112 Mr. Henry Holden on the 



A method of calculating the Electrostatic Capacity 

 of a Conductor. By Henry Holden, B.Sc, Bishop 

 Berkeley Fellow in Physics at the Owens College, 

 Manchester. Communicated by Prof. Schuster, 

 F.R.S. 



(Received February 21st, 1888.) 



The following paper contains a method for calculating 

 the capacity of a conductor, the condition of the dielectrical 

 medium being primarily considered. This method seems 

 to be the most natural one, and affords a simple explanation 

 of the meaning of the capacity of a conductor under any 

 circumstances. 



In works on electrostatics the capacity of a conductor 

 in the presence of other conductors is generally defined as 

 the quantity of electricity necessary to raise its potential by 

 unity, all the other conductors being connected to earth. 

 It is noted that this capacity does not depend on the nature 

 or mass of the conductor, but on its external shape, and 

 on the shape and position of the neighbouring conductors 

 (not on their nature or mass), and that the nature of the 

 dielectric between the conductors also affects the capacity 

 of the conductor considered. Thus it is evident that the 

 so-called capacity of a conductor is not one of its true 

 physical properties, and we may infer that a conductor has 

 really only an indirect influence in determining the value 

 of what is known as its capacity'. 



^ The first problem in calculating capacity usually considered in books on 

 Electrostatics is the case of a charged sphere at an infinite distance from any 

 other conductor. The capacity of such a charged sphere is generally calculated 

 somewhat as follows. It is first assumed that only the quantity of electricity 

 on the sphere need be considered since all other quantities of electricity are, by 

 hypothesis, infinitely distant. A previously-found expression for the potential 

 at a point is then used to prove that the potential at the centre of (and there- 

 fore throughout) the sphere is V = ^ where V is the increase of potential at the 



centre of the sphere of radius R due to a quantity Q of electricity on the 

 surface of the sphere. Substituting for Q its value CV (where C is the capacity 

 of the body) it follows that C = R. We are afterwards told that if the medium 

 surrounding the sphere be not air, the cajxicity is ecjual to KR where K is the 



