4 
Captain Kater’s account of the 
ations in length of the seconds' pendulum, doubts may be 
inferred of the accuracy of the method which I employed in 
the observations for ascertaining the length of the seconds’ 
pendulum in London, as well as in those which have been 
made with the invariable pendulum. It is asserted, that 
taking a mean between the disappearance and re-appearance 
of the disk, is a more correct method of observation than 
that which I have pursued ; and that the intervals between 
the coincidences obtained by observing the disappearances 
only of the disk, would be productive of error. 
With respect to the convertible pendulum, it will be seen 
on referring to the Philosophical Transactions for 1818, that 
the disk was made to subtend precisely the same angle as the 
tail-piece of the pendulum ; so that at the moment of disap- 
pearance of the last portion of the disk, its centre coincided 
with the middle of the tail-piece, a circumstance which, in 
my method of observing is indispensable, when the object is 
to obtain the true number of vibrations made by the pendu- 
lum in twenty-four hours. 
With the invariable pendulum, from causes unnecessary 
here to detail, the circumstances were somewhat different, the 
disk subtending a less angle than that of the tail-piece of the 
pendulum ; in consequence of which, the interval between the 
apparent coincidences was lessened, and the inferred number 
of vibrations in twenty-four hours diminished about two- 
tenths of a vibration ; but as the experiments with the inva- 
riable pendulum are intended to be merely comparative, and 
should therefore be made as nearly as possible in every 
respect under similar circumstances, no part of the apparatus 
being changed, nor any alteration made in the pendulum of 
