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 between the ether and matter, which, like that exercised on a pendulum, here produces a double effect, changing, on the one hand, the duration of this oscillation, and, on the other, gradually damping it.  He further supposed that ponderable matter is acted on by elastic forces.  The theory of Helmholtz has the great advantage of representing, not only the phenomena of dispersion, but also, as M. Carvallo has pointed out, the laws of rotatory polarization, its dispersion and other phenomena, among them the dichroism of the rotatory media discovered by M. Cotton.