strong, as the extreme case of a two-component system, in which the concentration of the second com- ponent approaches zero as its limit. Gibbs has shown that in a system of two phases, one component of which is very small, the chemical potential of the dilute component is proportional to the logarithm of its density. As the density of the smaller component becomes less and less, its potential tends to an infinite value, 104 which means that, at the limit, when concentration becomes evanescent, "the removal of the last traces of any impurity would demand infinite expenditure of avail- able energy." 105 From the view-point of mathematical chemistry there are many chemical substances that are relatively and approximately pure, but absolute purity of a chemical nature is, in Whetham's dictum, a more often a pious dream than an accomplished fact." 106 Ideal Oases and Qas-Mixtures. — It is in the physics of gases that the application of the molecular theory has proved most successful and the laws and equations relating to gaseous states are of considerable accuracy owing to the fact that practically all gases act alike. Al- though Gibbs made no explicit assumptions as to molecular dynamics, his treatment of gaseous states agrees so well with the kinetic theory that Boltzmann thought he must have had the latter constantly before his mind in framing his fundamental equations. 107 These equations are unique in that Gibbs subjected them to an unusual test of accuracy by comparing their calculated densities of gas mixtures with converti- ble components with the actual measurements for nitrogen peroxide, acetic and formic acids and phosphorus perchloride 108 by Sainte-Claire- Deville, Horstmann and others. In the case of nitrogen peroxide the difference between the observed and calculated densities scarcely ex- ceeded .01 on the average and was not greater than .03 in any case. 100 The agreement between the theoretical and actual values was equally striking for the other gases, and these results are among the most accurate and satisfactory in the history of physical chemistry. Inter- esting features of this section of Gibbs's work are his interpretation of m Tr. Connect, Acad., III., 194-7. "•Larmor, "Encycl. Britan.," 10th ed., XXVIII., 169.
- Whetham, " The Recent Developments of Physical Science," Philadelphia,
1904. m Aus vielen Stellen geht deutlich hervor, dass Gibbs auch diese molekular- theoretische Anschauung fortwahrend vor Augen hatte, wenn er auch von den Gleichungen der Molekularmechanik keinen Gebrauch machte." Boltzmann, "Vorles. fiber Gastheorie," Leipzig, 1898, II., 211. -•Gibbs, Am. J. So., 1879, 3. s., XVII., 277, 371. "• Tr. Conned. Acad., II., 240.