most important in
Astronomy, cannot be solved by the aid of mere observation on account of
the uncertainty of the early determinations of terrestrial latitude.
Laplace has supplied this defect by analysis. The great geometer has
demonstrated that no circumstance depending on universal gravitation can
sensibly displace the poles of the earth's axis relatively to the
surface of the terrestrial spheroid. The sea, far from being an obstacle
to the invariable rotation of the earth upon its axis, would, on the
contrary, reduce the axis to a permanent condition in consequence of the
mobility of the waters and the resistance which their oscillations
experience.

The remarks which I have just made with respect to the position of the
terrestrial axis are equally applicable to the time of the earth's
rotation which is the unit, the true standard of time. The importance of
this element induced Laplace to examine whether its numerical value
might not be liable to vary from internal causes such as earthquakes and
volcanoes. It is hardly necessary for me to state that the result
obtained was negative.

The admirable memoir of Lagrange upon the libration of the moon seemed
to have exhausted the subject. This, however, was not the case.

The motion of revolution of our satellite around the earth is subject to
perturbations, technically termed _secular_, which were either unknown
to Lagrange or which he neglected. These inequalities eventually place
the body, not to speak of entire circumferences, at angular distances of
a semi-circle, a circle and a half, &c., from the position which it
would otherwise occupy. If the movement of rotation did not participate
in such perturbations, the moon in the lapse of ages would present in
succession all the parts of its surface to the earth.

This event will not occur. The hemisphere of the moon which is actually
invisible, will remain invisible for ever. Laplace, in fact, has shown
that the attraction of the earth introduces into the rotatory motion of
the lunar spheroid the secular inequalities which exist in the movement
of revolution.

Researches of this nature exhibit in full relief the power of
mathematical analysis. It would have been very difficult to have
discovered by synthesis truths so profoundly enveloped in the complex
action of a multitude of forces.

We should be inexcusable if we omitted to notice the high importance of
the labours of Laplace on the improvement of the lunar