that same distance from the star. In the time of Halley, though it was known that the moon moved nearly in an ellipse, yet the elements of that ellipse, and the various irregularities to which it is subject, were very imperfectly ascertained. It had, however, been known even from the time of the Chaldeans, that some of these irregularities have a _period_, as it is called, of little more than eighteen years, that is, begin again in the same order after every eighteen years; the periods and quantities of several other errors had also been discovered with something like accuracy. To make good lunar tables, that is, tables from which the place of the moon might be correctly calculated beforehand, became the object of Halley’s ambition. He therefore observed the moon diligently during the whole of one of the periods of eighteen years, that is, from the end of 1721 to that of 1739, and produced tables which were published in 1749, after his death, and were of great service to astronomers. He also made another observation on the motion of the moon, which has since given rise to one of the finest discoveries of Laplace. In calculating from our tables the time of an ancient eclipse, observed at Babylon, B. C. 720, he found that, had the tables been correct, it would have happened three hours sooner than, according to Ptolemy, it did happen. This might have arisen from an error in the Babylonian observation; but on looking at other eclipses, he found that the ancient ones always happened later than the time indicated by his table, and that the difference became less and less as he approached his own time. From hence he concluded that the moon’s average daily motion is subject to a very small acceleration, so that a lunar month at present is in a very slight degree shorter than a month in the time of the Chaldeans. This was afterwards shown by Laplace to arise from a very slow diminution in the eccentricity of the earth’s orbit, caused by the attraction of the planets. For a further account of Halley’s astronomical labours, we may refer to the History of Astronomy in the Library of Useful Knowledge, page 79.