Page:Scientific Memoirs, Vol. 2 (1841).djvu/481

place of the circuit, brought into contact with $M$, has assumed when no new tension originates at this place of contact; under this supposition therefore

$u={\frac {r(u'-u)}{R}},$

whence we find

$u={\frac {ru'}{r+R}}.$

From this equation it results that the electroscopic force in the body $M$ will constantly be smaller than it was at the touched place before contact; and also that both will approximate the more to each other, the greater $r$ is in comparison to $R$. If we regard $R$ as a constant magnitude, the relation of the electroscopic forces $u$ and $u'$ to each other depends solely upon the magnitude of the space which the electricity occupies in the circuit; we can therefore bring the electroscopic force of the body $M$ nearer to its greatest value solely by increasing the capacity of the circuit, either by a general increase of its dimensions, or by attaching anywhere to it foreign masses. Upon the nature of these masses, when they are merely conductors of electricity, and do not give rise to new tensions, none of this effect, in my opinion, depends, but solely upon their magnitudes. If the attached masses occupy an infinitely great space, which case occurs when the circuit has anywhere a complete deduction, then the electroscopic force in the body $M$ will constantly be equal to that which the place of the circuit touched by it possesses.

To connect these effects with the action of the condenser, we have merely to bear in mind, that a condenser, whose magnitude is $R$, and whose number of charges is $m$, must be considered equal to a common conductor of the magnitude $mR$, yet with the difference that its electroscopic force is $m$ times that of the common conductor. If, therefore, we designate by $u$ the electroscopic force of the condenser, which is brought into connexion with a place of the circuit whose force is $u'$, we obtain

$u={\frac {mru'}{r+mR}},$

whence it follows that the condenser will indicate $m$ times the force of the touched place when $r$ is very great in comparison with $mR$; but that it will have a weakening action so soon as $r$ is