POTENTIAL OF A SPHERICAL SHELL. 



143 



If the axis coincides with the centre O of the shell, we have u = a 

 and sin a = i ; we get thus 



(45) 



2n+l 



2. 4. 6. ..(2+ 2) 



!Vf) 

 2)\r) 



These are the expressions which have been obtained above (768). 



775. MUTUAL INDUCTION OF Two CIRCULAR CURRENTS. Let 

 us in the first place consider two circumferences, HK and H'K' 

 (Fig. 145), having the same axis, of radii a and a', traversed by 



, Fig. 145. 



Fig. 146. 



parallel currents equal to unity. Take as origin a point C of 

 the axis, draw two spheres of radii u and u' which pass respectively 

 through the two currents, and replace these currents by two spherical 

 shells o- and o-' ; let a and a' be the angles subtended by the radii a 

 and a', V the potential of the shell o-'. 



The flow of force from an element cf into an element dv 



dV 

 of the first is equal to - d<r t and the coefficient of mutual 



induction is the integral of this expression extended to the entire 

 surface of the shell o-. 

 Putting again 



d<r 



