Page:Scientific Memoirs, Vol. 1 (1837).djvu/524

adopt it, in order to obtain from it a general basis for the arrangement of the different elements of the magnetic apparatus. I may be permitted here to state the fundamental principles of this theory.

1. In a closed voltaic circuit the same quantity of electricity passes across each section which is perpendicular to the direction of the current, whatever be the form or the matter of the different parts of the circuit.

2. Whatever change is made in one part of the circuit, this change affects the entire action of the pile, and is not confined merely to the place where the change takes place.

3. The voltaic action, in whatever manner measured, is in the direct ratio of the electro-motive power, and inversely as the resistances which oppose themselves to the passage of the current, or $A={\frac {E}{R}}$.

4. The resistances are composed of—

a) the resistance of the solid conductor or of the connecting wire. For the same substance this resistance is directly as the length of the wire, and inversely as the transversal section or as its thickness.

b) the resistance of the liquid conductor: this is in the direct ratio of the thickness of the liquid stratum which separates the positive and negative plates, and inversely as its transversal section, which coincides generally with the surface of the plates. During the action of the pile this last resistance increases, and at the same time the electro-motive power, or $E$, is affected by it. This is caused by chemical effects which take place and change by degrees the nature of the liquids, the surface of the metals, and the electric tension. But fixing any state of the pile, the law cited always exists. The difficulty of making electro-magnetic experiments comparable with each other, and the still greater difficulty in obtaining absolute measures, consist principally in the continual change of these elements. Thus in expressing by $r$ the resistance of the connecting wire, we shall have ${\frac {rl}{d}}$ for the resistance of a wire, of a length $l$, and of a thickness $d$; ${\frac {r'l'}{d'}}$ will likewise be the resistance of the liquid conductor, the surface and thickness of which are respectively expressed by $d'l'$. Therefore the action of the current, or the quantity of electricity passing through the pile, will be $A={\frac {E}{{\frac {rl}{d}}+{\frac {r'l'}{d'}}}}$.

5. The electromotive force is in the direct ratio of the number of voltaic pairs united in a pile, and at the same time the resistance $r'$ increases in the same proportion. Having one pile of $n'$ pairs, the force of the current will be expressed by $A={\frac {n'E}{{\frac {rl}{d}}+{\frac {n'r'}{d'}}}}$