THE CONTINUITY OF MOTION. 1S7 



eration and now retardation, yet the average speed is con- 

 stant through successive revolutions. Though the pendu- 

 lum comes to a momentary rest at the end of each swing, 

 and then begins a reverse motion; yet the oscillation, con- 

 sidered as a whole, is continuous: friction and atmospheric 

 resistance being absent, this alternation of states will go on 

 for ever. 



What, then, do these cases show us in common? That 

 which vision familiarizes us with in Motion, and that which 

 has thus been made the dominant element in our conception 

 of Motion, is not the element of which we can allege con- 

 tinuity. If we regard Motion simply as change of place; 

 then the pendulum shows us both that the rate of this 

 change may vary from instant to instant, and that, ceasing 

 at intervals, it may be afresh initiated. 



But if what we may call the translation-element in Mo- 

 tion is not continuous, what is continuous? If, watching 

 like Galileo a swinging chandelier, we observe, not its iso- 

 chronism, but the recurring reversal of its swing, we are 

 impressed with the fact that though, at the end of each 

 swing, the translation through space ceases, yet there is 

 something which does not cease ; for the translation recom- 

 mences in the opposite direction. And on remembering 

 that when a violent push was given to the chandelier it 

 described a larger arc, and was a longer time before the 

 resistance of the air destroyed its oscillations, we are shown 

 that what continues to exist during these oscillations is 

 some correlative of the muscular effort which put the chan- 

 delier in motion. The truth forced on our attention by 

 these facts and inferences, is that translation through space 

 is not itself an existence ; and that hence the cessation of 

 Motion, considered simply as translation, is not the cessa- 

 tion of an existence, but is the cessation of a certain sign of 

 an existence — a sign occurring under certain conditions. 



Still there remains a difficulty. If that element in the 

 chandelier's motion of which alone we can allege continuity, 



