132 Mr Sang on the Manner in xchkh 



This being premised, I proceed to consider the motion of the 

 watch-balance, when maintained by what is technically called 

 the chronometer escapement Disregarding the minute resist- 

 ances experienced in the repassing of the slender spring attached 

 to the detent lever, and in lifting the detent itself, the action of 

 this escapement may be thus described : 



If V represent the centre of the oscillations, VF = Vf the 



amount of friction, and A the point from which the oscillation 

 commences, the elasticity of the spring, acting with an inten- 

 sity proportional to VA, but diminished by the friction VF, 

 will cause the balance to describe an oscillation round F as a 

 vertex, and carry it to the distance FA^ = FA on the other 

 side. The time of this oscillation may be represented by the 

 half revolution A FA,. 



When the balance begins to return from A,, it encounters a 

 friction V/J and would clearly fall short of A, by a distance 

 double of ¥f. I'o prevent this, to restore the motion destroyed 

 and to be destroyed by the friction, the maintaining power of 

 the movement is introduced at the instant, we shall suppose, 

 when the balance has reached the position B. Having erected 

 the perpendicular BD, and cut it by the arc A^B from the 

 centre f, BD will represent the velocity at B, and the angle 

 A,J"D the time occupied in the description of the path A,B. 

 Bepresenting by the lineyM the intensity of the pressure com- 

 municated by the impulse tooth, M will clearly be the vertex 

 of the minute part of an oscillation performed by the balance 

 while under the influence of the maintaining power ; the ordi- 



