296 



on it may be considered as uniform. Then the sphere is uniformly 



3 8,-1 ^ 



polarized, the polarization being F, where 8- is the dielec- 



^ An B^-\-Z 



trie constant of the sphere and F is the uniform field acting on 

 the sphere. If q should denote the fraction of the volume of the 

 lattice which is occupied by the spheres themselves, the average 

 polarization is 



3(7 6.— 1 



Since now the effect of a uniformly polarized sphere at points 

 outside the sphere is equivalent to the effect of a doublet at the 

 centre of the sphere the contribution to F of the particles of powder 

 situated inside the large spherical hole vanishes by a well known 

 reasoning of LorEntz ^) and his result for F applies here so that 



4jr e„ — 1 



i.e. 



E 



F — 



\ — q 



f. + 2 



and 



37 E s — \ 



4jr 6, 4- 2 Ajt 



where e is the effective dielectric constant. 

 Thus 



f— 1 _ 1 



7(V^)"VT2 q ^^^ 



—^ — y(^-i) 



and letting 



*. = l + <f. (U) 



we have 



c— 1 _ 1 



^■^)'~' Pi ^^'^ 



~^ 3 



Thus the effective susceptibility of a powder is not proportional 

 1) H. A. LoBENTZ, Theory of Electrons, p. 308 



