V = (C1V1 − C2V2)
(C + C)

(16);

and hence if V is zero we have C1 : C2 = V2 : V1.

The method is carried out by charging the two condensers to be compared at the two sections of a high resistance joining the ends of a battery which is divided into two parts by a movable contact.[10] This contact is shifted until such a point is found by trial that the two condensers charged at the different sections and then joined as above described and tested on a galvanometer show no charge. Various special keys have been invented for performing the electrical operations expeditiously.

A simple method for condenser comparison is to charge the two condensers to the same voltage by a battery and then discharge them successively through a ballistic galvanometer (q.v.) and observe the respective “throws” or deflections of the coil or needle. These are proportional to the capacities. For the various precautions necessary in conducting the above tests special treatises on electrical testing must be consulted.

Fig. 2.

In the absolute determination of capacity we have to measure the ratio of the charge of a condenser to its plate potential difference. One of the best methods for doing this is to charge the condenser by the known voltage of a battery, and then Absolute determinations. discharge it through a galvanometer and repeat this process rapidly and successively. If a condenser of capacity C is charged to potential V, and discharged n times per second through a galvanometer, this series of intermittent discharges is equivalent to a current nCV. Hence if the galvanometer is calibrated by a potentiometer (q.v.) we can determine the value of this current in amperes, and knowing the value of n and V thus determine C. Various forms of commutator have been devised for effecting this charge and discharge rapidly by J.J. Thomson, R.T. Glazebrook, J.A. Fleming and W.C. Clinton and others.[11] One form consists of a tuning-fork electrically maintained in vibration of known period, which closes an electric contact at every vibration and sets another electromagnet in operation, which reverses a switch and moves over one terminal of the condenser from a battery to a galvanometer contact. In another form, a revolving contact is used driven by an electric motor, which consists of an insulating disk having on its surface slips of metal and three wire brushes a, b, c (see fig. 2) pressing against them. The metal slips are so placed that, as the disk revolves, the middle brush, connected to one terminal of the condenser C, is alternately put in conductive connexion with first one and then the other outside brush, which are joined respectively to the battery B and galvanometer G terminals. From the speed of this motor the number of commutations per second can be determined. The above method is especially useful for the determinations of very small capacities of the order of 100 electrostatic units or so and upwards.

Dielectric constant.—Since all electric charge consists in a state of strain or polarization of the dielectric, it is evident that the physical state and chemical composition of the insulator must be of great importance in determining electrical phenomena. Cavendish and subsequently Faraday discovered this fact, and the latter gave the name “specific inductive capacity,” or “dielectric constant,” to that quality of an insulator which determines the charge taken by a conductor embedded in it when charged to a given potential. The simplest method of determining it numerically is, therefore, that adopted by Faraday.[12] He constructed two equal condensers, each consisting of a metal ball enclosed in a hollow metal sphere, and he provided also certain hemispherical shells of shellac, sulphur, glass, resin, &c., which he could so place in one condenser between the ball and enclosing sphere that it formed a condenser with solid dielectric. He then determined the ratio of the capacities of the two condensers, one with air and the other with the solid dielectric. This gave the dielectric constant K of the material. Taking the dielectric constant of air as unity he obtained the following values, for shellac K = 2.0, glass K = 1.76, and sulphur K = 2.24.

Table I.—Dielectric Constants (K) of Solids (K for Air = 1).

Substance. K. Authority.
Glass, double extra dense flint, density 4.5 9.896 J. Hopkinson
Glass, light flint, density 3.2 6.72    ”
Glass, hard crown, density 2.485 6.61    ”
Sulphur 2.24 M. Faraday
2.88 Coullner
3.84 L. Boltzmann
4.0 P.J. Curie
2.94 P.R. Blondlot
Ebonite 2.05 Rosetti
3.15 Boltzmann
2.21 Schiller
2.86 Elsas
India-rubber, pure brown 2.12 Schiller
India-rubber, vulcanized, grey 2.69   ”
Gutta-percha 2.462 J.E. H. Gordon
Paraffin 1.977 Gibson and Barclay
2.32 Boltzmann
2.29 J. Hopkinson
1.99 Gordon
Shellac 2.95 Wällner
2.74 Gordon
3.04 A.A. Winkelmann
Mica 6.64 I. Klemenčič
8.00 P.J. Curie
7.98 E.M.L. Bouty
5.97 Elsas
Quartz—
    along optic axis 4.55 P.J. Curie
    perp. to optic axis 4.49 P.J. Curie
Ice at −23° 78.0 Bouty