122 Professor Airy on the Disturbances of Pendulums, 



will alter the rate. And with the usual form of the pallets no 

 law of resistance can be found which will make the vibrations 

 isochronous. 



In Cumming's escapements, the action of the wheels raises 

 a weight through a small space. It is then carried up by the 

 pendulum, and descends with the pendulum, till the latter has 

 arrived at its lowest point. This case, then, is almost exactly 

 the .same as the last, with this exception, that the force which 

 acts on the pendulum is independent of the irregularities in the 

 force transmitted through the wheel-work. If, however, the 

 length of the arc of vibration undergo any change, the time 

 of vibration will be changed. The principle of this construction 

 is, therefore, almost as bad as that of the former. 



We now come to the dead-beat escapement. Here the wheel 

 acts on the pallet for a small space near the middle of the vibration : 

 and during the remainder of the vibration it has no effect except 

 in producing a slight friction. The impact also at the beat does 

 not tend to accelerate or retard the pendulum. Neglecting then 

 the consideration of the friction, we have a constant force F, 

 which begins to act when x= -c, and ceases when x = c'. Taking 



Fx 



— /" 



between those limits, we have for the proportional increase of 

 time, 



This is a quantity extremely minute. For c and c' are generally 

 small compared with a, and c'-c may be made almost as small 



