Krall also argues that the expressions great and little year and their hieroglyphics referred to the rears of 365 and 360 days respectively, and adds:—

"If we inquire into the time at which the epagomenes were introduced, we can only fix approximate dates. If the calendars of the Mastabas, complete as they are, do not mention the epagomenes, whereas inscriptions of the period of the Amenamhāts refer to them, this can only be due to the circumstance that the epagomenes were only introduced in the meantime, but probably nearer the upper than the lower limit.... For the sake of completeness, we may mention that, according to Censorinus, the five epagomenes were introduced by the King Arminon.... Louth conjectures that Arminon is identical with Amenamhāt I., under whom the epagomenes are first met with. But since, between Nitokris and Amenamhāt I., there is a period of 500 years void of records, and the name Arminon has nothing to do with Amenamhāt, we can hardly share this view."

However this knotty point may subsequently be settled by Egyptologists, from the astronomers point of view the words of Ideler[70]—"Had ignorance lead to the establishment of a year of 360 days, yet experience would have led to its rejection in a few years"—will carry conviction with them. Indeed, one may ask whether it is not possible that the use of the 360-day year, and the complications which it involved, may have had something to do with the foundation of the solar temples.

Let us attempt to put ourselves, in imagination, in the place of the ancient Egyptians after the use of this 360-day year had been continued for any length of time. It is perfectly certain that now in this part of the Nile valley, now in that, everybody, from Pharaoh to fellah, must have got his calendar into the most hopeless confusion, compared with which "the year of confusion" was mere child's-play, and that the exact determination of the times, either of state functions or sowing, reaping, or the like, by means of such a calendar would have been next to impossible.

As each year dropped 5¼ days, it is evident that in about seventy years (365·25∕5·25) a cycle was accomplished, in which New Year's Day swept through all the months. The same month (so far as its name was concerned) was now in the inundation time, now in the sowing time, and so on. Of fixed agricultural work for such months as these there could be none.

It must have been, then, that there were local attempts to retain the coincidences between the true and the calendar year—intercalation of days or even of months being introduced, now in one place, now in another; and these attempts, of course, would make confusion worse confounded, as the months might vary with the district, and not with the time of year.

That this is what really happened is, no doubt, the origin of the stringent oath required of the Pharaohs in after times, to which I shall subsequently refer.

To acknowledge that the calendar year was wrong implied that they knew the length of the true one. How had they found it out? I think there can be no question that this knowledge had come to them by observations either of the solstices or the equinoxes. It is true they had the inundation; but, as we have seen, the rise is not absolutely regular, and the inundation takes many days to travel from Philæ to Cairo (Memphis). If, then, the inundation had fixed the beginning of the year, each nome would have its special New Year's Day, and this would never have been tolerated by a settled government embracing the whole Nile valley, especially as each king's reign was supposed to commence on New Year's Day.

It seems, then, that the solstitial temples and the pyramids were, if not actually requisite for settling the matter, at all events all that was necessary, if they existed.

But now comes in a most interesting and important point. If observations of the sun at solstice or equinox had been alone made use of, the true length of the year would have been determined in a few years. But the next scene in Egyptian history shows us that the true length of the year was not determined, but only an approximation to it.