CHAPTER XXV.

THE VAGUE AND THE SIRIAN YEARS.

During three thousand years of Egyptian history the beginning of the year was marked by the rising of Sirius, which rising took place nearly coincidently with the rise of the Nile and the Summer Solstice.

I have insisted upon the regularity of the rise of the Nile affording the ancient Egyptians, so soon as this regularity had been established, a moderately good way of determining the length of the year, but we have seen they did not so employ it.

It is also clear that so soon as the greatest northing and southing of the sun rising or setting at the solstices had been recognised, and the intervals between them in days had been counted, a still more accurate way would be open to them. The solstice _must_ have occurred with greater regularity than the rise of the river, so that as accuracy of definition became more necessary the solstice would be preferred. The solstice was common to all Egypt; the commencement of the inundation was later as the place of observation was nearer the mouth of the river. This means they also did not employ, at all events in the first instance. Of the three coincident, or nearly coincident, phenomena, the rise of the Nile, the Summer Solstice, and the rising of Sirius, they at first chose the last.

According to Biot the heliacal rising of Sirius _at the solstice_ took place on July 20 (Julian), in the year 3285 B.C.; and according to Oppolzer it took place on July 18 (Julian), in the year 3000 B.C.

But this is too general a statement, and it must be modified here. There was a difference of seven days in the date of the heliacal rising, according to the latitude, from southern Elephantine and Philæ, where the heliacal rising at the solstice was noted first, to northern Bubastis. There was a difference of four days between Memphis and Thebes, so that the connection between the heliacal rising and the solstice depended simply upon the latitude of the place. The further south, the earlier the coincidence occurred.

Here we have an _astronomical_ reason for the variation in the date of New Year's Day.

There no doubt was a time when the Egyptian astronomer-priests imagined that, by the introduction of the 365-days year, marking its commencement, as I have said, by the rising of one of the host of heaven, they had achieved finality. But, alas, the dream must soon have vanished.

Even with this period of 365 days, the true length of the year had not been reached; and soon, whether by observations of the beginning of the inundation, or by observations of the solstice in some of the solar temples when these had been built, it was found that there was a difference of a day every four years between the beginning of the natural and of the newly-established year, arising, of course, from the fact that the true year is 365 days _and a quarter of a day_ (roughly) in length.

With perfectly orientated temples they must have soon found that their festival at the Summer Solstice--which festival is known all over the world to-day--did not fall precisely on the day of the New Year, because, if 365 days had exactly measured the year, that flash of bright sunlight would have fallen into the sanctuary just as it did 365 days before. But what they must have found was that, after an interval of four years, it did not fall on the first day of the month, but on the day following it.

Recurrent solstices │ │ │ │ │ │ │ │ │ Recurrent 1st. of Thoth │ │ │ │ │ │ │ │ │ │

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.

The variation from the true tropical year brought about by the processional movement of Sirius or any other star, however, can be watched by noting its heliacal rising in relation to any physical phenomenon which marks the true length of the tropical year. Such a phenomenon we have in the solstice and in the rising of the Nile, which, during the whole course of historical time, has been found to rise and fall with constancy in each year, the initial rise of the waters, some little way above Memphis, taking place very nearly at the Summer Solstice.

Again, M. Biot has made a series of calculations from which we learn that the heliacal rising of Sirius AT THE SOLSTICE occurred on July 20 (Julian) in the year 3285 B.C., and that in the year 275 B.C., the _solstice_ occurred on June 27 (Julian), while the heliacal _rising of Sirius_ took place, as before, on July 20 (Julian), so that in Ptolemaic times, at Memphis, there was a difference of time of about 24 days between the heliacal rising of Sirius and the solstice, and therefore the beginning of the Nile flood in that part of the river. This, among other things, is shown on the next page.

We learn from the work of Biot and Oppolzer, then, that the precessional movement of the star caused successive heliacal risings of Sirius at the solstice to be separated by almost exactly 365¼ days--that is, by a greater period than the length of the true year. So that, in relation to this star, two successive heliacal risings at the 1st of Thoth vague are represented by a period of (365¼ × 4 =) 1461 years, while in the case of the solstices we want 1506.

Now in books on Egyptology the period of 1461 years is termed the Sothic period, and truly so, as it very nearly correctly measures the period elapsing between two heliacal risings at the solstice (or the beginning of the Nile flood) on the 1st of Thoth in the _vague_ year.

But it is merely the result of _chance_ that 365¼ × 4 represents it. It was not then known that the precessional movement of Sirius almost exactly made up the difference between the true length of the year and the assumed length of 365¼ days. It has been stated that this period had not any ancient existence, but was calculated back in later times. This seems to me very improbable. I look upon it rather as a true result of observation, the more so as _the period was shortened in later times_, as Oppolzer has shown.

It will be seen that our investigations land us in several astronomical questions of the greatest interest, and that the study is one in which modern computations, with the great accuracy which the work of Leverrier and others gives to them, can come to the rescue, and eke out the scantiness of the ancient records.

To consider the subject further, we must pass from the mere question of the year to that of chronology generally.