1886.] 



On Specific Inductive Capacity. 



453 



December 16, 1886. 



Professor STOKES, D.C.L., President, in the Chair. 



The Presents received were laid on the table, and thanks ordered 

 for them. 



The following Papers were read : — ■ 



1. " Note on Specific Inductive Capacity." By John HOPKINSON, 

 M.A., D.Sc, F.R.S. Received November 9, 1886. 



Consider a condenser formed of two parallel plates at distance x 

 from each other, their area A being so great, or the distance* as so 

 small, that the whole of the lines of force may be considered to be 

 uniformly distributed perpendicular to the plates. The space 

 between the plates is occupied by air, or by any insulating fluid. Let 

 e be the charge of the condenser and V the difference of potential 

 between the plates. If the dielectric be air, there is every reason to 

 believe that V<x e, that is, there is for air a constant of specific 

 inductive capacity. My own experiments ([1880] i Phil. Trans,' 

 vol. 172, p. 355) show that in the case of flint-glass the ratio of V to 

 e is sensibly constant over a range of values of V from 200 volts per 

 cm. to 50,000 volts per cm. From experiments in which the dielectric 

 is one or other of a number of fluids and values of V upwards of 

 30,000 volts per cm. are used, Professor Quincke concludes 

 ('Wiedemann, Annalen,' vol. 28, 1886, p. 549) that the value of e/V 

 is somewhat less for great electric forces than for small. From the 

 experiments described in that paper, and from his previous experi- 

 ments (' Wiedemann, Annalen,' vol. 19, 1883, p. 705, et seq.) he 

 also concludes that the specific inductive capacity determined from 

 the mechanical force resisting separation of the plates is 10 per cent, 

 to 50 cent, greater than that determined by the actual charge of the 

 condenser. The purpose of the present note is to examine the rela- 

 tions of these important conclusions, making as few assumptions as 

 possible. 



The potential difference V is a function of the charge e and 

 distance x, and if the dielectric be given of nothing else. The 



work done in charging the condenser with charge e is Yde. If the 



h 



distance of the plates be changed to x + dx, the work done in giving 



