116 Professor Airy on the Disturbances of Pendulums, 



Since the theory is applicable to every case in which a pen- 

 dulum is acted on by small forces, it can be applied to determine 

 the effect produced on the motion of the pendulum of a clock, or 

 the balance of a watch, by the machinery which serves to maintain 

 that motion. After describing generally the manner in which 

 the weight by the intermediation of the wheel-work acts on the 

 pendulum, and stating the principles to be observed in the con- 

 struction of escapements which follow from the investigations 

 above, we shall proceed to examine the escapements which are 

 most in use. 



If a pendulum vibrates uninfluenced by any external forces 

 except that of gravity, the resistance of the air and the friction 

 at the point of suspension reduce gradually the extent of vibra- 

 tion. But this diminution goes on very slowly. I have observed 

 a i)endulura suspended on knife edges vibrate more than seven 

 hours before its arc was reduced from two degrees to \t\\ of a degree. 

 In order to maintain vibrations of the same or nearly the same 

 length (which for clocks is indispensible) a force must act on 

 the pendulum : this force is generally given by the action of 

 a tooth of the seconds wheel on the inclined surfaces of small 

 arms or pallets carried by the pendulum: and the whole ap- 

 paratus is called the escapement. It is necessary, therefore, in 

 the theory of escapements, to consider the motion of the pendulum 

 when, besides the force arising from its own weight, it is acted 

 on by the resistance of the air, &c. and by the force impressed 

 by the machinery. The fact stated above shews that the first of 

 these forces, and consequently the second, are so small that our 

 approximate theory is abundantly sufficient for this investi- 

 gation. 



Now it appears from Examples 2, 3, 4, 5, and 6, that the 

 friction and the resistance of the air do not affect the time of 

 vibration. The maintaining force, therefore, mast be impressed 



