The moon travels in her orbit, swayed chiefly by the earth’s attraction. But the sun, though greatly more distant, yet, owing to the immensity of his mass, plays an important part in guiding our satellite. His influence tends to relieve the moon, in part, from the earth’s sway. Thus she travels in a wider orbit, and with a slower motion, than she would have but for the sun’s influence. Now the earth is not at all times equally distant from the sun, and his influence upon the moon is accordingly variable. In winter, when the earth is nearest to the sun, his influence is greatest. The lunar month, accordingly (though the difference is very slight), is longer in winter than in summer. This variation had long been recognised as the moon’s ‘annual equation;’ but Laplace was the first to point out that the variation is itself slowly varying. The earth’s orbit is slowly changing in shape—becoming more and more nearly circular year by year. As the greater axis of her orbit is unchanging, it is clear that the actual extent of the orbit is slowly increasing. Thus, the moon is slightly released from the sun’s influence year by year, and so brought more and more under the earth’s influence. She travels, therefore, continually faster and faster, though the change is indeed but a very minute one;—only to be detected in long intervals of time. Also the moon’s _acceleration_, as the change is termed, is only temporary, and will in due time be replaced by an equally gradual retardation. When Laplace had calculated the extent of the change due to the cause he had detected, and when it was found that ancient eclipses were now satisfactorily accounted for, it may well be believed that there was triumph in the mathematical camp. But this was not all. Other mathematicians attacked the same problem, and their results agreed so closely that all were convinced that the difficulty was thoroughly vanquished. A very noteworthy result followed from Laplace’s calculations. Amongst other solutions which had been suggested, was the supposition (supported by no less an authority than Sir Isaac Newton, who lived to see the commencement of the long conflict maintained by mathematicians with this difficulty), that it is not the moon travelling more quickly, but our earth rotating more slowly, which causes the observed discrepancy. Now it resulted from Laplace’s labours—as he was the first to announce—that the period of the earth’s rotation has not varied by one-tenth of a second per century in the last two thousand years. The question thus satisfactorily settled, as was supposed, was shelved for more than a quarter of a century. The result, also, which seemed to flow from the discussion—the constancy of the earth’s rotation-movement—was accepted; and, as we have seen, our national system of measures was founded upon the assumed constancy of the day’s duration.