396 Sir J. J. Thomson on the Scattering of 



If x, y, z are the displacements of the electron parallel to 

 OX, OY, OZ, 



# = J (cos #cos i/r cos cf> — sin <j> sin yjr) 



—n (cos 6 cos -v/rsin <£ + cos<£ sin ^) -f f sin 6 costy 



= Z [sin # cos 6 cos -v/r(c — a cos 2 cf> — b sin 2 (/>) 



:f(a — 6) sin sin i/r sin ^ cos 0], 

 where 



1.1 1 



e — 



A — nip 2 ' ±5 — wp 2 ' C — mp 2 ' 



y — *L [sin # cos# sin ^r{c — a cos 2 (/> — /> sin 2 <£) 



+ (a — &) sin # cos ty sin (/> cos </>] ; 

 # = Z (c cos 2 -f 6 sin 2 sin 2 </> + a sin 2 # cos 2 <£) . 



If Z varies as e lpt , the components of the acceleration 

 of the electron will be —p 2 %, —p 2 y, —p 2 z respectively. If 

 a, j3, y are the components at a time t of the magnetic force 

 at a point P due to the motion of an electron whose distance 

 from P is r, then when r is large compared with the wave- 

 length of the light, 



e e e 



u=~{jn — km}, j3 = - t {kl — hn}, y=~ {hm— jl}, 



where I, m, n are the direction cosines of the line joining 

 the electron to P, and li, j, k are the components of the 



acceleration of the electron at the time t — , where c is 



c 



the velocity of light and e the charge on the electron. 



The energy per unit volume of the scattered light at P is 



equal to 



= 4~p{* 2 +i 2 +* 2 -(^+™?+«*) 2 }. • • • (i) 



Now li, j, k are respectively —p 2 iv, — p 2 y, —p 2 z when 

 x, y, z have the values given above. Substituting these 

 values in (1) we get the energy in the scattered light from 

 a single atom. We cannot observe the effect of a single 

 atom or molecule ; we must take the sum of the effects 

 due to a large number of molecules with all possible values 

 for <9, <f), t/t. When the atoms are uniformly orientated 



