repair the derangements occasioned by the mutual action of the various
bodies. Euler, better instructed than Newton in a knowledge of these
perturbations, also refused to admit that the solar system was
constituted so as to endure forever.

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 completely established the perpetual variability of the
planetary ellipses. He demonstrated that the extremities of their major
axes make the circuit of the heavens; that independent of oscillation,
the planes of their orbits undergo displacements by which their
intersections with the plane of the terrestrial orbit are each year
directed toward different stars. But in the midst of this apparant
chaos, there is one element which remains constant, or is merely subject
to small and 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 varied most, on the principles held by Newton and
Euler. Gravitation, then, suffices to preserve the stability of the
solar system. It maintains the forms and inclinations of the orbits in
an average position, subject to slight oscillations only; variety does
not entail disorder; the universe offers an example of harmonious
relations, of a state of perfection which Newton himself doubted.

This condition of harmony depends on circumstances disclosed to Laplace
by analysis; circumstances which on the surface do not seem capable of
exercising so great an influence. If instead of planets all revolving in
the same direction, in orbits but slightly eccentric and in planes
inclined at but small angles toward each other, we should substitute
different conditions, the stability of the universe would be
jeopardized, and a frightful chaos would pretty certainly result. The
discovery of the actual conditions excluded the idea, at least so far as
the solar system was concerned, that the Newtonian attraction might be a
cause of disorder. But might not other forces, combined with the
attraction of gravitation, produce gradually increasing perturbations
such as Newton and Euler feared? Known facts seemed to justify the
apprehension. A comparison of ancient with modern observations revealed
a continual acceleration in the mean motions of the moon and of Jupiter,