PHYSICAL ASTRONOMY. 



When x = r, this expression becomes - - - , 



o 



which is therefore the attraction at the surface of 

 the sphere. 



The force of attraction or of gravity at the surfaces 

 of different spheres, are therefore as their densities 

 multiplied into their radii. 



The force with which a particle placed 

 any where within a sphere, is urged toward the 

 centre of the sphere, is proportional to its dis- 

 tance from that centre. 



From what goes before, it is plain, that it is not at- 

 tracted by any part of the sphere more distant 

 from the centre than itself. It is therefore attract- 

 ed only by the sphere at the surface of which it 

 is placed. 



. If a particle be placed any where in the 

 interior of an elliptic spheroid ; and if through 

 it there be described a spheroidal surface, simi- 

 lar and similarly situated to the surface of the 

 spheroid, the particle will be urged only by the 

 attraction of the spheroid contained within this 

 surface, and the force of that attraction will be 

 the force acting on a particle similarly situated 



on 



