and on the Theory of Escapements. 123 



as we please; consequently c'-\-c.c' — c is very small. If c and 

 c' were equal, the effect on the time would be absolutely nothing. 

 With this escapement, therefore, the effect of the maintaining 

 power on the rate of the pendulum may be made as small as 

 we please. 



It cannot, however, be made absolutely nothing. For the 

 wheel must be so adapted to the pallets, that when it is disengaged 

 from one it may strike the other, not on the acting surface, but 

 a little above it. That is, the instant of disengagement from a 

 pallet must follow the instant at which the pendulum is in its 

 middle position by a rather longer time than that by which the 

 instant of beginning to act preceded it. Therefore, c' must be 

 rather greater than c. But the difference may be made so small 

 that the effect on the clock's rate shall be almost insensible. 

 This escapement, therefore, approaches very nearly to absolute 

 perfection : and in this respect theory and practice are in exact 

 agreement. 



The impact at the beat indirectly affects the time of vibration 

 by producing, for a very short time, a considerable friction. This 

 cannot be estimated : but it will easily be seen that, as it takes 

 place after the pendulum has passed its lowest point, its effect 

 is to diminish the time of vibration. 



As the force of the spiral spring on a watch balance is (in 

 the best springs) proportional to the angular distance of the 

 balance from its position of rest, the same equations which ajjply 

 to the motion of a pendulum will apply also to the motion of 

 a balance. The comparative merits of watch escapements can, 

 therefore, be determined in the same manner as those of clock 

 escapements. The common crown wheel and verge escapement 

 is precisely similar in its action to the recoil escapement of 

 clocks, and has exactly the same defects. Mudge's detached es- 

 capement for watches is exactly similar in principle to Cumming's 



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