of the smallest decimals?

On the one hand, mathematical formulae, deduced from the principle of
universal attraction; on the other hand, certain irregularities observed
in the returns of the moon to the meridian.

An observing geometer who, from his infancy, had never quitted his
chamber of study, and who had never viewed the heavens except through a
narrow aperture directed north and south, in the vertical plane in which
the principal astronomical instruments are made to move,--to whom
nothing had ever been revealed respecting the bodies revolving above his
head, except that they attract each other according to the Newtonian law
of gravitation,--would, however, be enabled to ascertain that his narrow
abode was situated upon the surface of a spheroidal body, the equatorial
axis of which surpassed the polar axis by a _three hundred and sixth
part_; he would have also found, in his isolated immovable position, his
true distance from the sun.

I have stated at the commencement of this Notice, that it is to
D'Alembert we owe the first satisfactory mathematical explanation of the
phenomenon of the precession of the equinoxes. But our illustrious
countryman, as well as Euler, whose solution appeared subsequently to
that of D'Alembert, omitted all consideration of certain physical
circumstances, which, however, did not seem to be of a nature to be
neglected without examination. Laplace has supplied this deficiency. He
has shown that the sea, notwithstanding its fluidity, and that the
atmosphere, notwithstanding its currents, exercise the same influence on
the movements of the terrestrial axis as if they formed solid masses
adhering to the terrestrial spheroid.

Do the extremities of the axis around which the earth performs an entire
revolution once in every twenty-four hours, correspond always to the
same material points of the terrestrial spheroid? In other words, do the
poles of rotation, which from year to year correspond to different
stars, undergo also a displacement at the surface of the earth?

In the case of the affirmative, the equator is movable as well as the
poles; the terrestrial latitudes are variable; no country during the
lapse of ages will enjoy, even on an average, a constant climate;
regions the most different will, in their turn, become circumpolar.
Adopt the contrary supposition, and every thing assumes the character of
an admirable permanence.

The question which I have just suggested, one of the