where 
( 9 ) 
w=y e ^- 
m 
h 2 
n 0 2 — ri l -f- 2 km 
[cf. (4) and (5), § 1.]. Eliminating H x and H y between (7) and (8) 
we easily find 
(10) b 2 c 2 = 1 -|- S7vnb^-\- 4:Jin 2 b 2 %0. 
§ 4. It will be convenient first to consider the solution of equa¬ 
tion (10) in Art. 3 on the assumption that the term containing the 
quantity can be neglected. Later on, we shall return to the 
discussion of the exact solution. 
Let us assume that 
(1) be = v — lk ; 
from the expression (3), § 3, it appears*) that the quantity k re¬ 
presents the «coefficient of extinction» of the substance and that v 
may be called its «refractive index». 
Writing 
( 2 ) ® 1 -|- 
( 3 ) = 
v C 
and substituting (1), (2) and (3) in (10). § 3, we obtain 
(4) V 2 - K 2 + (£v + @ 
( 5 ) 2vk + + (Bk = oJ3. 
We shall write v 1 and k x when dealing with the right-handed cir¬ 
cularly polarized wave and v 2: k 2 when dealing with the left-handed 
circularly polarized wave. These quantities satisfy two pairs of 
equations which can be written down from (4) and (5). Eliminating 
between them the quantities ® and <a 18 we obtain two equations 
which after a little transformation take the form 
(6) {(*>! — *>,) — <2) (n +^ 2 ) + {© —(% — x % )} (x 1 + %) = 0 
(7) {© — (*! — >t 2 )} (*>, + v t ) — '{(*»! — v t ) — S) (*! + x s ) — 0. 
0 See Bulletin Int. de VAcad. d. Sc. de Gracovie, Cl. d. Sc. Mat. et Nat. 
for 1907, page 318. 
