CuAP. XXI.] THE HEAVENS. 245 



PEOPOSITION XIX. 



Theorem. — The revolving force of the sun's gravita- 

 tion in the orbits of the planets is directly as 

 the ratio which the velocities of the orbital and 

 lagging motions bear to each other in each orbit 

 respectively. 



Because the revolving force resulting from the 

 difference in the motive action of any two particles in 

 opposite hemispheres of the sun at corresponding 

 points in those hemispheres is inversely as the cube 

 of the planet's distance from the sun : for it is shown 

 by the table annexed that the ratio of forces acting 

 from R and s, close to the surface of the sun, differs so 

 little from that acting from y and z, near the respec- 

 tive centres of the opposite hemispheres, that for the 

 purpose of the present argument the aggregate action 

 of the two opposite hemispheres at the actual distance 

 of the planets may be treated as inversely as the 

 cube of the distance from the sun. And, by the same 

 table, the ratio of velocities also closely approximates 

 to the inverse cube of the distance with the minimum 

 lagging velocity indicated by the foregoing Proposi- 

 tion ; and a greater lagging velocity would make the 

 ratio of velocities more nearly approximate to the 

 inverse cube of the distance calculated from the centre 



