128 Professor Airy on the Disturbances of Pendulums, ^c. 



arcs than for small (supposing F to be unchanged) : if the action 



began after it, the contrary effect would take place. If we take 



for F a force sufficient to counteract the resistance of the air 



supposed to be as the square of the velocity ; since the diminution 



of the arc from that cause = »ja", and the increase from the action 



„ „ Fc _, , Fc , „ mn-a' AF . 



oi F = —r- , we must have -,- = wia , or F = ; .-. — 5- is 



na n a c a 



independent of a, and the clock's rate would be the same under 



all variations of the maintaining power. If the resistance be 



supposed to follow any other law, the clock's rate will not be 



independent of a, except the action takes place as is above 



described. 



The advantages which this escapement seems to offer are as 

 follows : 



1st. It would not require greater delicacy of workmanship, 

 perhaps less, than the common dead-beat. 



2d. It possesses in theory all the advantages of the detached 

 escapement in watches. 



3d. The clock would never be out of beat. 



Whether the shortness of the pendulum for a given rate of 

 beat would be any disadvantage, I do not know. The con- 

 struction would, however, I apprehend, be very convenient for 

 a portable clock. It is evident that by a repetition of tliis con- 

 struction, the clock might be made to beat at every vibration : 

 but several advantages would be lost by this complication. 



G. B. AIRY. 



Trinity College, 

 Nov. 10, 1827- 



