765 
been made. Indeed, besides the treatment in Drude's well known 
Optics 1 ), little work seems to have been done in connection with 
the theoretical study of these phenomena. 
Our discussion must from its nature depend on a general Theory 
of Photogyric Media; the analysis below in its essential results will 
easily be recognized as a particular case of the Theory given long 
ago by M. J. B o u s s i n e s q 2 ) and translated by Drude into 
electromagnetic language. For the sake of clearness, however, we 
must sketch the matter from the beginning. 
§ 1. Let e be the electric charge of an electron belonging to 
a definite class or category and let N represent the number of 
electrons of that class, per unit volume of the medium. Writing 
§, % f for the components of the displacement l of the electron, 
reckoned from its position of equilibrium, we have for the compo¬ 
nents of the electric polarization: 
P x = 2eÇN P y = 2er]N P z = 2eÇN-, (1) 
the summation is here extended to unit volume and has to include 
all classes of electrons present. 
Let us write down the equations of motion of an electron vi¬ 
brating in a naturally-active molecule. Making no assumptions re¬ 
garding the ultimate structure of such a molecule, we simply sup¬ 
pose that the force imposed upon the electron from without is a 
linear function of the first spacial differential coefficients of the 
electric force E (E x , E y , E z ) as well as of that force itself. Confin¬ 
ing ourselves to the case of isotropic media, we can easily show 
that the component in the direction of the axis x of that external 
force cannot involve other differential coefficients than 9E'j9y and 
9E y /9z and that these must occur in the combination 9EJ9y— 9E y /9z s ). 
Thus the equations of motion of the electron are — 
| + 2*f+ *,■! = £ 
... ß 
rj2kri-\- n 0 2 rj = — 
(2 a) 
(2 b) 
4 ) Lehrbuch der Optik, zweite Auflage, p. 404. Leipzig 1906. 
2 ) Journal de Mathématiques pures et appliquées II Série, tome XIII, page 
313 et suiv. Paris 1868. 
3 ) Drude, Lehrbuch der Optik , p. 390—892. 
Bulletin III. 
2 
