380 Sir W. Thomson on Periodic Motion 



12. Suppose now the pendulum of our ideal clock, with its 

 weight wound up very nearly to the top, to be started with 

 sufficient range to let it keep going. For simplicity let this 

 range be small enough to secure that when the weight is run 

 down, the augmented range of vibration will still be within the 

 limits allowed for proper action of the escapement mechanism. 

 Let the bottom of the clock-case be a rigid horizontal plane 

 fixed relatively to the framework bearing the wheel and pen- 

 dulum in exactly such a position that when the weight, in 

 running down, strikes it, the pendulum is at either end of its 

 range. The weight jumps up after the impact, and the clock 

 goes backwards, the energy-receivers return home from their 

 held stops at exactly the right times, retracing exactly every 

 step till the weight (wound up by the energy of the pendulum 

 and of the returning energy-receivers) passes through its 

 initial position. If it is allowed to go higher till it strikes 

 against an unadjusted stop, the clock may be stopped for a 

 time, with the pendulum vibrating through a moderately 

 small range, and one tooth of the wheel chattering against 

 one working facet of the escapement : but " sooner or later " 

 (very soon) the tooth will escape ; the clock will again go 

 forward ; the weight will run down, and again strike the 

 bottom and jump from it, this time not when the pendulum is 

 quite exactly at either end of its range. 



13. Complicated but quite orderly action will follow ; and 

 " sooner or later " a tooth will be hooked up by the escape- 

 ment and the clock will go backwards a beat or two ; but 

 after a very few beats, if more than one, it will go forward 

 till the weight strikes the bottom again. " Sooner or later " 

 the bottom will be struck at a time when the pendulum is 

 very nearly at rest at either end of its range and when several 

 energy-receivers are in such positions as to arrive home and 

 strike disks at right times ; and the clock will go backwards 

 for a good many beats. 



14. " Sooner or later," that is to say after some finite number 

 of millions of millions of years, the weight will strike the bottom 

 when the pendulum is so very nearly at rest at either end of 

 its range and all the sixty balls so very nearly striking each 

 its field-stop, that the clock will be driven back, winding up 

 the weight till it again strikes the top stop, and immediately, 

 or after a very few beats, begins again to go forward and 

 let the weight run down. But our subject is not the fortuitous 

 concourse of atoms. It is "periodic motion of a finite 

 system.'' 



15. Returning therefore to the end of § 12 ; let the top 

 stop be so adjusted that it is struck by the weight at an instant 



