where v has a value proportional to the strength of the field. More¬ 
over, if the relation (15) is supposed also to hold for the group a, 
we may put 
J x 2+) _ J x 2~) (*i) 
= «n 0 , B = 2 an 0 , 
with a positive constant «, so that we find 
2 (n-nj-ig 
C -k+ = i — 2(n—n i+ )-uj ’ 
— i s _ a __ 
2(n—ri2-)—uf ’ 
By this the values of S v 5, R, rj and-? have likewise become known. 
It is easily seen that 1 -+■ « = ft 0 *, when p 0 is the real index of refraction 
that would be found for n = n 0 if the particles were not put in motion 
in the modes of the group a, but only in those of the groups 
If, finally, we put 
« = P » 
MI ___ * 2 (n-nj+ig 
2 (n-nj-ig + . 
«»+ = , M8 _ = a 2 < K ~’ 12 il - . ' • • < 18 > 
4(n—n 2 +) +0 4 (h —w 2 _)+.'7 
we get 
n= ^+\- 2u ; .(19) 
1 — (M2+ + W2-) 
g- W2 — M2 + .(20) 
1—(M2++M2-) ’ 
and, after having calculated § by means of (12), 
(it)’ = (IS {1 - (« 24 - + «,_) \(l + i) .... (21) 
In the large majority of cases the absorption, even at the place 
in the spectrum where it is strongest, is very feeble along a distance 
of a wave-length. Consequently, the quantities u are very much 
smaller than 1. Equations (19) and (20) show that % £ are very 
small, and by (12) § is so likewise, so that (19), (20) and (21) may 
be written l ) 
r\ = m 2 + + « 2- — 2 Mj, 
£ ±= U2— — tt 2 + , 
&*) = ('. |i—5>2+ + “«-) + i|j. . ■ • ( 22 ) 
J ) Many of Voigt’s equations are free from these approximations. See also § 11 below. 
