Page:Scientific Memoirs, Vol. 2 (1841).djvu/497

Rh needle, under otherwise similar circumstances, is proportional to the magnitude of the current. But long since direct experiments have established the correctness of this supposition.

28. We will now proceed to the consideration of a multiple conduction existing at the same time. If, for instance, we imagine an open circuit, whose separated extremities are connected by several conductors, arranged by the side of each other, it may be asked, according to what law is the current distributed in the adjacent conductors? In answering this question, we might proceed directly from the considerations contained in §11 to 13; but we shall more simply attain the required object from the peculiarity of galvanic circuits ascertained in §25, in which case we will, for the sake of simplicity, suppose that none of the former tensions is destroyed by the opening of the circuit, nor a new tension produced by the conductor which is introduced.

For if $\lambda$, $\lambda'$, $\lambda''$, &c. represent the reduced lengths of the conductors brought into connexion with the extremities of the open circuit, and $$\alpha$$ the difference of the electroscopic forces at the extremities of the circuit, after the conductors have been introduced, the same difference will also occur at the ends of the single adjacent conductors, since, according to the supposition we have made, no new tension is introduced by the conductor. Since now, according to §13, the magnitude of the current in the circuit must be equal to the sum of all the currents in the adjacent conductors, we may imagine the circuit to be divided into as many parts as there are adjacent conductors; then, according to §25, the magnitude of the current in each adjacent conductor, and in the corresponding part of the circuit, will respectively be whence, in the first place, it results that the magnitude of the current in each adjacent conductor is in inverse ratio to its reduced length. If we now imagine a single conductor of such nature, that, being substituted for all the adjacent conductors in the circuit, it does not at all alter its current; then, in the first place, $\alpha$, according to §25, must retain the same value, and, if we designate by $$\Lambda$$ the reduced length of this conductor, must moreover be