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.
Since Faraday’s time, by improved methods, but depending essentially upon the same principles, an enormous number of determinations of the dielectric constants of various insulators, solid, liquid and gaseous, have been made (see tables I., II., III. and IV.). There are very considerable differences between the values assigned by different observers, sometimes no doubt due to differences in method, but in most cases unquestionably depending on variations in the quality of the specimens examined. The value of the dielectric constant is greatly affected by the temperature and the frequency of the applied electric force.
Table II.—Dielectric Constant (K) of Liquids.
| Liquid. | K. | Authority. |
| Water at 17° C. | 80.88 | F. Heerwagen |
| ” ” 25° C. | 75.7 | E. B. Rosa |
| ” ” 25.3° C. | 78.87 | Franke |
| Olive oil | 3.16 | Hopkinson |
| Castor oil | 4.78 | ” |
| Turpentine | 2.15 | P. A. Silow |
| ” | 2.23 | Hopkinson |
| Petroleum | 2.072 | Silow |
| ” | 2.07 | Hopkinson |
| Ethyl alcohol at 25° C. | 25.7 | Rosa |
| Ethyl ether | 4.57 | Doule |
| ” ” | 4.8 | Bouty |
| Acetic acid | 9.7 | Franke |
Table III.—Dielectric Constant of some Bodies at a very low
Temperature (−185° C.) (Fleming and Dewar).
| Substance. | K at 15° C. | K at −185°C. |
| Water | 80 | 2.4 to 2.9 |
| Formic acid | 62 | 2.41 |
| Glycerine | 56 | 3.2 |
| Methyl alcohol | 34 | 3.13 |
| Nitrobenzene | 32 | 2.6 |
| Ethyl alcohol | 25 | 3.1 |
| Acetone | 21.85 | 2.62 |
| Ethyl nitrate | 17.7 | 2.73 |
| Amyl alcohol | 16 | 2.14 |
| Aniline | 7.5 | 2.92 |
| Castor oil | 4.78 | 2.19 |
| Ethyl ether | 4.25 | 2.31 |
The above determinations at low temperature were made with either a steady or a slowly alternating electric force applied a hundred times a second. They show that the dielectric constant of a liquid generally undergoes great reduction in value when the liquid is frozen and reduced to a low temperature.[1]
The dielectric constants of gases have been determined by L. Boltzmann and I. Klemenčič as follows:—
Table IV.—Dielectric Constants (K) of Gases at 15° C. and 760 mm.
Vacuum = 1.
| Gas. | Dielectric Constant K. |
√K. | Optical Refractive Index. μ. |
| Air | 1.000590 | 1.000295 | 1.000293 |
| Hydrogen | 1.000264 | 1.000132 | 1.000139 |
| Carbon dioxide | 1.000946 | 1.000475 | 1.000454 |
| Carbon monoxide | 1.000690 | 1.000345 | 1.000335 |
| Nitrous oxide | 1.000994 | 1.000497 | 1.000516 |
| Ethylene | 1.001312 | 1.000656 | 1.000720 |
| Marsh gas (methane) | 1.000944 | 1.000478 | 1.000442 |
| Carbon bisulphide | 1.002900 | 1.001450 | 1.001478 |
| Sulphur dioxide | 1.00954 | 1.004770 | 1.000703 |
| Ether | 1.00744 | 1.003720 | 1.00154 |
| Ethyl chloride | 1.01552 | 1.007760 | 1.001174 |
| Ethyl bromide | 1.01546 | 1.007730 | 1.00122 |
In general the dielectric constant is reduced with decrease of temperature towards a certain limiting value it would attain at the absolute zero. This variation, however, is not always linear. In some cases there is a very sudden drop at or below a certain temperature to a much lower value, and above and below the point the temperature variation is small. There is also a large difference in most cases between the value for a steadily applied electric force and a rapidly reversed or intermittent force—in the last case a decrease with increase of frequency. Maxwell (Elec. and Magn. vol. ii. § 788) showed that the square root of the dielectric constant should be the same number as the refractive index for waves of the same frequency (see Electric Waves). There are very few substances, however, for which the optical refractive index has the same value as K for steady or slowly varying electric force, on account of the great variation of the value of K with frequency.
There is a close analogy between the variation of dielectric constant of an insulator with electric force frequency and that of the rigidity or stiffness of an elastic body with the frequency of applied mechanical stress. Thus pitch is a soft and yielding body under steady stress, but a bar of pitch if struck gives a musical note, which shows that it vibrates and is therefore stiff or elastic for high frequency stress.
Residual Charges in Dielectrics.—In close connexion with this lies the phenomenon of residual charge in dielectrics.[2] If a glass Leyden jar is charged and then discharged and allowed to stand awhile, a second discharge can be obtained from it, and in like manner a third, and so on. The reappearance of the residual charge is promoted by tapping the glass. It has been shown that this behaviour of dielectrics can be imitated by a mechanical model consisting of a series of perforated pistons placed in a tube of oil with spiral springs between each piston.[3] If the pistons are depressed and then released, and then the upper piston fixed awhile, a second discharge can be obtained from it, and the mechanical stress-strain diagram of the model is closely similar to the discharge curve of a dielectric. R. H. A. Kohlrausch called attention to the close analogy between residual charge and the elastic recovery of strained bodies such as twisted wire or glass threads. If a charged condenser is suddenly discharged and then insulated, the reappearance of a potential difference between its coatings is analogous to the reappearance of a torque in the case of a glass fibre which has been twisted, released suddenly, and then gripped again at the ends.
For further information on the qualities of dielectrics the reader is referred to the following sources:—J. Hopkinson, “On the Residual Charge of the Leyden Jar,” Phil. Trans., 1876, 166 [ii.], p. 489, where it is shown that tapping the glass of a Leyden jar permits the reappearance of the residual charge; “On the Residual Charge of
- ↑ See the following papers by J. A. Fleming and James Dewar on dielectric constants at low temperatures: “On the Dielectric Constant of Liquid Oxygen and Liquid Air,” Proc. Roy. Soc., 1897, 60, p. 360; “Note on the Dielectric Constant of Ice and Alcohol at very low Temperatures,” ib., 1897, 61, p. 2; “On the Dielectric Constants of Pure Ice, Glycerine, Nitrobenzol and Ethylene Dibromide at and above the Temperature of Liquid Air,” id. ib. p. 316; “On the Dielectric Constant of Certain Frozen Electrolytes at and above the Temperature of Liquid Air,” id. ib. p. 299—this paper describes the cone condenser and methods used; “Further Observations on the Dielectric Constants of Frozen Electrolytes at and above the Temperature of Liquid Air,” id. ib. p. 381; “The Dielectric Constants of Certain Organic Bodies at and below the Temperature of Liquid Air,” id. ib. p. 358; “On the Dielectric Constants of Metallic Oxides dissolved or suspended in Ice cooled to the Temperature of Liquid Air,” id. ib. p. 368.
- ↑ See Faraday, Experimental Researches, vol. i. § 1245; R. H. A. Kohlrausch, Pogg. Ann., 1854, 91; see also Maxwell, Electricity and Magnetism, vol. i. § 327, who shows that a composite or stratified dielectric composed of layers of materials of different dielectric constants and resistivities would exhibit the property of residual charge.
- ↑ Fleming and Ashton, “On a Model which imitates the behaviour of Dielectrics.” Phil. Mag., 1901 [6], 2, p. 228.
