133 
§ 3. We now proceed to consider the effect which an extra¬ 
neous magnetic field impresses on a wave propagated through it. 
Suppose a uniform magnetic field, of strength the lines of force 
being parallel to the axis of z. The equations of motion of an elec¬ 
tron vibrating in a molecule x ) are now 
S|- 2 ki + ft ± (Si '+ - a P„) £ ^ XV (la) 
Ü + *'** + V 9 = + âPÿgç- A X é • (lb) 
We assume as a solution 
Writing for brevity 
n 0 2 — n 2 -2 km = R ; 
we obtain 
I = ( E * + <5 P.) + * S (E s + <3 P,)) (3a) 
V = Vo e 
( 1 ) 
- e - x n = 8; — = y ( 2 ) 
me me 
Let 
n = {R{E„ + ùP a ) - . S (K+ÙP,)}. 
_ yçyyceNR 
V ~ ^ i 
R 2 — S 2 
yyceNS 
(3b) 
(4) 
From (3) and (4) we deduce 
p. = (E. + a P x ) F+ * (E, + <9 P,) W (5a) 
P„ = {E y +&P y )V-i (E x + ü P x ) W. (5b) 
Consider a right-handed circularly polarized wave and a left- 
handed circularly polarized wave. By a well-known proposition 
Py = ± * Px i Ey — ± * Ex î (6) 
here, and in all cases below, the upper sign refers to the right- 
q See, in the Bulletin Int. de VAcad. d. Sc. de Cracovie, Cl. d. Sc. M. et 
Nat., for April 1907, p. 316, a paper on the Electromagnetic Theory of Dispersion 
and Extinction. 
