The theory of the refractive indices of gases is distinctly more advanced, because their emission spectra can be studied without the radical change of state that would be necessary for solids. In the case of metallic vapours, such as sodium, the theory may be considered complete, though its practical verification is somewhat difficult. The spectrum of helium is known, and the measurement of its refraction has led to an interesting result. The lines of all atomic spectra fall into series which converge towards a finite limit Xh, but beyond this limit there is a region in which there is emission over a continuous range of wave lengths. Corresponding to this it is found that the refraction of helium requires an expression In the case of the ordinary permanent diatomic gases the spec trum is not so well-known, for an electric discharge is required in order that the gas should be luminous, and this breaks the molecules into atoms. Even without this knowledge, however, one feature can be predicted for a molecule composed of two identical atoms; the atomic vibrations which are of infra-red frequency will have no optical effects at all. This is confirmed by the dispersion formulae which for the permanent gases have only ultra-violet terms.
The Dispersion of Magnetic Gyration.—The dispersion of doubly refracting and naturally gyrating substances has been studied, and fits into the same general type of formula, but the theory is very complicated. On the other hand magnetic gyration is fairly completely understood, and, as it has thrown much light on the behaviour of atoms, we may consider it in more detail. We first take the simplest case, which is not in fact exhibited by many types of atom. In a magnetic field an electron experiences a force proportional to the field and to its own velocity, in a direction perpendicular to both, and we cannot therefore now limit the electron's motion to a single line. Taking the field along z (and omitting the damping factor by the exclusion of cases where it would be important), the motion will be The change in the denominators of these shows that there is a different magnitude of response to the two types of circular polarization, and this we saw would explain the gyration.
It is of some interest to see how the gyration behaves in the immediate neighbourhood of To simplify we will write = co, and it will be justifiable to write the denominator of the first solution as since for practicable fields is always negligible. In the second type of motion the denominator will be ) Considering the first solution we see that for values of v on opposite sides of — there will be a phase difference of 180°. On the other hand the second solution will not show this change at the same point, but at instead. This suffices to outline the behaviour of the gyration (see fig. 24). As v increases towards the value the gyration rapidly increases. At co the light is ab sorbed, but on the other side, where it is again observable, it gyrates strongly the opposite way. As p increases farther the gyration becomes less, though always negative, and then again increases as v approaches After passing this it is positive and large, and rapidly decreases as v recedes from By seeing which way the plane of polarization rotates, it is possible to find the sign of the electric charge e; this is negative as is that of the actual electron. It will be seen that our calculation in
dicates the presence of two regions of absorption, which implies that the original line v, has been split into two by the magnetic field. 'The phenomenon can also be observed in emission, and is then called the Zeeman effect (q.v.). This effect is much more complicated than our explanation would suggest, but, with the help of the quantum theory, it has been more or less completely elucidated. Most spectral lines do not split into only two mem bers, but into a pattern composed partly of line-waves and partly of circle-waves, and the circle-waves control the gyration. In the case of the two sodium lines, there are two pairs for one and one pair for the second.
The theory of the gyration of solids and liquids is less complete than that of metallic vapours, in just the same way as is that of refraction ; but it is known to bear a very similar relationship.
We can imagine that each vir tual electron has an appropriate eH/mc which determines its re sponse to the two types of circu larly polarized light. If the inci dent light has frequency far from any of the natural frequencies of the substance, it is found that the gyration depends on terms of the form this means that for ordinary substances it increases much more rapidly than does the refractive index, as the colour changes from red to blue. By a comparison of the gyration of any substance with its refraction, the values of e/m for its virtual electrons can be estimated, and they are usually a fraction (mostly between and 1) of the accepted value for an actual electron. The dis crepancy has not been explained, but it is to be attributed to a complication rather like that of the Zeeman effect which occurs in vapours.
In this account the principles of optics have been presented as a completed body of knowledge. Only where we leave the consideration of matter in bulk and come to atoms do we en counter more dubious questions. Since the beginning of the loth century atomic theories have been in a state of flux, and it is necessary that we should radically revise our conception of particles, and probably of time and space as well; but, however great the changes, and however new the language, we may be sure that the older work will stand, and that the new theory will accommodate within itself the wave-theory of light.