in terms of the Coefficients of Electrostatic Induction. 387 



Since, however, Maxwell's equations are linear, the value of 

 the capacity, in terms of q n , q 12 , .... given by this _ definition is 

 identical with that obtained by the use of Definition B, pro- 

 vided, of course, that the same conductors be insulated in the 

 two cases. 



Capacity between [1] and [2] when [3], ...[m] are insulated 

 and [m + 1], ... [n] are kept at zero potential. 



§ 13. Putting e x = — e 3 = e in equations (11), we obtain 



^A= e(A n + A 21 ), 



fc 2 A = - e (A 12 + A 22 ). 



Thus, if the capacity between [1] and [2] under the specified 

 conditions be denoted by X _ 2J we have 



Gl ~ 2 = ^^, = A u + A 12 + A 21 + A 22 (23) ' 



§ 14. When all the conductors except [1] and [2] are kept at 

 zero potential, we have, by (23), 



c _ guga - girt* 



§ 15. We may notice the relations between the capacity of 

 [1] and [2] "in parallel" and the capacity between [1] and [2]. 

 Thus, from (22) and (23), 



C 1+ , _ (A n + A 13 + A 21 + A. 22 ) 2 

 CU A n A 22 -A 13 A 21 



(A u + A 12 + A a + A 22 ) 2 

 AA lli22 



A 2 A 



C 1+2 . 0^ = AiiA2a _ Ai2A2i = An -; 2 • 



§ 16. In conclusion I wish to express my thanks to Mr A. 

 Russell for bringing the subject to my notice and for helping me 

 in framing the definitions of capacity adopted in the paper. My 

 thanks are also due to my former colleague, the Rev. P. E. Bateman, 

 for advice and assistance in connexion with the mathematical 

 methods employed, and to Mr G. T. Bennett for reading the 

 manuscript of the paper. 



