Page:A Treatise on Electricity and Magnetism - Volume 1.djvu/303

carrier when it is at the middle point of its passage, but $C,C'$ do not cover it so much.

We shall suppose $A,B,C$ to be connected with a Leyden jar of great capacity at potential $V$, and $A',B',C'$ to be connected with another jar at potential $-V'$.

$P$ is one of the carriers moving in a circle from $A$ to $C'$, &c., and touching in its course certain springs, of which a and a are connected with $A$ and $A'$ respectively, and $e,e'$ are connected with the earth.

Let us suppose that when the carrier $P$ is in the middle of $A$ the coefficient of induction between $P$ and $A$ is $-A$. The capacity of $P$ in this position is greater than $A$, since it is not completely surrounded by the receiver $A$. Let it be $A+a$.

Then if the potential of $P$ is $U$, and that of $A,V$, the charge on $P$ will be $(A+a)U-AV$.

Now let $P$ be in contact with the spring $a$ when in the middle of the receiver $A$, then the potential of $P$ is $V$, the same as that of $A$, and its charge is therefore $aV$.

If $P$ now leaves the spring $a$ it carries with it the charge $aV$. As $P$ leaves $A$ its potential diminishes, and it diminishes still more when it comes within the influence of $C'$, which is negatively electrified.

If when $P$ comes within $C$ its coefficient of induction on $C$ is $-C'$, and its capacity is $C'+c'$, then, if $U$ is the potential of $P$ the charge on $P$ is

$(C'+c')U+C'V'=aV.$

If

$C'V'=aV$

then at this point $U$ the potential of $P$ will be reduced to zero.

Let $P$ at this point come in contact with the spring $e'$ which is connected with the earth. Since the potential of $P$ is equal to that of the spring there will be no spark at contact.

This conductor $C'$, by which the carrier is enabled to be connected to earth without a spark, answers to the contrivance called a regenerator in heat-engines. We shall therefore call it a Regenerator.

Now let $P$ move on, still in contact with the earth-spring $e'$, till it comes into the middle of the inductor $B$, the potential of which is $V$. If $-B$ is the coefficient of induction between $P$ and $B$ at this point, then, since $U=0$ the charge on $P$ will be $-BV$.

When $P$ moves away from the earth-spring it carries this charge with it. As it moves out of the positive inductor $B$ towards the