It will be seen that our investigations land us in several astronomical questions of the greatest interest, and that the study is one in which modern computations, with the great accuracy which the work of Leverrier and others gives to them, can come to the rescue, and eke out the scantiness of the ancient records. To consider the subject further, we must pass from the mere question of the year to that of chronology generally. CHAPTER XXVI. THE SOTHIC CYCLE AND THE USE MADE OF IT. Although it is necessary to enter somewhat into the domain of chronology to really understand the astronomical observations on which the Egyptian year depended and the uses made of the year, I shall limit myself to the more purely astronomical part. To go over the already vast literature is far from my intention, nor is it necessary to attempt to settle all the differences of opinion which exist, and which are so ably referred to by Krall in his masterly analysis,[73] to which I own myself deeply indebted. The tremendously involved state of the problem may be gathered from the fact that the authorities are not yet decided whether many of the dates met with in the inscriptions really belong to a fixed or a vague year! Let us, rather, put ourselves in the place of the old Egyptians, and inquire how, out of the materials they had at hand, a calendar could be constructed in the simplest way. They had the vague year and the Sirius year, so related, as we have seen, that the successive coincidences of the 1st Thoth in both years took place after an interval of 1460 years. Now, for calendar purposes, they wanted not only to know the days of the years, but the years of the cycle. This latter is the only point we need consider here. How were they to do this? The _easiest_ way would be to conceive a great year or _annus magnus_, consisting of 1460 years, each day of which would represent four years in actual time; and further, to consider everything that happened, which had to be thus chronicled, to take place on the 1st of Thoth in each year. How would this system work? During the first four years, at the beginning of a cycle, the 1st Thoth vague would happen on the 1st Thoth of the cycle. During the next four years the 1st Thoth of the vague year would fall on the fifth epact, and so on; so, as the cycle swept onward, each group of four years would be marked by a date in the cycle, which would allow the place of the group of years in the cycle to be exactly defined. But as the cycle swept onward, the date would sweep backward among the months of the great sacred year until its end. To make this clear, it will be well to construct another diagram somewhat like the former one. [Illustration: THE DISTRIBUTION OF THE 1ST OF THOTH (REPRESENTING THE RISE OF SIRIUS) AMONG THE EGYPTIAN MONTHS IN THE 1460-YEAR SOTHIC CYCLE.]