134 
handed circularly polarized wave and the lower sign to the left- 
handed circularly polarized wave. Hence equations (5) take the form 
m P^_P, J _ jr+jv _ 
{> K E a i-ü{V+Wy 
§ 4. To make further progress, let us go back to the Max- 
well-Lorentz fundamental field-equations. As in the paper quoted 
above x ) we leave out of account the conduction current and (in 
the notation of the paper alluded to) we assume: 
(1) E z =0 H z = 0 P z = 0. 
We also suppose that the components 
(?) K, E y , E x , H y , P x and P y 
all contain the factor 
(3) exp. *«{*— (^F)*}- 
The field equations are satisfied provided that 
(II) {v — iKY — l = 4n^ = 4n 1 ^-. 
Ejy 
We have a plane, transverse wave, propagated in the direction of 
the axis of 3 ; x may be called the coefficient of extinction and v 
corresponds to the refractive index in transparent bodies. 
Let us apply these results to the case, considered in § 3., of 
two opposite circular vibrations. Groing back to (7) of § 3., we have 
for the two waves the equations 
(4) 
( v — lx ) 2 — 
4jt(V+ W) 
1 ~ 1 - d)(F + W)' 
From (4) 
and (2), § 3., we deduce 
(5) 
f=f w=a—i& 
where 
(Ilia) 
^ yceN(n 0 2 — n 2 + y%ri) 
^ ( n o 2 — n2 + y %n) 2 -\- 4k 2 n 2 
(Illb) 
? ^ yceN . 2kn 
^ ( n o 2 — w 2 dt yx n Y~\~4 k 2 n 2 
q Cf. Bulletin Int. for April 1907, p. 317. 
