288 ATTRACTION. OBLATE SPHEROID. 



When this is the case, 



zr ~ 



fore ^r' (r) -}- C . ty'" (r) + . . . = A, 



whatever c is, A being a constant independent of c ; therefore 



From the second condition, we have 



where -#, -#', and .#" arc constants. 



Hence ^' (r) or r/< (r) Jr = ' + 2J5" r ; 



therefore /< (r) dr = 



therefore 



with this value of </> (r) all the other equations of condition 

 are satisfied; hence the only law which satisfies tin- i-omlitiun 

 is that of the inverse square. 



226. To find the attraction of a homogeneous ol>lii< *pl 

 on a particle 'U mass, the law of attraction />< itcj that 



of the inverse square of the distance. 



Let a and c be the semi-axes, a being greater than < ; and 

 let the equation to the spheroid referred to its centre as origin 



*- ..................... <> 



t/, #, h be the co-ordinates of the attract. ,1 panic! 

 the distance from the attracted particle of any point of the 

 Z mass; 6 the angle which r makes with a straight 

 line parallel to the axis of z ; < the angle which the plane 



