Page:Scientific Memoirs, Vol. 2 (1841).djvu/470

 458 length $$l$$, and of the tension $$a$$, which is touched at any given place whose abscissa is $$\lambda$$, may be found for every other place.

If any constant and perfect adduction, from outwards to the galvanic circuit, were to be given instead of the permanent abduction outwards, so that the electroscopic force pertaining to the abscissa $$\lambda$$ were compelled to assume constantly a given energy, which we will designate by $$\alpha$$, we should obtain for the determination of the constant $$c$$ the equation and for the determination of the electroscopic force of the circuit at any other place the following:

We have seen how the constant $$c$$ may be determined when the electroscopic force is indicated at any place of the circuit by external circumstances; but now the question arises, what value are we to ascribe to the constant when the circuit is left entirely to itself, and this value can consequently no longer be deduced from outward circumstances? The answer to this question is found in the consideration, that each time both electricities proceed contemporaneously, and in like quantity from a previously indifferent state. It may, therefore, be asserted, that a simple circuit of the present kind, which is formed in a perfectly neutral and isolated condition, would assume on each side of the place of contact an equal but opposite electric condition, whence it is self-evident that their centre would be indifferent. For the same reason, however, it is also apparent that when the circuit at the moment of its origin is compelled by any circumstance to deviate from this, its normal state, it would certainly assume the abnormal one until again caused to change.

The properties of a simple galvanic circuit, such as we have hitherto considered them to be, accordingly consist essentially in the following, as is directly evident from the equation (d): a. The electroscopic force of such a circuit varies throughout the whole length of the conductor continually, and on like extents constantly to the same amount; but where the two extremities are in contact, it changes suddenly, and, indeed,