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

 we obtain from (B) by differentiation and subtraction, 



dZ 



(C) 



(^V.+^i- dy 



vr v «r 2 , fir 3 are the rotations of the elements of the medium round 

 axes parallel to those of coordinates. 



The disturbance which we are investigating is that caused and 

 maintained by the force Z acting within the space T. Accord- 

 ingly* 



-sx 3 =0, 



1 CCCdZe^' . . 



^=-^)})^j-r dxdydz > 



r being the distance between the element dx dy dz and the point 

 where w 1 is estimated, and 



*■-?-! W 



Since € ±ifcr will be finally multiplied by e iw ', and the disturbance 

 which we are dealing with is propagated outwards from T, it is 

 evident that the lower sign is to be employed. Now 



Ce~ ikr dZ , ?„€-**-] C r , d /e-*K , 



J— ^K z — H z ^(— H 



of which the term within brackets vanishes, because the value of 

 Z is only finite within the space T. Thus 



^ = ^¥ jJJ Z | (t") & * *• 



J / € -«r\ 



The factor -7- ( j within the space T is sensibly constant, so 



that, if Z stand for the mean value of Z over the volume T, 

 TZ d /e-^ 



4arb* dy 



-TZ rf/.J 



(*f> 



, e -ikr \ 



/ d d\ e-*** 



2 477-0* da?V r /* 



ifcr 



Helmholtz, Crelle's Journal, 1860. 



