Page:Scientific Memoirs, Vol. 2 (1841).djvu/479

$u=-O+C,$

which indicates that the electroscopic force in the whole extent of each other homogeneous portion of the circuit is everywhere the same, and merely changes suddenly from one part to the other to the amount of the entire tension prevailing at its place of contact.

To determine the constant $c$ in this equation, we will suppose the electroscopic force, at anyone place of the circuit, to be given. If we call this $u'$, and the sum of the tensions there abruptly passed over by the abscissa $O'$, we have

$u-u'=-(O-O').$

The difference of the electroscopic forces of any two places of an open circuit, i. e. a galvanic circuit interrupted by a non-conductor, is consequently equal to the sum of all the tensions situated between the two places, and the sign which has to be placed before this sum is always easily to be determined from mere inspection.

20. We will now notice another peculiarity of the galvanic circuit, which merits especial attention. To this end let us keep in view exclusively one of the homogeneous parts of the circuit, and imagine, for the sake of simplicity, the origin of the abscissæ placed in one end of it, and the abscissæ directed towards the other end. If we designate its reduced length by $\lambda$, and the reduced length of the other portion of the circuit by $\Lambda$, then

$u={\frac {A}{\Lambda +\lambda }}\centerdot y+c$

within the length $\lambda$; the following form may also be given to this equation:

$u={\frac {\frac {A\lambda }{\Lambda +\lambda }}{\lambda }}\centerdot y+c;$

the extent circuit is consequently similarly circumstanced to a simple homogeneous circuit, at whose ends the tension ${\frac {A\lambda }{\Lambda +\lambda }}$ occurs. If, accordingly, $A$ has a very sensible value, such as it can acquire in the voltaic pile, and if the ratio ${\frac {\lambda }{\Lambda +\lambda }}$ approaches to unity, then the tension ${\frac {A\lambda }{\Lambda +\lambda }}$ will likewise be still very per-