ATTRACTION. OBLATE SPHEROID. 



fore the attract! i on the particle 



218. T<> f ml the attraction of a 

 qftmafl eccentricity an a particle at it* equator. 



'*s the length of i it of the 



major axU of the generating ellipse. The spheroid roar be 



supposed to be the difference between a concentric sphere 



i and a shell, and the attractions of the sphere and 



fli'-ll may be separately calculated. Let a - made of 



the sphere and spheroid by a plane perpendicular to the straight 



ng the attracted pnrtid with tin* common centre of 



the sphere and siihcmid, an<l nt a distance x from the at- 



tracted particle ; thin plane will sphere in a 



area of which is iry", where y-2ax-x*, and it will cut the 



id in an ellipse of v 



y and r ^ , and the area of which is therefore - : - 



a a 



ferencc of the two areas is ir f 1 - H y*. If a section be 



made by a second plane par: and at a 



distance ox from it, the volume of the portion of the shell 



ted between the planes will be W 1 - - J /&r. The 



.ry particle <: ulus thus formed from the 



rticle is ar 



ted particle is approximately V(2or) ; and as the result- 

 annulus will act along the straight line join- 

 ing the attracted particle with the centre, it will approximately 



-"(-I) 

 --K-3 



J.M-i - 



fore the resultant attraction of the shell 



a - c ) 



