378 Mr Searle, On the Calculation of Capacities 



On the Calculation of Capacities in terms of the Coefficients 

 of Electrostatic Induction. By G. F. C. Searle, M.A., Peterhouse, 

 University Lecturer in Experimental Physics, and Demonstrator 

 in Experimental Physics. 



[Read 15 February 1904.] 



Introduction. 



§ 1. In elementary theoretical electrostatics we meet with 

 the capacity of an isolated body, such as a sphere in free space, 

 and with the capacity of a condenser. But, in dealing with the 

 problems connected with the distribution of electrical charges 

 upon the various conductors in a cable used for the transmission 

 of polyphase currents, it is convenient to so extend the definition 

 of the capacity of a conductor that we can employ the term even 

 though other conductors are in the neighbourhood. In like 

 manner it, is convenient to define the capacity between two con- 

 ductors in such a way that we can employ the term not only when 

 the two conductors do not form a theoretical condenser, but also 

 when other conductors are in the neighbourhood. 



Maxwell* contemplated the extensions of the definitions, which 

 are necessary in attacking the more complex problems, but he did 

 not pursue the matter except in a single instance. As the subject 

 is of some interest in practical electrical engineering, I propose to 

 give some definitions of capacity and to shew how to calculate 

 the capacities, so defined, in terms of Maxwell's coefficients 

 of induction. 



Capacity of a Conductor. 



| 2. The simplest case is that of a single conductor at an 

 infinite distance from all other bodies. In this instance, the 

 capacity of the conductor is defined by means of the relation 

 between the charge and the potential of the body. Thus, if C be 

 the capacity of the conductor and e and v be its charge and its 

 potential, then the capacity is defined by the relation 



C = - (1). 



v 



In practice, however, we do not have infinite distances to deal 



* Maxwell, Electricity and Magnetism, Vol. n. § 87, third edition. 



