IV. On the capacity and residual charge dielectrics as affected by temperature and time

Abstract

Before describing the experiments forming the principal subject of this communication, and their results, it may he convenient to shortly state the laws of residual charge. Let x t be the potential at any time t of a condenser, e. g . a glass flask, let y t be the time integral of current through the flask up to time t , or, in other words, let y t be the electric displacement, including therein electric displacement due to ordinary conduction. If the potential be applied for a short time ω , let the displacement at time t , after time ω has elapsed from the application of force x t - ω be x t - ω Ψ( ω ) dω ; this assumes that the effects produced are proportional to the forces producing them; that is, that we may add the effects of simultaneously applied electromotive forces. Generalise this to the extent of assuming that we may add the effects of successively-applied electromotive forces, then y t = ∫ ∞ 0 x t - ω Ψ( ω ) dω . This is nothing else than a slight generalisation of Ohm’s Law, and of the law that the charge of a condenser is proportional to its potential. Experiments were tried some years ago for the purpose of supporting this law of superposition as regards capacity. It was shown that the electrostatic capacity of light flint glass remained constant up to 5,000 volts per millimetre (‘Phil. Trans.,’ 1881, Part II., p. 365). The consequences of deviation from proportionality were considered (‘ Proc. Boy. Soc.,’ 1886, vol. 41, p. 453), and it was shown that, if the law held, the capacity as determined by the method of attractions was equal to that determined by the method of condensers; this is known to be the case with one or two doubtful exceptions ( ibid ., p. 458). Rough experiments have been made to show that residual charge is proportional to potential; they indicate that it is (‘Phil. Trans.,’ vol. 167, Part II.).