Mr. Atwood’s Investigations for determining 
162 
a — pts . of a second; 
cular arc, of which the sine = y/ . h x ” J . L = .09997752. 
z b + 2 n c 
Time shewn by the watch in 24/ 1 — 2 ? 4 ~ = 2 4 h °' 1 9 , '- 4 2 > 
giving a. daily rate of 19". 42 fast. 
Every thing else remaining, let the semiarc of vibration be 
diminished from 135 0 to 125 0 ; and make 
b = 2.1816616 = an arc of 125 0 to radius 1. 
c = 2.1991149 = an arc of 126°. 
The time of describing the semiarc B O will now be = 
— x a circular arc, of which the sine = 
1 
I/X n + 
7= 0.09997570 parts of a second. 
Time shewn by the watch in 24 h = 
b X n -f 1 
2 b 4 - 2 n c 
24 h 
24 h o' 
20".q6, 
giving a daily rate of - - - 20 ".96 fast, 
daily rate, when the semiarc of vibration was 135°= i9"-42 fast. 
Acceleration of daily rate in consequence of the . 
diminution of the semiarc of vibration from 
i35°.to 125 0 - - - i"- 54 » 
scarcely differing from the former determination in page 160. 
By having recourse to the figure, we may distinctly perceive 
the three quiescent positions of the arms GO and IO, (fig. 8.) 
in respect to the rods LM, Z W, which correspond with the 
several conditions assumed for the calculation of the preceding 
examples. In the first place, the crank AX Y D, and the arms 
GO, I O, being in their quiescent position, it is evident from 
the preceding observations, that when the arms G O, I O are 
adjusted so as just to touch the rods L M, Z W, the points of 
quiescence of the auxiliary springs u and v coincide with the 
point of quiescence of the balance spring O, (fig. 6.) and in 
