Page:Elementary Text-book of Physics (Anthony, 1897).djvu/310

formed by joining them together by conductors is easily found. It is assumed that the connecting conductors are fine wires, the capacities of which may be neglected. Then the charges of the respective bodies may be represented by $C_{1}V_{1},C_{2}V_{2},\dots C_{n}V_{n},$ and the capacity of the system by the sum ${C_{1}+C_{2}+\dots C_{n}}.$ Hence $V,$ the potential after connections have been made, is

$V={\frac {C_{1}V_{1}+C_{2}V_{2}+\dots C_{n}V_{n}}{C_{1}+C_{2}+\dots C_{n}}}\cdot$

In the case of two freely electrified bodies joined up together by a fine wire, we have $V={\frac {C_{1}V_{1}+C_{2}V_{2}}{C_{1}+C_{2}}}$ When $C_{1}$ is very great compared with $C_{2},$ we obtain $V=V_{1}+{\frac {C_{2}}{C_{1}}}V_{2}.$

Unless $V_{2}$ is so great that the term ${\frac {C_{2}}{C_{1}}}V_{2}$ becomes appreciable, the potential of the system is appreciably equal to the original potential of the larger body. The capacity of the earth, being equal to its radius, is very great in comparison with the capacity of any body used in our experiments, and hence the potential of the earth is not changed when it is connected with a charged body. This proposition justifies the adoption of the potential of the earth as the standard or zero potential.

261. Electroscopes and Electrometers.—An electroscope is an instrument used to detect the existence of a difference of electrical potential. It may also give indications of the amount of difference. It consists of an arrangement of some light body or bodies, such as a pith ball suspended by a silk thread, or a pair of parallel strips of gold-foil, which may be brought near or in contact with the body to be tested. The movements of the light bodies indicate the existence, nature, and to some extent the amount of the potential difference between the body tested and surrounding bodies.

An electrometer is an apparatus which gives precise measurements of differences of potential. The most important form is the absolute or attracted disk electrometer, originally devised by Harris,