1879.] 



of the Reflection and Refraction of Light. 



237 



lished in vol. xxi of the " Transactions of the Royal Irish Academv." 

 Following a slightly different line from his, I obtain, by a quaternion 

 and accompanying Cartesian analysis,, the same results as to wave 

 propagation, reflection, and refraction, as those obtained by M'Cullagh, 

 and which he developed into the beautiful theorem of the polar plane. 

 Of course, the resulting laws of wave propagation agree with those 

 obtained by Professor Maxwell from the same equations by a somewhat 

 different method. For isotropic media, the ordinary laws of reflection 

 and refraction are obtained, and the well-known expressions for the 

 amplitudes of the reflected and refracted rays. 



In the second part of the paper I consider the case of reflection at 

 the surface of a magnetised medium, adopting the expressions Pro- 

 fessor J. Clerk Maxwell has assumed in " Electricity and Magnetism," 

 vol. ii, Part IV, § 824, to express the kinetic energy of such a medium. 

 From this, following the same line as before, I have deduced the fol- 

 lowing equations to represent the superficial conditions : In them, 

 £ rj, have the same meaning as before, and the axes are x in the 

 intersections of the plane of incidence and the surface, y in the sur- 

 face, and z normal to it ; a, {3, 7, are the components of the strength of 



the vortex that Professor Maxwell assumes, and —z=za— + j3— - + 7— 



dh dx dy dz 1 



which, with these axes, reduces to a— +7^-; K and K x are the elec- 



dx dz 



trostatic inductive capacities of the two media in contact, and the 

 quantities referring to one of these which is supposed to be non- 

 magnetic are distinguished by the suffix 1; C is a constant, on which 

 the power of the medium to rotate the plane of polarisation of light 

 depends. 



dzi dxi ~K\dz dx) I dzdt dhdt J 



dzi K dz L dt\dz dx) dhdt J 



As these are unchanged by a simultaneous alteration of the signs of: 

 7] 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 polarised ray as composed of two oppositely circularly 

 polarised rays, each of which is reflected according to its own laws. 

 From these I further deduce that, when the magnetisation of the 

 medium is all in the direction of ^, there is no effect on reflection or 

 refraction produced by it. I consider next the cases of the magneti- 

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

 plane of incidence, and obtain the following result : When the inci- 

 dent ray is plane polarised, and the plane of polarisation is either in or 



