in every direction, but the prominence of the equatorial
diameter directed towards the earth became four times greater than that
of the diameter which we see perpendicularly.

The moon would appear then, to an observer situate in space and
examining it transversely, to be elongated towards the earth, to be a
sort of pendulum without a point of suspension. When a pendulum deviates
from the vertical, the action of gravity brings it back; when the
principal axis of the moon recedes from its usual direction, the earth
in like manner compels it to return.

We have here, then, a complete explanation of a singular phenomenon,
without the necessity of having recourse to the existence of an almost
miraculous equality between two movements of translation and rotation,
entirely independent of each other. Mankind will never see but one face
of the moon. Observation had informed us of this fact; now we know
further that this is due to a physical cause which may be calculated,
and which is visible only to the mind's eye,--that it is attributable to
the elongation which the diameter of the moon experienced when it passed
from the liquid to the solid state under the attractive influence of the
earth.

If there had existed originally a slight difference between the
movements of rotation and revolution of the moon, the attraction of the
earth would have reduced these movements to a rigorous equality. This
attraction would have even sufficed to cause the disappearance of a
slight want of coincidence in the intersections of the equator and orbit
of the moon with the plane of the ecliptic.

The memoir in which Lagrange has so successfully connected the laws of
libration with the principles of gravitation, is no less remarkable for
intrinsic excellence than style of execution. After having perused this
production, the reader will have no difficulty in admitting that the
word _elegance_ may be appropriately applied to mathematical researches.

In this analysis we have merely glanced at the astronomical discoveries
of Clairaut, D'Alembert, and Lagrange. We shall be somewhat less concise
in noticing the labours of Laplace.

After having enumerated the various forces which must result from the
mutual action of the planets and satellites of our system, even the
great Newton did not venture to investigate the general nature of the
effects produced by them. In the midst of the labyrinth formed by
increases and diminutions of velocity, variat