( 326 ) 
-^{K s ^ + >j)-^n s ^}^=^(l+ij)€> C o S ^ 1 * (U) 
from which we deduce by eliminating these components 
§ 2 (1 + V cos' *) - S fo - F> sin* & - £* (cos’ & + n ) -= 0 , . (12) 
or 
fg + n. (g - *&■ * + (£ # - £ 9 ) (1 + n) cos * * = 0. . (13) 
If the frequencies rc 0 , the frequencies nC*) (such as they are under 
the influence of the external magnetic field), the resistances g and 
the coefficients Bf*) are known, the quantities *S 1} S 2 , R and, by (10), 
ij and 5 will be wholly determined for any chosen value of the 
frequency n. After having calculated the value of I from equation 
(12), we can deduce from it, first, by means of (9), the complex 
index of refraction (p) and then, by means of (7), the real index of 
refraction p and the index of absorption h. 
Moreover, when g has been found, the equations (11) give the ratio 
between the components <£* and and also that between IV and 
which has the same value, because, on account of (8), 
The result is 
~ __ i »+ip , 14) 
£>*' * g(i + ij)«»# ’ ‘ ' ' * \ } 
it determines the state of polarization for any beam that can be 
propagated in the manner specified by (6), for arij r “principal beam”, 
as we shall say. 
Whereas the component <£ s > may very well be different from zero, 
the equations (8) show that £V = 0, as might have been expected 
beforehand. Hence, at every point of the system, the extremity of 
the vector I) describes an ellipse in a plane perpendicular to the 
direction of propagation. This line, which shows us the state of 
polarization of the principal beam, may be called its “characteristic 
ellipse ; equation (14) determines, not only its shape and position, 
but also the direction in which it is described. 
It must further be noticed that, on account of the relation (2), the 
• T) (F 
ratl ° ^ is equal to the ratios and the equality of which 
has already been mentioned. Hence, remembering that the components 
of ty are proportional to those of the displacement of the equivalent 
electron in a particle, one easily sees that, while a particle is made 
to vibrate in its different modes of motion (in the way determined 
by the sums in Q u Q 2 + and Q 2 _) the projection of the equivalent 
electron on the wave-front moves in an ellipse of the same form 
