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.
In the establishment of these theories, the language of ordinary optics has always been employed. The phenomena are looked upon as due to mechanical deformations or to movements governed by certain forces. The electromagnetic theory leads, as we have seen, to the employment of other images. M.H. Poincaré, and, after him, Helmholtz, have both proposed electromagnetic theories of dispersion. On examining things closely, it will be found that there are not, in truth, in the two ways of regarding the problem, two equivalent translations of exterior reality. The electrical theory gives us to understand, much better than the mechanical one, that in vacuo the dispersion ought to be strictly null, and this absence of dispersion appears to be confirmed with extraordinary precision by astronomical observations. Thus the observation, often repeated, and at different times of year, proves that in the case of the star Algol, the light of which takes at least four years to reach us, no sensible difference in coloration accompanies the changes in brilliancy.
§ 2. THE THEORY OF LORENTZ
Purely mechanical considerations have therefore failed to give an entirely satisfactory interpretation of the phenomena in which even the simplest relations between matter and the ether appear. They would, evidently, be still more insufficient if used to explain certain effects produced on matter by light, which could not, without grave difficulties, be attributed to movement; for instance, the phenomena of electrification under the influence of certain radiations, or, again, chemical reactions such as photographic impressions.
The problem had to be approached by another road. The electromagnetic theory was a step in advance, but it comes to a standstill, so to speak, at the moment when the ether penetrates into matter. If we wish to go deeper into the inwardness of the phenomena, we must follow, for example, Professor Lorentz or Dr Larmor, and look with them for a mode of representation which appears, besides, to be a natural consequence of the fundamental ideas forming the basis of Hertz's experiments.
The moment we look upon a wave in the ether as an electromagnetic wave, a molecule which emits light ought to be considered as a kind of excitant. We are thus led to suppose that in each radiating molecule there are one or several electrified particles, animated with a to-and-fro movement round their positions of equilibrium, and these particles are certainly identical with those electrons the existence of which we have already admitted for so many other reasons.
In the simplest theory, we will imagine an electron which may be displaced from its position of equilibrium in all directions, and is, in this displacement, submitted to attractions which communicate to it a vibration like a pendulum. These movements are equivalent to tiny currents, and the mobile electron, when animated with a considerable velocity, must be sensitive to the action of the magnet which modifies the form of the trajectory and the value of the period. This almost direct consequence was perceived by Lorentz, and it led him to the new idea that radiations emitted by a body ought to be modified by the action of a strong electromagnet.
An experiment enabled this prevision to be verified. It was made, as is well known, as early as 1896 by Zeeman; and the discovery produced a legitimate sensation. When a flame is subjected to the action of a magnetic field, a brilliant line is decomposed in conditions more or less complex which an attentive study, however, allows us to define. According to whether the observation is made in a plane normal to the magnetic field or in the same direction, the line transforms itself into a triplet or doublet, and the new lines are polarized rectilinearly or circularly.
These are the precise phenomena which the calculation foretells: the analysis of the modifications undergone by the light supplies, moreover, valuable information on the electron itself. From the direction of the circular vibrations of the greatest frequency we can determine the sign of the electric charge in motion and we find it to be negative. But, further than this, from the variation of the period we can calculate the relation of the force acting on the electron to its material mass, and, in addition, the relation of the charge to the mass. We then find for this relation precisely that value which we have already met with so many times. Such a coincidence cannot be fortuitous, and we have the right to believe that the electron revealed by the luminous wave which emanates from it, is really the same as the one made known to us by the study of the cathode rays and of the radioactive substances.