Page:A Treatise on Electricity and Magnetism - Volume 1.djvu/323

like figure of radius $r_{0}$, and nearly uniform thickness $z_{0}$, and of the part of the infinite plane of $xy$ which lies beyond this figure.

The surface-integral over the whole disk gives the charge of electricity on it. It may be found, as in the theory of a circular current in Part IV, to be

$Q=4\pi a\sigma 'c\left\{\log {\frac {8a}{r_{0}-a}}-2\right\}+\pi \sigma r_{0}^{2}$

The charge on an equal area of the plane surface is $\pi \sigma r_{0}^{2}$, hence the charge on the disk exceeds that on an equal area of the plane in the ratio of

$1+8{\frac {z}{r}}\log {\frac {8\pi r}{z}}$ to unity,

where $z$ is the thickness and $r$ the radius of the disk, $z$ being supposed small compared with $r$.

On Electric Accumulators and the Measurement of Capacity.

226.] An Accumulator or Condenser is an apparatus consisting of two conducting surfaces separated by an insulating dielectric medium.

A Leyden jar is an accumulator in which an inside coating of tinfoil is separated from the outside coating by the glass of which the jar is made. The original Leyden phial was a glass vessel containing water which was separated by the glass from the hand which held it.

The outer surface of any insulated conductor may be considered as one of the surfaces of an accumulator, the other being the earth or the walls of the room in which it is placed, and the intervening air being the dielectric medium.

The capacity of an accumulator is measured by the quantity of electricity with which the inner surface must be charged to make the difference between the potentials of the surfaces unity.

Since every electrical potential is the sum of a number of parts found by dividing each electrical element by its distance from a point, the ratio of a quantity of electricity to a potential must have the dimensions of a line. Hence electrostatic capacity is a linear quantity, or we may measure it in feet or metres without ambiguity.

In electrical researches accumulators are used for two principal purposes, for receiving and retaining large quantities of electricity in as small a compass as possible, and for measuring definite quantities of electricity by means of the potential to which they raise the accumulator.