CAPACITY. If the charge on an isolated con ductor is increased. so is its potential, because more work would he required to bring up a unit charge: if the charge is doubled, so is the poten tial. In mathematical language. the charge equals a constant times the potential. If c is the charge and V the potential, c= CV. This constant C depends naturally on the shape and size of the conductor and on the surrounding dieletrie: it is called the 'capacity' of the con ductor. Similarly, if a condenser is charged with -)-c and —c, and if the potentials of the two conductors are V, and there will he a constant relation between e and which may he expressed This con stant C depends upon the shape. size. and distance apart of the two entidnetors and on the nature of the dielectric which separates them: it is called the 'capacity of the condenser.' It was first observed by Cavendish and later by Faraday that the capacity of a condenser was different for different dieleetries, e. g. air. glass, etc. Thus, if the stone charge is given two con densers which are identical except in that one has air for its dielectric and the other glass, it is observed that 1lie difference of potential is greater in the former than in the latter, thus showing that the capacity of the latter is the greater. The ratio of the two eapaeities was
palled by Faraday the 'specific- inductive ea pacit•' of the glass with reference to air. if. in stead of using air as the dielectric, there had !wen a vaenum, the ratio of the capacity of the glass cmidenser to the vacuum one would be a constant which is characteristic of glass, and is called its Ilieleetric constant.' It can be shown easily that this constant is the li which at-curs in the formula for electric action. K is said to Inca-Lire the of the dielectric.
It may be proved from mathematical reason ing that the capacity of an isolated sphere of radius It in a medium whose dielectric con stant is Ii is 1:1Z; the capacity of it condenser of two parallel plate, of area -1 and at a distance apart d with a dielectric of constant K. is list 4rd ; ct•.