420 Proceedings of the 



it was abandoned for the better plan of endeavouring' to make the 

 arcs of vibration as small and as equal as possible. This is the 

 problem, which has for two centuries exercised the ingenuity of the 

 first mathematicians and mechanics of the world, and the best so- 

 lution of which it is our object to illustrate. 



The three difficulties presented by this problem are^ as before 

 stated: j ^ n ,;. 



1. The varying friction of the pendulum. qoi«? oV it«ilndqfij«i'i' 



2. The varying- resistance of the air. ."<*> gnio^ ayasffii ??' 



3. The varying impulse given to the pendulum; i^ii) •?^ivt>'^i^»' v^fi^ 

 For the first and second no compensation is attempted to be made ; 

 they are merely reduced as much as possible, and this has been 

 done so effectually, that a pendulum once set in motion, has vi- 

 brated thirty hours without any renewal of the first impulse. ' 



The third cause of error, the varying impulse given to the pendu-*' 

 lum, has been the great object of attack. The disturbance which 

 the pendulum is liable to, from its connection with the motive part 

 of the instrument, is of two kinds. In the first place, the pendulum 

 receives a new impulse at each vibration, in order to maintain its 

 motion ; that impulse, it is true, always proceeds from the same 

 weight or spring, but that impulse, will vary when the timekeeper 

 is close wound up, and when nearly down ; this, however, is trifling, 

 and can be very nearly compensated by other contrivances : but 

 the weight or spring has to operate through the train of wheels, 

 which, at different times, will have different degrees of friction, and 

 will, therefore, transmit different quantities of power to the escape 

 wheel from which the pendulum receives its impulse. 



This defect cannot be remedied, that is to say, the motive energy 

 residing in the escape wheel cannot be made uniform. The object 

 sought after has, therefore, been to render the impulse given to the 

 pendulum independent of the force existent in the wheel which 

 gives that impulse ; and this has been accomplished by means of 

 successive improvements in the escapement, so perfectly, that in- 

 creasing the weight attached to a good timekeeper an hundred fold 

 will not increase the impulse given to the pendulum. 



In order to understand these gradual improvements in the escape- 

 ment, we must now observe minutely its mode of operation. 



The business of the escapement is to act as a sort of mediator 

 between the escape wheel, (which is always tending to increase its 

 motion by the natural accelerating tendency of the weight or spring,) 

 and the pendulum, which is always tending to diminish its motion 

 from ffictioji, and the air's resistance, The business of the escape- 



