280 ATTRACTION. I.IM I snir.liOID. 



supposed made Up of a trifl sphere, the radius of which 



is c, and an exteri<>r sin -11 ; we shall calculate t linns 



of these portions separately. 



Let a section be made of the sphc heroic! by a 



perpendicular to the axis of revolution of the sp! 

 at a distance x fmm the attracted particle. This plane < -uts 

 the sphere and spheroid in concentric circles; the ana of the 



former being Try* and of the latter ~- t where y* = 2cx x*\ 



c 



the difference of these areas is TT f a a 1 J y\ If a section be 



made by a second plane, parallel to the former and at a 

 distance &x from it, the volume of the portion of tin- 



/a* \ 

 intercepted between the planes will be Trf -j Ijy'Sx. The 



distance of every particle of the annul us thus formed from 

 the attracted particle is approximately V(2c#), and, as the 

 resultant attraction of the annulus will act along the axis of 

 the spheroid, it will, approximately, 



'a* _ \ x y*8x 



7TO - 2 - 1 



H 2 (2c)* 



Therefore the resultant attraction of the shell 



4 _ , 

 ( 



If we suppose c = a (1 e), e being very small, we have 



a 7 c 2 = 2c*e approximately ; 

 therefore the resultant attraction of the shell 



Also the attraction 'of the sphere on the particle, by Art. 212, 



