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, it is not
surprising that there should have been but little temptation to doubt
it. On undertaking a new calculation of the same question, Professor
Adams found that Laplace had not pursued this approximation
sufficiently far, and that consequently there was a considerable
error in the result of his analysis. Adams, it must be observed, did
not impugn the value of the lunar acceleration which Halley had
deduced from the observations, but what he did show was, that the