in terms of the Coefficients of Electrostatic Induction. 379 



with, and thus we are obliged to consider a conductor in relation 

 to its surroundings ; when we do this, we find that the ratio of 

 the charge on a conductor to its potential no longer depends only 

 upon the form and magnitude of the conductor itself, but also 

 upon all the other conductors in its neighbourhood. To meet the 

 case, in which the field contains n conductors, we require a new 

 definition of capacity. When n — 1 conductors are kept at zero 

 potential, Maxwell defines the capacity of the remaining conductor 

 as its charge when its own potential is unity, but this extension 

 of the definition is not sufficient, for problems occur in which 

 some of the n — 1 conductors are insulated instead of being at 

 zero potential. The definition I propose is as follows : 



Definition A. Let there be the n conductors [1], [2], ... [n] in 

 the field and let them all be initially uncharged. Then, if the 

 potential of an insulated conductor [1] rise from zero to v x when a 

 charge e 1 is given to [1], the ratio of e x to v 1 is called the capacity 

 of [1] in the presence of [2], [3], ... [%]. 



The capacity of the conductor [1], as thus defined, depends in 

 general not only upon the forms and positions of the remaining 

 n — 1 conductors, but also upon their electrical conditions, and 

 thus it is necessary, as Maxwell hints, to specify in each case 

 which of the conductors [2], [3], . . . [n] are insulated and which 

 are kept at the constant potential zero. 



A problem, at first sight more general than the last, is that in 

 which, initially, the insulated conductors have given charges and 

 the other conductors have given potentials, which are maintained 

 constant while the charge on [1] is changed. In this case we 

 may say that if the potential of an insulated conductor [1] rises 

 by V 1 when its charge is increased by E 1} the ratio of E l to V x is 

 equal to the capacity of [1] in the presence of [2],...[w]. It 

 will, however, be seen that, since the n equations connecting the 

 potentials of the conductors with their charges are linear, the 

 value of the capacity of [1], yielded by the last definition, is 

 identical with that obtained by the use of Definition A, provided 

 that the same conductors be insulated in the two cases. It 

 will therefore suffice, in the present paper, to use the simpler 

 definition. 



Coefficients of Induction. 



§ 3. If, when [1] is at unit potential and all the other con- 

 ductors are at zero potential, the charge on [1] is q u , the quantity 

 q n is called the Coefficient of Self Induction for the conductor [1]. 

 We see at once that, according to Definition A, q u is the capacity 

 of [1] in the presence of [2], ...[n], when the latter conductors 

 are all kept at zero potential. 



25—2 



