Electromagnetic Theory of Light. 89 



and the expression for f x becomes 



— /* - 1 1 1 *o ^~ x e~ ikr dx dy dz\ . 

 For the sake of brevity we will write this 



/i=S[ KP ?-' iQ fl' • • • (35) 



where 



P= (Tj h AK- l e- ih 'dxdydz, 

 Q= 111 h Q ts^~ l e- ikr dx dy dz. 



(36) 



In like manner from (30) and (31), 



9l ~Wr 



[KPj], (37) 



Equations (35), (37), (38) express the electric displace- 

 ment in the secondary waves. Since af+fZg + yh=.Q, the dis- 

 placement is perpendicular to the direction of the secondary 

 ray. The general expression for the intensity is found by 

 adding the squares of/, g, h ; but it will be sufficient for our 

 present purpose to limit ourselves to the case where the second- 

 ary ray is perpendicular to the primary ray, i. e. to the case 

 « = 0. Then 



If P and Q are both finite, there is no direction along which 

 the secondary light vanishes. We find by experiment, how- 

 ever, that the light scattered by small particles on which pola- 

 rized light impinges does vanish in one direction perpendicular 

 to the original ray ; and thus either P or Q must vanish. Now, 

 when the particles are very small, we have 



V^hoAK-'e-^^dxdydz, QsA V~ 1 '~*JJJ<fa<fy<Z*3 C 40 ) 

 so that if P vanishes, AK = 0; and if Q vanishes, A/4 = 0. 

 The optical evidence that either AK or A/4 vanishes is thus 

 very strong; while electrical reasons lead us to conclude that 

 it is A/4. 



If we write T for the volume of the small particle, we get 



