Page:Scientific Memoirs, Vol. 2 (1841).djvu/493

Rh simple circuits, merits peculiar attention in this place, from the numerous and varied experimental results obtained by its means.

If $$A$$ represent the sum of the tensions of a closed galvanic circuit, and $$L$$ its reduced length, the magnitude of its current is, as we have found, Now, if we imagine $$n$$ such circuits perfectly similar to the former, but open, and constantly bring the end of each one in direct connexion with the commencement of the next following one, in such a manner that between each two circuits no new tension occurs, and all the previous tensions remain afterwards as before, then the magnitude of the current of this voltaic combination, closed in itself, is evidently consequently equal to that in the simple circuit. This equality of the circuit, however, no longer exists when a new conductor, which we will call the interposed conductor, is inserted in both. If, namely, we designate the reduced length of this interposed conductor by $$\Lambda$$, then, when no new tension is produced by it, the magnitude of the current in the simple circuit will be and in the voltaic combination, consisting of $$n$$, such elements therefore in the latter circuit it is constantly greater than in the former, and, in fact, a gradual transition takes place from equality of action, which is evinced when $$\Lambda$$ disappears, to where the voltaic combination exceeds $$n$$ times the action of the simple circuit, which case occurs when $$\Lambda$$ is incomparably greater than $$n L$$. If by $$\Lambda$$ we represent the relative length of the body upon which the circuit is to act by the force of its current, then from the observations just brought forward it results that it is most advantageous to employ a powerful simple circuit when $$\Lambda$$ is very small in comparison to $$L$$; and, on the contrary, the voltaic pile, when $$\Lambda$$ is very great in comparison with $$L$$.