Page:Scientific Memoirs, Vol. 2 (1841).djvu/438

 426 portion. Consequently, if merely such circuits are compared in which the fluid parts have the same actual lengths and the same conductibilities, then the magnitude of the current in these circuits is in direct ratio to the section of the fluid portion. However, it must not be overlooked, that a more complex definition must take the place of this simple one when the reduced length of the metallic portion can no longer be regarded as evanescent towards that of the fluid, which case occurs whenever the metallic portion is very long and thin, or the fluid portion is a good conductor, and with unusually large terminal surfaces.

From the equation we can easily perceive that, when a portion is taken from the galvanic circuit, and is replaced by another, and after this change the sum of the tensions as well as the energy of the current still remains perfectly the same, these two parts have the same reduced length, ''consequently their actual lengths are as the products of their conductibilities and sections. The actual lengths of such parts are therefore, when they have like sections, as their conductibilities, and when they have like conductibilities as their sections.'' By the first of these two relations we are enabled to determine the conductibilities of various bodies in a far more advantageous manner than by the previously mentioned process, and it has already been employed by Becquerel and myself for several metals. The second relation may serve to demonstrate experimentally the independence of the effect on the form of the section, as has previously been done by Davy, and recently by myself.

In the voltaic pile, the sum of the tensions, and the reduced length of the simple circuit, is repeated as frequently as the number of elements of which it consists expresses. If, therefore, we designate by $$A$$ the sum of all the tensions in the simple circuit, by $$L$$ its reduced length, and by $$n$$ the number of elements in the pile, the magnitude of the current in the closed pile is evidently