4 6 Capt. Kater’s experiments for determining the 
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 registered. 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 arcs, it 
became necessary to apply a correction to determine what 
they would have been in an arc infinitely small. For this 
correction I might have used a formula depending on the 
decrease of the arcs in geometrical progression, whilst the 
times decrease in arithmetical ; but as there is an uncertainty 
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 arc, being nearly as the square of the arc, if the 
mean of the observed arcs at the commencement and end of 
each interval be taken, and its square multiplied by 1 ,635 
(the difference between the number of vibrations made by the 
pendulum in 24 hours, in a cycloid and in an arc of one 
degree, ) the required 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 coin- 
cidences, the number of vibrations in 24 hours was obtained 
