and on the Tlieory of Escapements. 121 



the same vibration : then, as it is required that the acceleration 

 produced by the maintaining power shall be invariable, we must 

 have 



2 F Ja'-e ^ ^ 2 C „ Ca^ 



. — ; . -5^ — J — = a constant = ■ — , , or F *= , „ . 



The increase of the arc in consequence will be 



No resistance expressed in positive powers of the velocity will 

 give a diminution of the arc of this form, and therefore it is im- 

 possible to make the vibrations isochronous. 



Besides the forces already considered, there is the impact on 

 the pallet which takes place at the beat. As this depends on 

 the weight of the wheels, &c., it is impossible to measure it, but 

 we can discover the nature of the effect which it will produce. 

 It may be represented by a force - G, acting through a very 

 small space h at the distance c. It will therefore diminish the 

 time of vibration by 



1 Ghc 



This evidently diminishes as a is increased, and therefore this 

 force produces the same effect as the others. 



We have now sufficient data to enable us to form a judgment 

 of the merits of this escapement. It appears that the maintaining 

 power will always enter into the expression for the time of vi- 

 bration : consequently, any obstruction or friction of the wheel- 

 work will affect the rate of the clock. The arc also generally 

 enters, and therefore any alteration of the extent of vibration 



Fo/. III. Part I. ' Q 



