Page:Scientific Memoirs, Vol. 2 (1841).djvu/492

the powers of conduction, therefore, of both bodies are directly proportionate to their lengths, and inversely proportionate to their sections. If it is intended to employ this relation in the determination of the powers of conduction of various bodies, and we choose for the experiments prismatic bodies of the same section, which indeed is requisite for the sake of great accuracy, their lengths will enable us to determine accurately their conductibilities.

25. In the preceding paragraph we have deduced the magnitude of the current from the general equation given in § 18,

$u={\frac {A}{L}}y-O+c,$

and have found that it is expressed by ${\frac {A}{L}}$, the coefficient of $y$.

To ascertain the value ${\frac {A}{L}}$ it is in general requisite to possess an accurate knowledge of all the single parts of the circuit, and their reciprocal tensions; but our general equation indicates a means of deducing this value likewise from the nature of any single part of the circuit in the state of action, which we will not disregard, as it will be of great service to us hereafter. If, namely, we conceive in the above equation $y$ to be increased by any magnitude $\Delta y$, and designate by $\Delta O$ the corresponding change of $O$, and by $\Delta u$ that of $u$, there results from that equation

$\Delta u={\frac {A}{L}}\Delta y-\Delta O,$

and we thence find

${\frac {A}{L}}={\frac {\Delta u+\Delta O}{\Delta y}};$

we find, therefore, the magnitude of the electric current by adding to the difference of the electroscopic forces at any two places of the circuit the sum of all the tensions situated between these two places, and dividing this sum by the reduced length of the part of the circuit which lies between these same places. If there should be no tension within this portion of the circuit, then $\Delta O=0$, and we obtain

${\frac {A}{L}}={\frac {\Delta u}{\Delta y}}.$

26. The voltaic pile, which is a combination of several similar