ON THE ACTIOX OF MAGNETISM ON LIGHT. 351 



Since (hi, ho, h^) ave small we may employ in the terms containing them 

 the approximate values of (^, ?;, 4) which neglect the rotatory action, viz., 



which satisfy ^_ — eyM {I, v, 4)=0, and so obtain finally, for disturb- 

 ances of period 2ir/r, the equations 



d'^u „, , ^ '^ fi dh, , , dl , . dl\ 

 dF = '^'''^r^7u{'^d.-^\ly+^^dz} 



Thus for a wave travelling along the axis of z 



but the rotatory effect given by these equations, if sensible for waves of 

 moderate length, would be quite insensible for light- waves. 



On the other hand, if we add rotational terms of the type employed 

 by Maxwell we should have similarly 



d^u _ ^2 ,-, d'^v , d^w . d\ 



where the condition for transverse undulations determines X by the 

 equation 



so that 



dxdt\ ' dx^ 

 that is, 



dt^ 



dtl ^dz^dx dzj ^dy\dy dxj i 



d' A d-'E,, d^r, dH\ 

 V'dx^^^'dp-^^'dz^)' 



,.. = .V».«»-|(.,g.,|,..3£) 



Thus the equations arrived at in these two ways are not, as Drude 

 seems to hastily assume without examination, of the same type. 



It is however difficult to see why equations arrived at in this manner 

 are worthy of the detailed discussion and refutation to which Drude 

 subjects them : though it is to be said that they agree formally with the 

 equations of the earliest attempt to explain magnetic reflexion, that of 

 Lorentz based on the Hall effect. The form of the rotational terms in 

 the first of them Heaving out of account the character of the coefficient 

 ^^3/^^) is the same as the one to which we have been already guided as 

 the correct type, by various lines of argument ; and in fact the equations 

 adopted by Brude himself are obtained by adding on these terms, some- 

 what empirically, to the ordinary electro-magnetic equations of type 



dt^^\dy dz) 



-y 



