CiiAP. XXL] THE HEAVENS. 275 



and aphelion might occur together outside ; or the 

 points of perigee and perihelion might be for ever 

 changing their relative positions. 



6. Throughout these problems we have dealt 

 with the motions caused by the revolving forces and 

 controlled by the forces of astral gravitation brought 

 into action by the motions : but in those motions the 

 heavenly bodies are held in equilibrium between the 

 forces of astral gravitation and the direct forces 

 of the gravitation of the bodies round which they 

 are revolved ; therefore the study of gravitation, as 

 followed by Newton and subsequent astronomers, 

 must show its action to harmonise with the motions 

 caused by the revolving forces. 



But as the laws of vis-inertia? have indicated the 

 cause of the motions which have been the objects of 

 study, it is evident that the science of astronomy 

 must be simplified and more easily extended by the 

 use of this new power of reasoning from cause to 

 effect than by the former process of demonstrating 

 the necessary connection of concomitant effects, pro- 

 ceeding from an unknown cause. ^ 



But, as regards the revolution of the apsides, one 

 part of the force which determines it will probably 

 have to be ascertained, by analogy, from its effects. 



' The paper on the Secular Acceleration of the Moon's Motion 

 which forms Chapter XIII. of The New Princij)les of Natural 

 Philosojyhy , is an extension of the argument of these Propositions, 

 and forms a practical corroboration of the above remarks. 



T 2 



