to assign their nature and
in a few rare cases their numerical value, was the object which Newton
proposed to himself in writing his famous book, the 'Principia
Mathematica Philosophiae Naturalis' [Mathematical Principles of Natural
Philosophy], Notwithstanding the incomparable sagacity of its author,
the 'Principia' contained merely a rough outline of planetary
perturbations, though not through any lack of ardor or perseverance. The
efforts of the great philosopher were always superhuman, and the
questions which he did not solve were simply incapable of solution
in his time.

Five geometers--Clairaut, Euler, D'Alembert, Lagrange, and
Laplace--shared between them the world whose existence Newton had
disclosed. They explored it in all directions, penetrated into regions
hitherto inaccessible, and pointed out phenomena hitherto undetected.
Finally--and it is this which constitutes their imperishable glory--they
brought under the domain of a single principle, a single law, everything
that seemed most occult and mysterious in the celestial movements.
Geometry had thus the hardihood to dispose of the future, while the
centuries as they unroll scrupulously ratify the decisions of science.

If Newton gave a complete solution of celestial movements where but two
bodies attract each other, he did not even attempt the infinitely more
difficult problem of three. The "problem of three bodies" (this is the
name by which it has become celebrated)--the problem of determining the
movement of a body subjected to the attractive influence of two
others--was solved for the first time by our countryman, Clairaut.
Though he enumerated the various forces which must result from the
mutual action of the planets and satellites of our system, even the
great Newton did not venture to investigate the general nature of their
effects. In the midst of the labyrinth formed by increments and
diminutions of velocity, variations in the forms of orbits, changes in
distances and inclinations, which these forces must evidently produce,
the most learned geometer would fail to discover a trustworthy guide.
Forces so numerous, so variable in direction, so different in intensity,
seemed to be incapable of maintaining a condition of equilibrium except
by a sort of miracle. Newton even suggested 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