374 ELECTKOSTATICS AND MAGNETISM. [PT. II. CH. IX. 



field. This is a consequence of the distributions on the ends 

 being infinitely distant. We may then measure K as the ratio of 



FIG. 77. 



the longitudinal magnetization to force, a method often used in 

 practice, and accurate only when the cylinder is extremely long. 



196. Ellipsoid of Revolution. In the case of an ellipsoid 

 of revolution the form of the integrals simplifies, and inserting in 

 the formulae of 116 the eccentricity e=*/a? fr/a we obtain for a 

 prolate ellipsoid 



T"-^ 1 "^! 1 ! l +e 



fl I - e 2 



(2) M=N=*TT i _ 'log 



" i e 

 and for an oblate ellipsoid 



(3) L = 4-7T j- 2 g sin" 1 e [ , 





For e all these expressions become indeterminate, but on 

 evaluating the indeterminate form they take the common value 

 already found for the sphere. For e 1 the expressions for the 

 prolate ellipsoid become indeterminate, and on evaluation we find 



