RESIDUAL DISCHARGE.] ELECTRICI T Y 3<J the rate of loss is much less than before, being now very nearly constant, and not far from the limit above mentioned It would appear, therefore, that this constant limit, which on favourable days is very small, represents the loss due to convection and conduction in the usual way, and that the larger varying loss is due to some other cause. When an accumulator, let us say a Leyden jar, has been repeatedly charged up to potential V, until the rate of dissipation has become constant, we shall say that it is saturated. If we discharge a saturated jar, by con necting the knob for a fraction of a second with a good earth communication, and then insulate the knob, the outer coating being supposed throughout in connection with the earth, we find that the instant after the discharge the potential of the knob is zero; after a little, however, it begins to rise, and by and by it reaches a value which is a considerable fraction of Y, and has the same sign. This phenomenon justifies the assumption we made as to the peculiar nature of the variable loss of potential experienced by a freshly charged jar. The charge which reappears in this way subsequent to the instantaneous discharge is called the residual discharge. 1 If at any time during the appearance of the residual charge the jar be discharged, the potential of the knob becomes for a short time zero, but begins to rise again ; and this may be repeated many times before all trace of charge disappears. Faraday made a variety of experiments on the subject, and established that whenever a charge of positive electricity disappeared or became latent in this way, an equal negative charge disappeared in a similar way. He concluded that the cause of the phenomenon was an actual penetration of the two electricities (Exp. fies., 1245) by conduction into the dielectric. This is not the view which is favoured by the best authorities of the present day ; it ia indeed (see Maxwell, Elect, and Mag., vol. i. 325) at variance with the received theories of conduction, and alike untenable, as far as we know, whether we adopt the theories of Weber, of Maxwell, or of Helmholtz. Faraday established that time was a necessary condition for the development of the phenomenon ; and he was thus enabled to eliminate its inHuence in the experiments on the specific inductive capacity of sulphur, glass, and shellac. The phenomenon is most marked in the last of these ; and in spermaceti, which relatively to those is a tolerably good conductor, the phenomenon is very marked, and develops very rapidly, esti- Kohlrausch 2 studied the residual disharge in an ordinary Leyden jar, in a jar whose outside and inside coatings were at one time quicksilver and at another acidulated water, and in a Franklin s pane, one side of which was coated with tinfoil in the usual way, while the other was silvered like
- piece of looking-glass He showed, by taking measure
ments with an electrometer and a galvanometer, that the r-.itio of the free or disposable charge to the potential is con stant. By the disposable charge is meant the charge which is instantaneously discharged when the knob of the j ir is connected with the earth. This ratio is the capacity of the jar, and it appears tliat it is independent of the residual" or "latent" charge. He showed that the " latent " charge is not formed by a temporary recession of the electricity to the uncovered glass about the neck and upper part of the jar ; and that it does not to any great extent depend on the material used to fasten the armature to the glass, or on the air or other foreign matter between them. On the other hand, his results led him to suspect that the " latent " charge depended on the thickness of the glass, being greater for- thick plates than for thin. This 1 Wheu we think of the part of the charge that has disappeared, i.e., ceased Lo etlect the potential of the knob, we may talk of the " lateut charge. 1 This part of the charge is sometimes said to be absorbed.
- Fogg. Ann., xci., 1851.
conclusion has been questioned, however. 3 He separated by a graphical method the loss by latent charge from the loss by conduction, &c., and found that the amount of charge which becomes latent, or, which amounts to the same thing, the loss of potential owing to the forming of latent charge in a given time, is proportional to the initial potential so long as we operate with the, same jar. Kohlrausch recognized the insufficiency of Faraday s His explanation of the residual charge, and sought to account theory. for it by extending Faraday s own theory of the polariza tion of the dielectric. The residual charge is due according to him to a residual polarization of the molecules of the dielectric, which sets in after the instantaneous polarization is complete, and which requires time for its development. This polarization may consist in a separation of electricity in the molecules of the dielectric, or in a setting towards a common direction of the axes of a number of previously polarized molecules, analogous to that which Weber assumes in his theory of induced magnetism. It is easy to see that such a theory will to a great extent account for the gradual reduction of the potential of a freshly charged jar, and the gradual reappearance of the residual charge. If the charge, and consequently the potential, of the jar were kept constant at Q , the residual charge tends to a limit pQ (p const.). Kohlrausch assumes that the difference Tt-pQo between the residual charge actually formed and the limit decreases at a rate which is at each instant proportional to this difference, and further more, to a function of the time, which he assumes to be a simple power. In any actual case, where the jar is charged and then insulated, the charge varies, owing to conduction, &c., and to the formation of residual charge, so that the limit of r* is continually varying, and we must write Q ( for Q , Q t denoting the charge at time t. The equation for residual charge is then. From this he deduces the formula which he finds to represent his results very closely, m lias very nearly the same value (-0 5744, or -A nearly) in all his experi ments, p had the values 4289, 5794, 2562 ; and b 0397, 0223, 044G in his three cases. Kohlrausch called attention to the close analogy between Aualo- the residual discharge and the " elastic recovery" (elastische gous Nachwirkung) of strained bodies, which had been invest!- pheuo- gated by Weber 4 in the case of a silk fibre, and which has ni of late excited much attention. The instantaneous strain which follows the application of a stress is analogous to the initial charge of the jar, and the gradually increasing strain which follows to the gradual formation of the latent or residual charge. The sudden return to a position near that of unconstrained equilibrium corresponds to the in stantaneous discharge, and the slow creeping back to the original state of equilibrium to the slow appearance of the residual discharge. Another analogy may be found in the temporary and residual or subpermaneut magnetism of soft iron or steel. If we wish to make the analogy still more complete, we have only to introduce the permanent polarity of tourmaline, the permanent set of certain solids when strained, and the permanent magnetism of hard steel. The phenomena of polarization furnish yet another analogy. In justifying the introduction of a power of the time Effect of into his equation for the residual discharge, Kohlrausch duration makes the important remark that the time which a residual of charge, charge of given amount takes to reappear fully may be different according to the way that charge is produced. The charge reappears more quickly when it is produced in a short time by an initial charge of high potential, than when produced by a charge uf lower potential acting 3 Wullner, Pogg. Ann., N.F. i. pp. 272, 369.
4 Dsjlli bomlycini vi elastica, Gottingaa, 184L