Page:Scientific Memoirs, Vol. 2 (1841).djvu/496

without committing any sensible error, be considered equal to the limit value.

Since the action of a coil of the circuit is ${\frac {A}{L}}$, while the action of the multiplier, in connexion with the same circuit, is ${\frac {A}{\lambda }}$, it is evident that the two actions are in the same ratio to each other as the reduced length $\lambda$ and $L$; if, therefore, we are acquainted with the two actions, and with one of the two reduced lengths, the other may be found, and in the same manner one of the two actions may be deduced from the other, and the two reduced lengths.

Since the limit of the action of the multiplier is ${\frac {A}{\lambda }}$, it increases when $\lambda$ is invariable in the same proportion as the sum of the tensions $A$ in the circuit increases; we may, therefore, by comparing the extreme actions of the same multiplier in various circuits, arrive at the determination of their relative tensions. At the same time we perceive that the extreme action of the multiplier increases, when several simple circuits are formed into a voltaic combination, and, indeed, in direct proportion to the number of the elements. In this manner it is always in our power, in cases where the multiplier in connexion with the simple circuit produces a weakening effect, to cause it to indicate any increase of force whatever.

If we call the actual length of a coil of the multiplier $l$, its conductibility $\chi$, and its section $\omega$, then $\lambda ={\frac {l}{\chi \omega }}$, and consequently the extreme action of the multiplier

$\chi \omega \cdot {\frac {A}{l}},$

whence it results that in the same circuit the extreme actions of two multipliers of coils of equal diameter, are in the ratio to each other of the products of their conductibility and their section. These extreme actions are, therefore, in two multipliers, which differ only in being formed of two distinct metals, in proportion to the conductibility of these metals; and when the multipliers consist of similar convolutions, and of one metal, their extreme actions are proportional to their sections.

But all these determinations are based upon the supposition that the action of a portion of the circuit on the magnetic