Page:Scientific Memoirs, Vol. 2 (1841).djvu/422

410 completely the figure $$F\, G\, H\, I$$ in every case, and also to distinguish perfectly the mode of electrical separation in the ring. All the peculiarities, hitherto considered separately, of the ring composed of two heterogeneous parts, may be summed up in the following manner: In a galvanic circuit consisting of two heterogeneous prismatic parts, there takes place in regard to its electrical state a sudden transition from the one part to the other at each point of excitation, forming the tension there occurring, and from one extremity of each point to the other a gradual and uniform transition; and the dips of these two transitions are inversely proportional to the products of the conductibilities and sections of each part.

Proceeding in this manner, we are able without much difficulty to inquire into the electrical state of a ring composed of three or more heterogeneous parts, and to arrive at the following general law: In a galvanic circuit consisting of any indefinite number of prismatic parts, there takes place in regard to its electrical state at each place of excitation a sudden transition, from one part to the other, forming the tension there prevailing, and within each part a gradual and uniform transition from the one extremity to the other; and the dips of the various transitions are inversely proportional to the products of the conductibilities and sections of each part. From this law may easily be deduced the entire figure of the separation for each particular case, as I will now show by an example.

Let $$A\, B\, C\, D$$ (fig. 3) be a ring composed of three heterogeneous parts, open at one of its places of excitation, and extended in a straight line. The straight lines $$F\, G$$, $$H\, I$$, $$K\, L$$ represent by their position the mode of separation of the electricity in each individual part of the ring, and the lines $$A\, F$$, $$B\, G$$, $$B\, H$$, $$C\, I$$, $$C\, K$$, and $$D\, E$$ drawn through $$A,\, B,\, C$$ and $$D$$ perpendicular to $$A\, D$$ such quantities that $$G\, H$$, $$K\, I$$ and $$L\, M$$ or $$D\, L - A\, F$$ show by their length the magnitude of the tensions occurring at the individual places of excitation. From the known magnitude of these tensions, and from the given nature of the single parts $$A\, B$$, $$B\, C$$, and $$C\, D$$, the figure of the electrical separation has to be entirely determined.

If we draw straight lines parallel to $$A\,D$$, through the points $$F,\, H$$ and $$K$$, meeting the line drawn through $$B,\, C$$ and $$D$$ perpendicular to $$A\, D$$, in the points $$F'$$, $$H'$$, $$K'$$, then according to what has already been demonstrated, the lines $$G\, F'$$, $$I\, H'$$ and