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XIX. The Residual Charge of the Leyden Jar. By J. Hopkinson, M.A., I). Sc. Com- 
municated by Sir William Thomson, F.R.S., Professor of Natural Philosophy in 
the University of Glasgow. 
Received February 24, — Read March 30, 1876. 
1. Suppose that the state of a dielectric under electric force* is somewhat analogous to 
that of a magnet, that each small portion of its substance is in an electropolar state. 
Whatever be the ultimate physical nature of this polarity, whether it arises from con- 
duction, the dielectric being supposed heterogeneous (see Maxwell’s 4 Electricity and 
Magnetism,’ vol. i. arts. 328-330), or from a permanent polarity of the molecules ana- 
logous to that assumed in Weber’s theory of induced magnetism, the potential at points 
external to the substance due to this electropolar state will be exactly the same as that 
due to a surface distribution of electricity, and its effect at all external points may be 
masked by a contrary surface distribution. Assume, further, that dielectrics have a pro- 
perty analogous to coercive force in magnetism, that the polar state does not instantly 
attain its full value under electric force, but requires time for development and also for 
complete disappearance when the force ceases. The residual charge may be explained 
by that part of the polarization into which time sensibly enters. A condenser is charged 
for a time, the dielectric gradually becomes polarized ; on discharge the two surfaces of 
the condenser can only take the same potential if a portion of the charge remain suffi- 
cient to cancel the potential, at each surface, of the polarization of the dielectric. The 
condenser is insulated, the force through the dielectric is insufficient to permanently 
sustain the polarization, which therefore slowly decays ; the potentials of the polarized 
dielectric and of the surface charge of electricity are no longer equal, the difference is 
the measurable potential of the residual or return charge at the time. It is only neces- 
sary to assume a relation between the electric force, the polarization measured by 
the equivalent surface distribution, and the time. For small charges a possible law may 
be the following: — For any intensity of force there is a value of the polarization 
proportional to the force to which the actual polarization approaches at a rate pro- 
portional to its difference therefrom. Or we might simply assume that the difference 
of potentials E of the two surfaces and the polarization are connected with the time by 
two linear differential equations of the first order. If this be so, E can be expressed in 
terms of the time t during insulation by the formula E=(A-f-Bs“ Mi! )a _Ai , where X and g, 
* To define the electric force within the dielectric it is necessary to suppose a small hollow space excavated 
about the point considered ; the force will depend on the form of this space ; but it is not necessary for the 
present purpose to decide what form it is most appropriate to assume. 
MDCCCLXXVI. 3 Y 
