i,5B Mr. Atwood's Investigations for determining 
1= 1 93 
f= o .9562754 
— — x into a circular arc, of which the sine is 
If Xn + 1 
c.X» + 1 — 
parts of a seconfl. 
0 . 0995147 2 
2 b -f z n c 
/ a x a circular arc, of which the sine is 
v 2 if 
d __ _ 
b z + nc 2 
O.OOO5O949 
The time of a semivibration 
.10002421 
Time shewn by the watch in 24* = x , 00 2 0 ” i — 2 3 h 59' 39 " -°8 
giving a daily rate of 20". 92 slow. 
Daily rate, when the semiarc of vibration was 135* 19". 4 ° ^ ow - 
Retardation of the daily rate in consequence of 
the diminution of the semiarc of vibration from 
135° to 125 0 - 1 ’ 52 ’.. 
In these examples, the point of quiescence of the auxiliary 
spring Q is situated in the first semiarc of vibration between B 
and O ; and in consequence of this position, the daily rate of the 
time-keeper is retarded by a separation of the points of qui- 
escence, while the semiarc of vibration remains the same ; 1. e. 
135 0 ; secondly, the separation of the points of quiescence 
remaining unaltered, a diminution of the arc of vibration causes 
a further retardation of the rate. Opposite effects on the daily 
rate take place when the point of quiescence Q is situated in 
the latter semiarc of vibration, (fig. 5.) between O and E. 
The arc O Q remaining = T as before, this case produces an 
acceleration instead of a retardation of the rate. 
