en. 11.] RHYTHM. 299 



The illustration is a very trite one, being approximately 

 realized in every case of planetary revolution, but the space 

 here given to it is justified by the supreme importance of the 

 principle 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 unvary- 

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

 moving in independent directions and exerting attractive 

 forces upon each other, must for ever move in directions 

 which rhythmically vary, and with velocities which are 

 rhythmically augmented and diminished. Thus the rhythm 

 of motion is a corollary from the persistence of force. Our 

 only alternatives are rhythm, or invariable velocity in an 

 invariable direction. The latter alternative being excluded 

 by the fact that in the known universe innumerable bodies 

 coexist, it follows that we must adopt the former, and admit 

 that all motion is and must be rhythmical. 



The direct dependence of this conclusion upon the axiom 

 of the persistence of force is still further illustrated by the 

 case of the pendulum. Let us imagine, for the sake of 

 definiteness, a heavy bob at the end of a rigid wire. When 

 the bob is raised to leftward of the perpendicular, and then 

 left to the action of gravity, it at once begins to descend. 

 But while it is descending, gravity is at each instant adding 

 to its momentum, so that, when it reaches the perpendicular, 

 it cannot stop, but is carried along to rightward until 

 all the added momentum is lost again ; that is, until it has 

 ascended to a height equal to that from which it began to 

 descend. Being now left to the unhindered action of gravity, 

 the same series of motions will occur in the reverse direction, 

 and so on for ever. Strictly speaking, no such case can be 

 realized ; since all the lost momentum is not expended in 

 neutralizing gravity, but part of it is employed in communi- 

 cating motion to the environing atmosphere, and part of it is 



