OUTLINES OF NATURAL PHILOSOPHY. 



on the surface of the exterior spheroid, as the 

 transverse axis of the interior to the transverse 



axis of the exterior spheroid. 



. 



296. If in an oblate spheroid differing little 

 from a sphere, b be the polar semi-axis, b + c the 

 radius of the equator, and <p the angle which a 

 line drawn from the centre to a given point on 

 the surface makes with the axis of the sphe- 

 roid^ the force with which the given point is 

 attracted by the spheroid ; 



4 * b f c 4 sin* <p\ 

 /= ~3~V + b' 5~~J' 



At the equator, where q> = 90, this becomes 



c 3\ 



/T 5/ * {&$**. P ' wnere ^ = > 



For a very elementary demonstration of this theorem, 

 see the Notes on NEWTON'S Principia, by MADAME 

 DU CHASTELLET, Principes, &c. torn. n. p. 237, 



> 297' If in an oblate spheroid, a be the semi- 

 transverse axis, and e the eccentricity of the 

 meridian j then, if gravity at the surface, in the 



plane 



