Page:A Treatise on Electricity and Magnetism - Volume 1.djvu/317

 of the electrometer, and if $$V, V'$$ denote the potentials of these bodies before making 1 contact, then their common potential after making contact will be

$\bar{V}=\frac{KV-K'V'}{K+K'} $

Hence the original potential of the conductor was

$V=\bar{V}+\frac{K'}{K}(\bar{V}-V') $

If the conductor is not large compared with the electrometer, $$K'$$ will be comparable with $$K$$, and unless we can ascertain the values of $$K$$ and $$K'$$ the second term of the expression will have a doubtful value. But if we can make the potential of the electrode of the electrometer very nearly equal to that of the body before making contact, then the uncertainty of the values of $$K$$ and $$K'$$ will be of little consequence.

If we know the value of the potential of the body approximately, we may charge the electrode by means of a 'replenisher' or otherwise to this approximate potential, and the next experiment will give a closer approximation. In this way we may measure the potential of a conductor whose capacity is small compared with that of the electrometer.

To Measure the Potential at any Point in the Air.

221.] First Method. Place a sphere, whose radius is small compared with the distance of electrified conductors, with its centre at the given point. Connect it by means of a fine wire with the earth, then insulate it, and carry it to an electrometer and ascertain the total charge on the sphere.

Then, if $$V$$ be the potential at the given point, and $$a$$ the radius of the sphere, the charge on the sphere will be $$-Va=Q $$, and if $$V'$$ be the potential of the sphere as measured by an electrometer when placed in a room whose walls are connected with the earth, then

$Q=V'a $

whence

$V+V'=0 $

or the potential of the air at the point where the centre of the sphere was placed is equal but of opposite sign to the potential of the sphere after being connected to earth, then insulated, and brought into a room.

This method has been employed by M. Delmann of Creuznach in