200. Of his numerous contributions to astronomy, which touched almost every branch of the subject, his work on comets is the best known and probably the most important. He observed the comets of 1680 and 1682; he worked out the paths both of these and of a number of other recorded comets in accordance with Newton’s principles, and contributed a good deal of the material contained in the sections of the _Principia_ dealing with comets, particularly in the later editions. In 1705 he published a _Synopsis of Cometary Astronomy_ in which no less than 24 cometary orbits were calculated. Struck by the resemblance between the paths described by the comets of 1531, 1607, and 1682, and by the approximate equality in the intervals between their respective appearances and that of a fourth comet seen in 1456, he was shrewd enough to conjecture that the three later comets, if not all four, were really different appearances of the same comet, which revolved round the sun in an elongated ellipse in a period of about 75 or 76 years. He explained the difference between the 76 years which separate the appearances of the comet in 1531 and 1607, and the slightly shorter period which elapsed between 1607 and 1682, as probably due to the perturbations caused by planets near which the comet had passed; and finally predicted the probable reappearance of the same comet (which now deservedly bears his name) about 76 years after its last appearance, _i.e._ about 1758, though he was again aware that planetary perturbation might alter the time of its appearance; and the actual appearance of the comet about the predicted time (chapter XI., § 231) marked an important era in the progress of our knowledge of these extremely troublesome and erratic bodies. 201. In 1693 Halley read before the Royal Society a paper in which he called attention to the difficulty of reconciling certain ancient eclipses with the known motion of the moon, and referred to the possibility of some slight increase in the moon’s average rate of motion round the earth. This irregularity, now known as the =secular acceleration of the moon’s mean motion=, was subsequently more definitely established as a fact of observation; and the difficulties met with in explaining it as a result of gravitation have rendered it one of the most interesting of the moon’s numerous irregularities (cf. chapter XI., § 240, and chapter XIII., § 287).