agreeing with the value (28) which we have given for a ray perpen¬ 
dicular to the lines of force and having its vibrations along these 
lines. At the same time q — y'q'—l may be replaced by — , so that 
% 
hji approaches the limit (29). 
On the other hand, when # is made smaller and ultimately becomes 
equal to ^ (<2 = i), both hi and hu have the limiting value 
or, if (37) is taken into account, 
2v coa&.+ff 
4v s + g* 
• 02 ), 
h L- 2r g sm 2 4- g z 
cg 4r 8 -f- g* 
This lies between the values (28) and (29). 
As for the directions of the vibrations in the principal beams, 
these are determined by Xi = 0 and ~ .-r in the extreme cases 
4 
& = — n an d £ = # x . The former of these results was to be expected, 
and the latter shows that for # = & x both directions coincide with 
the line bisecting the angle X'OY. We shall denote this line by OX. 
$ 8. It appears from what precedes that for the state of 
things is wholly different from the one existing when & = 0, which 
is characterized by a circular polarization of the principal beams. 
The transition between these phenomena is formed by those which 
are observed when # <[ d- x . 
In this case q < 1, so that we may put 
9 
sin* & _ cosaj 
by which some of our formulae are simplified. The mode of vibration 
of the principal beams is determined by the relation 
==s e±*" w , 
(43) 
following from (35), and we may therefore say that if we have at 
some point of the system 
=r ae*\"*+P), 
with real a and p, the other component of the dielectric displacement 
will be given by 
2V = a#( nt +P± W ). 
