in
the same substance. The index of refraction varies with the duration
of the period, or, if you will, with the length of wave _in vacuo_
which is proportioned to this duration, since _in vacuo_ the speed of
propagation is entirely the same for all vibrations.

Cauchy was the first to propose a theory on which other attempts have
been modelled; for example, the very interesting and simple one of
Briot. This last-named supposed that the luminous vibration could not
perceptibly drag with it the molecular material of the medium across
which it is propagated, but that matter, nevertheless, reacts on the
ether with an intensity proportional to the elongation, in such a
manner as tends to bring it back to its position of equilibrium. With
this simple hypothesis we can fairly well interpret the phenomena of
the dispersion of light in the case of transparent substances; but far
from well, as M. Carvallo has noted in some extremely careful
experiments, the dispersion of the infra-red spectrum, and not at all
the peculiarities presented by absorbent substances.

M. Boussinesq arrives at almost similar results, by attributing
dispersion, on the other hand, to the partial dragging along of
ponderable matter and to its action on the ether. By combining, in a
measure, as was subsequently done by M. Boussinesq, the two
hypotheses, formulas can be established far better in accord with all
the known facts.

These facts are somewhat complex. It was at first thought that the
index always varied in inverse ratio to the wave-length, but numerous
substances have been discovered which present the phenomenon of
abnormal dispersion--that is to say, substances in which certain
radiations are propagated, on the contrary, the more quickly the
shorter their period. This is the case with gases themselves, as
demonstrated, for example, by a very elegant experiment of M.
Becquerel on the dispersion of the vapour of sodium. Moreover, it may
happen that yet more complications may be met with, as no substance is
transparent for the whole extent of the spectrum. In the case of
certain radiations the speed of propagation becomes nil, and the index
shows sometimes a maximum and sometimes a minimum. All those phenomena
are in close relation with those of absorption.

It is, perhaps, the formula proposed by Helmholtz which best accounts
for all these peculiarities. Helmholtz came to establish this formula
by supposing that there is a kind of friction be