Page:Scientific Memoirs, Vol. 2 (1841).djvu/500

and we hence obtain by integration

$S^{2}=c^{2}+\chi ^{2}\omega ^{2}\beta ^{2}u^{2}$

where $c$ represents a constant remaining to be determined. If we designate by $u'$ the smallest absolute value which $u$ occupies in the circumference of the circuit, and by $S'$ the corresponding value of $S$, and determine, in accordance with this, the constant $c$, we obtain

$S^{2}-S'^{2}=\chi ^{2}\omega ^{2}\beta ^{2}(u^{2}-u'^{2}).$

It may easily be deduced from this equation, that the current of a circuit, which is influenced by the atmosphere, is weakest where the electroscopic force, without regard to the sign, is smallest, and that it is of the same magnitude at places with equal but opposite electroscopic forces.

 

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APPENDIX.

ON THE CHEMICAL POWER OF THE GALVANIC CIRCUIT.

On the Source and character of the Chemical Changes in a Galvanic Circuit, and on the Nature of the Fluctuations of its Force dependent thereon.

30. In the present Memoir we have constantly supposed that those bodies, which are under the influence of the electric current, remain unchangeable; we will now, however, take into consideration the action of the current on the bodies subjected to it, and the alterations in their chemical constitution thence resulting in any possible manner, as also the changes of the current itself produced by reaction. If what we here give does by no means exhaust the subject, nevertheless our first attempt shows that we are advancing in this path towards important conclusions respecting the relation of electricity towards bodies.

To proceed on sure ground, let us return to what has been enounced in §1 to 7, and connect our present considerations with those expressions and developments. We will suppose, therefore, two particles, and designate by $s$ their mutual distance, by $u$ and $u'$ their electroscopic forces, which we admit to be of equal intensity in all points of the same particle; then, as may easily be deduced from what has been previously stated,