and an equally striking diminution of the mean motion of Saturn. These
variations led to a very important conclusion. In accordance with their
presumed cause, to say that the velocity of a body increased from
century to century was equivalent to asserting that the body continually
approached the centre of motion; on the other hand, when the velocity
diminished, the body must be receding from the centre. Thus, by a
strange ordering of nature, our planetary system seemed destined to lose
Saturn, its most mysterious ornament; to see the planet with its ring
and seven satellites plunge gradually into those unknown regions where
the eye armed with the most powerful telescope has never penetrated.
Jupiter, on the other hand, the planet compared with which the earth is
so insignificant, appeared to be moving in the opposite direction, so
that it would ultimately be absorbed into the incandescent matter of the
sun. Finally, it seemed that the moon would one day precipitate itself
upon the earth.

There was nothing doubtful or speculative in these sinister forebodings.
The precise dates of the approaching catastrophes were alone uncertain.
It was known, however, that they were very distant. Accordingly, neither
the learned dissertations of men of science nor the animated
descriptions of certain poets produced any impression upon the public
mind. The members of our scientific societies, however, believed with
regret the approaching destruction of the planetary system. The Academy
of Sciences called the attention of geometers of all countries to these
menacing perturbations. Euler and Lagrange descended into the arena.
Never did their mathematical genius shine with a brighter lustre. Still
the question remained undecided, when from two obscure corners of the
theories of analysis, Laplace, the author of the 'Mecanique Celeste,'
brought the laws of these great phenomena clearly to light. The
variations in velocity of Jupiter, Saturn, and the moon, were proved to
flow from evident physical causes, and to belong in the category of
ordinary periodic perturbations depending solely on gravitation. These
dreaded variations in orbital dimensions resolved themselves into simple
oscillations included within narrow limits. In a word, by the powerful
instrumentality of mathematical analysis, the physical universe was
again established on a demonstrably firm foundation.

Having demonstrated the smallness of these periodic oscillations,
Lapla