Scattering of Light by Small Dielectric Spheres. 417 



plane of fig. 1, which contains therefore the electric force, E, 

 oscillating in the x direction. In the path of this beam of 

 light is placed a sphere of dielectric constant k and of radius R 

 small compared with the wave-length X. In each moment 

 we may consider the sphere as surrounded by a uniform 

 electric field, E. Now, if a dielectric sphere is placed in a 

 uniform field, there will be induced in the sphere a uniform 

 field also, and the original field outside the sphere will 

 be disturbed as if the sphere were replaced by a doublet of 

 moment 



where q represents the charge in one pole and I the distance 

 between the two poles of the doublet. If the field is alter- 

 nating according to the equation e = E sin 2irnt^ the doublet 

 w r ill oscillate according to : 



/z = E^— ^R 3 sin27r^ 



£ + 2 



or fju = ql sin 2 irnt 



and ^ = -(27r^) 2 E^iR 3 sin27r^. . . (1) 



If the doublet oscillates it will emit electric waves which 

 have been studied by H. Hertz. In the neighbourhood of 

 the doublet the oscillations are fairly complicated, but at 

 large distances we find simple spherical waves, in which the 

 electric and magnetic forces can be studied by the pulse 

 method as follows : — 



The variable moment jul is either equal to 



fx = ql sin 2irnt = qx 



or equal to />t = gsin 2irnt .l = q v .l. 



In the latter case the charge is considered variable, and the 

 length I constant ; in the former case the charge q is con- 

 sidered constant while oscillating in simple harmonic motion 

 through an interval 21. This corresponds to the oscillation 

 of a charge around a centre of attraction, and we have 



da ch,! d 2 /jb d 2 x 



di =q dt> d? =q d? =( i' f ' • • • ( 2 ) 



where /is the acceleration. 



Phil Mag. S. 6. Vol. 39. No. 232. April 1920. 2 E 



