Page:Scientific Papers of Josiah Willard Gibbs.djvu/367

surface of the tube multiplied by $\varsigma ''$, the superficial tension of liquid water in contact with the tube at the pressure at which the water and its vapor would be in equilibrium at a plane surface. In this sense, the total weight of water which can be supported by the tube per unit of the perimeter of its surface is directly measured by the value of $-\varsigma$ for water in contact with the tube.

Modification of the Conditions of Equilibrium by Electromotive Force.—Theory of a Perfect Electro-Chemical Apparatus.

We know by experience that in certain fluids (electrolytic conductors) there is a connection between the fluxes of the component substances and that of electricity. The quantitative relation between these fluxes may be expressed by an equation of the form

$De={\frac {Dm_{\text{a}}}{a_{\text{a}}}}+{\frac {Dm_{b}}{a_{\text{b}}}}+{\text{etc.}}-{\frac {Dm_{\text{g}}}{a_{\text{g}}}}-{\frac {Dm_{\text{h}}}{a_{\text{h}}}}-{\text{etc.,}}$

(682)

where $De,Dm_{\text{a}}$, etc. denote the infinitesimal quantities of electricity and of the components of the fluid which pass simultaneously through any same surface, which may be either at rest or in motion, and $a_{\text{a}},a_{\text{b}}$, etc., $a_{\text{g}},a_{\text{h}}$, etc. denote positive constants. We may evidently regard $Dm_{\text{a}},Dm_{\text{b}}$, etc., $Dm_{\text{g}},Dm_{\text{h}}$, etc. as independent of one another. For, if they were not so, one or more could be expressed in terms of the others, and we could reduce the equation to a shorter form in which all the terms of this kind would be independent.

Since the motion of the fluid as a whole will not involve any electrical current, the densities of the components specified by the suffixes must satisfy the relation

${\frac {\gamma _{\text{a}}}{a_{\text{a}}}}+{\frac {\gamma _{\text{b}}}{a_{\text{b}}}}+{\text{etc.}}={\frac {\gamma _{\text{g}}}{a_{\text{g}}}}+{\frac {\gamma _{\text{h}}}{a_{\text{h}}}}+{\text{etc.}}$

(683)

These densities, therefore, are not independently variable, like the densities of the components which we have employed in other cases. We may account for the relation (682) by supposing that electricity (positive or negative) is inseparably attached to the different kinds of molecules, so long as they remain in the interior of the fluid, in such a way that the quantities $a_{\text{a}},a_{\text{b}}$, etc. of the substances specified are each charged with a unit of positive electricity, and the quantities $a_{\text{g}},a_{\text{h}}$, etc. of the substances specified by these suffixes are each charged with a unit of negative electricity. The relation (683) is accounted for by the fact that the constants $a_{\text{a}},a_{\text{h}}$, etc. are so small that the electrical charge of any sensible portion j the fluid varying sensibly from the law expressed in (683) would be enormously great, so that the formation of such a mass would be resisted by a very great force.