126 Professor Airy on the Disturbances of Pendulums, 



carries the seconds' hand : it is represented in the figure with 

 60 pins perpendicular to its plane : instead of a wheel with pins, 

 a crown wheel can be used. B is the crutch for the pendulum, 

 in its position of rest. C the pallet, carried by the arm CD : in 

 the position of rest it will be between two pins of the wheel. 

 E a small ,pin carried by the arm CD. FG a spring fixed at F: 

 flexible towards F, and stiff in the remaining part: it carries 

 a tooth H concealed in fig. 1, by the rim of the wheel, but shewn 

 in fig. 2 : this tooth stops the wheel J by catching one of its 

 pins. KL a very weak spring attached at K to the under side 

 of FG : the part at L projects beyond the rest, that it may be 

 touched by the pin E. The action of this escapement is very 

 simple. When the pendulum moves so that C approaches the 

 center of the wheel, the pin F touches L, and (as the spring KL 

 is very weak) passes it without any sensible retardation. When 

 it returns, immediately before the middle of its vibration, the 

 same pin touches the under side of L, and as L cannot yield 

 without raising FG, it lifts the tooth H from the pin of the 

 wheel which it held, and the wheel thus set at liberty immediately 

 acts on the pallet C. Before it has finished its action, the pin 

 -F has let go the spring L, and H has descended so as to catch 

 another tooth as soon as the action shall have ceased. The pen- 

 dulum, it is plain, receives but one impulse in two vibrations, 

 and, therefore, for a seconds' beat, a half second pendulum would 

 be necessary. 



To investigate the effect of these actions on the time of vi- 

 bration, omitting nothing, let z be the distance of the pendulum 

 from its middle point when the action on the pallet begins, z+c 

 that when it ends, z — e the mean tlistance at which the resistance 

 of the spring FG takes place, and z-k that at which the resistance 

 of KL takes place as the pendulum returns. Let the action on 

 the pallet be supposed constant and = F: and for the springs, 



