773 
M. Cotton. We now require to know how from the value of cp 
the quantity — % 2 , in the notation of §§ 4 and 5, can be eval¬ 
uated. We have first 
a l5 a 2 being the amplitudes of the two opposite circular vibrations 
and X the wave-length (in vacuo) to which n applies. Moreover, 
recalling formula (19) in Art. 1 of the paper «On the elliptic po¬ 
larization...» J ), we infer that 
exp - {+ x ( % — **) *} = = ( 45 ° — v) » ( 3 ) 
where we are to read — or -)- in the left-hand member according 
as the difference a l k 2 is positive or negative. 
§ 8. Combining (1), § 6, with (12), § 4, we find now 
Ip = 4:71 
n * 2 z 
l 2 * 
e 2 N 
m 
h(n 0 2 — n 2 ) 
( n 0 2 — n 2 ) 2 -j- 4 k 2 n 2 
or, what is equivalent, 
where 
D = ^l^N hz r = W' 
c 2 m tic 
(1) 
( 2 ) 
(3) 
It is interesting to note that the constant coefficient T has here 
the same value as the quantity denoted by the same symbol in 
§ 8 of the previous paper On the Electromagnetic Theory of Dis¬ 
persion and Extinction 2 ). 
Again, from (3), § 7 and (13), § 4, it follows 
-F logio tg (45° — <p)_ 2 DTX 
log l0 e (P-to'F + r*** { > 
where we are to read — or -f- in the left-hand member according 
as the constant h (or D) is positive or negative. 
9 Bulletin Int. for March 1908, page 132. 
2 ) Bulletin Int. for Avril 1907, page 323; cf. ibidem pp. 324—325. 
