the Times of Vibration of Watch Balances. 149 
Suppose that when the balance is quiescent, the main spring 
being unwound, the branch or crank A X Y D is in the posi- 
tion represented in fig. 8, A X being parallel to C O ; if the 
quiescent points of the auxiliary springs coincide with that of 
the balance spring, the arm G O will just touch the rod L M ; 
and in like manner the arm I O will just touch the rod W Z ; 
the two arms G O and I O, in this position, are parallel to the 
line CO. This position of the balance and auxiliary springs 
remains as long as the main spring of the machine continues 
unwound ; but whenever the action of the main spring sets the 
balance wheel in motion, a tooth thereof meeting with one or 
other of the pallets p or q, will wind up one of the auxiliary 
springs ; suppose it should be the auxiliary spring u : the arm 
G O being carried into the position G h, by the force of the 
balance wheel acting on the pallet y>, remains in that position 
as long as the tooth of the balance wheel continues locked by 
the projection at the extremity of the pallet p : and the balance 
itself not being at all affected by the motion of the arm G O, 
nor by the winding up of the spring u, remains in its quiescent 
position ; consequently no vibration can take place except by 
the assistance of some external force to set the machine in mo- 
tion. Suppose an impulse to be given to the balance sufficient 
to carry it through the semiarc O B, which is about* 1 35 0 , ac- 
cording to Mr. Mudge's construction. 
The balance during this motion carries with it the crank 
A X Y D, and the affixed rods L M, Z W. When the balance 
has described an angle of about *.27° = to the angle O C h 
or O G h, the rod L M meets with the arm G h, and by 
turning the axis T R, and the pallet p , in the direction of the 
arc O h } releases the tooth of the balance wheel from the pro- 
* Vide infra the note in page 150. 
