Intelligence and Miscellaneous Articles, 217 



why the results should apply at least approximately to conductors. 

 In the first part of the paper the media are not assumed to be iso- 

 tropic as regards electrostatic inductive capacity ; so that the results 

 are generally applicable to reflection and refraction at the surfaces 

 of crystals. I use the expression given by Professor J. Clerk Max- 

 well in his ' Electricity and Magnetism/ vol. ii. part 4, chap. 11, for 

 the electrostatic and electrokinetic energy of such media. By assu- 

 ming three quantities £, ?7, and £, such that, t representing time, 



_, —, and — are the components of the magnetic force at any 

 dt dV dt l & J 



point, I have thrown these expressions for the electrostatic and 

 electrokinetic energy of a medium into the same forms as M'Cullagh 

 assumed to represent the potential and kinetic energy of the scther, 

 in " An Essay towards a Dynamical Theory of Crystalline Reflection 

 and Refraction," published in vol. xxi. of the Transactions of the 

 Royal Irish Academy. Following a slightly different line from his, 

 I obtain by a quaternion and accompanjdng 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. 

 Eor 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 magnetized medium, adopting the expressions 

 Professor J. Clerk Maxwell has assumed in ' Electricity and Mag- 

 netism,' vol. ii. part 4, § 824, to express the kinetic energy of such 

 a medium. From this, following the same line as before, I have 

 deduced the following equations to represent the superficial condi- 

 tions. 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 surface, and z normal to it ; a, /5, y are the com- 

 ponents of the strength of the vortex that Professor Maxwell 

 assumes, and 



d __ d a d d 



dh dec dy dz 



which, with these axes, reduces to 



a— + — • 



doo dz ' 



K and K x are the electrostatic 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 ; C is 

 a constant, on which the power of the medium to rotate the plane 

 of polarization of light depends. 



