RHYTHM 



position alongside of b, its momentum is con- 

 siderably in excess of b's attraction, and it is 

 consequently carried on toward a point in the 

 rear of b. The same rhythmical decrease and 

 increase in a's momentum continues until the 

 curve is completed, and a has reached the posi- 

 tion from which it started. Thus our attracted 

 body, instead of moving in a straight line, 

 moves in a closed curve of which one of the 

 foci must coincide in position with the common 

 centre of gravity of the attracted and attracting 

 bodies. The result which we have here ob- 

 tained by supposing a to be so much smaller 

 than b that its reciprocal influence upon b's 

 motion might be left unconsidered is not al- 

 tered if we suppose a and b to be equal in size. 

 In this case the common centre of gravity lies 

 midway between the two bodies, and is the 

 common focus of the two closed curves respec- 

 tively described by them. 



The illustration is a very trite one, being ap- 

 proximately realized in every case of planetary 

 revolution, but the space here given to it is jus- 

 tified by the supreme importance of the princi- 

 ple now to be generalized from it. To Galileo's 

 first law of motion there is now to be added a 

 supplemental law. As a single moving body, in 

 an otherwise empty universe, would move for- 

 ever with unvarying velocity in an unvarying 

 direction ; so, on the other hand, two or more 



165 



