142 COEFFICIENTS OF INDUCTION. 



As equation (25) enables us to eliminate all these integrals, and 

 seeing that the limit of /x is cos a, 



(42) 



774. POTENTIAL OF A SPHERICAL SHELL. The potential V at 

 the point P of a uniform magnetic shell of unit power, limited to the 

 same contour as the preceding layer, will be given (364) by the 

 expression 



v 



V() ~ u 



We obtain thus 



n+1 



Lastly, the potential V of a shell at a point P at a distance r and 

 in a direction which makes the angle 6 with the axis, is from equation 

 (23), replacing /* by cos a, 



V= -2Tr\i -co3a + -sin 2 aX' 1 (a)X 1 (6>) + . +-- 

 (44) 



The first series is converging for ^-< ^, and the second for u< r. 

 At the surface of the sphere where r=u, the two series have the 

 same value if we have 0>a that is to say, if the point P is outside 

 the shell ; but when we have 0< a that is to say, for points of the 

 shell itself the difference of the two series is equal to 471-. 



The potential of a circular shell, or of a circular current, is thus 

 referred to an origin C situate at any given point of the axis. 



