176 THE WORLD-ENERGY 



toward the sun was a process of accumulating energy 

 by which they were able to resist actually falling into 

 the central body, and by which also they are now seen 

 to actually "fall" away from that body. 



Centripetal force is direct attraction. Centrifugal 

 force is energy of motion, due to attraction, but hav- 

 ing a tangential direction, this tangential direction 

 itself being due to the complexity of gravitative rela- 

 tion inherent in the group of the assumed three 

 bodies. 



It ought to be remarked, finally, that the movement 

 away from the central body on the part of the smaller 

 masses necessarily takes place in opposition to the attraction 

 between them and the central body. Hence, their velocity 

 must now diminish until, their centrifugal force becoming 

 less than the force of attraction between them and the 

 central body, they gradually return upon their path of 

 approach toward the central body, to repeat the same 

 round. 



It is easy to see, too, from the relations of force here 

 developed, that the path of a smaller body revolving 

 about a larger one must approximate an ellipse, and that, 

 as was discovered by Kepler, the radius vector must 

 describe equal areas in equal times. 



Such, it seems perfectly safe to assume, is the nature 

 of all curvilinear motion, and hence of all motion what- 

 ever, throughout space. It may be rendered incalculably 

 complex by multiple attractions. But in every case the 

 perturbations in the movements of the heavenly bodies 

 are but the further illustration of the same law of rela- 

 tion necessarily applying as between all the force-centers 

 of the material universe, as has been repeatedly and 



