in the mean motions of the moon and of Jupiter, 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, Laplace next succeeded in determining the absolute dimensions of the orbits.  What is the distance of the sun from the earth?  No scientific question has occupied the attention of mankind in a greater degree.  Mathematically speaking, nothing is more simple:  it suffices, as in ordinary surveying, to draw visual lines from the two extremities of a known base line to an inaccessible object; the remainder of the process is an elementary calculation.  Unfortunately, in the case of the sun, the distance