+ 



Now 



ON THE ACTION OF MAGNETISM ON LIGHT. 343 



j.n/' '^ —■ ^ \ fdu dv dw\ 

 \ ^ dz ' dyj \dx dy dz J 



r\ J { d d \ fdv_du\_f d _ d\ fdu_dw\ "1 



^XV'Tz ''dxJUx Ty) V'dx "'TyJ \dz dx)]' 



1 d d n r> ■'^^^ 



when w, -— , -=. are null, ir^ — k^ — ; 

 ax ay dz^ 



d d p d^iv 



"' dx' dz " 'W' 



" ' dy/' dz 



hence L-M=l, G=0. 



P=0; 



This expression for P,. with the correlative ones for P,, and P^ is the 

 most general form which the magnetic terms can assume in an isotropic 

 medium, independently of any condition of exact transversality of the 

 vibrations: transversality requires in addition that L and N shall be null. 



The equations of vibration of an elastic medium loaded with spinning 

 molecular gyrostats, whose axes follow the rotations of the elements 

 of the medium, have been formed, ' and it is of interest to observe that 

 the rotatory terms come under this special type for which L, N are null 

 as well as G. The reason is clear : the action of the gyrostats depends 

 solely on the rotations of the elements of the medium, while the terms 

 involving L and N have no rotational character. 



7. Before application of these magneto-optic terms to problems of 

 reflexion at a magnet, the type of the unmodified equations of propagation 

 of light, to which they are to be added, must first be settled. The form 

 of these equations which gives most satisfactory results for reflexion at 

 the interface separating transparent media is (equivalent partially to Lord 

 Kelvin's labile fether theory) expressed most simply both as to bodily 

 equations and as to boundary conditions by the principles of the electro- 

 magnetic theory of light ; and it has been shown that the introduction of 

 electric conducting quality into these equations gives a tolerable account 

 of the phenomena of metallic reflexion.^ It is therefore natural to add on 

 these rotatory terms to the equations of the electro-magnetic theory, and to 

 try to explain the phenomena of magnetic reflexion by their aid, with the 

 boundary conditions appropriate to that theory. This is what has been 

 done in all attempts that have had any success ; though there is room for 

 diversity in the electrical basis which has to be supplied for the rotational 

 terms. 



Dynamical Theories based on the Form of the Energy-function. 



8, The subject of magnetic rotation has been treated by G. F. Fifz- 

 Gerald^ from the point of view of an additional magneto-optic term in 

 the energy-function of the electro-magnetic medium. According to 



' J. Larmor, Proc. Lond. Math. Soc, xxii. 1891. 



^ Cf. J. J. Thomson, ' Eecent Advances in Electricity and Magnetism,' 1893, 

 §§ 352, seq. 



' G. F. FitzGerald, ' On the Electro-magnetic Theory of the Reflection and Re- 

 fraction of Light,' Phil. Trans., 1880. 



