accurately calculated.  At the present time, and for thousands of years past, as well as for thousands of years to come, the eccentricity of the earth’s orbit is diminishing, and consequently the orbit described by the earth each year is becoming more nearly circular.  We must, however, remember that under all circumstances the length of the longest axis of the ellipse is unaltered, and consequently the size of the track which the earth describes around the sun is gradually increasing.  In other words, it may be said that during the present ages the average distance between the earth and the sun is waxing greater in consequence of the perturbations which the earth experiences from the attraction of the other planets.  We have, however, already seen that the efficiency of the solar attraction for disturbing the moon’s movement depends on the distance between the earth and the sun.  As therefore the average distance between the earth and the sun is increasing, at all events during the thousands of years over which our observations extend, it follows that the ability of the sun for disturbing the moon must be gradually diminishing.

[Plate:  Cambridge observatory.]

It has been pointed out that, in consequence of the solar disturbance, the orbit of the moon must be some what enlarged.  As it now appears that the solar disturbance is on the whole declining, it follows that the orbit of the moon, which has to be adjusted relatively to the average value of the solar disturbance, must also be gradually declining.  In other words, the moon must be approaching nearer to the earth in consequence of the alterations in the eccentricity of the earth’s orbit produced by the attraction of the other planets.  It is true that the change in the moon’s position thus arising is an extremely small one, and the consequent effect in accelerating the moon’s motion is but very slight.  It is in fact almost imperceptible, except when great periods of time are involved.  Laplace undertook a calculation on this subject.  He knew what the efficiency of the planets in altering the dimensions of the earth’s orbit amounted to; from this he was able to determine the changes that would be propagated into the motion of the moon.  Thus he ascertained, or at all events thought he had ascertained, that the acceleration of the moon’s motion, as it had been inferred from the observations of the ancient eclipses which have been handed down to us, could be completely accounted for as a consequence of planetary perturbation.  This was regarded as a great scientific triumph.  Our belief in the universality of the law of gravitation would, in fact, have been seriously challenged unless some explanation of the lunar acceleration had been forthcoming.  For about fifty years no one questioned the truth of Laplace’s investigation.  When a mathematician of his eminence had rendered an explanation of the remarkable facts of observation which seemed so complete,