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.

PLANETARY THEORY.
76. IN the same manner in which thp ',,
(apparently) round the Earth disturbs the
round the Earth, each of the planets revolving round the
Sun disturbs every other planet revolving round the Sun.
But though the principle of perturbation is the same in
both cases, the circumstances upon which the nature and
magnitude of its effect depend are so different as to require
investigations very different in form.
The disturbing force on the Moon is a resolved part of
the Sun's attraction, that is, of the attraction of the largest
body in the solar system. The disturbing force on a planet
is the attraction of another planet, and the largest of these
is very inconsiderable when compared with the Sun. The
perturbations of the Moon are consequently very much
greater than those of any planet: and this circumstance
alone makes an important difference in the process of calculation. For the disturbing force depends itself upon the
situation of the disturbed body. Now the disturbance of a
planet is so small that for all ordinary purposes we may,
in calculating the disturbing force, use the place in which
the planet would have been if not disturbed, instead of that
where it really is, without producing any sensible error.
But we should in the lunar theory obtain most inaccurate
results, if we expressed the forces in terms of any thing
but the true co-ordinates of the Moon. The motion of the
perihelion of a planet is scarcely sensible in ten years: the
Moon's perigee has in that time gone through every sign of
the zodiac. In this respect then the planetary theory is
simpler than the lunar theory.
On the other hand we must observe that the expansions
of P, T, S, or the equivalent expressions, are much shorter
in the lunar than in the planetary theory. For these expan