Page:Scientific Memoirs, Vol. 2 (1841).djvu/483

$A$ and $B$, and at the same time $1-{\frac {1}{2m}}$ for $n$, which is permitted when $m$, as is usually the case, denotes a very large number, we obtain

${\begin{aligned}A&=md+{\frac {1}{2}}u,\\B&=-md+{\frac {1}{2}}u+{\frac {1}{2}}d.\end{aligned}}$

Or when $m$ is a very large number, and n not much greater than $d$, we may, without committing any perceptible error, place

${\begin{aligned}A&=md,\\B&=-md,\end{aligned}}$

in which is expressed the known law, that when two different places of a voltaic pile are brought into connexion with the two plates of an insulated condenser, each plate takes the same charge as if the other plate, and the corresponding place of the pile, had been touched deductively. At the same time our considerations show that this law ceases to be true when $u$ can no longer be regarded as evanescent towards $md$. This case would occur if, for instance, two places, near the insulated upper pole of a voltaic pile, constructed of a great number of elements, came in contact with the plates of the condenser, while the inferior pole of this pile remained in deductive connexion with the earth.

The determinations hitherto given respecting the mode in which the galvanic circuit imparts its electricity to foreign bodies, and which appear to me to leave nothing more to be wished for in the explanation of this subject, might, however, give rise to researches of a very different kind, and of no slight interest. For it is placed beyond all doubt, both from theoretical considerations, as well as from experiments, that electricity in motion penetrates into the interior of bodies, and its quantity accordingly depends on the space occupied by the bodies; while, on the other hand, it is no less ascertained that static electricity accumulates at the surface of bodies, and its quantity therefore is dependent on the extent of surface. But it would hence result, that in the closed galvanic circuit, $r$ in the above formulæ would express the volume of the circuit; in the open circuit, on the contrary, the magnitude of its surface, on which point, in my opinion, experiments might decide without great difficulty.

22. We have hitherto kept in view a circuit on which the surrounding atmosphere exercised no influence, and which has

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