INFLUENCE OF THE CASE. 177 



If the product mm is replaced by its approximate value fd 2 , and 



R 2 

 by , we get 



//' sin a ( d~ 



(10) / i- - =C(A + a). 



When the radius R of the sphere is great enough in reference to 



-n 2 



the distances / and /', we may replace x by D or , which gives 



//'sin o 



~ 



3 ~] 



J 



Comparing with equation (2), we see that the factor of correction 



/ 

 is equal to ( 



Let us still suppose the masses equal, and the balls of the same 

 radius, and let V be the potential of each ball produced by the 

 mass m. The true potential will be 



Replacing m by the approximate value given by the first of the 

 equations (4), we have 



< 



R 2 

 If x further be replaced by , to have an idea of the im- 



portance of the correction, we get 



Making / = -R, and adopting the same numerical values as 



4 

 above, the correction is about 0*15. 



VOL. II. N 



