﻿its Polarization and Colour. Ill 



may be sure that i varies directly as T and inversely as r, and 

 must therefore be proportional to T-r-A, 2 r, T being of three di- 

 mensions in space. In passing' from one part of the spectrum 

 to another X is the only quantity which varies, and we have the 

 important law : — 



When light is scattered by particles which are very small com- 

 pared with any oj 'the 'wave-lengths ', the ratio of the amplitudes of the 

 vibrations of the scattered and incident light varies inversely as the 

 square of the ivave-length, and the intensity of the lights themselves 

 as the inverse fourth powei\ 



I will now investigate the mathematical expression for the 

 disturbance propagated in any direction from a small particle 

 which a beam of light strikes. 



Let the vibration corresponding to the incident light be ex- 



pressed by A cos — bt. The acceleration is 



U-7 C0S T^ 



so that the force which would have to be applied to the parts 

 where the density is D', in order that the wave might pass on 

 undisturbed, is, per unit of volume, 



_ ( ]y_D)A(P) 2 co S fw.; 



To obtain the total force which must be supposed to act over the 

 space occupied by the particle, the factor T must be introduced. 

 The opposite of this conceived to act at (the position of the 

 particle) gives the same disturbance in the medium as is actu- 

 ally caused by the presence of the particle. Suppose, now, that 

 the ray is incident along Y, and that the direction of vibration 

 makes an angle a with the axis of sc, which is the line of the 

 scattered ray under consideration — a supposition which involves 

 no loss of generality, because of the symmetry which we have 

 shown to exist round the line of action of the force. The ques- 

 tion is now entirely reduced to the discovery of the disturbance 

 produced in the sether by a given periodic force acting at a fixed 

 point in it. In his valuable paper " On the Dynamical Theory 

 of Diffraction"*, Professor Stokes has given a complete investi- 

 gation of this problem ; and I might assume the result at once. 

 The method there used is, however, for this particular purpose 

 very indirect, and accordingly I have thought it advisable to 

 give a comparatively short cut to the result, which will be found 

 at the end of the present paper. It is proved that if the total 



force acting at in the manner supposed be F cos — bt, the re- 



* Camb. Phil. Trans, vol. ix. 



