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 the earth were sufficiently sensible not to be confounded with the errors of observation.  It was accordingly necessary to find the general formula of perturbations of this nature, in order to be able, as in the case of the solar parallax, to eliminate the unknown quantity.

The ardour of Laplace, combined with his power of analytical research, surmounted all obstacles.  By means of an investigation which demanded the most minute attention, the great geometer discovered in the theory of the moon’s movements, two well-defined perturbations depending on the spheroidal figure of the earth.  The first affected the resolved element of the motion of our satellite which is chiefly measured with the instrument known in observatories by the name of the transit instrument; the second, which operated in the direction north and south, could only be effected by observations with a second instrument