Mr Larmor, On the origin of magneto-optic rotation. 181 



On the origin of magneto-optic rotation. By Mr J. Larmor. 

 \Raad March 6.] 



It is known {Phil. Mag., Dec. 1897) that when in a material 

 molecule there exists an independently vibrating group of ions or 

 electrons, for all of which the ratio e/m of electric charge to 

 inertia is the same, then the influence of a magnetic field H on 

 the motions of this group is precisely the same as that of a rotation 

 with angular velocity w, equal to ^eH/mC' 2 , imposed on the group 

 around tbe axis of the field, on the hypothesis that the extraneous 

 forces acting on the ions are symmetrical with respect to this 

 axis. This result involves the main features of the Zeeman effect ; 

 it requires that the separations of the doublets representing the 

 spectral lines arising from such a grouj} must all be equal when 

 measured in difference of frequency, or be inversely as the square 

 of the wave-length in vacuum when measured in difference of 

 wave-length, a relation which Preston has recently found to obtain 

 for the natural series of lines in ordinary spectra. 



The object of this note is to point out that it is possible to 

 deduce the Faraday effect from the Zeeman effect by general 

 reasoning as regards any medium in which the optical dispersion 

 is mainly controlled by a series of absorption bands for which the 

 Zeeman effect obeys the above law, without its being necessary to 

 introduce any special dynamical hypothesis. For this law ensures 

 that the effect of the magnetic field on the periods of the corre- 

 sponding free vibrations of the molecules is the same as that of a 

 bodily rotation, say with angular velocity a>, round its axis : while 

 the complete circular polarizations of the Zeeman doublets, viewed 

 in the direction of the axis, shew that their states of vibration 

 are symmetrical with respect to that axis. Thus, 12 being the 

 angular velocity of the displacement vector in a train of circularly 

 polarized waves traversing the medium along the axis, the state of 

 synchronous vibration which it excites in the molecules will have 

 exactly the same formal relation to this train when the magnetic 

 field is off, as it would have to a train with the very slightly 

 different angular velocity Q ± &> when the magnetic field is on, 

 the sign being different, according as the train is right-handed or 

 left-handed. Now change of this angular velocity O means 

 change of period of the light : thus the propagation of a circularly 

 polarized wave-train, when the field is on, is identical with that of 

 the same wave-train when the period is altered by its being 

 carried round with angular velocity + &> and there is no influencing 

 magnetic field. 



