cannot be depended on
certainly, no magnitudes in astronomy can), we find, _that the moon does
not fall from the tangent of her orbit, as much as the theory requires_.
As this is of vital importance to the integrity of the theory we are
advocating, we have made the computation on Newton's own data, except
such as were necessarily inaccurate at the time he wrote; and we have
done it arithmetically, without logarithmic tables, that, if possible,
no error should creep in to vitiate the result. We take the moon's
elements from no less an authority than Sir John Herschel, as well as
the value of the earth's diameter.

Mass of the moon 1/80
Mean distance in equatorial radii 59.96435
Sidereal period in seconds 2360591

The vibrations of the pendulum give the force of gravity at the surface
of the earth, and it is found to vary in different latitudes. The
intensity in any place being as the squares of the number of vibrations
in a given time. This inequality depends on the centrifugal force of
rotation, and on the spheroidal figure of the earth due to that
rotation. At the equator the fall of a heavy body is found to be
16.045223 feet, per second, and in that latitude the squares of whose
sine is 1/3, it is 16.0697 feet. The effect in this last-named latitude
is the same as if the earth were a perfect sphere. This does not,
however, express the whole force of gravity, as the rotation of the
earth causes a centrifugal tendency which is a maximum at the equator,
and there amounts to 1/289 of the whole gravitating force. In other
latitudes it is diminished in the ratio of the squares of the cosines of
the latitude; it therefore becomes 1/434 in that latitude the square of
whose sine is 1/3. Hence the fall per second becomes 16.1067 feet for
the true gravitating force of the earth, or for that force which retains
the moon in her orbit.

The moon's mean distance is 59.96435 equatorial radii of the earth,
which radius is, according to Sir John Herschel, 20.923.713
feet. Her mean distance as derived from the parallax is not to be
considered the radius vector of the orbit, inasmuch as the earth also
describes a small orbit around the common centre of gravity of the earth
and moon; neither is radius vector to be considered as her distance from
this common centre; for the attracting power is in the centre of the
earth. But the mean distance of the moon moving around a movable centre,
is to the s