1 6o 
Mr. Atwood's Investigations for determining 
Farti of i ttteni. 
circular arc of which the sine is v / b ~ d x ” ± -1=0.09946662 
2 b -f 2 n c 
./ . . . --- x a circular arc of which the sine 
2 If X 1 +. z « 
IS 
y 
<P X 1 
ft 1 -f n c z - 2 « 
Time of a semivibration in the arc B O 
24* 
Time shewn by the watch in 24 h 
giving a daily rate of 
•9997574 
= .00050913 
= -09997574 
= 24,fco'2o".9i, 
Qo".gi fast. 
Daily rate when the semiarc of vibration was 
135 ° - - - 19 "-S 8 fast. 
Acceleration of the rate in consequence of the 
diminution of the semiarc of vibration from 135 0 
to 125 0 = - _ " ■ 1 -53 
The theorem from which this latter result has been calcu- 
lated is founded on a supposition, that the arc B N (fig. 5.) is 
described by the accelerative forces of the balance spring and 
the auxiliary spring w, and that the arc NO is described by 
the accelerative forces of the two springs just mentioned, com- 
bined with the retarding force of the other auxiliary spring v, of 
which the point of quiescence is situated at N (fig. 5-) - ^ 
possibly be thought, that this supposed action of the auxiliary 
spring which retards the balance while it describes the arc from 
N to O, cannot take place, because by the peculiar construction 
of Mr. Mudge's invention, when the balance vibrates from B 
towards E, the retarding force of the auxiliary spring is re- 
moved from acting on the balance while it describes the arc 
k = 27 0 (fig. 5.), including the said arc NO ; but it is to be 
considered, that this removal of the retarding force from 
