Page:Scientific Papers of Josiah Willard Gibbs.djvu/406

within the films as well as without are the same, and the surfaces of the films are also the same, there will be no difference of tension. Nor will the tension of the same film be altered, if a part of the interior drains away in the course of time, without affecting the surfaces. If the thickness of the film is reduced by evaporation, its tension may be either increased or diminished, according to the relative volatility of its different components.

Let us now suppose that the thickness of the film is reduced until the limit is reached at which the interior ceases to have the properties of matter in mass. The elasticity of the film, which determines its stability with respect to extension and contraction, does not vanish at this limit. But a certain kind of instability will generally arise, in virtue of which inequalities in the thickness of the film will tend to increase through currents in the interior of the film. This probably leads to the destruction of the film, in the case of most liquids. In a film of soap-water, the kind of instability described seems to be manifested in the breaking out of the black spots. But the sudden diminution in thickness which takes place in parts of the film is arrested by some unknown cause, possibly by viscous or gelatinous properties, so that the rupture of the film does not necessarily follow.

Electromotive force.—The conditions of equilibrium may be modified by electromotive force. Of such cases a galvanic or electrolytic cell may be regarded as the type. With respect to the potentials for the ions and the electrical potential the following relation may be noticed:—

When all the conditions of equilibrium are fulfilled in a galvanic or electrolytic cell, the electromotive force is equal to the difference in the values of the potential for any ion at the surfaces of the electrodes multiplied by the electro-chemical equivalent of that ion, the greater potential of an anion being at the same electrode as the greater electrical potential, and the reverse being true of a cation.

The relation which exists between the electromotive force of a perfect electro-chemical apparatus (i.e., a galvanic or electrolytic cell which satisfies the condition of reversibility), and the changes in the cell which accompany the passage of electricity, may be expressed by the equation

$d\epsilon =({\text{V}}'-{\text{V}}'')de+td\eta +d{\text{W}}_{\text{G}}+d{W}_{\text{P}},$

(30)

in which $d\epsilon$ denotes the increment of the intrinsic energy in the apparatus, $d\eta$ the increment of entropy, $de$ the quantity of electricity which passes through it, ${\text{V}}'$ and ${\text{V}}''$ the electrical potentials in pieces of the same kind of metal connected with the anode and cathode respectively, $d{\text{W}}_{\text{G}}$ the work done by gravity, and $d{\text{W}}_{\text{P}}$ the work done by the pressures which act on the external surface of the apparatus. The term $d{\text{W}}_{\text{G}}$ may generally be neglected. The same is true of $d{\text{W}}_{\text{P}}$, when gases are not concerned. If no heat is supplied or withdrawn