152 PARTICULAR CASES OF EQUILIBRIUM. 



of small spheres of radius a 19 and assume with Poisson that the 

 electrification of each of them is not influenced by the electrification 

 of the adjacent spheres, and only depends on the strength of the 

 field. If n is the number of small spheres contained in the large 

 one, the value of the potential at a distance, which is very great 

 compared with a, is 



_ r na\ 



or putting h = , that is to say calling h the ratio of the space, occu- 

 pied by the small spheres, to the volume of the whole sphere, 



cos 



If the sphere were homogeneous, and of the specific inductive 

 capacity /*, the potential V at the same distance would be 



The action of the two systems is identical if we have 



which gives 



this value of ft represents the apparent inductive capacity of the 

 sphere made up as we have supposed. 



If we assume that the small spheres are conductors, we must 

 make a, = oo ; we have then 



I + 2/1 



