424 An Account of Experiments for determining the Length of 
On the contrary, if the second coincidence or return of the 
brass pendulum to the lowest point of the arc, should have taken 
place nine-tenths of a second before the second at which the 
disappearance of the disk was noted, the error in the number of 
vibrations in 24 hours would amount to the same quantity, and 
would now be in excess. 
If the first and third coincidences take place accurately at the 
time of the observed disappearance of the disk, and the observa- 
tion of the second coincidence should differ nine-tenths of a se- 
cond from the truth, it is obvious that the number of vibrations 
in 24 hours deduced from each interval will be erroneous about 
0°56, the one being in excess, the other in defect. The mean of 
both will be the truth, though the observed difference between 
the two amounts to so considerable a quantity as 12. 
The last coincidence of each set takes place when the are of 
vibration is much reduced. It is therefore not impossible that 
an error of one second may sometimes, though rarely, occur in 
determining the time of this coincidence. This would occasion 
an error of about 0-63 in the number of vibrations in 24 hours, 
which divided by 4 as before, would influence the mean result 
0:15 of a vibration. 
In estimating these errors, | have taken an extreme case, as it 
is probable they would in most instances be compensated by the 
succeeding intervals, Supposing them however to be combined, 
the greatest effect on the mean result of any one set of experi- 
ments might amount to about 0:5 of a vibration in 24 hours, and 
the difference between the number of vibrations in either position 
of the pendulum, might have been double this quantity, and yet, 
when the great weight was below, not have differed from the truth 
more than 0°35 of a vibration. 
It appears then, that if the experiments have been conducted 
with sufficient care, no greater difference should be found be- 
tween the mean, and any one of the resulting lengths of the pen- 
dulum contained in the preceding table, than might have been 
occasioned by a difference of 0-3 of a vibration in 24 hours, and 
this is found to be about 0:0003 of an inch. 
In fact, on referring to the table we perceive that the experi- 
ments A and D, which differ most from the mean, give, the one, 
“00029 of an inch in excess, and the other ‘OU026 in defect. 
In considering the sources of error, it may not be unnecessary 
to remark, that had the bar of the pendulum been made too thick, 
and the Knife edges not been placed accurately at right angles to 
it, an error, though very minute, might have arisen from the ef- 
fect of the obliquity in diminishing the distance of the centre of 
oscillation from the axis. This was sufficiently guarded against 
by 
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a, ee 
