Page:A history of the theories of aether and electricity. Whittacker E.T. (1910).pdf/474

From the occurrence of the factor (κ² – mn²) in the denomi. nator of the expression for the magneto-optic constant σ, it may be inferred that the magnetic rotation will be very large for light whose period is nearly the same as a free period of vibration of the electrons. A large rotation is in fact observed^[1] when plane-polarized light, whose frequency differs but little from the frequencies of the D-lines, is passed through sodium vapour in a direction parallel to the lines of magnetic force.

The optical properties of metals may be explained, according to the theory of electrons, by a slight extension of the analysis which applies to the propagation of light in transparent substances, It is, in fact, only necessary to suppose that some of the electrons in metals are free instead of being bound to the molecules: a supposition which may be embodied in the equations by assuming that an electric force E gives rise to a polarization P, where

$\mathbf {E} =\alpha \mathbf {\ddot {P}} +\beta \mathbf {\dot {P}} +\gamma \mathbf {P}$;

the term in α represents the effect of the inertia of the electrons; the term in β represents their ohmic drift; and the term in γ represents the effect of the restitutive forces where these exist. This equation is to be combined with the customary electromagnetic equations

${\text{curl }}\mathbf {H} =\mathbf {\dot {E}} /c^{2}+4\pi \mathbf {\dot {P}} ,\qquad -{\text{curl }}\mathbf {E} =\mathbf {\dot {H}}$.

In discussing the propagation of light through the metal, we may for convenience suppose that the beam is plane-polarized

1. The phenomenon was first observed by D. Macaluso and O. M. Corbino, Comptes Rendus, cxxvii (1898), p. 548, Rend. Lincei (5) vii (2) (1898), p. 293. The theoretical explanation was supplied by W. Voigt, Gött. Nach., 1898, p. 349, Ann. d. Phys. lxvii (1899), p. 345. Cf. also P. Zeeman, Proc. Amst, Acad. v (1902), p. 41, and J. J. Hallo, Arch. Néerl. (2) x (1905), p. 148.
   Voigt also predicted that if plane-polarized light, of period nearly the same as that of the D radiation, were passed through sodium vapour in a magnetic field, in a direction perpendicular to the lines of magnetic force, the velocity of propagution would be found to depend on the orientation of the plane of polarization, so that the sodium vapour would behave as a uniaxal crystal. This prediction was confirmed experimentally by Voigt and Wiechert: cf. Voigt, Gött. Nach., 1898, p. 355: Ann. d. Phys. lxvii. (1899), p. 345. Cf. also A. Cotton, Comptes Rendus, cxxviii (1899), p. 294, and J. Goest, Arch. Néerl. (2), x (1905), p. 291.