( 335 ) 
Taking the real parts of these expressions, namely 
£V = a cos (n t + p db to) , = a cos {nt + p), ^ 
we may conclude that both principal beams are elliptically polarized, 
with the same characteristic ellipse, one of whose axes has the 
direction of the line OL mentioned above. The difference between 
the two beams lies merely in this, that the characteristic ellipses are 
described in opposite directions. In order to see this, we have only 
to observe that, if x is the angle between © and OX', 
_ cosjnt + p) 
' -cos{nt+p±a>y 
cos 2 x dt cos* {nt + p db to) 
In the beam to which the upper signs refer, the direction of the 
motion corresponds to that of propagation. For this reason we shall 
distinguish all quantities relating to it by the index + an ^ ^ ose 
which relate to the other beam by the index —. 
We need hardly add that the characteristic ellipse coincides with 
the straight line OL when # = # x , and that it becomes a circle 
when # = 0. 
We can further deduce from (43), (36) and (22) 
_ / 2 p»co$& . \ 
“ V 41?*+/ Sm 40 ) ’ 
showing that, for n~n 0 and for any direction between & = and 
^ = 0, the two principal beams are equally absorbed, just like the 
two circularly polarized beams in the extreme case # = 0. The 
common index of absorption, for which we shall henceforth write 
h, diminishes as d increases; for £ = (co = 0) it takes the value 
(42), and for # = 0 (co = the value (26;. How far these extreme 
values are different, depends on the relative magnitude of v and g. 
$ 9. The difference between the velocities with which a left-handed 
and a right-handed circularly polarized beam travel along the lines 
of force, leads to the well known rotation of the plane of polarization. 
On account of the unequality of the velocities of propagation deter¬ 
mined bv (44), there is a similar rotation in the interval from # = 0 
to ft = +, w ith some difference in the details, however, owing to 
23* 
