Page:Scientific Memoirs, Vol. 2 (1841).djvu/507

Rh when $$z = 0$$, or $$z = 1$$, i. e. when the body to be decomposed is not compound; thirdly, when $$m \beta - n z = 0$$, i. e. when the densities of the constituents are proportional to the latent electroscopic forces which they possess, which circumstance can never occur with constituents of opposite electric nature.

All the expressions here given for the decomposing force of the circuit refer to the entire section belonging to the respective place; if we wish to reduce the value of the decomposing force to the unity of surface, the expression must be divided by the magnitude of the section, to which attention has been already called in § 30, in a similar example.

33. If this decomposing force of the circuit is able to overcome the coherence of the particles in the disc, a coherence produced by their electric opposition, this necessarily occasions a change in the chemical equivalent of the particles. But such a change in the physical constitution of the circuit must, at the same time, react on the electric current itself, and give rise to alterations in it, with which a more accurate acquaintance is desirable, and which we will therefore spare no trouble to acquire.

For this purpose we will imagine a portion of the galvanic circuit to be a homogeneous fluid body, in which such a decomposition actually takes place; then, at all points of this portion, the elements of one kind will tend to move with greater force towards one side of the circuit than those of the other kind; and since we suppose that, by the active forces, the coherence is overcome, it follows, if we pay due attention to the nature of fluid bodies, that the one constituent must pass to one side, those of the other constituent, on the contrary, towards the other side of the portion, which necessarily produces on one side a preponderance of the constituent of one kind, and on the other side a preponderance of the other kind of constituent. But as soon as a constituent is predominant on one side of any disc, it will oppose by its preponderance the movement of the like constituent in the disc towards the same side, in consequence of the repulsive force existing between both; the decomposing force, therefore, has now not merely to overcome the coherence between the two constituents in the disc, but also the reacting force in the neighbouring discs. Two cases may now occur; the decomposing force of the electric current either constantly overcomes all the forces opposed to it,