the mean radius of the
terrestrial orbit--of the distance of the sun--then becomes one of the
most simple operations of algebra. Such is the happy combination by the
aid of which Laplace has solved the great, the celebrated problem of
parallax. It is thus that the illustrious geometer found for the mean
distance of the sun from the earth, expressed in radii of the
terrestrial orbit, a value differing but slightly from that which was
the fruit of so many troublesome and expensive voyages.

The movements of the moon proved a fertile mine of research to our great
geometer. His penetrating intellect discovered in them unknown
treasures. With an ability and a perseverance equally worthy of
admiration, he separated these treasures from the coverings which had
hitherto concealed them from vulgar eyes. For example, the earth governs
the movements of the moon. The earth is flattened; in other words, its
figure is spheroidal. A spheroidal body does not attract as does a
sphere. There should then exist in the movement--I had almost said in
the countenance--of the moon a sort of impress of the spheroidal figure
of the earth. Such was the idea as it originally occurred to Laplace. By
means of a minutely careful investigation, he discovered in its motion
two well-defined perturbations, each depending on the spheroidal figure
of the earth. When these were submitted to calculation, each led to the
same value of the ellipticity. It must be recollected that the
ellipticity thus derived from the motions of the moon is not the one
corresponding to such or such a country, to the ellipticity observed in
France, in England, in Italy, in Lapland, in North America, in India, or
in the region of the Cape of Good Hope; for, the earth's crust having
undergone considerable upheavals at different times and places, the
primitive regularity of its curvature has been sensibly disturbed
thereby. The moon (and it is this which renders the result of such
inestimable value) ought to assign, and has in reality assigned, the
general ellipticity of the earth; in other words, it has indicated a
sort of average value of the various determinations obtained at enormous
expense, and with infinite labor, as the result of long voyages
undertaken by astronomers of all the countries of Europe.

Certain remarks of Laplace himself bring into strong relief the
profound, the unexpected, the almost paradoxical character of the
methods I have attempted to sketch. What are