JOSIAH WILLARD GIBBS 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, 

 " more often a pious dream than an accomplished fact." 106 



Ideal Gases and Gas-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. 109 

 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 



104 Tr. Connect. Acad., III., 194-7. 



106 Larmor, " Encycl. Britan.," 10th ed., XXVIII., 169. 



loe Whetham, " The Recent Developments of Physical Science," Philadelphia, 

 1904. 



107 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. liber Gastheorie," Leipzig, 1898, II., 211. 



10s Gibbs, Am. J. 8c, 1879, 3. s., XVII., 277, 371. 

 109 Tr. Connect. Acad., II., 240. 



