Mathematical tracts on the lunar and planetary theories, the figure of the earth, precession and nutation, the calculus of variations, and the undulatory theory of optics.

DETERMINED BY OBSERVATION. 81
Eliminating c, e may be found. This method is not considered to be practically accurate: the determination of difference of longitude being attended with great difficulty.
81. The method which on account of its great facility
is now very extensively used, is that of observing the intensity of gravity in different latitudes, by means of the
pendulum. It is usual to observe the number of vibrations
made in a day by the same pendulum, in the different
places at which it is proposed to compare the force of
gravity; and likewise the number of vibrations made at
London or Paris. The observations are commonlv made
by causing the experimental pendulum to vibrate in front
of a clock-pendulum, and by observing the interval between
the times at which the two pendulums pass the centers of
the arcs of vibration at the same instant and in the same
direction: then, since one of the pendulums has in that time
gained exactly two vibrations upon the other, the ratio of
the actual times of vibration is accurately known: and the
time of vibration of the clock-pendulum is found from astronoiical observations: and thus the time of vibration of
the experimental pendulum, and the number of vibrations
which it makes in a day, are found with great accuracy.
In some experiments the clock-pendulum itself has been
observed. The comparative number of vibrations being
found, the comparative force of gravity, or the comparative
length of the second's pendulum, can be found: and, as the
length of the second's pendulum has been very accurately
determined at London and Paris, its length is known at all
the places of observation. The French astronomers have used
a method more direct, but less convenient, and probably
less accurate: it is described at length in the Additions to
Biot's Astronomie Physique, p. 138.
82. Let p and p' be the lengths of the seconds' pendulum in latitudes L and 1', P that at the equator. Since
these lengths are proportional to the intensities of gravity,
we have, by (63),
p= P( +n sin21l) I 5m
p = P( +n sin2l' were 2 =