POISSON'S HYPOTHESIS. 151 



and therefore 



2) -2(/X-l) 2 /? ' 



The force in the interior at the surface S x is 



The force is constant inside S p but it is not constant between S x 

 and S 2 , nor outside S 2 . The value of the force in the interior of S x is 

 a fraction of the strength of the field, which would be equal to unity 

 for ft = i, and to zero for ft= oo. With dielectrics whose coefficient 

 ft does not differ much from 2, the fraction is always very near 

 unity; if the layer is a conductor, the coefficient /* may be 

 considered as infinite, and F T becomes zero. 



We shall afterwards see the importance of this question in 

 magnetism. 



167. POISSON'S HYPOTHESIS ON THE CONSTITUTION OF DIELEC- 

 TRICS. Poisson's hypothesis, as revived by Faraday for electricity, 

 consists, as we have already said (no), in assuming the dielectric to 

 be formed of small conducting spheres disseminated in an insulating 

 medium. 



The results already obtained enable us to explain the method 

 adopted by Poisson for calculating, at any rate approximately, the 

 consequences of his hypothesis. 



Consider a sphere of radius a lt and of specific inductive capacity 

 fij , situate in a field of strength <f> 2 , and of specific inductive capacity 

 ft 2 ; from equations (25) and (28) the force on the interior of the 

 electric layer is 



and the external potential of this layer on a point at a distance r is 

 equal to 



Let us suppose that a sphere of radius a contains a large number 



