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XXXIX. On the Theory and Measurement of Residual 

 Charges, By Prof. A. Anderson, M.A., and T. Keane, B.A.* 



THE following attempt to throw light on the action in a 

 dielectric which results in a residual charge is based 

 on Maxwell's treatment of the subject. He pictured the 

 medium as varying from point to point, both in specific 

 inductive capacity and in specific resistance, and worked out 

 the solution for the case of a dielectric of lamellar structure 

 in which there were discontinuities in the values of these 

 quantities at the bounding surfaces. The case of a single 

 dielectric between two parallel plate electrodes, in which the 

 specific inductive capacity and specific resistance are finite 

 and continuous functions of the distance from one of the 

 plates, admits of easy treatment. We shall only have occa- 

 sion to require the solution for the steady state acquired by 

 the dielectric after a difference of potential between the 

 plates has been established and kept constant. Let the 

 potential of one plate be V, and that of the other zero. 

 Then, if r denote the specific resistance and K the specific 

 inductive capacity at a point whose distance from the first 

 plate is x, we have 



L S S) = °> and L ( K S) = - inp ' 



where p is the volume density of electricity. Hence 



— --=—, w T hich is equal to the current c per unit area, is 



t dx ' l r 



constant, and therefore 



Hence, by integration, the whole quantity of electricity 

 stored in the dielectric is 



Ac 



A being the area of one of the plates. Here K x and K are 

 the specific inductive capacities, and r x and t q the specific 

 resistances, at the surfaces of the dielectric. Hence the 

 amount of electricity stored, or the amount of what is known 

 as the residual charge, or the residual discharge, depends, at 

 any rate in the case under consideration, on the state of the 



* Communicated by the Authors. 

 Phil Mag. S. 6, Vol. 24, No, 141. SepU 1912. 2 G 



