150 PARTICULAR CASES OF EQUILIBRIUM. 



Whence 



' 



The law of the terms is evident. Connecting these equations 

 with the identities 



& -**+*!, 



(28) 4> 2 



we could determine the values of Fj , F 2 , F 3 . . . The problem is thus 

 completely solved. 



165. Let us suppose that there are two layers bounded by the 

 surfaces Sj and S 2 , in a uniform external field of strength <, where 

 the dielectric is air. We may simply put 



Equations (28) give then 



/XY 

 Substituting in (25) and (26), and putting /?=( ) we have 



F!) = ft (< + F 2 - 2FJ, 



+ 2 - 



equations which would determine the forces F x and F 2 as functions 

 of the data of the problem. 



166. Suppose, further, that the internal nucleus is also air, which 

 would amount to determining the state of a spherical layer ; /^ must 

 also equal i. Let us denote by ft the specific inductive capacity of 

 the medium previously denoted by /* 2 , equations (29) would become 



From this is deduced 



