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 body subtends only a small solid angle. Now we know that when light vibrating in the plane of incidence falls on a reflecting surface at an angle of 45°, light is sent out according to the law of ordinary reflection, whose direction of vibration is perpendicular to that in the incident ray. And not only is this so in experiment, but it has been proved by Green to be a consequence of the very same view as to the nature of the difference between media of various refrangibilities as has been adopted in this paper. The apparent contradiction, however, is easily explained. It is true that the disturbance due to a foreign body of any size is the same as would be caused by forces acting through the space it fills in a direction parallel to that in which the primary light vibrates; but these forces must be supposed to act on the medium as it actually is—that is, with the variable density. Only on the supposition of complete uniformity would it follow that no ray could be emitted parallel to the line in which the forces act. When, however, the sphere of disturbance is small compared with the wave-length, the want of uniformity is of little account, and cannot alter the law regulating the intensity of the vibration propagated in different directions.

Having disposed of the polarization, let us now consider how the intensity of the scattered light varies from one part of the spectrum to another, still supposing that all the particles are many times smaller than the wave- length even of violet light. The whole question admits of analytical treatment; but before entering upon that, it may be worth while to show how the principal result may be anticipated from a consideration of the dimensions of the quantities concerned.

The object is to compare the intensities of the incident and scattered rays; for these will clearly be proportional. The number ($$i$$) expressing the ratio of the two amplitudes is a function of the following quantities:—$$T$$, the volume of the disturbing particle; $$r$$, the distance of the point under consideration from it; $$\lambda$$, the wave-length; $$b$$, the velocity of propagation of light; $$D$$ and $$D'$$, the original and altered densities: of which the first three depend only on space, the fourth on space and time, while the fifth and sixth introduce the consideration of mass. Other elements of the problem there are none, except mere numbers and angles, which do not depend on the fundamental measurements of space, time, and mass. Since the ratio $$i$$, whose expression we seek, is of no dimensions in mass, it follows at once that $$D$$ and $$D'$$ only occur under the form $$D:D'$$, which is a simple number and may therefore be omitted. It remains to find how $$i$$ varies with $$T,\,r,\,\lambda,\,b.$$

Now, of these quantities, $$b$$ is the only one depending on time; and therefore, as $$i$$ is of no dimensions in time, $$b$$ cannot occur in its expression. We are left, then, with $$T,\,r,$$ and $$\lambda$$; and from what we know of the dynamics