Page:Scientific Memoirs, Vol. 2 (1841).djvu/508

496 and then evidently the action terminates by a total separation of the constituents, the entire mass of the one passing to the one end of the portion, and the entire mass of the other constituent being impelled towards the other end of this portion; or such a relation takes place between the forces in action, that the forces opposing the separation ultimately maintain the decomposing force in equilibrium; from this moment no further decomposition will occur, and the portion will be, in a remarkable state, a peculiar distribution of the two constituents occurring, into the nature of which we will now inquire. If we call $$Z$$ the decomposing force of the current in any disc of the portion in the act of decomposition, $$Y$$ the magnitude of the reaction by which the neighbouring discs oppose the decomposition by the electric current, and $$X$$ the force of the coherence of the two constituents in the same disc, then evidently the state of a permanent distribution within the supposed portion, will be determined by the equation and it is already known, from the preceding paragraph, that or if we substitute $$\chi \omega \frac$$ for $$S$$,

Before we proceed further, we will add to what has been above said the following remarks. At the limits of the portion in question, we imagine the circuit so constituted, that insuperable difficulties there oppose themselves to any further motion; for it is obvious that otherwise the two extreme strata of both constituents, which it is evident could never of themselves arrive at equilibrium, would quit the portion in which we have hitherto supposed them, and either pass on to the adjacent parts of the circuit, or from any other causes separate entirely from the circuit. We will not here follow the last-mentioned modification of the phænomenon any further, although it frequently occurs in nature, as sufficiently shown by the decomposition of water, the oxidation of the metals on the one side, and a chemical change of a contrary kind occurring on the metals at the other side of the portion hitherto less