.Chap. XXI.] THE HEAVENS. 229 



minor question until, after elucidating the general 

 principles, greater accuracy becomes requisite for 

 matters of detail. 



Corollary. — Subject to the foregoing Definition, 

 the fraction of the sun's direct force of gravitation at 

 any distance, which acts as a revolving force, is in- 

 versely as the distance, as shown by the table on 

 page 82, as regards the actual distances of the planets 

 from the sun. 



PEOPOSITION IV. 



Theorem. — The revolving force of the gravitation of 

 a sphere is inversely as the cube of the distance 

 from it. 



Because the direct force of gravitation is in- 

 versely as the square of the distance, and the ratio 

 which the revolving force bears to the direct force is 

 inversely as the distance (Proposition III.) ; therefore 

 the revolving force of the gravitation of a sphere is, 

 at different distances, inversely as the cubes of the 

 distances.^ 



^ This is demonstrated also by the Table of Forces and Velocities 

 given in Proposition XIX., which also shows the slight difference 

 in the ratio of forces, at the actual distances of the planets, acting 

 from the centres of the opposite hemispheres of the sun and from 

 the svirfaces of the same. 



