MAGNETISM AND LIGHT 329 



and at first sight it appears somewhat artificial. But it appears 

 more natural if we assume, as we surely must, that there is some 

 sort of motion round the lines of force in a magnetic field. Then 

 a resolution into circular motion would seem to be appropriate. 



An electron theory of the rotation. We have now to 

 .show that if we suppose that in a circularly polarised ray the 

 electrons are whirled round with the frequency of the waves (i.e. a 

 number of times per second equal to the number of waves passing a 

 point per second), then the velocity will be different for the t\vo 

 directions of whirling if a magnetic field exists parallel to the path 

 of the ray. 



According to Sellmciers mechanical theory, the velocity of a 

 train of light waves in a medium depends on the nearness of the 

 wave frequency to the natural frequencies of vibration of the 

 molecular or atomic systems constituting the medium. By 

 the natural frequencies we mean those of the different types of 

 motion of each system if it is disturbed and then left to vibrate 

 without auv external action. 



I jet N 1? N 2 , c., be the natural periods of the constituents of 

 the medium. The velocity v of a train of waves of frequency n 

 is given bv 



where K, /3,,/3 2 , &c., are constants for the medium.* 



For simplicity we shall suppose that there is only one mode of 

 natural vibration N, and that this takes place under an acceleration 

 towards a centre at distance d equal to io 2 d or 4<7r 2 N 2 d. The 

 velocity of a train of waves is given in this case by 



\Ylicn n N, the formula makes v 0. The physical inter- 

 pretation is that there is at this value "resonance," and the waves 

 spend their energy in setting the constituent systems of the 

 medium into 'vibration so that they are absorbed and not trans- 

 mitted. There will be absorption too, in a real system, for some 

 little range on each side of n = N. As we rise from n = 0, i.e. 

 from waves of infinite length towards n = N, l/r> 2 , which is pro- 

 portional to jUL 2 where JUL is the refractive index, gradually increases 

 and becomes great as n nears N. When n has just passed N, l/v 2 

 i> at first negative or /m is unreal. But when l/v 2 becomes positive 

 and IUL re.il it increases as n increases. There is, however, a limit K 

 towards which it tends as n goes on increasing. 



* Sue Schnst.-r's Theory of Optics for an account of the theory of dispersion and 

 of majrni'to-optirs. Voitft, who has very largely contributed to the theory, is the 

 author of a work on M>ii/net<>- and Elclrtro-optilt, Teubner, 1908. 



