1902.] of FresneVs Polarisation-vector. 43 



mined by the magnetic field, the propagational speeds o>i, w 2 of the 

 waves are given by 



= o- -1 + - o- (Ibi + mk 2 + nb 3 ) ~ — <r' + - cr (Ibi + m& 2 + nb s ) , 

 oo 2 = cr -1 - - cr (^i + m6 2 + W&s) T7 = ~ ~ °" (^1 + + W& 3 ) y~ • 



T Li T -Li 



Whence, approximately, 



cr -2 = co x 2 - — (Ibi + mb-2 + nb 3 ) ~ = co 2 2 + ^ (Z&i + w6 2 + nb B ) , 



cr' -2 = cox 2 - — (/Ji 4- m& 2 + mbs) = co 2 2 + ^ (Z&i + ?rti 2 + nb s ) ^- • 

 Proceeding as in the last case we have instead of (11), 



— — 27T — 



(an - co 2 ) a + a i2 /? + a u y = FZ - t— - (/^ + m& 2 + nb$) (my - 



(13), 



and two similar equations ; and applying the principle of interference 

 we obtain the equations 



(if, v, w) 



2 /_a d_ _9\ 12 _/i_ _3 JLVi A A 



8v ' divj \dx ' 8y ' dz/\dx ' du dy ' dv dz ' dw. 



I ^ + b ^ +b- ^ ^ ^ ^ ^ 



1 dx " dy dz I \ dy dz ' dz dx ' dx dy/ 



which may be written in the form 



D = - curl curlE + BVD. 



The interface being the plane x = 0, the boundary conditions are 

 the continuity of *r 2 j ^3, dti/dv + biw, d&jdw -biv, to which we may 

 add the continuity of u and wi - b 2 du/dy - b 3 du/dz, since within the 

 transition-layer div. D = 0, div. (i<r - BvD) = : the number of 

 independent conditions is, however, only four, as required for the 

 treatment of magneto-optic reflection and the Kerr effect, since 



dw% dw 



w ~ ai 



7 du j die d /3G 7 \ d /dil 7 • \ 

 wi - b-2 _ - h 5- = ( u hv ) - I + b lW ). 



oy cz cy \ow j cz \cv J 



