404 Sir J. J. Thomson on the Scattering of 



Take the case when Y' = 0, X'=X cos 5*. 

 Then, integrating these equations, we get 



a = a + — 



X f cos {q + n)t cos (q—?i)t~\ 

 np 2 \ q + n q — n J ' 



X f 



e coso) = 



X [sin (q + n)t sin (q — n) t\ 

 nap 2 \ q + n q — n J ' 



J , /cos (jt? + 1 n + q) t c os (p+ In— ff)A 

 2najt? \ 2 V Qo + 1) w + £ r (/) + l)7i — gr / 



, /cos (p — ln + <?)£ cos(p — In — ff)* \\ 

 \ ip — l)n + g (p~l)n — 9 /J * 



esm & =~^-fjc / sin(p+ln + g> sin (y + ln-g)A 

 2nap\ 2 V (p+l)n + q (p + l)n — q / 





, / sin(p-ln + g )^ sin (p-ln-g) \\ 

 "H (p-l)n + fl V ( p -l)n-c JS 



(p—l)n + q (p—1) 



Substituting these values in the expression for #, we 

 find that 



* = X cos at< 2 1 h^(p-l) , V(p + 1) \ 



* V(n 2 -^ 2 ) >{^(p- 1) 2 -<f} + p{n 2 (^ + l) 2 ~<? 2 } J 



-Xcos(2n + g)*.-o * 2 



v 7/ p 2 n 2 — (n + q) 2 



— X cos (2n — q)t. -*-z — 7-? ^ 9 



v *y p 2 n 2 —(n—q) 2 



-t-a Q cos nt. 



To calculate the intensity of the scattered light of the 

 same colour as the incident we need only consider the term 

 containing cospt. As this term is proportional to the 

 applied force, we see that an electron rotating in an orbit 

 acts, so far as its contribution to specific inductive capacity 

 is concerned, like a statical system, where the displacement 

 of the electron is proportional to the force. Hence for 

 forces in the plane of the electron we have, using the 

 notation of p. 396, 



a = h = *__. Wj p-l) V(p + 1) 



Wh6re , 1.1, 11 



kl=Z 2 + p> h = p~2- 



