Page:Scientific Memoirs, Vol. 1 (1837).djvu/636

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

consequently, by division,

$1={\frac {L+\lambda }{L+{\frac {\lambda }{m'}}}}\cdot {\frac {\sin .{\frac {1}{2}}\alpha }{\sin .{\frac {1}{2}}\alpha '}}\quad {\mbox{or}}\quad L+{\frac {\lambda }{m'}}=(L+\lambda ){\frac {\sin .{\frac {1}{2}}\alpha }{\sin .{\frac {1}{2}}\alpha '}}$

$1={\frac {L+\lambda }{L+{\frac {\lambda }{m''}}}}\cdot {\frac {\sin .{\frac {1}{2}}\alpha }{\sin .{\frac {1}{2}}\alpha ''}}\quad {\mbox{or}}\quad L+{\frac {\lambda }{m''}}=(L+\lambda ){\frac {\sin .{\frac {1}{2}}\alpha }{\sin .{\frac {1}{2}}\alpha ''}}$

$1={\frac {L+\lambda }{L+{\frac {\lambda }{m'''}}}}\cdot {\frac {\sin .{\frac {1}{2}}\alpha }{\sin .{\frac {1}{2}}\alpha '''}}\quad {\mbox{or}}\quad L+{\frac {\lambda }{m''''}}=(L+\lambda ){\frac {\sin .{\frac {1}{2}}\alpha }{\sin .{\frac {1}{2}}\alpha '''}}$,

from which equations $m',\,m'',$ and $m'''$ may be found.

For our case, $L$ is ${}=849$ inches, $\lambda =84.1$, $\alpha =21^{\circ }\;52'$, $\alpha '=17^{\circ }\;36'$, $\alpha ''=15^{\circ }\;34'$, $\alpha '''=18^{\circ }\;20'$, hence we have

Capacity of conduction of	copper	= 1·00000,
———————————	iron or $m'$	= 0·27321,
———————————	platina or $m''$	= 0·18370,
———————————	brass or $m'''$	= 0·32106.

We might still find these values more exactly if the lengths of the wires were greater; but this investigation did not properly come within the scope of this paper, I therefore defer it till another occasion.

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Consequences of the Laws already established in respect to the Construction of Electromotive Spirals.

In the following experiments I suppose the magnet for the production of the electric current to be given here, therefore the question is to determine those spirals of a certain metal which act most advantageously with this magnet and its cylindrical armature, which is likewise given. Further, I suppose the spirals, together with their free, not wound ends, to consist of one and the same wire; moreover, it is self-evident that every other property of the ends of the wires not belonging to the electromotive spirals may be reduced to those above mentioned, if we know the length, the diagonal, and the conducting power of the pieces of wire brought into the circle.

It is easy to see that by increasing the convolutions ad infinitum we do not also increase the strengths of the current ad infinitum. In the first place,—the number of convolutions of a given wire is limited by