Recent Progress in Theoretical Physics. 247 



tion possible for the magnetic rotation of the plane of polarized 

 light is that, in magnetization there must be molecular electrical 

 currents, and that the components of these currents can be dynam- 

 ically compounded with the angular velocity acquired by an ele- 

 ment of the medium, during the passage through it of a ray of 

 circularly-polarized light. 



47rC • i^ 



On making in formula (2), m = and neglecting ^rzCy ■ 



vp^ vpX, 



because it is very small, being essentially the amount of the rota- 

 tion of the plane of polarization after passing through a thickness 

 of the medium only equal to half a wave length of the light em- 

 ployed, we have formula (1), 



Before showing the manner in which formula (2) is derived by 

 Maxwell, from Thompson's explanation of the magnetic rotation 

 of the plane of polarized light, it may be best to recall one or two 

 elementary propositions relating to polarized light, and also to 

 circular motion. In the first place, experiment shows that two 

 rays of light circularly polarized in opposite directions, and 

 of the same intensity, become, when united, a plane polarized 

 ray, the plane of polarization of which will depend upon whether 

 the periods of the component circular vibrations are the same or 

 not. If, from any cause, the phase of one of the circularly-polar- 

 ized rays is accelerated, then the plane of polarization of the re- 

 sultant ray, is turned round through an angle equal to half the 

 angle of acceleration of the phase. 



So also in certain cases, such as reflection from metallic sur- 

 faces, or total reflection in glass at certain angles, as in Fresnel's 

 rhombs, or in the passage of light through thin laminas of double 

 refracting crj^stals, as in quarter-wave laminne of mica, two plane 

 vibrations may give rise to one circular one, right handed or left- 

 handed, according as one or the other plane component is ad- 

 vanced in phase by a quarter of a complete oscillation. 



This is only what might be expected from the well-known 

 theorem in pure motion, that " two uniform circular vibrations of 

 the same amplitude, having the same periodic time and in the 

 same plane, but revolving in opposite directions, are equivalent, 



