If we compare these with the zodiacal periods given by Alfraganus, we see that Dante has taken those of Saturn, Jupiter, and Mars at the nearest whole number of years and halved them, but with the sun he seems to have used that more exact value with which we have already seen that he was acquainted. For to divide the 365¼ days of Alfraganus by 2 would have given him exactly 182 days 15 hours; but dividing 365 days 5 hours, and neglecting minutes gives 182 days 14 hours. The large oscillations of Venus and Mercury would make their periods of visibility very irregular, but the mean period would be, as Dante says, about the same as that of the sun. He has made a slip with the moon, for of course it is her sidereal period of 27 days 7¾ hours which he should have taken, giving a half period of less than 14 days, whereas he has evidently taken the mean synodic period of 29 days 12¾ hours, and ignored the hours. All the printed editions of Alfraganus give the sidereal period in this passage, except the Paris edition of 1546; but that gives the synodic,[596] so it doubtless appeared on some mediæval MSS. Dante must have had the misfortune to possess or consult one of these. ------------------------------------------------------------------------ [596] Toynbee, “Dante’s Obligations to Alfraganus in _Vita Nuova_ and _Convivio_,” in _Romania_ xxiv. 95. ------------------------------------------------------------------------ As for the stars, one third of their sphere would not yet have been seen. This is not difficult to understand if we remember what the movement of the star sphere was supposed to be, and how long it was since man had first begun to look upon it, according to Dante’s chronology. The movement which makes the equinoctial point shift its place among the stars was thought to be a movement of revolution of the whole star sphere, and its rate to be one degree in a century; the age of the world, we learn from _Par._ xxvi. 118-123, was over sixty centuries when Dante wrote. For Adam said that he had spent 930 years on Earth and 4302 in the Limbo, so that Dante evidently counted 5232 years from the Creation to the Crucifixion, that is (5232-33 =) 5199 to the beginning of our era at the birth of Christ, which is the date given by Orosius; adding 1300 years to this, we find that the age of the world in Dante’s day was more than 6000 years. Therefore the star sphere had revolved, since the beginning of the world, through more than 60 degrees.