the Times of Vibration of Watch Balances. 121 
In time-keepers, the irregular forces, both of impulse and re- 
sistance, are much diminished by the exactness of form and 
dimension which is given to each part of the work ; and 
they are further corrected by the maintaining power derived 
from the main spring : for whatever motion is lost by the ba- 
lance from resistance of any kind, almost the same motion is 
communicated by the maintaining power, so as to continue the 
arc of vibration, as nearly as possible, of the same length. 
In these machines, the real measure of time is the balance, 
all the other work serving only to continue the motion of the 
balance, and to indicate the time as measured by its vibrations. 
The regularity of a time-keeper will therefore depend on that 
of the time in which the balance vibrates : to investigate this 
time of vibration, from the several data or conditions on which 
it depends, is the object of the ensuing pages. 
Let P MN S (Tab. XIV. fig. 1.) represent the circumference 
of a watch balance, which vibrates by the action of a spiral * 
spring, on an axis passing through the centre C. Let O D B E 
be the circumference of a concentric circle, considered as fixed, 
to which the motion of the balance may be referred. In the 
circumference of this circle let any point O be assumed, and 
when the balance is in its quiescent position, suppose a line 
to be drawn through C and O, intersecting the circumference 
of the balance in the point A ; the radius C A will be an index, 
by which the position of the balance, and its motion through 
any different arcs of vibration, will be truly defined. In the 
ensuing pages, the motion of the balance, and the motion of 
the index C A, will be used indifferently, as terms conveying 
* In these investigations it is indifferent whether the balance is supposed to vibrate 
by the action of a spiral or helical spring. 
MDCCXCIV. R 
