of a Finite Conservative System. 379 



and the corresponding next tooth falls on the other side of 

 the escapement. But there is a loss of energy by impacts and 

 slipping, both on the non-working and on the working faces 

 of the escapement. The loss on the working faces could be dis- 

 pensed with : but the loss on the non -working faces is essential 

 to the going of the clock. In our idealized clock we suppose 

 each recoil to exactly reverse the relative motion of tooth and 

 escapement in the direction perpendicular to the common 

 tangent plane of the two surfaces at their point of impact ; 

 and we suppose the surfaces to be perfectly Motionless, so 

 that the infinitely great mutual force at the instant of each 

 impact is exactly in that direction. The jumping action thus 

 produced would keep stopping the clock and letting it go on 

 again : and would utterly prevent any regularity of going. 

 Therefore I add the following arrangement of energy-receivers 

 to annul the shocks on the non-working faces of the escape- 

 ment : — Prolong the shaft of the escapement-wheel, and fix 

 on it, in helical order, sixty little arms each carrying at its 

 end a disk, with its front face in a plane through the axis. 

 Adjust the escapement-wheel on its shaft, so that when each 

 of its thirty teeth strikes one or other of the two branches of 

 the escapement, the lowest one of those sixty disks has its front 

 face vertical. On a horizontal plane below the prolongation 

 of the shaft place sixty little balls (energy-receivers) in such 

 positions that each shall be struck by a disk^'wstf before the 

 corresponding tooth touches the corresponding branch of the 

 escapement. Let the mass of each ball be equal to the proper 

 inertia-equivalent"* of A, (the escapement-wheel, &c, and 

 driving-weight). Each ball struck by it, receives the whole 

 kinetic energy which A had before the impact ; and leaves A 

 at rest, with a tooth of the escapement-wheel pressing on a non- 

 working face of the escapement. Fix sixty rigid stops to pre- 

 vent the balls from, in any circumstances, (§ § 13 ... 16), going 

 too far behind the positions in which they are initially placed. 

 Each of these stops must be slotted, to allow the proper disk 

 of the escapement-shaft to strike the ball and afterwards pass 

 clear through with its carrying arm. For brevity these 

 forked stops will be called the home-stops. Fix also sixty 

 other stops, (field-stops we shall call them) in such positions 

 that the balls shall strike them all simultaneously and at 

 exactly the instant (§12) when the weight strikes the bottom 

 of the clock-case. 



* Let r. be the radius of the cord-drum : W the driving-weight : h the 

 radius of gyration, and w the weight of the whole rotating body con- 

 sisting of cord-drum, escapement-wheel, shaft, and 60 arms and disks : a 

 the length of each arm reckoned from the axis to the point of its disk 

 which strikes the ball. The " proper inertia-equivalent " is (Wr 2 -\-ivli 2 ) Id 2 . 



