118 Professor Airy on the Disturbances of Pendulums, 



The escapements of docks in general use may be divided 

 into the three following classes: recoil escapements, dead-beat 

 escapements : and the escapements in which the action of the 

 wheels raises a small weight which by its descent accelerates 

 the pendulum. The last may be called, from the name of their 

 tirst proposer, Cumming's escapements. 



I shall first observe that the friction which in the recoil and 

 dead-beat escapements takes place during the whole vibration does 

 not appear to affect the time lof vibration. This friction may be 

 separated into two parts: that which is properly called friction, 

 arising from the rubbing of two bodies, and that which arises 

 from the viscidity of the oil. The former of these is generally 

 considered to be constant, and the latter to vary nearly as the 

 velocity. Consequently, by Examples 2 and 3, they do not alter 

 . the time of oscillation. It is undoubtedly important that friction 

 .should be avoided if possible, as a smaller maintaining power 

 is then required, and the irregularities which it may occasion 

 in the pendulum's motion are proportionally diminished. In 

 the dead-beat escapement this friction is interrupted during the 

 time in which the wheel is acting on the pallets. We may, 

 however, suppose a retarding force to act during this time, pro- 

 vided we add to the maintaining power an equal force. In 

 Cumming's escapement the friction is nothing. 



In the recoil escapement, soon after the pendulum has passed 

 its lowest position a force begins to retard it till it reaches the 

 extremity of its vibration: then (acting still in the same direction) 

 it accelerates it till it has again passed the lowest point by the 

 same distance as before : then another retarding force commences 

 its action, &c. We may then consider the action of the force 

 as divided into two parts, of which one retards the ascent of the 

 pendulum and accelerates its descent, and the other accelerates 

 the pendulum a little before and a little after it has reached its 

 lowest point. The former of these, by Example 9, has no effect 



