156 Mr. Atwood's Investigations for determining 
cond when adjusted to mean time ; the daily rate will therefore 
in this case be = o. 
Now let Q (fig. 4 and 8.), or the point of quiescence of the 
auxiliary spring deviate from O, the point of quiescence of the 
balance spring, by an arc O Q ; suppose this arc O O to be = 
i° ; and let the point Q be situated in the first semiarc of vi- 
bration between O and B. The time of describing the semi- 
arc B O will be ascertained on these conditions, by referring 
to the investigation (page 140), and making the following 
substitutions : 
a = 1.5707963 = an arc of 90° to radius = 1 * 
b = 2.3561945 = an arc of 135 0 
c = 2.3387412 = an arc of 134 0 
b — c = d = 0.0174533 = an arc of T 
1 = 193 
/= 0.9562754 
nution only, not having any memorandum of experiments made to ascertain the exact 
proportion. 
If therefore, the actual rate of the watch should be observed when the balance vi- 
brates by the action of the auxiliary springs only, it is probable that the time shewn 
by the watch in 60 seconds of mean time might differ somewhat from that which has 
been here stated.. 
Since these notes were written, I have been favoured by his Excellency Count B a v h l 
with an account of an observation made on the rate of Mr. Mu doe’s first time- 
keeper when the balance vibrated by the action of the auxiliary springs only, the ba- 
lance spring being removed. According to this observation, the watch shewed twelve 
minutes by the motion of the. hands in one hour of mean time, which corresponds to 
an interval of 12 seconds of time, shewn by the watch in 60 seconds, or one minute of 
mean time. According to the calculation, 13 seconds of time are shewn by the 
watch in one minute. A nearer agreement between the theory and matter of fact could) 
scarcely be expected in the circumstances of the experiment. 
* In all the following calculations the radius is also 5: 
