the Times of Vibration of Watch Balances. 
*53 
balance wheel is that which subsists while the pallet is disen- 
gaged from the tooth ; an instant of time in a practical sense 
almost evanescent : it should also be remarked, that the pres- 
sure of the tooth against the projection of the pallet is dimi- 
nished before the tooth is released, by the counteraction of the 
other pallet on the opposite tooth of the balance wheel ; which 
action takes place just before the tooth of the balance wheel 
first mentioned is released from the pallet : by this diminution 
of pressure, the tooth is the more easily detached from the pro- 
jection of the pallet. These circumstances concur in giving to 
the machine facility and lightness of motion. 
The preceding investigations are in the next place to be ap- 
126. If we can ascertain the arc described by the balance while the tooth of the ba- 
lance wheel is released from the projection of the pallet, the portion of time in which the 
balance is connected with the wheel-work of the machine will be known. By an ex- 
periment made on a very exact model of Mr. Mudge’s construction, it appeared that 
the balance described an arc of about 8°, while the tooth was released from the pal- 
let. And since the balance describes 108 0 of its semivibration before the pallet begins 
to be moved, it will have described 1 16 0 before the tooth is released; we are therefore 
to find the times in which the balance describes severally the two arcs 108° and 1 16° : 
the difference of these times will be the time in which, the balance wheel is released 
from the pallet. By the theorem referred to 
. . a Parts of a second. 
The time in which the balance describes an arc of 1 16 0 is - 0.091 01 
Time of describing an arc of 1 o8° is - 0.08718 
The difference, or time during which the balance is connected with the 
other parts of the machine, - 0.00383 
which is about part of a second of mean time, the effects of friction not being here 
considered. 
If therefore the time of a semivibration is supposed to be divided into 100 equal 
parts, or physical instants, during the first 91 of them the balance will describe 108® 
from the extremity of the arc of vibration, to the contact of the arm connected with the 
pallet- During the 4 succeeding instants the pallet will be released, and during the 5 
instants following, the balance will describe the remaining arc of the semivibration. 
Thus it appears, that the balance moves perfectly free and unconnected with the wheel- 
work of the machine during g 6 parts in 100 of the time of each vibration. 
MDCCXCIV. X 
