454 The Theory of Aether and Electrons in the 



From the occurrence of the factor (KT - mw) in the denomi- 

 nator of the expression for the magneto-optic constant <r, 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* 

 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 sub- 

 stances. 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 



E = a P + /3P + 7 P ; 



the term in a represents the effect of the inertia of the electrons ; 

 the term in ]3 represents their ohmic drift ; and the term in y 

 represents the effect of the restitutive forces where these exist. 

 This equation is to be combined with the customary electro- 

 magnetic equations 



curl H = E/c 2 + 47rP, - curl E = H. 



In discussing the propagation of light through the metal, we 

 may for convenience suppose that the beam is plane-polarized 



* The phenomenon was first observed by D. Macaluso and 0. M. Corbino,. 

 Comptes Rendus, cxxvii (1898), p. 548, Rend. Lincei (5) vii (2) (1898), p. 293. The 

 theoretical explanation was supplied by AV. Voigt, Gott. Nach., 1898, p. 349, 

 Ann. d. Phys. Ixvii (1899), p. 345. Cf. also P. Zeeman, Proc. Amst. Acad. 

 v (1902), p. 41, and J. J. Hallo, Arch. N6erl. (2) x (1905), p. 148. 



Voigt also predicted that if plane-polarized light, of period nearly tbe 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 propa- 

 gation 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, Gott. Nach., 1898, 

 p. 355: Ann. d. Phys. Ixvii. (1899), p. 345. Cf. also A. Cotton, Cornpte* 

 Rendus, cxxviii (1899), p. 294, and J. Geest, Arch. Neerl. (2), x (1905), p. 291. 



