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.