constant condition (V being constant) when it is extended. Integrating the previous equation, we have
.
Lippmann found that when the external electromotive force was applied, the surface-tension increased at first, until, when the external electromotive force amounted to about one volt, the surface-tension attained a maximum value, after which it diminished. He found that d2γ/dV2 was sensibly independent of V, so that the curve which represents the relation between γ and V is a parabola.[1]
The theory so far is more or less independent of assumptions as to what actually takes place at the electrode: on this latter question many conflicting views have been put forward. In 1878 Josiah Willard Gibbs,[2] of Yale (b. 1839, d. 1903), discussed the problem on the supposition that the polarizing current is simply all ordinary electrolytic conduction-current, which causes a liberation of hydrogen from the ionic form at the cathode. If this be so, the amount of electricity which passes through the cell in any displacement must be proportional to the quantity of hydrogen which is yielded up to the electrode in the displacement; so that dγ/dV must be proportional to the amount of hydrogen deposited per unit area of the electrode.[3]
A different view of the physical conditions at the polarized electrode was taken by Helmholtz,[4] who assumed that the ions of hydrogen which are brought to the cathode by the polarizing current do not give up their charges there, but remain in the vicinity of the electrode, and form one face of a quasi-condenser
- ↑ Lippman, Comptes Rendus, xcv (1882), p. 686.
- ↑ Trans. Conn. Acad. iii (1876-1878), pp. 108, 343; Gibbs' Scientific Papers, i, p. 55.
- ↑ This is embodied in equation (690) of Gibbs' memoir.
- ↑ Berlin Monatsber., 1881, p. 945; Wiss. Abl. i, p. 925; Ann. d. Phys. xvi. (1882), p. 31. Cf. also Planck, Ann. d. Phys. xliv (1891), p. 385.
