306 EQUATION WHICH V SATISFIES. 



suppose a ;iln'd in T il shall include 



the attracted and let I' - I",-' I',, when- I"., n-t'cr- to 



the sphere and Fj to the remainder of tin- attracting body; 

 then 



<PF d*V d*V 



da 9 + dV + ~3c 



db dc 



I d'V, d*]\ 

 ~ "" 



by what has been already proved. 



Now the centre of the sphere may be chosen as near the 

 attracted particle as we please, and the radius of the sphere 

 may be taken so small that its density may be considered 

 ultimately uniform, and equal to that at the point (a, b, c). 



Let a, /?, 7 be the co-ordinates of the centre of the sphere ; 

 then the attractions of the sphere on the particle parallel to 

 the axes are, by Art. 212, 



<U\ 

 ^' 



. - 

 therefore 



, f d*V d*V d'V 



therefore +_+_ 



240. A ' >n to the Sphere. In Art. 237 we havi 



calculated V by direct integration in the case of a body com 



