Page:Scientific Memoirs, Vol. 2 (1841).djvu/427

the kind hitherto mentioned, the quantity of electricity passing through a section of it in a given time is everywhere the same, because at all places and in each moment the same quantity in the section leaves it on the one side as enters it from the other, but in different circuits this quantity may be very different: therefore, in order to compare the actions of several galvanic circuits inter se, it is requisite to have an accurate determination of this quantity, by which the magnitude of the current in the circuit is measured. This determination may be deduced from figure 3 in the following manner. It has already been shown that the force of the electric transition in each instant from one element to the adjacent one is given by the electric difference between the two existing at that time, and by a magnitude dependent upon the kind and form of the particles of the body, viz. the conductibility of the body. But the electrical difference of the elements in the part $BC$, for instance, reduced to a constant unit of distance, will be expressed by the dip of the line $HI$ or by the quotient ${\frac {IH'}{BC}}$; if, therefore, we now indicate by $\chi$ the magnitude of the conductibility of the part $BC$,

${\frac {\chi \cdot IH'}{BC}}$

will express the force of the transition from element to element, or the intensity of the current in the part $BC$; consequently if $\omega$ represent the magnitude of the section in the part $BC$, the quantity of electricity passing in each instant from one section to the adjacent one, or the magnitude of the current, will be expressed by

${\frac {\chi \cdot \omega \cdot IH'}{BC}}$;

or if $S$ represent this magnitude of the current, we have

$S={\frac {\chi \cdot \omega \cdot IH'}{BC}}$,

and if we substitute for $IH'$ its value ${\frac {A\cdot \lambda '}{L}}$

$S={\frac {A}{L}}\cdot {\frac {\chi \cdot \omega \cdot \lambda '}{BC}}$.

Hitherto the letters $\lambda$, $\lambda '$, $\lambda ''$ have represented lines which are proportional to the quotients formed of the lengths of the parts $AB$, $BC$, $CD$, and the products of their conductibilities and their sections. If we restrict for the present this determination,