This was known long before the time of Laplace, but it did not directly convey any explanation of the lunar acceleration.  It no doubt amounted to the assertion that the moon’s periodic time was slightly augmented by the disturbance, but it did not give any grounds for suspecting that there was a continuous change in progress.  It was, however, apparent that the periodic time was connected with the solar disturbance, so that, if there were any alteration in the amount of the sun’s disturbing effect, there must be a corresponding alteration in the moon’s periodic time.  Laplace, therefore, perceived that, if he could discover any continuous change in the ability of the sun for disturbing the moon, he would then have accounted for a continuous change in the moon’s periodic time, and that thus an explanation of the long-vexed question of the lunar acceleration might be forthcoming.

The capability of the sun for disturbing the earth-moon system is obviously connected with the distance of the earth from the sun.  If the earth moved in an orbit which underwent no change whatever, then the efficiency of the sun as a disturbing agent would not undergo any change of the kind which was sought for.  But if there were any alteration in the shape or size of the earth’s orbit, then that might involve such changes in the distance between the earth and the sun as would possibly afford the desired agent for producing the observed lunar effect.  It is known that the earth revolves in an orbit which, though nearly circular, is strictly an ellipse.  If the earth were the only planet revolving around the sun then that ellipse would remain unaltered from age to age.  The earth is, however, only one of a large number of planets which circulate around the great luminary, and are guided and controlled by his supreme attracting power.  These planets mutually attract each other, and in consequence of their mutual attractions the orbits of the planets are disturbed from the simple elliptic form which they would otherwise possess.  The movement of the earth, for instance, is not, strictly speaking, performed in an elliptical orbit.  We may, however, regard it as revolving in an ellipse provided we admit that the ellipse is itself in slow motion.

It is a remarkable characteristic of the disturbing effects of the planets that the ellipse in which the earth is at any moment moving always retains the same length; that is to say, its longest diameter is invariable.  In all other respects the ellipse is continually changing.  It alters its position, it changes its plane, and, most important of all, it changes its eccentricity.  Thus, from age to age the shape of the track which the earth describes may at one time be growing more nearly a circle, or at another time may be departing more widely from a circle.  These alterations are very small in amount, and they take place with extreme slowness, but they are in incessant progress, and their amount admits of being