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



and two similar equations, where f, rj, f are the displacements 

 parallel to the coordinate axes, 



8 — <% + ^L + d X 

 dx dy dz 



„ d ( d\ d ( d\ d ( d\ 



^-A n rJ + dy\ n Ty) + ^A n Tz)' 



If n and D were constant, equations (1) would be satisfied by 



e-^.8-% i ( 2) 



In the application that we have to make, n and D may be sup- 

 posed to be constant except within a small space T at the origin 

 of coordinates, where they assume the values n + Aw, D + AD. 

 In consequence of this variation the equations of motion are no 

 longer satisfied by (2) ; but we may take as the true values of the 

 displacements, f , tj, £ -f f, S, where f , rj, £ 8 are small quan- 

 tities of the order T, which are to be neglected when multiplied 

 by An, AD*. Substituting in equations (1) and dropping the 

 factor relating to the time, we get 



;|(«8) + V.9 + D*W, =0, 



5 (m8) + V. f+D«'{ + V. to + Dm o =0, 

 and j._2w , 2 n 



or, since 



Vn S> = Va»S) + Vn5» 



Dr =(D+AD)r =DS,+AD.5 )) 

 and 



v„to+»* 2 r„=o, 

 l* M+vf+J , + l*£ 



s s (»*) + vr+*M- J VA»r„+ 4? *•$,=<>. 



7f» 7 "^ 



Hence if w 3 = -^ — -7- &c. be the rotations of the medium, 

 * The effect of this is subsequently considered. 



(3) 



