It has been rendered, I hope, quite clear in Chapter XXIII. that there is a difference of fifteen or sixteen days between the arrival of the inundation at Elephantine and at Memphis. Hence, if in Pepi's time a Nile rise were observed at Silsilis, there might easily be a difference of fifteen days between the rise of the Nile at Silsilis and the Memphic 1st of Thoth. If both at Silsilis and Memphis the Nile rise marked 1st Thoth, the day of the rise at Memphis would correspond to 15th Thoth at Silsilis, so that a king reaching Silsilis with Memphis local time would be struck with this difference, and anxious to record it. May not this, then, have been the important datum recorded in the sacred books? If so, it would not touch the question of the fixed or vague year at all. Let it, then, be for the present conceded that there was a vague year, and that at least some of the inscriptions which suggest the use of only a fixed year in these early times may be explained in another way. CHAPTER XXVII. THE CALENDAR AND ITS REVISION. In the last chapter the so-called Sothic cycle was discussed, and dates of the commencement of the successive cycles were suggested. These dates were arrived at by taking the very simplest way of writing a calendar in pre-temple times, and using the calendar inscriptions in the most natural way. The dates for the coincidence of the heliacal rising of Sirius and the 1st Thoth of the vague year at, or near, the solstice, were-- 270 B.C. 1728 B.C. 3192 B.C. Here, _in limine_, we meet with a difficulty which, if it cannot be explained, evidently proves that the Egyptians did not construct and use their calendar in the way we have supposed. We have it on the authority of Censorinus that a Sothic period was completed in 139 A.D., and that there was then a vague year in partial use. It is here that the work of Oppolzer is of such high value to us; he discussed all the statements made by Censorinus, and comes to the conclusion that his account is to be depended upon. It has followed from the inquiries of chronologists that in this year the 1st of Thoth took place on July 20 (Julian), the date originally of the heliacal rising of Sirius, the beginning of the year. This being so, then, in the year 23 A.D.--in which the Alexandrine reform of the calendar, of which more presently, was introduced--the 1st of Thoth would take place on August 29, a very important date. Censorinus also said that in his own time (A.D. 238) the 1st of Thoth of the vague year fell on June 25. The diagram will show the connection of these three dates in reference to the vague year. The relations of the statements made as to the years 139 and 238 are very clearly discussed by Prof. Oppolzer. [Illustration: JULIAN DATES OF THE 1ST OF THOTH (VAGUE) FROM 23 A.D. AND 240 A.D.]