days, regulated by the revolutions of the moon, did not long meet the needs of the Egyptian people; it did not correspond with the length of the solar year, for it fell short of it by five and a quarter days, and this deficit, accumulating from twelvemonth to twelvemonth, caused such a serious difference between the calendar reckoning and the natural seasons, that it soon had to be corrected. They intercalated, therefore, after the twelfth month of each year and before the first day of the ensuing year, five epagomenal days, which they termed the "five days over and above the year."[*] * There appears to be a tendency among Egyptologists now to doubt the existence, under the Ancient Empire, of the five epagomenal days, and as a fact they are nowhere to be found expressly mentioned; but we know that the five gods of the Osirian cycle were born during the epagomenal day (cf. p. 247 of this History), and the allusions to the Osirian legend which are met with in the Pyramid texts, prove that the days were added long before the time when those inscriptions were cut. As the wording of the texts often comes down from prehistoric times, it is most likely that the invention of the epagomenal days is anterior to the first Thinite and Memphite dynasties. The legend of Osiris relates that Thot created them in order to permit Nuit to give birth to all her children. These days constituted, at the end of the "great year," a "little month," which considerably lessened the difference between the solar and lunar computation, but did not entirely do away with it, and the six hours and a few minutes of which the Egyptians had not taken count gradually became the source of fresh perplexities. They at length amounted to a whole day, which needed to be added every four years to the regular three hundred and sixty days, a fact which was unfortunately overlooked. The difficulty, at first only slight, which this caused in public life, increased with time, and ended by disturbing the harmony between the order of the calendar and that of natural phenomena: at the end of a hundred and twenty years, the legal year had gained a whole month on the actual year, and the 1st of Thot anticipated the heliacal rising of Sothis by thirty days, instead of coinciding with it as it ought. The astronomers of the Graeco-Roman period, after a retrospective examination of all the past history of their country, discovered a very ingenious theory for obviating this unfortunate discrepancy. If the omission of six hours annually entailed the loss of one day every four years, the time would come, after three hundred and sixty-five times four years, when the deficit would amount to an entire year, and when, in consequence, fourteen hundred and sixty whole years would exactly equal fourteen hundred and sixty-one incomplete years. The agreement of the two years, which had been