Page:Scientific Memoirs, Vol. 1 (1837).djvu/635

of wires of different substances, but in every other respect placed in exactly the same circumstances, is completely the same for all these substances"^[1].

Hence again it immediately follows that in two perfectly equal wire rings of different substance, surrounding the magnetic armature, the electric currents which are produced by taking the armature off or placing it on the magnet, are in direct proportion as the capacities of the substances for conducting electricity. Silver and copper wires therefore are the most advantageous.

From the latter observations we shall easily be able to deduce the capacity of the four metals for conducting, if we make a second similar observation, in which instead of bringing into the circle of the electric current two spirals of different metals, we make use of two of the already used copper spirals, and then place either of them on the armature, and determine the angle of deviation. Let this angle be called $\alpha$; and, for the other spirals, in the order in which they followed in the observation (therefore the copper spiral, with that of iron, platina, and brass), let these angles be designated by $\alpha ',\,\alpha ''\,$ and $\alpha '''$. Further, let the combined lengths of the wire of the multiplier of the conducting wires and that of the connecting wire of both spirals (all reduced to the diameter of the wire of the multiplier) be called $L$; but the lengths, which are equal in all the spirals, reduced also to the same diameter, be $\lambda$; we will further designate by $1,\,m',\,m'',\,m'''$, the conductive power of the metals in the above order, where that of the copper is also expressed by $1$.

If we take the general formula (A.), namely

$x=(L+l+\lambda )p\cdot \sin .{\frac {1}{2}}\alpha$,

we must here, since the wires are no longer of the same kind, substitute for the resistance $(L+l+\lambda )$, the resistances^[2]

$(L+\lambda ),\quad \left(L+{\frac {\lambda }{m'}}\right),\quad \left(L+{\frac {\lambda }{m''}}\right),\quad {\mbox{and}}\quad \left(L+{\frac {\lambda }{m'''}}\right),$

since they stand in inverse proportion to the capacities of conduction; we have therefore four equations (in which, according to the law just found, $x'=x''=x'''$ are ${}=x$),

$x=(L+\lambda )p\cdot \sin .{\frac {1}{2}}\alpha$
$x=\left(L+{\frac {\lambda '}{m'}}\right)p\cdot \sin .{\frac {1}{2}}\alpha '$

1. After I had made the above experiment I saw from No. 5 of Poggendorff's Annalen, which I had then just received, that this last law had already been demonstrated, although in a different way, by Faraday. My experiment may therefore serve to confirm it.
2. In the following expressions I consider the resistance $l$ jointly with that of $L$, since in the multiplier last employed the conducting wires consisted of one piece with the wire of the multiplier, therefore $L+\lambda$ must always remain constant.