of the ether, and imagined the molecules to be attached to the
ether surrounding them, but free to vibrate about their mean positions
within a limited range. Thus the ether within the dispersive medium is
loaded with molecules which are forced to perform oscillations of the
same period as that of the transmitted wave. It can be shown
mathematically that the velocity of propagation will be greatly
increased if the frequency of the light-wave is slightly greater, and
greatly diminished if it is slightly less than the natural frequency
of the molecules; also that these effects become less and less marked
as the difference in the two frequencies increases. This is exactly in
accordance with the observed facts in the case of substances showing
anomalous dispersion. Sellmeier's theory did not take account of
absorption, and cannot be applied to calculate the dispersion within a
broad absorption band. H. von Helmholtz, working on a similar
hypothesis, but with a frictional term introduced into his equations,
obtained formulae which are applicable to cases of absorption. A
modified form of Helmholtz's equation, due to E. Ketteler and known as
the Ketteler-Helmholtz formula, has been much used in calculating
dispersion, and expresses the facts with remarkable accuracy. P. Drude
has obtained a similar formula based on the electromagnetic theory,
thus placing the theory of dispersion on a much more satisfactory
basis. The fundamental assumption is that the medium contains
positively and negatively charged ions or electrons which are acted on
by the periodic electric forces which occur in wave propagation on
Maxwell's theory. The equations finally arrived at are
____
\ D[lambda]^2([lambda]^2 - [lambda]_m^2)
n^2(1 - [kappa]^2) = 1 + > ------------------------------------------,
/___ ([lambda^2 - [lambda]_m^2) + g^2[lmabda]^2
____
\ Dg[lambda]^3
2n^2[kappa]^2 = > -------------------------------------------,
/___ ([lambda]^2 - [lambda]_m^2) + g^2[lmabda]^2

where [lambda] is the wave-length in free ether of light whose
refractive index is n, and [lambda]_m the wave-length of light of the
same period as the electron, [kappa] is a coefficient of absorption,
and D and g are constan