due to the Scattering of Light by Electrons. 723 



molecule are those due to the forces in the electrical 

 wave, 



A — = cos — - {ct— x Q )(n^ey —n^ez ) 



dt 



-f ^sin^(<tf-^)(« 3 M-7! 2 N), 



A. A, 



so that 



1 9 7T 



- -cos" (rf- .r )(« 3 M — t? 2 N), 



6' A. 



with symmetrical expressions for B&> 2 , ^ w a- 



The velocity of a particle due to these rotations has for 

 components \ arallel to x' ', //, z\ 



&)oc' — a) 3 j/', ©ga/ — ft)]*', Wiy' — Wyx' : 



hence the velocity parallel to the fixed axis z/ is 



»i 1 (w 2 :'- W;-.//') -J- m 2 (&> 3 ./ — a>i^') + m 3 (*»j^' — ©^ )• 



Y the electric force parallel toy is, as we see by equation (1), 

 proportional to the sum of these expressions. 



Now to find the rotation we require the term in Y which 

 is of the same phase as Z, i. e. we require the term in 



27T 2tt 



cos— -('/ — x) and do not need that in sin— {ct — x). 



A, A, 



But, as we have explained, owing to the different positions 



2-7T 



of the moving electrical charge, a term cos — (c£— x 9 ) in the 



A, 



expression for the velocity of a particle whose coordinate is 

 x r will give rise to a term 



2tt. " 2tt . 2tt, 



cos — [ct — x ) — x r — sin — (ct — Xq ) 



27T 



iii the expression for the electric force ; while sin*". (ct—x ) 

 will give rise to 



9 7T ->7T '>TT 



Sin — (ct — X ) + X r — COS- (m— X ). 



Remembering this we see that the contribution of the rth 



