44 Capi. Kater’s experiments for determining the 
brass pendulum, in the same interval, may be known by 
considering that it must have made two oscillations less than 
the pendulum of the clock. Hence by simple proportion, as 
the vibrations made by the pendulum of the clock, are to the 
number of vibrations made by the brass pendulum, so are the 
vibrations made by the pendulum of the clock in 24, hours, to 
those of the brass pendulum in the same period.* 
Many experiments were made in order to select such a 
distance of the knife edges as might give an interval which 
would allow of the determination of the time of coincidence 
without an error of a single second, -f* and yet afford a con- 
venient number of intervals before it should become neces- 
sary to renew the motion of the pendulum. At the first coin- 
cidence, the velocity of the brass pendulum, at the lowest part 
of the arc, must not exceed that of the pendulum of the 
clock, otherwise the disk would disappear for an impercepti- 
ble time, and then re-appear ; and this limits the extent of 
the arc of vibration. 
Again ; th6 observations must not be continued beyond a 
certain diminution of the arc of vibration, otherwise the space , 
which the pendulum of the clock has to gain on the brass 
pendulum in one vibration, becomes so small as to render the 
observation of the time of coincidence in some degree uncer- 
tain ; and, should the space be so far diminished as to be less 
than the error or deviation from a right line, which would 
* In order to render the calculation more easy, the clock has always been supposed 
to keep mean time, or to make 86400 vibrations in 24 hours, and the variation from 
this number, or the rate of the clock (being a very small quantity) has been after- 
wards applied as a correction. 
f The principle on which this method of coincidences is founded, was employed 
by Dr. Wollaston, in May 1808, in some experiments in which he was then engaged, 
the moment of coincidence being determined however by sound instead of sight. 
