the Times of Vibration of Watch Balances. 15 1 
of the balance wheel from the pallet qr ; the balance wheel accord- 
ingly revolves, and the upper tooth meeting with the pallet p, 
winds up the auxiliary spring u as before. The balance with 
the crank proceeding to describe the remaining semiarc k E, 
winds up the spring v through the further angle k C E = 108° ; 
the balance returns through the semiarc EO, by the joint action 
of the balance spring and the auxiliary spring v, both of which 
cease to accelerate the balance the instant it has arrived at O, 
It is remarkable, according to this construction, that no force 
or impulse whatever is communicated to the balance from the 
main spring, and yet the vibrations are continued of their due 
length : on further consideration it appears that the maintain- 
ing power of the machine, instead of communicating any force 
or impulse, acts by removing a part of the force which retards the 
balance while it is describing the latter semiarc of each vibration. 
In the preceding account it has been shewn, that the balance 
describes the semiarc from B to O by the joint action of the two 
springs; now for a moment let it be supposed that the balance 
vibrated through the entire arc B OE {fig. 7 and 8.) by the joint 
action of the two springs, in the same manner as if one balance 
spring only was applied of the same strength with both ; in 
this case, the balance commencing its vibration at the extre- 
mity of the arc B, after having passed the semiarc B O with an 
accelerated motion, would describe an equal arc O E on the 
other side of O, by retarded motion, provided it was not ob- 
structed by friction or other irregular resistances ; but such 
resistances taking place will cause the latter semiarc, which is 
described by retarded motion, to fall short of the arc O E by 
some small difference ES. There are two modes by which 
this latter semiarc may be restored to its due length O E ; 
either by communicating an impulse to the balance from the 
