( 4.3P, ) 



§ 6. Wo >lia]l iKiw sliow liow our o-onoral oqimtions (T,A — (Y,.) 

 iimv ho. iipjilitMl to oj)tio:il ))lienoinon:i. For tliis purpose we oonsiilcr 

 a system of ponderahle bodies, tlie ions in ■wiiicli are oapablf of 

 vil)rating fibont determinato positions of ocinilibrium. If the system 

 be traversed by waves of light, tliere will be oscillations of the 

 ions, accompanied by electric vibrations in the aether. For cnn- 

 venience of treatment we shall snppose that, in the absence of light- 

 waves, there is no motion at all ; this amounts to ignoring all 

 molecular motion. 



Our first step will be to omit all terms of the second order. 

 Thus, we shall put /.•^=1, and the electric force acting on ions at 

 rest will become a' itself. 



We shall further introduce certain restrictions, by means of which 

 we get rid of the last term in (h) and of the terms containing 

 i\r, i>v' ^-V- in (\c). 



The first of these restrictions relates to the magnitude of the 

 displacements a from the positions of equilibrium. We shall suppose 

 them to be exceedingly small, even relatively to the dimensions of 

 the ions and we shall on this ground neglect all quantities which 

 are of the second order with respect to a. 



It is easily seen that, in consequence of the displacements, the 

 electric density in a fixed point will no longer have its original 

 value (Jq^ but will have become 



(> = t'o — y- (Co ^:r) — — ((',1 «//) — Y' *-i'n "--)• 



d'' oy o-r 



Here, the last terns, which evidently must be taken into account, 

 have the order of magnitude -^ , if <■ denotes the amplitude of 



rt 



the vibrations; consequently, the first term of the right-hand member 

 of (To) will contain (piantities of the order 



Ylllo (3^ 



a 



On the other hand, if T is the time of vibration, the last term 

 in (Ic) will be of the order 



'^, (4) 



