It would be interesting to know where Dante found this value, which is practically the only astronomical datum not given in Alfraganus. Ptolemy, following Hipparchus, had given the tropical year as ¹/₃₀₀ part of a day less than 365¼; Albategnius gave a more accurate figure, and one which agrees well with the “centesma,” for his tropical year differs from the Julian by a little less than ¹/₁₀₆ of a day; but he also improved the value of precession, and Dante does not seem to have known this, so he was probably not acquainted with this astronomer’s work. The Alfonsine Tables gave a value which was very close indeed to the correct one, making the tropical year only 30 seconds longer than the modern value, and the difference between the Julian and true year ¹/₁₃₄ of a day. (The correct value is ¹/₁₂₈). Either of these figures may have been known to Dante indirectly: perhaps he had obtained the Alfonsine value in conversation with Brunetto Latini, who had visited Alfonso’s court. His fraction was evidently only approximate, but it is interesting to know that he had found out more than popular books could tell him about the period of the sun’s revolution, and that he had been sufficiently struck by the small difference between the calendar and astronomical years to mention it in a picturesque way in his poem. It is possible that he had heard of Roger Bacon’s appeal to the Pope in 1267 to correct the calendar because the date of the spring equinox was of importance in connection with the observation of Easter. It is hardly necessary to remind my readers that this was done by another Pope three hundred years later, before January had made much more advance towards becoming a spring month. The hundredth part of a day, of which Beatrice complained, is now subtracted from the year by omitting to make century years leap years; but as the error was really not quite so great as she said, an exception is made for century years divisible by 400. Thus 1600 was a leap year, but not 1700, 1800, or 1900. [Illustration: Fig. 40. The Zodiac and the Months.] Dante seems to have connected any season of the year with the sun’s path in the zodiac as readily as with the name of a month. The sun’s yearly course through the signs is shown diagrammatically in figure 40, and a glance at this will make clear a number of allusions without any explanation. Starting from the first point of Aries at the spring equinox, which in Dante’s time fell in the middle of March, and taking one-twelfth of the year to traverse each sign, it is evident that during the end of March and beginning of April the sun was in Aries; he entered Cancer and reached the summer solstice in June, the autumnal equinox in Libra in September, and the winter solstice when he entered Capricornus in December. The six signs above the horizontal line are northern, the six below are southern. The following are a few typical examples.