Page:Scientific Memoirs, Vol. 2 (1841).djvu/482

equal to, or smaller than $R$. Masses attached anywhere to the circuit will accordingly make the indications of the condenser approximate to its maximum in proportion as they are greater, and a circuit touched at any place will constantly produce in the condenser the maximum of increase.

The preceding determinations suppose that one plate of the condenser remains constantly touched deductively. We will now take into consideration the case where the two plates of an insulated condenser are connected with various points of a galvanic circuit. In the first place, it is evident that the two plates of the condenser will assume the same difference of free electricity which the various places of the circuit with which they are in contact require unconditionally, from the peculiar nature of galvanic actions. Consequently, if $d$ represents the difference of the electroscopic force at the two places of the circuit, and $u$ the free electricity of one plate of the condenser, then $u+d$ is the free electricity of the other plate, and everything will depend on finding, from the known free electricities existing in the plates of the condenser, those actually present in them. If, for this purpose, we call $A$ the actual intensity of electricity in the plate, whose free electricity is $u+d$, then $A-u-d$ represents the portion retained in the same plate; in the same manner $B-u$ designates the portion of electricity retained in the plate, whose free electricity is $u$, when $B$ represents the actual intensity of the electricity in this plate. If now we represent by $n$ the relation between the electricity retained by one plate, and the actual electricity of the other plate, the following two equations arise:

${\begin{aligned}&A-u-d+nB=0,\\&B-u+nA=0,\end{aligned}}$

from which the values $A'$ and $B$ result, as follows:

${\begin{aligned}A&={\frac {d+u(1-n)}{1-n^{2}}},\\B&={\frac {u(1-n)-nd}{1-n^{2}}}.\end{aligned}}$

But from the theory of the condenser, it is well known that $1-n^{2}={\frac {1}{m}}$, if $m$ is the number of charges of the condenser; if, therefore, we substitute ${\frac {1}{m}}$ for $1-n^{2}$ in the expressions for