1918]
SCATTERING OF LIGHT BY A CLOUD OF SMALL PARTICLES
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the vibrations are perpendicular to the primary vibrations. All that we are then concerned with are certain resolving factors, and the integration over angular space required to take account of the random orientations. In virtue of the postulated symmetry, a revolution of a particle about its own axis has no effect, so that in the integration we have to deal only with the direction of this axis. It is to be observed that the system of vibrations scattered by a particle depends upon the direction of primary vibration without regard to that of primary propagation. In the case of a spherical particle the system of scattered vibrations is symmetrical with respect to this direction and the amplitude of the scattered vibration is proportional to the cosine of the angle between the primary and secondary vibrations. When we pass to unsym-metrical particles, we have first to resolve the primary vibrations in directions corresponding to certain principal axes of the disturbing particle and to introduce separate coefficients of radiation for the different axes. Each of the three component radiations is symmetrical with respect to its own axis, and follows the same law as obtains for the sphere*.
In Fig. 1 the various directions are represented by points on a spherical surface with centre 0. Thus in the rectangular system XTZ, OZ is the direction of primary vibration, corresponding (we may suppose) to primary propagation parallel to OX. The rectangular system UVW represents in like manner the principal axes of a particle, so that UV, VW, WU are quadrants. Since symmetry of the particle round W has been postulated, there is no loss of generality in taking U upon the prolongation of ZW. As usual, we denote ZWby d, and XZW by <f>.
The first step is the resolving of the primary vibration Z in the directions U, V, W. We have
cos ZU = — sin 0, cos ZV= 0,
Fig. l.
cos ZW = cos 0.
.(1)
The coefficients, dependent upon the character of the particle, corresponding to U, V, W may be denoted by A, A, (7; and we seek the effect along the scattered ray OF, perpendicular to both primary vibration and primary propagation. The ray scattered in this direction will not be completely polarized, and we consider separately vibrations parallel to Z and to X. As regards the former, we have the same set of factors over again, as in (1), so that the vibration is A sin2 6 + C cos2 6, reducing to G simply, if A = G. This is the result for a single particle whose axis is at W. What we are aiming
* Phil. Mag. Vol. XLIV. p. 28 (1897); Scientific Papers, Vol. iv. p. 305.onless." I have repeated this experiment, using oil which is believed to have come direct from Italy. A drop of this placed upon a clean water-surface at once drives dust to the boundary in forming the mono-molecular layer, and in addition flattens itself out into a disk of considerable size, which rapidly undergoes the transformations well described and figured by Devaux. The same oil, purified by means of alcohol on Miss Pockels' plan, behaves quite differently. The first spreading, driving dust to the boundary,