998 Mr. Gr. H. Livens on a Theory of the 



Now the equation (2) gives at once 



e y ' 



B,{l + «(l-9»)}-*^(l-9»)B r =0, 



E y {l + <l-^)}+i^(l-^)Ex=0, 

 which are equivalent to the two equations 



(E I+ iE y )[( ? 2 -l)( a -^2)-l]=0, 



(E I -iE y )[( 3 2 -l)(«+^-l]=0. 



These equations can be* satisfied in two ways: 



(1) Either by 



E x + iE y = Q and tf-l)L+&¥\-l=0, 



(2) or by 



E,-iE y = and (q 2 -l)L-^i\-l = 0. 



Now examine what this means : let q 1 and q 2 be the respec- 

 tive roots of the two cubics in (1) and (2), and consider the 

 propagation of a beam of light which starts with the electric 

 force polarized in the plane of the axis of y and with an 

 amplitude E 



E,=E^, E^=0. 



The medium splits this beam into two oppositely circularly 

 polarized beams, in the one of which 



E^IE^, E yi =-?E«?»< 



initially, and in the other 



E, 2 =iE,»", E ya =|E«K 



The first of these beams, in which E zl + £E yi = 0, is propagated 

 through the medium with a velocity equal to the real part 



