To these twelve months, as already said, five days were added, and the year thus formed is generally known as the “=vague= (or wandering) =year=,” and the “=calendar year=.” Now it is clear that since this vague year of 365 days was shorter than the true year, or “=solar year=,” of 365¼, by nearly a quarter of a day, every fourth vague year would be shorter than the true year by nearly a whole day. Moreover, given a sufficient number of years, the vague year would work backward through all the months of the year, until at length the first day of the vague year would coincide with the first day of the solar year. Thus, supposing the first day of the vague and solar years to have coincided on January 1, B.C. 2000, two hundred years later the first day of the vague year would have worked back about 50 days; and five hundred years later, _i.e._, about B.C. 1300, the first day of the vague year would fall in the height of the summer instead of in the depth of winter. This defect in their year of 365 days would soon become apparent, and we may be sure that they were not long in discovering some means for correcting it. According to some authorities the Egyptians knew the length of the true, or solar, year with considerable exactitude, and if this be so they were well able to plan their farming operations without any reference to the vague year. According to others the Egyptians were ignorant of the solar year, but were acquainted with a =Sothic year=, which is so called because it began on the day when the star =Sepṭ= (or =Sirius=, or =Sothis=, or the =Dog Star=) rose heliacally, that is to say, with the sun. This happened on July 19 or 20, and as this date was very near the time when the Inundation began, the Egyptians considered it most convenient for their year and the Inundation to begin at the same time. The =Sothic year= contained practically 365¼ days, _i.e._, a few minutes more than the true, or solar, year; and the =Sothic Period=, _i.e._, the length of the time which must elapse between two risings of Sothis heliacally, contained 1,460 Sothic years, or 1,461 vague, or calendar, years.