Then Meton made his celebrated discovery that nineteen tropical years correspond almost exactly with 235 synodic months (the difference is in fact only a few hours), and a cycle of 19 years was arranged, which was adopted by all Greek states and dependencies. Some of the years had twelve and some thirteen months, and some of the months 29 and others 30 days, but all followed in a regular order, and when one cycle was completed another was begun. The total number of days in each cycle was 6940, and as this is only 9½ hours longer than 19 true tropical years, it follows that the average year in the Metonic cycle was only half an hour longer than it should have been.[58] The average month was not quite two minutes longer than the true synodic month. ------------------------------------------------------------------------ [58] It therefore really approached more nearly the sidereal year, although the cycle was based on the tropical year. ------------------------------------------------------------------------ An improvement even on Meton’s cycle was made by Calippus, who proposed to correct its too great length by quadrupling the period, and then deducting one day from the whole. This would have given a cycle of 76 calendar years, in which the average year was 365¼ days, or only 11¼ minutes too long. It does not seem, however, to have been ever brought into actual use as a calendar, but Ptolemy often refers to the Calippic epoch as a date from which to calculate celestial phenomena. [Sidenote: Theon of Alexandria _c._ 380 A.D.] After Ptolemy, the Alexandrian school of astronomy produced only copyists and commentators, the last of whom was Theon, who saw his daughter Hypatia murdered and the library burned by fanatical mobs. It only remains for us to see how the Greek system of astronomy, brought to so great perfection in the _Almagest_, was neglected for many centuries, and by whom it was at length rediscovered and made to live again. _VI. ASTRONOMY UNDER IMPERIAL AND CHRISTIAN ROME._ B.C. 46 TO A.D. 1000. _Vos O clarissima mundi_ _Lumina labentem cœlo quæ ducitis annum._ Georgic I. No new school of astronomy arose under the Roman Empire, nor do we even know of one Roman who devoted his life to the science. The genius of this people lay in other directions, and Dante truly says:— ‘“Nature ordained in the world a place and a people for universal command ... to wit, Rome and her citizens or people. The which our poet too has touched upon right subtly in the sixth [Virgil, in the sixth book of the Æneid], introducing Anchises admonishing Æneas, the father of the Romans, thus:—