Page:Scientific Memoirs, Vol. 2 (1841).djvu/421

 Rh the lines $$F\, G$$ and $$H\, I$$ in the portions $$A\, B$$ and $$B\, C$$, composed of like substance, will be inversely to each other as the areas of the sections of these parts. By this the figure $$F\, G\, H\, I$$ is now fully determined.

When the parts $$A\, B$$ and $$B\, C$$ of the ring have the same section but are composed of different substances, the transition of the electricity will then no longer be dependent solely on the progressive change of electricity in each part from element to element, but at the same time also on the peculiar nature of each substance. This difference in the distribution of the electricity, caused solely by the material nature of the bodies, whether it have its origin in the peculiar structure or in any other peculiar state of the bodies to electricity, establishes a distinction in the electrical conductibility of the various bodies; and even the present case may afford some information respecting the actual existence of such a distinction and give rise to its more accurate determination. In fact, since the ring composed of the two parts $$A\, B$$ and $$B\, C$$ differs from the homogeneous one only in this respect, that the two parts are formed of two different substances, a difference in the dip of the two lines $$F\, G$$ and $$H\, I$$ will make known a difference in the conductibility of the two substances, and one may serve to determine the other. In this way we arrive at the following position, supplying the place of a definition: In a ring consisting of two parts $$A\, B$$ and $$B\, C$$, of like sections but formed of different substances, the dips of the lines $$F\, G$$ and $$H\, I$$ are inversely as the conducting powers of the two parts. If we have once ascertained the conducting powers of the various substances, they may be employed to determine the dips of the lines $$F\, G$$ and $$H\, I$$ in every case that may occur. By this, then, the figure $$F\, G\, H\, I$$ is entirely determined. The determination of the conductibility from the separation of the electricity is rendered very difficult from the weak intensity of galvanic electricity, and from the imperfection of the requisite apparatus; subsequently we shall obtain a more easy means of effecting this purpose.

From these two particular cases we may now ascend in the usual way to the general one, where the two prismatic parts of the ring neither possess the same section nor are constituted of the same substance. In this case the dips of the two parts must be in the inverse ratio of the products of the sections and powers of conduction. We are hereby enabled to VOL. II.