﻿452 The Hon. J. W. Strutt on the Scattering 



w 3 =0, 



D'-D a? 



(8) 



which correspond to the results already obtained. Since the 

 optical density is proportional to the square of the refractive 

 index, 



In a note to my previous paper I mentioned that no change 

 is required in (8), even though the terms containing the square 



and higher powers of — ^r — are retained. As I there showed, 



the density of a medium may always be supposed to be changed, 

 even in the most arbitrary manner, if suitable bodily forces pro- 

 portional to the variation of density and to the actual accelera- 

 tion are conceived to act upon it, while the motion remains ab- 

 solutely the same as before. The waves thrown off from a small 

 particle which lies in the path of a beam of light are those due 

 to a set of forces proportional to D' — D, and parallel to the 

 actual vibrations acting through the space T occupied by the 

 particle. In calculating the effect of the forces, the variation of 

 density is to be taken into account, unless we are content to neg- 

 lect the square of D f — D. But by a second application of our 

 principle we see that the density within the space T may be sup- 

 posed to be D instead of D', provided we introduce a second set 

 of forces proportional to J) 1 — D and to the acceleration at T. 

 Now it may be proved (Thomson and Tait, p. 569), that the effect 

 of a bodily force applied through a small space T to an elastic 

 medium diminishes without limit with T even within the region 

 of application. Accordingly the acceleration at T caused by our 

 first set of forces is of a higher order of magnitude than the 

 forces themselves, and thus, whether D'— D be small or not, the 

 effect of the second set is to be neglected. The error caused by 

 taking, in the calculation of the first set the undisturbed instead 

 of the actual acceleration is evidently smaller still. 



If it were desired to continue the approximation, some further 

 supposition would be necessary as to the shape of the disturbing 

 particles. The leading term, we have seen, depends only on the 

 volume; but the same would not be true for those that follow. 

 However, little exception could be taken to the assumption of a 

 spherical form ; and in that case there is no difficulty in proceed- 



