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.
[Illustration: CONDITIONS OF THE HELIACAL RISING OF SIRIUS FROM 4000
B.C. TO 600 A.D.
The diagram shows (1) by white horizontal lines the Gregorian and
Julian dates for the rising at Thebes and at Memphis; (2) by the full
diagonal line the Julian date of the solstice or beginning of the
inundation in each century, at a point of the river near Memphis. The
fainter lines show the Julian dates for other places where the time
of the beginning of the flood differs by three days from the Memphis
dates. The interval between each line represents a difference of three
days in the arrival of the flood; (3) the interval in days between
the heliacal rising and the inundation at different periods and at
different points of the river. This can be determined for each century
by noticing the interval between the proper diagonal line and that
indicating the heliacal rising; (4) by dots at the top of the diagram
the commencement of the Sothic period as determined by Oppolzer, Biot,
and the author.]
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.