15© Mr. Atwood's Investigations for determining 
jection at the extremity of the pallet p ; the balance wheel im- 
mediately revolves, and the lower tooth meeting with the 
pallet q winds up the auxiliary spring z>, and carries the arm 
I O with a circular motion through the angle O I k about 27 0 ; 
in which position the arm I O remains as long as the tooth 
of the balance wheel is locked by the pallet q. "W hile the 
spring v is winding up through the arc O k, the balance de- 
scribes the remaining part of the semiarc h B, and during this 
motion the rod L M carries round the arm G b, causing it to 
describe an angle h C B, or h G B*, which is measured by the 
arc h B = f 108° : when the balance has arrived at the extre- 
mity of the semiarc O B = 135 0 , the auxiliary spring u will 
have been wound up through the same angle = 135 ,i.e. 27 , 
by the force of the main spring acting on the pallet p, and 108’ 
by the balance itself carrying along with it the arm G O or 
G b 9 while it describes the arc b B. The balance therefore 
returns through the arc B O by the joint action of the balance 
spring, and the auxiliary spring u ; the acceleration of both 
springs ceasing the instant the balance arrives at the quiescent 
point O ; when the balance has proceeded in its vibration about 
27° beyond the point O to the position C k, the rod Z W meets 
with the arm I k, and by carrying it forward releases the tooth 
* The angle h G B is not expressed in the figure for want of room, but is easily 
imagined, being precisely equal to the angle h C B represented on the balance. 
f This magnitude of the arc h B has been inferred from the following circum- 
stances communicated by Mr. Mu d g h. ist. “ The whole arc of vibration is about | of 
t < a circle, or 270°, consequently the semiarc of vibration is 135°. zdly. The ac- 
“ tion of the balance by carrying round the arm O G from b to B winds up the auxi- 
„ liary spring through an angle about four times greater than the angle OC b through 
« which it is wound up by the action of the balance wheel on the pallet.” Where- 
fore if O B, or 1 35 0 , is divided into five parts, one of them will be Oi> = 27 0 , and the 
other four parts, or b B == xo8°. 
