CHAPTER H. 



EHYTHM. 



The third corollary from the persistence of force may best 

 be introduced by a reconsideration of the simplest case of 

 motion contemplated by the preceding corollary. The reali- 

 zation of Galileo's first law of motion — the law that a 

 moving body must for ever continue in a straight line with 

 uniform velocity — obviously postulates the non-existence of 

 any other matter than that contained in the body in ques- 

 tion. If there were but one body in the universe, that body, 

 when once set in motion, would never alter its direction, or 

 undergo any increase or diminution of velocity. The intro- 

 duction of a second body, attracting the first and attracted 

 by it, alters the result in a way which now demands brief 

 consideration. If the motion with which the two bodies 

 start is such as would carry them along a straight line 

 toward each other, they must obviously rush together, and 

 the case is thus again reduced to that of a single moving 

 body. But this case is too simple to have been ever actually 

 realized. What we have to deal with is the case of two 

 bodies which are moving in independent directions. For 

 the sake of simplicity, let us suppose that the second body, 

 B, is so much heavier than the first body, A, that the 

 commcn centre of gravity of the two lies within B's peri- 



