135 
Writing 
en= 1 — 2i5a-|-M s 
(IV) 
we obtain from (4) and (5) the two pairs of equations 
*2 1 = 4 ™^ a à (a* + ®2) j 
(Va) 
0 
2vu = 
die 
(Vb) 
We will write v ly x ly and 8fft x for the right-handed circu¬ 
larly polarized wave and v 2l u 2 . ^2 an( ^ ^4 f° r left-handed 
circularly polarized wave. These quantities are now subject to ma¬ 
thematical conditions identical in form with those satisfied by the 
v , jc, & and cVT of a medium free from extraneous magnetic 
force 1 ); so that many of the results proved in §§ 6. and 7. of the 
paper quoted above have also an application in our present case. 
For example, if we assume k = 0 for all classes of electrons pre¬ 
sent, we obtain Lorentz’ theorem modified into the type — 
v 2 — 1 
v*+~2 
-J TVSt 
with 
yceN 
— n 2 + y%n' 
( 6 ) 
From this it follows 
_ 4n (?q 2 ~j— 2) —j— 2 ) {ßl x — ^2) 
9 Oi + v*) 
( 7 ) 
If we suppose that v 1 and v 2 are but slightly different from unity, 
we get from (7) approximately 
Vl - V2 = -4 nc%n ^- —J 
y 2 eN 
{n o 2 — n i£ Y — 
Therefore the quantity, say defined by (see (5), § 1) 
&i = i~ 
Z% 
will be found to have the value 
31 = — 2 mi' 
! V 
y 2 eN 
Oc 
n l y 
y*Z n* 
(B) 
(9) 
( 10 ) 
0 Cf. Bulletin Int. for April 1907, p. 321 and 322. 
