CONCENTRIC SPHERICAL LAYER IN A UNIFORM FIELD. 149 



Let us consider the inner sphere S r If the medium of specific 

 inductive capacity fi 2 , which surrounds it, were unlimited and formed 

 a uniform field of strength </> 2 , this sphere would be covered with a 

 layer of displacement M 15 giving in the interior a constant force Fj 

 and a uniform field </> : = < 2 + l ; and for a point P x on the surface 

 in the direction w, we should have the equation 



cos to = * < - 2 cos o> 

 or 

 (25) 



But the uniform field of strength < 2 , situate on the outside of the 

 sphere S 19 is that which would be produced for the interior of the 

 sphere S 2 by an external uniform field of strength < 3 , and by the 

 internal force F 2 due to the fictive layer distributed on the surface 

 according to the same law, which would give 



For a point P 2 of this surface we have to consider not merely the 

 action < 3 of the external field, and that of the layer M 2 , but also 

 the action of the layer M 1 of the internal sphere S r 



The law of the conservation of the flow of induction would give 

 a relation between these quantities analogous to the equation (25) 

 and which we may write directly in the following manner, suppressing 

 the common factor cos w : 



whence 



(26) ^, = ft fa, - 2 F 2 ) + a (ft, - 



The same reasoning applies to surface S 3 ; for a point P 3 of its 

 surface we should then have to take into account the strength ^ of 

 the external field, together with the actions of the three internal layers 

 M 3 , M z and M r 



We shall thus have 



