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: the same 
and position as the characteristic ellipse, and described 
dir A s tl0 ( l 2) gives two values of |, there are two principal beams, 
differing from each other by their states of polarization, their velocities 
of propagation and their indices of absorption. All these details depend 
on the angle 9 and in general on the value chosen for the frequency ». 
4 4 The magnetic components belonging to one of the members 
of a definite group «, b, or c etc. lie within a narrow strip of the 
spectrum which we shall likewise denote by the letter a, b, or c 
ete We shall confine ourselves to the propagation of light belonging 
pne of these parts, say to a, and we shall assume that the 
distances of this part from the parts b, c etc. are very great in 
comparison both with the breadth of a and with that of b, c . 
On this assumption the part 
"* ( n +^)) ("-nWj-iny 
of (1), which relates to the group b for instance, may be simplified 
by writing n 0a instead of n, n 0 b for each and 
for each denominator. The result 
The quantities Q 2 +, may be treated in the same way and 
d .. what we have done with b. 
we can repeat for the groups 
If we assume that for each group ■*) 
2 J300 == -S £(*) + = 2 2 
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the parts contributed by the groups b, c,.. taken together, to the 
quantities Q„ Q a+ , may be represented by s, i J s, where s 
is a real quantity, constant through the region a. As for the paits 
due to the group a, in these we may replace every denominator by 
2n„(n — *«) — *».P- 
understanding by «„ the value n„„. We shall simplify still further by 
assuming that the group « is a magnetic triplet, so that >t comprises 
but one mode of vibration *i, one mode *2+ and one in¬ 
frequencies of the free vibrations in these modes are 
n 2 + = '». + *, • 
See § 51 of the Article in the Math. Encjkl. cited above. 
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