274 ELECTROSTATICS. [PT. II. CH. VI. 



i.e., when the ellipsoid is oblate, and 



f ^ =^=10 



Jo (a 2 + s) V c 2 + s Vc 2 -a 2 



when the ellipsoid is prolate. The capacity is 



1 1 ir -< 'rl 



Va 2 - c 2 ' 

 sin" 1 



a 

 Vc 2 - a 2 



ir ., 

 , prolate ellipsoid. 



For a very long prolate ellipsoid, neglecting f-J , 



c 



= 



so that as a approaches zero, the capacity approaches zero, but 

 more slowly, viz., logarithmically*. 



In the limiting case of an oblate ellipsoid, for c = 0, we have a 

 circular disc, whose capacity is 



If in the expression for the surface density we eliminate c by 

 the equation of the ellipsoid, 



a 2 b* 



/**(- a? f* 



V a 4+ 6 4+ 7A a 2 "^ 



