Page:Scientific Memoirs, Vol. 2 (1841).djvu/489

Rh and that it at last entirely vanishes; the permanent state of the circuit has then occurred. This moment can, as is evident from the form of the expression, be retarded by a diminished power of conduction, and in a far greater degree by an increased length of the circuit.

This expression found for $$u$$, however, holds perfectly only so long as the circuit, which we have supposed, is not induced by any external disturbance to change its natural state. If the circuit is at any time compelled by any external cause, for instance, by deductive contact at any place, to approximate to an altered permanent state, the above method has to undergo some changes, which I intend to develope on another occasion. I will, moreover, observe, that it is in this last class of galvanic circuits, in which the peculiar phænomena of dry piles, and, in general, of circuits of unusually great length, have to be sought for; to which class likewise belong the circuits of very great length employed in the experiments of Basse, Erman, and Aldini, if the influence of their great length be not annulled by an increased goodness of conduction, or by an increased section.

C. Phænomena of the Electric Current.

24. According to what was advanced in paragraph 12, the magnitude of the electric current, in a prismatic body, will in general be expressed for each of its places by the equation where $$S$$ denotes the magnitude of the current, and $$u$$ the electroscopic force at that place of the circuit whose abscissa is $$x$$, while $$\omega$$ represents the section of the prismatic body, and $$\chi$$ its power of conduction at the same place. To connect this equation with the general equation found in § 18 for any circuit, composed of any number of parts, we write it thus: and substitute for $$\frac$$ the value $$\frac$$ resulting from that general equation, and for $$\frac$$ the value $$\frac$$ easily deducible from the same paragraph, both which values are valid for each place,