In the first case, i.e. when the angle between the ray and the 
lines of force is not too small, the ratio (35) is real, namely 
^ = .(38) 
The vibrations of the two principal beams will therefore be 
rectilinear, the angles X z and Xjjr which they make with the axis 
OX', and which we shall reckon positive in the direction from OX' 
towards OT, being given by 
sin 2Y,!=isin2Xu = - .( 39 ) 
9 
Both angles lie between 0 and i n, and the smaller of the two, 
which we shall call Xj, corresponds to the under sign in (38), so 
that we may write 
Equation (36) shows that § has now an imaginary value for both 
principal beams, and, since the same is true of u%+ -l - u 2 —> we see 
from (22) and (7) that the two beams have the same real index 
of refraction fi 0 (and therefore the same velocity of propagation), but 
different indices of absorption, namely 
! (2+ *'?’- 
(40) 
^ = ' • <41) 
It appears from this that the absorption is strongest for the beam 
whose vibrations make the smaller angle with the lines of force. 
This might have been expected on the ground of the elementary 
theory of the ZEEMAN-effect. _ _____ „ 
The difference between the expressions q + Vq *—1 and q \/q*—\ 
which occur in hj; and h n increases as q becomes greater. Now, 
if for a fixed value of —, the angle # is made to approach the limit 
4*, (34) shows that q increases indefinitely. When it has become 
very great, we may replace q + Vf —1 by 2 q, and since q cos & 
tends towards the value — , as may be seen from (34), we have at 
, 9 
the limit 
hj _ n o 
Proceedings Royal Acad. Amsterdam. Vol. XII. 
