98 An Account of Experiments for determining the Length of 
would occasion an error of only 0°63 in the number of vibrations 
in 24 hours. 
Here it must be evident that no sensible alteration could take 
place in the knife edge during the experiments without its be- 
coming perceptible at every coincidence, since the number of 
vibrations in 24 hours deduced from each interval, must vary 
with any change in the form of the knife edge. 
The following was the method pursued in making the obser- 
vations. The small weight or slider being placed with its index 
at a certain distance (say one inch and a half) from the middle 
of the pendulum towards the great weight, and the second weight 
about five inches from the knife edge, the Ys of the support were 
elevated, the knife edge of the pendulum was placed in them, 
with the great weight alove, and the frame gently lowered till 
the knife edge was left on the surface of the agate. The requi- 
site adjustments of the telescope having been made, the pendu- 
lum was set in motian in an are not exceeding one degree and 
four-tenths, in order that its velocity might not be greater than 
that of the pendulum of the clock. 
The minute and second, at which the disk ceased to be visible, 
was then carefully noted; and the arc of vibration seen through 
the telescope, the height of the barometer, and the temperature 
indicated by a thermometer suspended on the clock-case near 
the middle of the brass pendulum, were also observed and re- 
gistered, Five successive coincidences were thus taken, and the 
number of vibrations in 24 hours was deduced from them in the 
manner before described; but the vibrations thus obtained being 
made in different.ares, it became necessary to apply a correction 
to determine what they would have been in an are infinitely 
small. For this correction I might have used a formula depend- 
ing on the decrease of the ares in geometrical progression, whilst 
the times decrease in arithmetical; but as there is an uncer- 
tainty in observing the arc of vibration amounting to one or two 
hundredths of a degree, this method, though more perfect in 
theory, would have been an unnecessary refinement in practice, 
The error arising from the greater length of the vibration in 
a circular are, being nearly as the square of the are, if the mean 
of the observed arcs at the commencement and end of each in- 
terval be taken, and its square multiplied by 1:635, (the dif- 
ference between the number of vibrations made by the pendulum 
in 24 hours, in a cycloid and in an arc of one degree,) the re- 
quired correction will be obtained, to be added to the number 
of vibrations before computed. 
‘The mean of these last results being taken, and also the mean 
of the observed temperatures at the first and last coincidences, 
the number of vibrations in 24 hours was obtained at a certain 
temperature, 
