Page:A history of the theories of aether and electricity. Whittacker E.T. (1910).pdf/399

of which the other face is the electrode itself.^[1] If σ denote the surface-density of electricity on either face of this quasicondenser, we have, therefore,

$de=-d(S\sigma );\qquad {\text{so}}\qquad \sigma =d\gamma /dV$.

This equation shows that when dγ/dV is zero—i.e., when the surface-tension is a maximum—o must be zero; that is to say, there must be no difference of potential between the mercury and the electrolyte. The external electromotive force is then balanced entirely by the discontinuity of potential at the other electrode H₀; and thus a method is suggested of measuring the latter discontinuity of potential. All previous measurements of differences of potential had involved the employment of more than one interface; and it was not known how the measured difference of potential should be distributed among these interfaces; so that the suggestion of a means of measuring single differences of potential was a distinct advance, even though the hypotheses on which the method was based were somewhat insecure.

A further consequence deduced by Helmholtz from this theory leads to a second method of determining the difference of potential between mercury and an electrolyte. If a mercury surface is rapidly extending, and electricity is not rapidly transferred through the electrolyte, the electric surface-density in the double layer must rapidly decrease, since the same quantity of electricity is being distributed over an increasing area Thus it may be inferred that a rapidly extending mercury-surface in an electrolyte is at the same potential as the electrolyte.

This conception is realized in the dropping-electrode, in

1. The conception of double layers of electricity at the surface of separation of two bodies had been already applied by Helmholtz to explain various other phenomena—e.g., the Volta contact-difference of potential of two metals, frictional electricity, and "electric endosmose," or the transport of fluid which occurs when an electric current is passed through two conducting liquids separated by a porous barrier. Cf. Helmholtz, Berlin Monatsherichte, February 27, 1879; Ann. d. Phys. vii (1879), p. 337; Helmholtz, Wiss. Abh. 1, p. 855.