Page:Scientific Memoirs, Vol. 2 (1841).djvu/439

${\frac {n\mathrm {A} }{n\mathrm {L} }}$,

while in the simple closed circuit it is

${\frac {\mathrm {A} }{\mathrm {L} }}$.

If we now introduce into the simple circuit, as well as into the pile, one and the same new part $\Lambda$ of the reduced length, upon which the current is to act, the magnitude of the current thus altered in the simple circuit will be

${\frac {\mathrm {A} }{\mathrm {L} +\Lambda }}$,

and in the voltaic pile

${\frac {n\mathrm {A} }{n\mathrm {L} +\Lambda }},\quad {\text{or}}\;{\frac {\mathrm {A} }{\mathrm {L} +{\frac {\Lambda }{n}}}}$.

It is hence evident that the current is constantly greater in a voltaic pile than in the simple circuit, but it is merely imperceptibly greater so long as $\Lambda$ is very small in comparison with $\mathrm {L}$; on the contrary, this increase approximates the nearer to $n$ times, the greater $\Lambda$ becomes to $n\mathrm {L}$, and consequently the more so in comparison with $\mathrm {L}$. Besides this mode of increasing the magnitude of the galvanic current, there is a second one, which consists in shortening the reduced lengths of the simple circuit, which may be effected by increasing its section, or placing several simple circuits by the side of each other, and connecting them in such a way that together they only form one single simple circuit. If we now retain the same signs, so that

${\frac {\mathrm {A} }{\mathrm {L} +\Lambda }}$

again denotes the magnitude of the current in one element, then, in the above-mentioned combination of $n$ elements into a single circuit, the magnitude of the current is evidently

${\frac {\mathrm {A} }{{\frac {\mathrm {L} }{n}}+\Lambda }},\quad {\text{or}}\;{\frac {n\mathrm {A} }{\mathrm {L} +n\Lambda }}$,

which indicates a slight increase in the action of the new combination when $\Lambda$ is very great in comparison with $\mathrm {L}$; on the contrary, a very powerful one when $\Lambda$ is very small in comparison with ${\frac {\mathrm {L} }{n}}$, and consequently the more so in comparison with $\mathrm {L}$. It hence

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