Page:Scientific Memoirs, Vol. 2 (1841).djvu/467

 Rh with equal energy over the metals, and thus re-establishes in the fluid the conditions upon which our calculation is founded. But it is a very different matter when the prismatic fluid is only touched in disproportionately small portions of its surfaces by the metals, as the electricity arriving there can only advance slowly and with considerable loss of energy to the untouched surfaces of the fluid, whence currents of various kinds and directions result. The existence of such currents has been sufficiently demonstrated by Pohl's manifoldly varied experiments, and nothing more now stands in the way of their determination by analysis, after the additions which it has received from the successful investigations respecting the theory of heat, than the complexities of the expressions. Since their determination exceeds the limits of this small work, which has for its object to investigate the current only in one dimension, we will defer them to a more fit occasion.

We will now proceed to the application of the formulæ advanced, and divide, for the sake of a more easy and general survey, the whole into two sections, of which the one will treat of the electroscopic phænomena, and the other of the phænomena of the electric current.

B. Electroscopic Phænomena.

15. In our preceding general determinations we have constantly confined our attention to prismatic bodies, whose axes, upon which the abscissæ have been taken, formed a straight line. But all these considerations still retain their entire value, if we imagine the conductor constantly curved in any way whatsoever, and take the abscissæ on the present curved axis of the conductor. The above formulæ acquire their entire applicability from this observation, since galvanic circuits, from their very nature, can but seldom be extended in a straight line. Having anticipated this point, we will immediately proceed to the most simple case, where the prismatic conductor is formed in its entire length of the same material, and is curved backwards on itself, and conceive the seat of the electric tension to be where its two ends touch. Although no case in nature resembles this imaginary one, it will nevertheless be of great service in the treatment of the other cases which do really occur in nature.