122 COEFFICIENTS OF INDUCTION. 



The value of H at the point P' is the integral of this expression 

 extended to the whole surface S, which gives 



H= -2/vr \JS/.r. 



We have then 



IHo-tfS' = - 2^0-0-' \d S' \d$l . r = 



Js' J J 



or 



R, being the geometrical mean distance of the sections S and S' of 

 the two conductors. 



In like manner we have 



If //- is the coefficient of magnetic permeability of the first 

 conductor, the value of H at the point P, where is the element dS, is 



H = 2/r dS^l . r^ 



an expression in which ^/S 1 denotes any other given element of the 

 surface S. It follows that 



("HO-^S = - 2/xo- 2 



S Si/. r- - 2/J 2 /. R 2 , 



R 2 being the geometrical mean distance from the surface S. 

 We have, finally, 



|HWS'= -2/*T/.R;. 



Js' 



Substituting these values in the expression (8) of the energy, we 



get 



2 w 



