( 340 ) 
£<> = — 
4ftv c 
4v' + 
Substituting these values in (47), 
d 
where we have put 
^ 1 + ««• 
The new term to which our present approximation leads us, 
namely (1— i) £ 0 rf, is thus seen to be of the order of magnitude £„'/*, 
so that it will be allowable to neglect quantities of the order l'. 
Such are: first, the difference between the values of given by 
(37) and (46), and secondly, the change that would be brought about 
in our results if we took into account the difference between rj,S 
and rj 0 ,£ t . Moreover, we may neglect the products vfe, and in 
formula (14), and we may again use for the complex index of 
refraction the equation (22), substituting in it, on account of (24), 
(25) and (37), 
_ig r _±. r 
» _L A ,.* 0 ~ A ' 
V + «2-) = - 
A 4v 
Finally we deduce from (48) 
£ ==* — * £ o «*» ^ ± (1 — ») r d, 
from (14) 
COS -O’. 
and from (22) 
0*) = f*. 
>lqp-(l+9- 
i±-(l-l)£ 0 d 
The result is that in this special case, like in the general one, 
there are two distinct principal beams, with different characteristic 
ellipses, both deviating somewhat from the straight line OL mentioned 
at the end of § 7. Between the two there is a slight difference, both 
in velocity of propagation and in index of absorption. 
The regions of the longitudinal and the transverse ZEEMAN-effeet 
are thus found not. to be sharply separated from each other, as we 
concluded in § 10, but to overlap to a certain extent. This shows 
that, strictly speaking, the consideration of additional terms of the 
order £,*/* is necessary, not only in the case & = but also for 
other directions of propagation lying within a small angle on both 
sides of the direction determined by the angle . 
