Dante seems to have taken some trouble to find out the exact period of the sun’s revolution. His text-book, the _Elementa_ of Alfraganus, only gives it as 365¼ days nearly:—“Sol ... orbem confecit diebus 365 et propè ¼.” Ristoro d’Arezzo and Brunetto Latini were content to repeat this rough estimate, and call the year 365 days 6 hours, but Dante wished to be more exact, and somehow contrived to obtain a value which was much nearer the modern estimate of 365 days, 5 hours, 48 minutes, 46 seconds. We know this from two passages. In the _Convivio_ he gives the half period as less than 182 days 15 hours; and in the _Paradiso_ Beatrice says that January will in time cease to be a winter month, because of a neglected fraction of time. “Prima che gennaio tutto si sverni Per la centesma ch’ è laggiù negletta.”[224] ------------------------------------------------------------------------ [224] “Ere January be unwintered wholly By the centesimal on Earth neglected.” _Par._ xxvii. 142-143. (_Longfellow_). ------------------------------------------------------------------------ January was in fact receding from the winter, and steadily though slowly advancing towards the spring, because the Julian year (as we saw, p. 171) was 11 minutes 14 seconds longer than the true solar tropical year. When Julius Cæsar reformed the Calendar, March 25 was made (as of old) to coincide with the spring equinox, but by Dante’s time this date was 13 days late, and the true equinox fell on March 12. Consequently though the day called January 1 still came 84 days before March 25, it was only 71 days before the spring equinox. If Beatrice meant to speak with scientific precision, and was correct in her hundredth part of a day per annum, that is, if the difference between the astronomical and the Julian year was one day in a hundred years, it would be 7100 years before the first of January came to coincide with the spring equinox, and January became a spring month. But the error quoted is really rather too large, for a hundredth part of a day is 14 minutes 24 seconds, and it was in fact only 11 minutes 14 seconds.