diameters, making with each other considerable angles, the equator and the poles would change places on the Earth; and the ocean, flowing continually towards the new equator, would alternately overwhelm and then abandon the highest mountains; but all the investigations which I have made upon this change of position in the poles, convince me that it is insensible. CHAP. XIV. On the Libration of the Moon, We have now only to explain the cause of the libration of the Moon, and of the nodes of its equator. The Moon, in virtue of its motion of rotation,is a little flattened at its poles; but the attraction of the Earth, must have lengthened a little that axis which is turned towards it. If the Moon were homogeneous and fluid, it would (to be in equilibrio) assume the form of an ellipsoid, of which the lesser axis passed through the poles of rotation; the greater axis would be directed to the Earth, and in the plane of the lunar equator, and the mean axis would be situated in the same plane perpendicular to the other two. The excess of the greatest above the least axis would be quadruple the excess of the mean above the least, and nearly equal the least axis being taken as unity. We may easily conceive that if the greater axis of the Moon deviates a little from the direction of the radius vector, which joins its centre with that of the Earth, the terrestrial attraction will tend to bring it down to this radius, in the same manner as gravity brings a pendulum towards the vertical. If the primitive motion of rotation of this satellite, had been sufficiently rapid to have overcome this tendency, the period of its rotation would not have been perfectly equal to that of its revolution, and the difference would have discovered to us successively every point in its surface. But at their origin the angular motions of rotation and revolution having differed but little; the force by which the greater axis of the Moon tended to deviate from the radius vector, was not sufficient to overcome the tendency of this same axis towards the radius, due to the terrestrial gravity, which by this means has rendered their motions rigorously equal and in the same manner as a pendulum, drawn aside from the vertical by a very small force, continually returns, making small vibrations on each side of it, so the greater axis of the lunar spheroid ought to oscillate on each side of the mean radius vector of its orbit. Hence would arise a motion of libration, of which the extent would depend on the primitive difference be. tween the angular motions of rotation and revolution of the Moon. This difference must have been very small, since it has not been perceived by observation. Thus we see that the theory of gravitation explains in a sufficiently satisfactory manner, the rigorous equality of these two mean motions of rotation and revolution in the Moon. It would be against all probability to suppose, that these two motions had been at their origin perfectly equal, but for the explanation of this phenomenon, it is enough that their primitive difference was but small, and then the attraction of the Earth would establish the equality which at present subsists. The mean motion of the Moon being subject to great secular inequalities, which amount to several circumferences, it is evident that if its mean motion of rotation were perfectly uniform, this satellite would, by virtue of these inequalities, present successively to the Earth every point on its surface, and its apparent disk would change by imperceptible degrees, in proportion as these inequalities were developed; the same observers would see it always pretty nearly the same, and there would be no considerable difference but to observers separated by an interval of several ages. But the cause which has thus established an equality between the mean motions of revolution and rotation, should take away all hope from the inhabitants of the Earth,of seeing the opposite side of the lunar hemisphere. The terrestrial attraction, by continually drawing towards us the |
