EXPERIMENTAL VERIFICATIONS.

2

355

401. In an isotropic medium, K1 = K2 = K ̧, and N is zero; whence (14) become

ƒ=(μK)¬1▼2ƒ, ÿ=(μK)-1▼2g, h= (μK)−1▼2h.......(29).

From these equations we see, that the velocity of propagation Vis equal to (uK). If the medium is air, and we adopt the electrostatic system of units, K=1, and μ=v2, where v is the number of electrostatic units in one electromagnetic unit, whence V=v; or the velocity of propagation of light is equal to the number of electrostatic units in one electromagnetic unit. If on the other hand we adopt the electromagnetic system, K = v2, and μ1, so that the equation Vv is still true.

=

402. The methods of determining v are explained in Maxwell's Electricity and Magnetism, Vol. II. Ch. XIX., and are quite independent of the methods for determining the velocity of light; hence the agreement or disagreement of the values of V and v furnishes a test of the electromagnetic theory of light.

The following table, taken from Maxwell, gives the values of V and v in C. G. S. units.

From these results we see, that the velocity of light, and the ratio of units are quantities of the same order; but none of them can be considered to be determined with such a degree of accuracy as to enable us to assert, that one is greater than the other1.

403. In all transparent media the magnetic permeability is very nearly equal to that of air, hence refraction must depend principally upon differences of specific inductive capacity. According to the electromagnetic theory, the dielectric capacity of a transparent medium is equal to the square of its index of refraction. But the index of refraction of light is different for different colours, being greater for light of short period; we must therefore select the index of refraction, which corresponds to waves of longest period, since these are the only waves whose motion can

See also the note, p. 379.

be compared to the slow processes, by which the capacity of a dielectric can be determined.

The square root of the value of K for paraffin' is 1.405; whilst the index of refraction for waves of infinite period is about 1-422.

404. In discussing these experimental results Maxwell concludes as follows:-"The difference between these numbers is greater than can be accounted for by errors of observation, and shows that our theories of the structure of bodies must be much improved, before we can deduce their optical from their electrical properties. At the same time, I think, that the agreement between the numbers is such, that if no greater discrepancy were found between the numbers derived from the optical and the electrical properties of a considerable number of substances, we should be warranted in concluding that the square root of K, although it may not be the complete expression for the index of refraction, is at least the most important term in it."

405. In 1873, which was the date of publication of the first edition of Maxwell's treatise on Electricity and Magnetism, paraffin was the only transparent dielectric, whose electrostatic capacity had been determined. Since that date, the capacity of a variety of other media have been determined, and it has been found that for many substances, the square of the refractive index differs considerably from the value of the electrostatic capacity.

The experiments of Hopkinson' give the following results for the electrostatic capacity of Chance's glasses.

In this table, p is the density, K is the electrostatic capacity,

and μ is the index of refraction of the double line D of the

spectrum.

1 Gibson and Barclay, Phil. Trans. 1871, p. 573.

2 Phil. Trans. 1878, p. 17.

HOPKINSON'S EXPERIMENTS.

357

A further series of experiments was made by Hopkinson', which gave the following results.

406. In the last paper an account is given of experiments made upon certain liquids; and the results are shown in the following table. The value of μ is calculated by means of Cauchy's formula

μ2 = μ2 + b/x2.

From these tables it appears, that the vegetable and animal oils do not agree with Maxwell's theory, but the hydrocarbon oils do. But in the electrical experiments, the determination was effected by the charge and discharge of a condenser; and it must be recollected, that even when the time of charge and discharge is only 5 x 10 of a second, this period is many million times longer than the period of the waves of any portion of the visible spectrum.

407. The capacities of Iceland spar, fluor spar and quartz have been examined by Romich and Nowak, and give results which

1 Phil. Trans. 1881, p. 355.

2 Wiener. Sitzb. vol. LXX. part ii. 1

are much in excess of the square of the refractive index. On the other hand, the same observers, and also Boltzmann, obtain for crystallized sulphur, a value of the capacity in reasonable accord with theory.

The experimental determinations of electrostatic capacities, made by Boltzmann for paraffin, colophonium and sulphur1, and also for various gases; by Silow for turpentine and petroleum3; by Schiller and Wüllner for plate glass, will be found in the papers referred to below.

Hertz's Experiments.

408. The rapidity of the propagation of electrical effects across space or any insulating medium, which has until recently eluded all attempts at measurement, early suggested to natural philosophers, that it might be connected with the mode of propagation of light across space. For all kinds of mechanical tremors in the matter of bodies are propagated comparatively slowly, in the manner of sound waves; while the propagation of free gravitation was shown long ago by Laplace, to be extremely rapid, even compared with that of light itself.

This suggested connection was enormously strengthened when Maxwell, who was the first to try to express the known equations. of electrodynamic action in a form, which suggested and implied propagation across a medium, found that his system gave rise to electric waves of the same transverse character as waves of light, whose velocity of propagation is an electric constant, which on measurement turns out to be for a vacuum the same as the velocity of light. Nor is the fact that, except for media of simple and homogeneous chemical constitution, this agreement in velocities is not very generally observed, a serious drawback to the theory, when we consider the great difficulty of unravelling the complex effect of the molecules of matter on the propagation of light, and on the character of electric actions.

1 Pogg. Ann. (1874), vol. CLI. pp. 482 and 531; vol. CLIII. p. 525.

2 Ibid. (1875), vol. cLv. p. 403.

3 Ibid. (1875), vol. CLVI. p. 389; (1876), vol. CLVIII. p. 306.

4 Ibid. (1874), vol. CLII. p. 535.

5 Ibid. New Series, vol. 1. pp. 247 and 361.

6 I am indebted to Mr Larmor for §§ 408-409.

HERTZ'S EXPERIMENTS.

359

409. There remained however another side of the subject to explore, in the detection and systematic examination of actual electric vibrations propagated across space. The difficulties in the way were (i) to obtain a vibrating electric system, with periods high enough to give waves of manageable length; (ii) to obtain some method of detecting their propagation. These difficulties have been successfully surmounted within the last few years by Hertz'. The vibrations were set up by the snap of an electric discharge between two conductors, whose capacity and self-induction were so arranged as to give a wave-length of the order of magnitude of ordinary waves of sound, or even down to a few inches. The detector in one form consists of a wire circuit, with a minute spark-gap in it. When placed in a field across which waves are travelling, whose period is the same as that of the free electric oscillations of the circuit itself, the latter acts as a resonator, and reveals the presence of the waves by sparking. It was found by Hertz, that such a resonator was excited at equidistant positions in front of the vibrator, corresponding to half a wavelength; and that the circumstances corresponded in all respects to the mode of propagation of the transverse electric waves of Maxwell's theory. It is now pretty certain, that the radiation from the vibrator contains a wide spectrum of wave-lengths. The vibrator being worked by a rapid torrent of sparks from an induction coil, each spark sets up an electric vibration swaying in it, which is very rapidly damped by radiation, even in a very few swings. The succession of sparks thus sends out a succession of disturbances, which have no single definite period, but are capable of being decomposed in Fourier's manner into a whole spectrum of simple waves travelling out into the medium. Of these the resonator takes up the appropriate one, and reinforces it; thus the observed wave-length corresponds to the period of the resonator, and is in fact different for different resonators. This mode of explanation appears to require, that when an electric vibration is started in a resonator, it persists sensibly over the period between two successive sparks of the primary; and therefore that the resonator should present a small surface for radiation.

At any rate, Hertz's experiments have firmly established that electric radiation does exist; and that its properties are exactly on the lines indicated by the appropriate a priori electric theories.

1 Wied. Ann, vols. xxxI. to XXXVI.