430 Dr. H. Stanley Allen on Optical Rotation, 



circularly polarized waves travelling through the medium 

 with different velocities, according as the rotation is right- 

 handed or left-handed, and in consequence the plane of 

 polarization will rotate uniformly about the direction of 

 propagation of the light, the amount of the rotation per 

 unit length being 



8=2*ry/X», 



where \ is the wave-length of the light (in vacuum), 



and f-t-P* 



1 



(?)' 



Here N denotes the number of electrons of the type con- 

 sidered; in unit volume, r is 1J2it times the period of 

 vibration of the light, and ta is 1/2tt times the natural free 

 period of the electron. 



It is not claimed that the foregoing discussion gives a 

 complete account of the behaviour of ring-electrons under 

 the influence of light-waves. There are other actions which 

 may be briefly referred to. In connexion with the magnetic 

 rotation of the plane of polarization, Drude has given a theory 

 based on the hypothesis of molecular currents, as conceived 

 by Ampere and Weber. It is assumed that these molecular 

 currents are made parallel to one another by the action of 

 the external field. Drude points out that the displacement 

 of the molecular current when a light-wave falls upon it, 

 produces a displacement of the magnetic lines of force which 

 arise from it, so that a peculiar induction effect takes place. 

 It is to be observed that this theory calls for rotations of 

 opposite sign on opposite sides of an absorption band. It 

 would seem that a complete theory of the action of light- 

 waves on an assemblage of ring-electrons would have to take 

 into consideration also the " Hall effect," which has been 

 found to yield a satisfactory explanation of rotatory disper- 

 sion in a magnetic field. Thus the hypothesis of the Hall 

 effect explains the result that the rotation is in the same 

 direction on opposite sides of the absorption band in the case 

 of sodium vapour, and also predicts an effect when the rays 

 of light are perpendicular to the lines of magnetic force. 

 I have discussed elsewhere* the possibility of accounting for 

 the Zeeman effect by means of the ring- electron. 



* H. S. Allen, Proc. Phys. Soc. Lond. vol. xxxi. p. 49 (1919). 



