There is yet another inscription, also known to be of a still earlier period, referring to the rising of Sirius on the 27th of Epiphi. We may neglect the difference of one day in the cycle (representing four years); and again, if the use of the Sothic cycle were the origin of the identity of dates, we have this time, according to Oppolzer, a period of 1460 years to add: this gives us (1580 + 1460 =) 3040 B.C. Again under which king? Here we are face to face with one of the difficulties of these inquiries, to which reference has already been made. It may be stated, however, that the inscription is ascribed to Pepi, and that, according to various authorities, that king reigned some time between 3000 and 3700 B.C. We come, then, to this: that one of the oldest dated inscriptions known seems to belong to a system which continued in use at Philæ up to about 100 B.C., and it was essentially a system of a vague year, the 1st Thoths of which were represented as days on a 1460-years' cycle. Now, assuming that the approximate date of the earliest inscription is 3044 B.C., and that it represented the heliacal rising of Sirius on the 27th of Epiphi, the year 3044 must have been the [(5 + 30 + 3) x 4 =] 152nd after the beginning of the cycle. The cycle, then, must have commenced (3044 + 152 =) 3196 B.C. If we assume that the real date of Pepi, who, it is stated, reigned 100 years, included the year 3044 B.C., it may be, then, that the inscriptions to which I have directed attention give us three Sothic cycles beginning-- 122 + 148 = 270 B.C. 1580 + 148 = 1728 B.C. 3044 + 148 = 3192 B.C. According to Biot's calculation, the first heliacal rising of Sirius at the solstice took place in the year 3285 B.C.; it is possible, then, that the Egyptians utilised this heliacal rising within a hundred years of the date on which it would have been first possible for them to do so. This shows how keenly alive they were in these matters, and also, I think, that they had been trained by watching some other star previously. It would also follow that the vague year was in common use. There is ample evidence to show, however, that by this time the priests were fully acquainted with the true year, which was called the sacred year, and that every four years an additional epact was interpolated. Their solar temples, then, at last had been utilised. One argument which has been used to show that a vague year was not in use during the time of the Ramessids has been derived from some inscriptions at Silsilis which refer to the dates on which sacred offerings were presented there to the Nile-god. As the dates 15th of Thoth and 15th of Epiphi are the same in all three inscriptions, although they cover the period from Rameses II. to Rameses III.--120 years--it has been argued by Brugsch that a fixed year is in question.