e already remarked that the
determination of the contemplated distance appeared to demand
imperiously an extensive base, for small bases would have been totally
inadequate to the purpose. Well, Laplace has solved the problem
numerically without a base of any kind whatever; he has deduced the
distance of the sun from observations of the moon made in one and the
same place!

The sun is, with respect to our satellite, the cause of perturbations
which evidently depend on the distance of the immense luminous globe
from the earth. Who does not see that these perturbations would diminish
if the distance increased; that they would increase on the contrary, if
the distance diminished; that the distance finally determines the
magnitude of the perturbations?

Observation assigns the numerical value of these perturbations; theory,
on the other hand, unfolds the general mathematical relation which
connects them with the solar parallax, and with other known elements.
The determination of the mean radius of the terrestrial orbit 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 only in a slight
degree from that which was the fruit of so many troublesome and
expensive voyages. According to the opinion of very competent judges the
result of the indirect method might not impossibly merit the
preference.[36]

The movements of the moon proved a fertile mine of research to our
great geometer. His penetrating intellect discovered in them unknown
treasures. He disentangled them from every thing which concealed them
from vulgar eyes with an ability and a perseverance equally worthy of
admiration. The reader will excuse me for citing another of such
examples.

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
like a sphere. There ought then to exist in the movement, I had almost
said in the countenance of the moon, a sort of impression of the
spheroidal figure of the earth. Such was the idea as it originally
occurred to Laplace.

It still remained to ascertain (and here consisted the chief
difficulty), whether the effects attributable to the spheroidal figure
of th