the Dead Escapement. 23 



and the number of teeth of the wheel the pallets take over; and 

 that the escapement may be constructed to lead the pendulum an 

 equal quantity, with the pallets made to take over a few teeth, 

 and with a low angle of lead ; or with the pallets made to take 

 over a greater number of teeth, and with a high angle of lead. 

 It may further be noticed, that the lower the angle of the inclined 

 planes, the less will be the friction upon them, and consequently 

 the easier the action of the wheel upon the pallets : because the 

 lower the angle the shorter the inclined planes : and, on the con- 

 trary, the higher the angle and the longer the inclined planes, the 

 greater the friction, and the more unfavourable the action of the 

 wheel on the pallets. At the same time it is to be observed, that 

 the less the friction on the inclined planes, the greater the friction 

 on the rests. Supposing the case of two dead escapements, si- 

 milar in every respect except the angle of lead, of which the pen- 

 dulums are made to vibrate equal angles, (here the angle of vi- 

 bration must not be confounded with the angle of lead,) and the 

 pallets of the one constructed with a low angle of lead taking 

 over a few teeth, and the pallets of the other with a high angle 

 and taking over a greater number of teeth ; there will in the first 

 case be less friction on the inclined planes and more on the rests, 

 and in the second more friction on the inclined planes and less on 

 the rests ; and consequently, in the case of the pallets with a low 

 angle of lead, of the total space of time which is occupied by 

 each vibration of the pendulum, a less portion will be engaged 

 during the advance of the wheel and the giving the impulse, than 

 during the action of the wheel on the rests of the pallets ; whereas, 

 in the case of the pallets made with a high angle of lead, the 

 direct contrary will occur; unless, indeed, which is a possible 

 case, the angle of lead should lead the pendulum exactly half the 

 angle of vibration, when the portion of time the wheel is engaged 

 on the inclined planes will be equal to that it is engaged on the 

 rests of the pallets. This observation is made on the supposition 

 that the whole vibration of the pendulum is made with equal ve- 

 locity, which is not the case; but as the pendulum is acted upon 

 by the clock through the inclined planes of the pallets, both 



