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

 suiting disturbance in the ray propagated along X is 



«, F sin a 2ir n , . 



Substituting for F its value, we have 



r^MU ?= A — jy- ^2 sin a cos — {bt-r), 



Sxju 



an equation which includes all our previous results and more. 



One reservation, however, must not be omitted. Since we 

 have supposed the medium uniform throughout, whereas it 

 really has a different density at the place where the force acts, 

 our investigation does not absolutely correspond to the actual 

 circumstances of the case. As before remarked, no error is on 

 that account to be feared in the law determining the intensity of 

 the vibration in different directions ; but it is probable that the 

 coefficient, so far as it depends on D : D', may be changed*, and 



27T 



there may be a change in the phase comparable with — x the 



linear dimension of the particle, which is of importance when the 

 scattered and primary waves have to be compounded. 



So much for a single particle. In actual experiments, as, for 

 instance, with Professor TyndalPs " clouds," we have to deal 

 with an immense number of such particles ; and the question 

 now is to deduce what their effect must be from the results 

 already obtained. Were the particles absolutely motionless, the 

 partial waves sent out in any direction from them would have 

 permanent relations as to phase, and the total disturbance would 

 have to be found by compounding the vibrations due to all the 

 particles. Such a supposition, however, would be very wide of 

 the mark; for, in consequence of the extreme smallness of X, the 

 slightest motion of any particle will cause an alteration of phase 

 passing through many periods in a less time than the eye could 

 appreciate. Our particles are, then, to be treated as so many 

 unconnected sources of light ; and instead of adding the vibrations, 

 we must take the intensities represented by their squares. Only 

 in one direction is a different treatment necessary, namely along 

 the course of the primary light. I mention this because it would 

 not otherwise appear how the reduction in the intensity of the 

 transmitted light is effected ; but we do not require to follow the 

 details of the process, because, when once we know the intensity 

 of the light emitted laterally, the principle of energy will tell us 

 what the primary wave has lost. 



* I find that no alteration of any kind is needed. — Jan. 20. 



