48 THE POPULAR SCIENCE MONTHLY and the equations of Ostwald and van der Waals. 121 But perhaps his most important contributions to the theory of electricity are the two papers on electrochemical thermodynamics which he sent to the British Association in 1886 and 1888; Helmholtz, in his well-known formula for electromotive force, gives a relation such that if a cell be set up, and the reversible heat measured, the electromotive force need not be measured, but may be calculated from these data, or vice versa. In Gibbs's rendement of the perfect (or reversible) galvanic cell, both the electromotive force and the reversible heat can be predicted from his equation without the necessity of setting up any cell at all. "Pro- duction of reversible heat," says Gibbs, "is not anything incidental, superposed or separable, but belongs to the very essence of the opera- tion." 122 In discussing the matter in 1887, Sir Oliver Lodge raised the question whether Professor Gibbs was not regarding a galvanic cell as " too simply a heat engine " or assuming that the union of the elements in a cell primarily produces heat and secondarily propels a current. 128 Gibbs replied that "in supposing such a case we do not exceed the liberty usually allowed in theoretical discussions" and proceeded to show, in an ingenious demonstration, that Helmholtz's equation flows as a natural consequence from his own earlier results. 124 The accuracy of his reasoning is sustained by such developments of the subject as the " Peltier effect," in which it is demonstrated that the thermoelectric effect in systems of conductors, in which no chemical action takes place, is still proportional to the absolute temperature at any junction. In general the properties of a thermoelectric system are determined by the entropy function, and the entropy and energy in a thermoelectric net- work are not, as previously supposed, stored in the conductors, but, as we see in the electric transmission of motor power from a waterfall like Niagara to an engine or railway car, actually travel with the moving charge of electricity itself. In short, " entropy can be located in an electric charge." 125 Such are a few of the mathematical and physical consequences flow- ing from the single idea of entropy, and they are sufficient to define the position of Gibbs in the history of thermodynamics. In the establish- ment of the dynamical theory of heat, says Larmor, "The name of Carnot has a place by itself; in the completion of its earlier physical stage the names of Joule and Clausius and Kelvin stand out by common consent; it is, perhaps, not too much to say that, by the final adaptation of its ideas to all reversible natural operations, the name of Gibbs takes a place alongside theirs." 126 m See Bancroft, J. Phys. Chem., 1903, VII., 416-427. m " Report British Association for the Advancement of Science," 1886, 388. m Loo. cit.
- " Report British Association for the Advancement of Science," 1888, 343-6.
m See Bryan, " Thermodynamics," Leipzig, 1907, 174, 198.
- " Proc. Roy. Soc. Lond., 1905, LXXV., 292.
(To be oontinued)