422 



Put I 



54) 



55) 



VIII. NEWTONIAN POTENTIAL FUNCTION 

 c, a being the axis of revolution, 



du 1 /TT- 



1 J (i 



X = 



56) 

 where 



Put 



C - - j 



J (V + u}(a*+uY< 

 a 



co 



y C -- du / _ 



y (6H) f y f +~ 



_ 1 



" 



ds. 



When u = oo, s = 0; when u = 6, s =1/ , 2 , a > 



so that 



57) r~,aVf- -W-W -- 

 ^7 s s (6 2 - a ! )V(6 s - a 8 ) (1 - s 8 ) 



ds 



no\ TT- 



= 



59) X = 2*aVxT ___ 



J S 8(ft2 



4:7cab 2 x / s*ds 



~A / " ~ 



(& 2 -a 2 )2,y (l-s 2 ) 



Now 



/s 2 ds s 



^l == W 



