Scattering of Light by Small Dielectric Spheres. 421 



If, however, we investigate the scattered light proceeding 

 in the direction z of the original beam, we have to take into 

 account the phases as well as the intensities of the electric 

 forces. Let us consider a layer dz of equal particles, of 



Fig. 3. 



index of refraction 7, and calculate the resultant electric 

 force e s at any point P on the path of the original beam 

 where sin 3=1, due to all the doublets in the stratum. The 

 volume of an infinitesimal ring will be (fig. 3) 



dr — dz 2irp dp ^=dz2irr dr 



as 



? + z* = r\ 



For sin 3=1 and E = l we get from (4) 



e s = 



13ttV1 . 2tt. n 



sm — {ct — r)* 



k-r2 X 



The resultant electric force due to all particles in dr is 

 therefore 



7/ N AT 7 k— 1 3ttV . 27r / . ^2irrdr 

 d(e s ) r = N dz ] , — - — sm — (ct - r) —— , 



