The dawn of astronomy / A study of the temple-worship and mythology of the ancient Egyptians

by Sir Norman Lockyer

The true year and the newly-established year of 365 days, then, behaved to each other as shown in the following diagram, when the solstice, representing the beginning of the calendar year, occurred on the 1st Thoth of the newly-established calendar year. We should have, in the subsequent years, the state of things shown in the diagram. The solstice would year by year occur later in relation to the 1st of Thoth. The 1st of Thoth would occur earlier, in relation to the solstice; so that in relation to the established year the solstice would sweep forwards among the days: in relation to the true year the 1st of Thoth would sweep backwards.

Let us call the true natural year a fixed year: it is obvious that the months of the 365-day year would be perpetually varying their place in relation to those of the fixed year. Let us, therefore, call the 365-day year a vague year.

Now if the fixed year were exactly 365¼ days long, it is quite clear that, still to consider the above diagram, the 1st of Thoth in the vague year would again coincide with the solstice in 1,460 years, since in four years the solstice would fall on the 2nd of Thoth, in eight years on the 3rd of Thoth, and so on (365 × 4 = 1460).

But the fixed year is not 365¼ days long exactly. In the time of Hipparchus 365·25 did not really represent the true length of the solar year; instead of 365·25 we must write 365·242392—that is to say, the real length of the year is a little less than 365¼ days.

Now the length of the year being a little less, of course we should only get a second coincidence of the 1st of Thoth vague with the solstice in a longer period than the 1460-years cycle; and, as a matter of fact, 1506 years are required to fit the months into the years with this slightly shortened length of the year. In the case of the solstice and the vague year, then, we have a cycle of 1,506 years.

The variations between the fixed and the vague years were known perhaps for many centuries to the priests alone. They would not allow the established year of 365 days, since called the vague year, to be altered, and so strongly did they feel on this point that, as already stated, every king had to swear when he was crowned that he would not alter the year. We can surmise why this was. It gave great power to the priests; they alone could tell on what particular day of what particular month the Nile would rise in each year, because they alone knew in what part of the cycle they were; and, in order to get that knowledge, they had simply to continue going every year into their Holy of Holies one day in the year, as the priests did afterwards in Jerusalem, and watch the little patch of bright sunlight coming into the sanctuary. That would tell them exactly the relation of the true solar solstice to their year; and the exact date of the inundation of the Nile could be predicted by those who could determine observationally the solstice, but by no others.

But now suppose that, instead of the solstice, we take the heliacal rising of Sirius, and compare the successive risings at the solstice with the 1st of Thoth.

But why, it will be asked, should there be any difference in the length of the cycles depending upon successive coincidences of the 1st of Thoth with the solstice and the heliacal rising of Sirius? The reason is that stars change their places, and the star to which they trusted to warn them of the beginning of a new year was, like all stars, subject to the effects brought about by the precession of the equinoxes. Not for long could it continue to rise heliacally either at a solstice or a Nile flood.

Among the most important contributors to the astronomical side of this subject are M. Biot and Professor Oppolzer. It is of the highest importance to bring together the fundamental points which have been made out by their calculations. We have determinate references to the heliacal rising of Sirius, to the 1st of Thoth, to the solstice, and to the rising of the Nile in connection with the Egyptian year; but, so far as I have been able to make out, we find nowhere at present any sharp reference to the importance of their correlation with the times of the tropical year at which these various phenomena took place. The question has been complicated by the use by chronologists of the Julian year in such calculations; so the Julian year and the use made of it by chronologists have to be borne in mind. Unfortunately, many side-issues have in this way been raised.

The heliacal rising of Sirius, of course—if in those days a true tropical year was being dealt with—would have given us a more or less constant variation in the time of the rising over a long period, on account of its precessional movement; and M. Biot and others before him have pointed out that the variation, produced by that movement, in the time of the year at which the heliacal rising took place was almost exactly equal to the error of the Julian year as compared with the true tropical or Gregorian one. The Sirius year, like the Julian, was about eleven minutes longer than the true year, so that in 3,000 years we should have a difference of about 23 days. Biot showed by his calculations, using the solar tables extant before those of Leverrier, that from 3200 B.C. to 200 B.C. in the Julian year of the chronologists, Sirius had constantly, in each year, risen heliacally on July 20 Julian = June 20 Gregorian. Oppolzer, more recently, using Leverrier's tables, has made a very slight correction to this, which, however, is practically immaterial for the purposes of a general statement. He shows that in the latitude of Memphis, in 1600 B.C., the heliacal rising took place on July 18·6, while in the year 0 it took place on July 19·7, both Julian dates.