the. Pendulum vibrating Seconds in the Latitude of London. 97 
and second at which this total disappearance is observed, must 
be noted. The pendulums will now be seen to separate, and 
after a time will again approach each other, when the same 
phenomenon will take place. The interval between the two 
- coincidences in seconds, will give the number of vibrations made 
by the pendulum of the clock ; and the number of “oscillations 
of 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 vibra- 
tions 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*, 4 
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 convenient number of in- 
tervals before it should become necessary to renew the motion 
of the pendulum. At the first coincidence, the velocity of the 
brass pendulum, at the lowest part of the are, must not exceed 
that of the pendulum of the clock, otherwise the disk would’ 
disappear for an imperceptible time, and then re-appear; and 
this limits the extent of the are of vibration. 
Again; the observations must not be continued beyond a cer- 
tain diminution of the are 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 uncertain; and, should 
the space be so far diminished as to be less than the error or devia- 
tion from a right line, which would probably take place in the ad- 
justment of the sides of the diaphragm, the end of the pendulum, 
and the disk, the results would be erroneous, as the interval would 
go on increasing till the pendulum came to a state of rest. 
The interval which best fulfilled these conditions was found 
to be about 530 seconds. This admitted five coincidences (af- 
fording four intervals) to be taken before the are became too 
small for the observations to be continued with safety. With 
this interval an error vf one second in the time of coincidence 
* In order to render the calculation more easy, the clock has always been 
supposed to keep mean time, or to make 86,400 vibrations in 24 hours, and 
the variation from this number, or the rate of the clock (being a very small 
quantity) has been afterwards applied as a correction. 
+ The principle on which this method of coincidences is founded, was em- 
ployed 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. 
Vol. 52. No, 244. Aug. 1818. G would 
