﻿110 The Hon. J. W. Strutt on the Light from the Sky, 



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 appa- 

 rent 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 vi- 

 brates ; 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 ray ; for these will clearly be proportional. The num- 

 ber (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 ; 

 X, 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 ele- 

 ments 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 f , which is a simple number 

 and may therefore be omitted. It remains to find how i varies 

 with T, r, X, 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 X ; 



and from what we know of the dynamics of the question, we 



* Camb. Phil. Trans, vol. vii. 



