299 

 Ë E, 



e. 



-1 



we obtain 



having let 



^ -f /^ 1 



Aj6j-i + /i,«,-i p ^ qe-'^ 



A, + /i, /il + /i, 



Tiiis number e„ is tlie effective dielectric constant for the component 

 normal to the laminae. 



(II) Parallel component. 



For this it is clear that the effective dielectric constant is 



(III) Both components present. 



E 



The electric displacement is — (8„ cos 0-, e,, sin ^) where d' is the 



angle made bj the mean electric intensity with the normal to the 



laminae. Since the directions of the normals to the laminae are 



entirely arbitrary with respect to the direction of the mean electric 



intensity, the component of the electric displacement perpendicular 



to the mean electric intensity is distributed at random. The only 



component to be considered is then that pai-allel to the mean electric 



E 

 intensity which is — {sncos* >'J -\- ^p siif &). The effective dielectric 



constant is 



Hence we get 



1 1 +-ip(f 



— ^ ^ (3) 



To within the first power of ö this is the same as (2) or (1') so 

 that in this case the conclusions drawn as to a force on a sphere 

 are still valid. Rewriting (3) in the form 



e— 1 1 

 = (3') 



3 -h 2p6 



it becomes apparent that the value of e obtained from (3) lies between 

 the values obtained from (1') and (2). 



