discoveries which emanated from these two men, each gifted with
extraordinary genius.

Laplace's most famous work is, of course, the "Mecanique Celeste," in
which he essayed a comprehensive attempt to carry out the principles
which Newton had laid down, into much greater detail than Newton had
found practicable. The fact was that Newton had not only to
construct the theory of gravitation, but he had to invent the
mathematical tools, so to speak, by which his theory could be applied
to the explanation of the movements of the heavenly bodies. In the
course of the century which had elapsed between the time of Newton
and the time of Laplace, mathematics had been extensively developed.
In particular, that potent instrument called the infinitesimal
calculus, which Newton had invented for the investigation of nature,
had become so far perfected that Laplace, when he attempted to
unravel the movements of the heavenly bodies, found himself provided
with a calculus far more efficient than that which had been available
to Newton. The purely geometrical methods which Newton employed,
though they are admirably adapted for demonstrating in a general way
the tendencies of forces and for explaining the more obvious
phenomena by which the movements of the heavenly bodies are
disturbed, are yet quite inadequate for dealing with the more subtle
effects of the Law of Gravitation. The disturbances which one planet
exercises upon the rest can only be fully ascertained by the aid of
long calculation, and for these calculations analytical methods are
required.

With an armament of mathematical methods which had been perfected
since the days of Newton by the labours of two or three generations
of consummate mathematical inventors, Laplace essayed in the