THE DIELECTRIC.] ELECTRICITY 37 Fig. 17. Faraday assumed that the electrical action is propagated from molecule to molecule by actions whose sphere of immediate activity is very small. He denied the existence of "action at a distance," and regarded his results about induction in curved lines as at variance with it. Thomson 1 showed, however, that Faraday s results were perfectly consistent with the theory of action at a distance, pro vided the polarization of the dielectric be taken into account, and that the mathematical treatment of the subject is identical with Poisson s theory of induced magnetism. The theory of action at a distance as ap plied to this subject will be found under MAGNETISM. Helmholtz, whose memoirs we ha~ already mentioned, takes this view of the matter. We do not propose to follow Faraday s theory any further at present ; its main features are involved in Maxwell s theory, to which we shall afterwards allude. W. Siemens 2 examined and confirmed the conclusions of Faraday. He used voltaic electricity in comparing the capacities of condensers. By means of a kind of self-acting commutator 3 (Sclbstthdtige Wippe), the armatures of the condenser were connected alternately with a battery of DanielPs cells and with each other; so that the condenser was charged and discharged about 60 times per second. Figure 17 gives a scheme of the arrangement. F and G are two insulated metal screws, with which the vibrat ing tongue E of the Wippe comes alter nately into contact ; CD and AB are the armatures of the con denser, H the battery, and K the galvano meter. Theory indicates, and experiment confirms, that the deflec tion will be the same whether the galvanometer is put in the charge or in the discharge circuit. The former arrangement is that indicated in the figure. The amount of electricity which flows through the galvanometer each time the condenser is charged, is pro portional to the product of the capacity C of the condenser and the electromotive force E of the battery. E is propor tional to the number of cells in the battery. If, therefore, the speed of the Wippe be constant, the galvanometer deflection, or its sine or tangent as the case may be, will be proportional to EC. By varying E and C inde pendently, we can verify the laws that regulate the charge of condensers. If we keep E the same, and the speed the same, we can compare the capacities of two condensers, or of the same condenser with two different dielectrics, and thus find the specific inductive capacities of various sub stances with respect to air. Siemens found that C is independent of E ; and concluded that the effect of solid dielectrics on the capacity of a condenser is not to be explained by a penetration of the electricity into the dielectrics. We shall give some of his values of the specific inductive capacity farther on. Gaugain 4 studied the effect of the insulator on the capacity of condensers. He used in his researches the discharging electroscope (see art. ELECTROMETER), an in strument which does not at first sight look likely to lead to very accurate results, but which seems to have worked satisfactorily in his hands. Many of Gaugain s results concerning the gradual increase of the charge arc very interesting ; their bearing on theory is difficult to estimate, however, owing to the mixture of effects due to surface and body conduction. His results concerning the "limit- 1 Camb. and Dub. Math. Jtnim., 1845, or Reprint of Papers, p. 15. 2 Pogg. Ann., cii. , 1857. 3 Fora description of this instrument, see Wiedeniann s Galvanismus, Bd. i. 451. 4 Ann. tie Chim. et tie Phys., 4 ser. t. ii. (1862V ing " value of the specific inductive capacity are at variance with those of subsequent experimenters who have worked with more delicate instruments. In their experiments on the specific inductive capacity Gibson of paraffin, Gibson and Barclay 5 employed a method due to and Sir William Thomson, in which an instrument called the Platyme.ter is used in conjunction with the quadrant elec- m eter. trometer. They found for the specific inductive capacity of paraffin 1 97, and showed that this value alters very little, if at all, with the temperature. The most extensive measurements of this kind that have been made of late are those of Boltzmann 6 and Schiller. 7 Boltzmann used a sliding condenser, whose plates could be Boltz- placed at measured distances apart. Plates of different mann> insulating materials were introduced between the parallel plates of the condenser, so as to be parallel with them and at different distances from one of them. According to the mathematical theory, the capacity of the con denser is independent of the position of the plate, and varies inversely as m - n + ^ , where m is the distance between the plates of the condenser, and n the thickness of the plate of insulat ing material whose specific inductive capacity is K. In other words, the plate may be supposed replaced by a plate of air of thickness 71 JT-. If therefore A denote in absolute measure the reciprocal of tho capacity of the condenser, then where G is a constant. The capacity of the condenser was mea sured by charging it with a battery of 6 to 18 Daniell s cells, and then dividing its charge with the electrometer. One pole of the battery and one armature of the condenser are connected to earth. The other pole of the battery is first connected with the electrode A of the electrometer, whose other electrode B is connected to earth. Let the reading thus obtained be E, then E is proportional to the potential of the battery pole. The condenser is next charged by connecting its insulated armature with the battery ; the battery connection is then removed, and the electrode A of the electrometer, which has meanwhile been connected with the earth, is now con nected with the condenser. If C be the capacity of the condenser, C that of the electrometer (in certain cases artificially increased), we have, if F be the common potential of the condenser and con nected parts of the electrometer, (C + C )F CE , and C=7T FCT E - F 1 -r"c - But F is proportional to the second reading of the electrometer, hence A is known in terms of C . As only relative measures are wanted, C is not required. Boltzmann made a variety of experi ments, all of which confirmed the theory, and showed the applica bility of the above formula. If we make three measurements, first with the plates at distance m^, secondly, at distance m v with only air between in each case; and thirdly, at distance m 3 , with an insulating plate of thickness n between, we have, if A x , A 2 , A 3 be the corresponding values of A, G = 2 ra, , and - ( -
n 1 -t-n. The advantage of this procedure is that only differences of m lt m v m 3 come in, and no absolute length has to be measured. Measure ments were also made with condensers, in which there was no air between the armatures and the insulating plates ; in them the armatures were formed by means of mercury. To give an idea of the agreement of the results by different methods, we give K for paraffin as determined on plates of different thickness; with the ordinary condenser, K = 2 28, 2 34, 2 31 for plates I., II., and III. ; and K = 2 31, 2 33 for plates I. and II. used with mercury armatures. Boltzmann convinced himself that, in the case of ebonite, Effect of paraffin, sulphur, and rosin, the time during which the time, condenser was charged was without sensible influence. He found that the result was the same whether the charge 6 Phil. Trans., 1871. fi Pogg. Ann., cli., 1874, or Sitzb. der Wiener Akad., Lxvii. 7 Pogg. Ann., clii. 8 It is supposed that the plates are near enough to allow tie to
neglect the effect of the rims.