ions in the forms of the
orbits, changes of distances and inclinations, which these forces must
evidently produce, the most learned geometer would fail to discover a
trustworthy guide. This extreme complication gave birth to a
discouraging reflection. Forces so numerous, so variable in position, so
different in intensity, seemed to be incapable of maintaining a
condition of equilibrium except by a sort of miracle. Newton even went
so far as to suppose that the planetary system did not contain within
itself the elements of indefinite stability; he was of opinion that a
powerful hand must intervene from time to time, to repair the
derangements occasioned by the mutual action of the various bodies.
Euler, although farther advanced than Newton in a knowledge of the
planetary pertubations, refused also to admit that the solar system was
constituted so as to endure for ever.

Never did a greater philosophical question offer itself to the inquiries
of mankind. Laplace attacked it with boldness, perseverance, and
success. The profound and long-continued researches of the illustrious
geometer established with complete evidence that the planetary ellipses
are perpetually variable; that the extremities of their major axes make
the tour of the heavens; that, independently of an oscillatory motion,
the planes of their orbits experienced a displacement in virtue of which
their intersections with the plane of the terrestrial orbit are each
year directed towards different stars. In the midst of this apparent
chaos there is one element which remains constant or is merely subject
to small periodic changes; namely, the major axis of each orbit, and
consequently the time of revolution of each planet. This is the element
which ought to have chiefly varied, according to the learned
speculations of Newton and Euler.

The principle of universal gravitation suffices for preserving the
stability of the solar system. It maintains the forms and inclinations
of the orbits in a mean condition which is subject to slight
oscillations; variety does not entail disorder; the universe offers the
example of harmonious relations, of a state of perfection which Newton
himself doubted. This depends on circumstances which calculation
disclosed to Laplace, and which, upon a superficial view of the subject,
would not seem to be capable of exercising so great an influence.
Instead of planets revolving all in the same direction in slightly
eccentric orbits, and