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 reversibje 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. 123 

 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." 123 



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. 



122 " Report British Association for the Advancement of Science,!' 1886, 388. 



123 Loo. tit. 



124 " Report British Association for the Advancement of Science," 1888, 343-6. 



125 See Bryan, " Thermodynamics," Leipzig, 1907, 174, 198. 

 135 Proc. Roy. Soc. Lond., 1905, LXXV., 292. 



(To be continued) 



