They would, therefore, have to search in the heavens for an apparent sign of its return, and they imagined they had found this sign when the sun returned to the same position, relatively to some remarkable star. Thus they applied themselves, like almost all nations who are beginning this inquiry, to observe the heliacal risings and settings of the stars. We know that they chose particularly the heliacal rising of Sirius, at first, doubtless, on account of the beauty of the star; and, especially, because, in those ancient times, this rising of Sirius being nearly coincident with the solstice, and indicative of the inundation, was to them the most important phenomenon of this kind. Hence it was that Sirius, under the name of Sothis, occupied so conspicuous a place in their mythology, and in their religious ceremonies. Supposing, therefore, that the return of the heliacal rising of Sirius and the tropical year were of the same duration, and believing, at length, that this duration was 365 days and a quarter, they would imagine a period after which the tropical year and the old year, the sacred year of 365 days only, would return to the same day; a period which, according to these incorrect data, was necessarily 1461 sacred years, and 1460 of those improved years to which they gave the name of years of Sirius. They took for the point of departure of this period, which they named the Sothiac or great year, a civil year, the first day of which was, or had been, also that of a heliacal rising of Sirius; and it is known, from the positive testimony of Censorinus, that one of these great years had ended in the 138th year of the Christian era[182]. It had consequently commenced in the 1322d before Christ, and that which preceded it in the 2782d. In fact, the calculations of M. Ideler shew, that Sirius was heliacally risen on the 20th July of the Julian year 139, a day which corresponded that year to the first of Thot, or the first day of the Egyptian sacred year[183]. But not only is the position of the sun, with relation to the stars of the ecliptic, or the sidereal year different from the tropical year, on account of the precession of the equinoxes. The heliacal year of a star, or the period of its heliacal rising, especially when it is distant from the ecliptic, differs still from the sidereal year, and differs in various degrees according to the latitudes of the places where it is observed. What is very singular, however, and the observation has already been made by Bainbridge[184] and Father Petau[185], it happens, by a remarkable concurrence in the positions, that, in the latitude of Upper Egypt, at a certain epoch, and during a certain number of ages, the year of Sirius was really within very little of 365 days and a quarter; so that the heliacal rising of this star returned in fact to the same day of the Julian year, the 20th July, in the year 1322 before, and the year 138 after Christ[186].