248 



THE OCEAls^. 



[Book X. 



Appakent Velocities, 



The ratios above are inversely as the cubes of the 

 distances of the planets from the sun, or dn-ectly as 

 the sun's revolving force in each orbit (approxi- 

 mately), as shown by the table on p. 246. 



The ratios of real velocities and lagging, with 

 the maximum correction for the latter alluded to 

 in Proposition III., is also given in the table just 

 mentioned. 



PROPOSITION XX. 



Iheorem. — The relative velocities of the lagging 

 motions of the planets are as the square roots of 

 the ratio which vis-inertise bears to the direct 

 and revolving force of the sun's gravitation in 

 their respective orbits. 



For the ratio of forces is as the fifth power of the 

 distance (Proposition XI Y.) 



