Electromagnetic Theory.—A discussion of these and other questions upon the basis of the electromagnetic theory of light is given in the Phil. Mag., 1881, 12, p. 81. Here we must be content with a statement of some of the results. So long as the particles are supposed to be very small and to differ little from their envi ronment in optical properties, there is little difference between the electric and the elastic solid theories. Whatever may be the shape or size of the particles, there is no scattered light in a direction parallel to the primary electric displacements. In order to render an account of Tyndall's "residual blue" it is necessary to pursue the approximation further, taking for simplicity the case of spheri cal shape. We learn that the light dispersed in the direction of primary vibration is not only of higher order in the difference of optical quality, but is also of order Pe in comparison with that dispersed in other directions, where c is the radius of the sphere, and k= 27r/X. The incident light being white, the intensity of the component colours scattered in this direction varies as the inverse eighth power of the wave-length, so that the resultant light is a rich blue.
As regards the polarization of the dispersed light as dependent on the angle at which it is emitted, we find that although, when terms of the second order are included, the scattered light no longer vanishes in the same direction as before, the peculiarity is not lost but merely transferred to another direction. The angle 0 through which the displacement occurs is measured backwards, i.e., towards the incident ray, and its value is given by AK being the difference of dielectric constants.
Experiments upon this subject are not difficult. In a darkened room a beam of sunlight (or electric light) is concentrated by a large lens of 2 or 3 ft. focus ; and in the path of the light is placed a glass beaker containing a dilute solution of sodium thio sulphate (hyposulphite of soda). On the addition, well stirred, of a small quantity of dilute sulphuric acid, a precipitate of sul phur slowly forms, and during its growth manifests exceedingly well the phenomena under consideration. The more dilute the solutions, the slower is the progress of the precipitation. A strength such that there is a delay of 4 or 5 minutes before any effect is apparent will be found suitable, but no great nicety of adjustment is necessary.
Polarization.—In the optical examination we may, if we prefer it, polarize the primary light; but it is usually more con venient to analyze the scattered light. In the early stages of the
precipitation the polarization is complete in a perpendicular direc tion, and incomplete in oblique directions. After an interval the polarization begins to be incomplete in the perpendicular direc tion, the light which reaches the eye when the nicol is set to minimum transmission being of a beautiful blue, much richer than anything that can be seen in the earlier stages. This is the moment to examine whether there is a more complete polariza tion in a direction somewhat oblique; and it is found that with 0 positive there is, in fact, a direction of more complete polariza tion, while with 0 negative the polarization is more imperfect than in the perpendicular direction itself.
The polarization in a distinctly oblique direction, however, is not perfect, a feature for which more than one reason may be put forward. In the first place, with a given size of particles, the direction of complete polarization indicated by (23) is a function of the colour of the light, the value of 0 being 3 or 4 times as large for the violet as for the red end of the spectrum. The experiment is, in fact, much improved by passing the primary light through a coloured glass. Not only is the oblique direction of maximum polarization more definite and the polarization itself more com plete, but the observation is easier than with white light in conse quence of the uniformity in the colour of the light scattered in various directions. If we begin with a blue glass, we may observe the gradually increasing obliquity of the direction of maximum polarization; and then by exchanging the blue glass for a red one, we may revert to the original condition of things, and observe the transition from perpendicularity to obliquity over again. The change in the wave-length of the light has the same effect in this respect as a change in the size of the particles, and the comparison gives curious information as to the rate of growth.
But even with homogeneous light it would be unreasonable to expect an oblique direction of perfect polarization. So long as the particles are all very small in comparison with the wave-length, there is complete polarization in the perpendicular direction; but when the size is such that obliquity sets in, the degree of obliquity will vary with the size of the particles, and the polariza tion will be complete only on the very unlikely condition that the size is the same for them all. It must not be forgotten, too, that a very moderate increase of dimensions may carry the particles beyond the reach of our approximations.