Page:A Treatise on Electricity and Magnetism - Volume 1.djvu/328

(6) Let $A$ and $A'$ be connected with an electroscope $E$.

We may express these connexions as follows:–

${\begin{array}{lllclclclcl}(1)&&0=C=B'&=&A'&|&A&=&B=C'&=&J.\\(2)&&0=C=B'&=&A'&|&A&=&B=C'&|&J.\\(3)&&0=C=B'&|&A'&|&A&|&B=C'.\\(4)&&0=C=B'&|&A'&|&A&|&B=C'&=&0.\\(5)&&0=C=B'&|&A'&=&A&|&B=C'&=&0.\\(6)&&0=C=B'&|&A'&=E=&A&|&B=C'&=&0.\end{array}}$

Here the sign of equality expresses electrical connexion, and the vertical stroke expresses insulation.

In (1) the two accumulators are charged oppositely, so that $A$ is positive and $A'$ negative, the charges on $A$ and $A'$ being uniformly distributed on the upper surface opposed to the large disk of each accumulator.

In (2) the jar is removed, and in (3) the charges on $A$ and $A'$ are insulated.

In (4) the guard-rings are connected with the large disks, so that the charges on $A$ and $A'$, though unaltered in magnitude, are now distributed over their whole surface.

In (5) $A$ is connected with $A'$. If the charges are equal and of opposite signs, the electrification will be entirely destroyed, and in (6) this is tested by means of the electroscope $E$.

The electroscope $E$ will indicate positive or negative electrification according as $A$ or $A'$ has the greater capacity.

By means of a key of proper construction, the whole of these operations can be performed in due succession in a very small fraction of a second, and the capacities adjusted till no electrification can be detected by the electroscope, and in this way the capacity of an accumulator may be adjusted to be equal to that of any other, or to the sum of the capacities of several accumulators, so that a system of accumulators may be formed, each of which has its capacity determined in absolute measure, i. e. in feet or in metres, while at the same time it is of the construction most suitable for electrical experiments.

This method of comparison will probably be found useful in determining the specific capacity for electrostatic induction of different dielectrics in the form of plates or disks. If a disk of the dielectric is interposed between $A$ and $C$, the disk being considerably larger than $A$, then the capacity of the accumulator will