POISSON'S HYPOTHESIS. 153 



_jv _ 



If, finally, the external medium is of air, /* 2 = i, and we get 



I +2/1 



For those dielectrics, whose specific inductive capacity is near 

 2, we should have 



2 + 2 4 



This result may give some idea of the degree of exactitude to 

 which Poisson's reasoning tends. 



In a conducting sphere, the interior force due to the induced 

 layers is equal to the action of the external field. The external 

 action of a polarized sphere is very small compared with the internal 



AA 3 

 action, for the ratio of the forces (158) is at most equal to 2( - J 



and tends towards zero when the spheres are infinitely small. But if 

 the volume occupied by the conducting spheres is a quarter of the 

 total volume, the action which each of them exerts upon the adjacent 

 ones can no longer be neglected in comparison with the internal 

 force, and the field is thus modified. The maximum ratio of the 

 sum of the volumes of the spheres which touch, to the total space is 



equal to -= or sensibly = . If this ratio is reduced to - , the 

 3v/2 v/2 4' 



distance of the centres of two adjacent spheres is about equal to the 



3 /~T~ 

 diameter multiplied by * / =. The action exerted by the electrical 



layer of one of the spheres, at the centre of the nearest one, might 

 thus attain a fraction of the internal force equal to 



It is true that if the reciprocal action of the sphere tends to 

 increase the electrification parallel to the force of the field, it tends 

 to diminish it in a perpendicular direction, so that we are not far from 

 the truth in assuming, with Poisson, that this reciprocal influence may 

 be neglected. 



