Chap. VII.] GRAVITATION AND INERTION. 



83 



These actual velocities, deduced from tlie approxi- 

 mate measurements of tlie relative distances and 

 periods, are the same as those in the theoretical 

 table ; for : 



The first of the foregoing tables shows that the 

 fraction of the sun's direct force which acts as a 

 revolving force is, approximately, inversely as the 

 distance from the sun. And, as the total of the 

 direct force is itself inversely as the square of the 

 distance, the revolving force of the sun's gravitation 

 is, therefore, inversely as the cube of the distance 

 from the sun, approximately ; and, this being so, it 

 is then a mere matter of fact that the square roots 

 of the revolving forces in the different orbits of the 

 planets represent, approximately, the actually appa- 

 rent velocities with which, if viewed from the sun, 

 they would be seen to move, threading their way east- 

 wards among the fixed stars. Or, in other words, 

 the rapidity with which an orbital revolution is 

 accomplished increases or decreases directly as the 



G 2 



