218 Intelligence and Miscellaneous Articles. 



^ c^ L K \dz dxj x [ dz dt 



dz x K dz ^ l \ r dt\dz dxy dhdt] 



As these are unchanged by a simultaneous alteration of the signs 

 of rj and C, I show that the method adopted in my former paper on 

 Magnetic Reflection, in the 'Proceedings of the Royal Society' for 

 1876, No. 176, is justified, and that it is legitimate to consider an 

 incident plane-polarized ray as composed of two oppositely circu- 

 larly polarized rays, each of which is reflected according to its own 

 laws. From these I further deduce that, when the magnetization 

 of the medium is all in the direction of /?, there is no effect on reflec- 

 tion or refraction produced by it. I consider next the cases of the 

 magnetization being all normal to the surface, and all in the surface 

 and the plane of incidence, and obtain the following result : — When 

 the incident ray is plane polarized, and the plane of polarization is 

 either in or perpendicular to the plane of incidence, the effect of 

 magnetization is to introduce a component into the reflected ray 

 perpendicular to the original plane of polarization, whose ampli- 

 tude, c, is given in the several cases by the following equations, in 

 which i is the angle of incidence, and r of reflection, and k a small 

 constant depending principally on C and the intensity of the inci- 

 dent ray 1. When the magnetization is normal to the reflecting 

 surface. If the incident ray be polarized in the plane of incidence, 

 _ 7 (1 + cos 2 r) sin 2 i sin 2i\ 



C — A?. -J ; ; • 



sin r . sin 2 (i-\-r) . cos (i—r) 

 If it be polarized in a plane perpendicular to the plane of incidence, 



, cos 2 r . sin 2 i sin 2? 

 c — fa m 



sin r . sin 2 (i + r) . cos (i — r)' 

 2. When the magnetization is parallel to the intersection of the 

 surface and the plane of incidence, and the plane of polarization of 

 the incident ray is either in or perpendicular to the plane of inci- 

 dence, 



7 cos r sin 2 i sin 2i 

 sm 2 (i + r) cos (i — r) 



This vanishes at the grazing and normal incidences, and, in the case 

 of iron, attains a maximum at about the angle of incidence i= 63° 20'. 

 I do not obtain any change of phase by reflection in any case ; 

 and this was to be expected, as this change of phase probably depends 

 on the nature of the change from one medium to another, which, 

 following M'Cullagh, I have uniformly assumed to be abrupt. 

 Apart from this question of change of phase, my results conform 

 completely to Mr. Kerr's beautiful experiments on the reflection 

 of light from the pole of a magnet, as published in the Philoso- 

 phical Magazine for May 1877 and March 1878. — Proceedings of 

 the Roycd Society, January 9, 1879. 



