prolongation of the entrance passage to its place of opening out on the
northern face. But as the pyramid rose layer by layer above its
basement, there must be ascending passages of some sort towards the
south, the most important part of the sky in astronomical research.
The astronomers who planned the pyramid would specially require four
things. First, they must have the ascending passage in the absolutely
true meridian plan; secondly, they would require to have in view, along
a passage as narrow as the entrance tunnel, some conspicuous star, if
possible a star so bright as to be visible by day (along such a tunnel)
as well as by night; thirdly, they must have the means of observing the
sun at solar noon on every day in the year; and fourthly, they must also
have the entire range of the zodiac or planetary highway brought into
view along their chief meridional opening.
The first of these points is at once the most important and the most
difficult. It is so important, indeed, that we may hope for significant
evidence from the consideration of the methods which would suggest
themselves as available.
Consider:--The square base has been duly oriented. Therefore, if each
square layer is placed properly, the continually diminishing square
platform will remain always oriented. But if any error is made in this
work the exactness of the orientation will gradually be lost. And this
part of the work cannot be tested by astronomical observations as exact
as those by which the base was laid, unless the vertical boring by which
the middle of the base, or a point near it, was brought into connection
with the entrance passage, is continued upwards through the successive
layers of the pyramidal structure. As the rock rises to a considerable
height within the interior of the pyramid,[44] probably to quite the
height of the opening of the entrance passage on the northern slope, it
would only be found necessary to carry up this vertical boring on the
building itself after this level had been reached. But in any case this
would be but an unsatisfactory way of obtaining the meridian plane when
once the boring had reached a higher level than the opening of the
entrance passage; for only horizontal lines from the boring to the
inclined tunnelling would be of use for exact work, and no such lines
could be drawn when once the level of the upper end of the entrance
passage had been passed by the builders.
A plan would be available, however (not yet noticed, so far as I know,
by any who have studied the astronomical relations of the great
pyramid), which would have enabled the builders perfectly to overcome
this difficulty.
Suppose the line of sight down the entrance passage were continued
upwards along an ascending passage, after reflection at a perfectly
horizontal surface--the surface of still water--then by the simplest of
all optical laws, that of the reflection of light, the descending and
ascending lines of sight on either side of the place of reflection,
would lie in the same vertical plane, that, namely, of the entrance
passage, or of the meridian. Moreover, the farther upwards an ascending
passage was carried, along which the reflected visual rays could pass,
the more perfect would be the adjustment of this meridional plane.
To apply this method, it would be necessary to temporarily plug up the
entrance passage where it passed into the solid rock, to make the
stone-work above it very perfect and close fitting, so that whenever
occasion arose for making one of the observations we are considering,
water might be poured into the entrance passage, and remain long enough
standing at the corner (so to speak) where this passage and the
suggested ascending passage could meet, for Alpha Draconis to be
observed down the ascending passage. Fig. 2 shows what is meant. Here D
C is the descending passage, C A the ascending passage, C the corner
where the water would be placed when Alpha Draconis was about to pass
below the pole. The observer would look down A C, and would see Alpha
Draconis by rays which had passed down D C, and had been reflected by
the water at C. Supposing the building to have been erected, as Lepsius
and other Egyptologists consider, at the rate of one layer in each year,
then only one observation of the kind described need be made per annum.
Indeed, fewer would serve, since three or four layers of stone might be
added without any fresh occasion arising to test the direction of the
passage C A.
[Illustration: Fig. 2.]
It is hardly necessary to remind those who have given any attention to
the subject of the pyramid that there is precisely such an ascending
passage as C A, and that as yet no explanation of the identity of its
angle of ascent with the angle of descent of the passage D C has ever
been given. Most pyramidalists content themselves by assuming, as Sir E.
Beckett puts it, "that the same angle would probably be used for both
sets of passages, _as there was no reason for varying it_," which is not
exactly an explanation of the relation. Mr. Wacherbarth has suggested
that the passages were so adjusted for the purpose of managing a system
of balance cars united by ropes from one passage to another; but this
explanation is open, as Beckett points out, to the fatal objection that
the passages meet at their lowest point, not at their highest, so that
it would be rather a puzzle "to work out the mechanical idea." The
reflection explanation is not only open to no such objections, but
involves precisely such an application of optical laws as we should
expect from men so ingenious as the pyramid builders certainly were. In
saying this, let me explain, I am not commending myself for ingenuity in
thinking of the method, simply because such methods are quite common and
familiar in the astronomy of modern times.
While I find this explanation, which occurred to me even while this
paper was in writing, so satisfactory that I feel almost tempted to say,
like Sir G. Airy of his explanation of the Deluge as an overflow of the
Nile, that "I cannot entertain the slightest doubt" of its validity, I
feel that there ought to be some evidence in the descending passage
itself of the use of this method. We might not find any traces of the
plugs used to stop up, once a year or so, the rock part of the
descending passage. For they would be only temporary arrangements. But
we should expect to find the floor of the descending passage constructed
with special care, and very closely fitted, where the water was to be
received.
Inquiring whether this is so, I find not only that it is, but that
another hitherto unexplained feature of the great pyramid finds its
explanation in this way,--the now celebrated "secret sign." Let us read
Professor Smyth's account of this peculiar feature:--
"When measuring the cross-joints in the floor of the
entrance-passage, in 1865, I went on chronicling their angles, each
one proving to be very nearly at right angles to the axis, until
suddenly one came which was _diagonal_; another, and that was
diagonal too; but, after that, the rectangular position was
resumed. Further, the stone material carrying these diagonal joints
was harder and better than elsewhere in the floor, so as to have
saved that part from the monstrous excavations elsewhere
perpetrated by some moderns. Why, then, did the builders change the
rectangular joint angle at that point, and execute such unusual
angles as they chose in place of it, in a better material of stone
than elsewhere; and yet with so little desire to call general
attention to it, that they made the joints fine and close to that
degree that they escaped the attention of all men until 1865 A.D.
The answer came from the diagonal joints themselves, on discovering
that the stone between them was opposite to the butt end of the
portcullis of the first ascending passage, or to the hole whence
the prismatic stone of concealment through 3000 years had dropped
out almost before Al Mamoun's eyes. Here, therefore, was a secret
sign in the pavement of the entrance-passage, appreciable only to a
careful eye and a measurement by angle, but made in such hard
material that it was evidently intended to last to the end of human
time with the great pyramid, and _has_ done so thus far."
Whether Professor Smyth is right in considering that this
specially-prepared position of the floor was intended not for any
practical purpose, but to escape the notice of the careless, while yet,
when the right men "at last, duly instructed, entered the passage," this
mysterious floor-sign should show them where a ceiling-stone was
movable, on perceiving which they "would have laid bare the beginning of
the whole train of those sub-aërial features of construction which are
the great pyramid's most distinctive glory, and exist in no other
pyramid in Egypt or the world," I leave the reader to judge. I would
remark, only, that, if so, the builders of the pyramid were not
remarkably good prophets, seeing that the event befell otherwise, the
ceiling-stone dropping out a thousand years or so before the floor-sign
was noticed; wherefore we need not feel altogether alarmed at their own
prediction (according to Professor Smyth), that the end of the world is
to come in 1881, even as Mother Shipton also is reported to have
prophesied. For my own part, I am quite content with my own
interpretation of the secret sign; as showing where the floor of the
descending passage was purposely prepared for the reception of water, on
the still surface of which the Pole-star of the day might be mirrored
for one looking down the ascending passage.
Albeit, I cannot but think that this ascending passage must also have
been so directed as to show some bright star when due south. For if the
passage had only given the meridian plane, but without permitting the
astronomer to observe the southing of any fixed star, it would have
subserved only one-half its purposes as a meridional instrument. It is
to be remembered that, supposing the ascending passage to have its
position determined in the way I have described, there would be nothing
to prevent its being also made to show any fixed star nearly at the same
elevation. For it could readily be enlarged in a vertical direction, the
floor remaining unaltered. Since it is not enlarged until the great
gallery is reached (at a distance of nearly 127 feet from the place
where the ascent begins), it follows, or is at least rendered highly
probable, that some bright star was in view through that ascending
passage.
Now, taking the date 2170 B.C., which Professor Smyth assigns to the
beginning of the great pyramid, or even taking any date (as we fairly
may), within a century or so on either side of that date, we find no
bright star which would have been visible when due south, through the
ascending passage. I have calculated the position of that circle among
the stars along which lay all the points passing 26° 18' above the
horizon when due south, in the latitude of Ghizeh, 2170 years before the
Christian era; and it does not pass near a single conspicuous star.[45]
There is only one fourth magnitude star which it actually
approaches--namely, Epsilon Ceti; and one fifth magnitude star, Beta of
the Southern Crown.
When we remember that Egyptologists almost without exception assert that
the date of the builders of the great pyramid _must_ have been more than
a thousand years earlier than 2170 B.C., and that Bunsen has assigned to
Menes the date 3620 B.C., while the date 3300 B.C. has been assigned to
Cheops or Suphis on apparently good authority, we are led to inquire
whether the other epoch when Alpha Draconis was at about the right
distance from the pole of the heavens may not have been the true era of
the commencement of the great pyramid. Now, the year 3300 B.C., though a
little late, would accord fairly well with the time when Alpha Draconis
was at the proper distance 3-2/3° from the pole of the heavens. If the
inclination of the entrance-passage is 26° 27', as Professor Smyth made
it, the exact date for this would be 3390 B.C.; if 26° 40', as others
made it before his measurements, the date would be about 3320 B.C.,
which would suit well with the date 3300 B.C., since a century either
way would only carry the star about a third of a degree towards or from
the pole.
Now, when we inquire whether in the year 3300 B.C. any bright star would
have been visible, at southing, through the ascending passage, we find
that a very bright star indeed, an orb otherwise remarkable as the
nearest of all the stars, the brilliant Alpha Centauri, shone as it
crossed the meridian right down that ascending tube. It is so bright
that, viewed through that tube, it must have been visible to the naked
eye, even when southing in full daylight.
But thirdly, we must consider how the builders of the pyramid would
arrange for the observation of the sun at noon on every clear day in the
year.
They would carry up the floor of the ascending passage in an unchanged
direction, as it already pointed south of the lowest place of the noon
sun at mid-winter. They would have to turn the tunnel into a lofty
gallery, to increase the vertical range of view on the meridian. It
seems reasonable to infer that they would prefer so to arrange matters
that the upper end of the gallery would be near the middle of the
platform which would form the top of the pyramidal structure from the
time when it was completed for observational purposes. The height of the
gallery would be so adjusted to its length, that the mid-winter's sun
would not shine further than the lower end of the gallery (that is, to
the upper end of the smaller ascending passage). In fact, as the moon
and planets would have to be observed when due south, through this
meridional gallery, and as they range further from the equator both
north and south than the sun does, it would be necessary that the
gallery should extend lower down than the sun's mid-winter noon rays
would shine.
As it would be a part of the observer's work to note exactly how far
down the gallery the shadow of its upper southern edge reached, as well
as the moment when the sun's light passed from the western to the
eastern wall of the gallery, and other details of the kind; besides, of
course, taking time-observations of the moment when the sun's edge
seemed to reach the edge of the gallery's southern opening; and as such
observations could not be properly made by men standing on the smooth
slanting floor of the gallery, it would be desirable to have
cross-benches capable of being set at different heights along the
sloping gallery. In some observations, indeed, as where the transits of
several stars southing within short intervals of time had to be
observed, it would be necessary to set some observers at one part of the
gallery, others at another part, and perhaps even to have several sets
of observers along the gallery. And this suggests yet another
consideration. It might be thought desirable, if great importance was
attached (as the whole building shows that great importance must have
been attached) to the exactness of the observations, to have several
observations of each transit of a star across the mouth of the gallery.
In this case, it would be well to have the breadth of the gallery
different at different heights, though its walls must of necessity be
upright throughout--that is, the walls must be upright from the height
where one breadth commences, to the height where the next breadth
commences. With a gallery built in this fashion, it would be possible to
take several observations of the same transit, somewhat in the same way
that the modern observer watches the transit of a star across each of
five, seven, or nine parallel spider threads, in order to obtain a more
correct time for the passage of the star across the middle thread, than
if he noted this passage alone.
How far the grand gallery corresponds with these requirements can be
judged from the following description given by Professor Greaves in
1638:--"It is," he says, "a very stately piece of work, and not
inferior, either in respect of the curiosity of art, or richness of
materials, to the most sumptuous and magnificent buildings," and a
little further on he says, "this gallery, or corridor, or whatever else
I may call it, is built of white and polished marble (limestone), the
which is very evenly cut in spacious squares or tables. Of such
materials as is the pavement, such is the roof and such are the side
walls that flank it; the coagmentation or knitting of the joints is so
close, that they are scarce discernible to a curious eye; and that which
adds grace to the whole structure, though it makes the passage the more
slippery and difficult, is the acclivity or rising of the ascent. The
height of this gallery is 26 feet" (Professor Smyth's careful
measurements show the true height to be more nearly 28 feet), "the
breadth of 6.870 feet, of which 3.435 feet are to be allowed for the way
in the midst, which is set and bounded on both sides with two banks
(like benches) of sleek and polished stone; each of these hath 1.717 of
a foot in breadth, and as much in depth." These measurements are not
strictly exact. Smyth made the breadth of the gallery above the banks or
ramps as he calls them, 6 feet 10-1/5 inches; the space between the
ramps, 3 feet 6 inches; the ramps nearly about 1 foot 8-1/14 inches
broad, and nearly 1 foot 9 inches high, measured transversely, that is
at right angles to the ascending floor.
As to arrangements for the convenience of observers in the slippery and
difficult floor of this gallery, we find that upon the top of these
benches or ramps, near the angle where they meet the wall, "there are
little spaces cut in right-angled parallel figures, set on each side
opposite one another, _intended no question for some other end than
ornament_."
The diversity of width which I have indicated as a desirable feature in
a meridional gallery, is a marked feature of the actual gallery. "In the
casting and ranging of the marbles" (limestone), "in both the side
walls, there is one piece of architecture," says Greaves, "in my
judgment very graceful, and that is that all the courses or stones,
which are but seven (so great are these stones), do set and flag over
one another about three inches; the bottom of the uppermost course
overlapping the top of the next, and so in order, the rest as they
descend." The faces of these stones are exactly vertical, and as the
width of the gallery diminishes upwards by about six inches for each
successive course, it follows that the width at the top is about 3-1/2
feet less than the width, 6 feet 10-1/5 inches, at the bottom, or agrees
in fact with the width of the space between the benches or ramps. Thus
the shadow of the vertical edges of the gallery at solar noon just
reached to the edges of the ramps, the shadow of the next lower
vertical edges falling three inches from the edges higher up the ramps,
those of the next vertical edges six inches from these edges, still
higher up, and so forth. The true hour of the sun's southing could thus
be most accurately determined by seven sets of observers placed in
different parts of the gallery, and near mid-summer, when the range of
the shadows would be so far shortened, that a smaller number of
observers only could follow the shadows' motions; but in some respects,
the observations in this part of the year could be more readily and
exactly made than in winter, when the shadows' spaces of various width
would range along the entire length of the gallery.
Similar remarks would apply to observations of the moon, which could
also be directly observed. The planets and stars of course could only be
observed directly.
The grand gallery could be used for the observation of any celestial
body southing higher than 26° 18' above the horizon; but not very
effectively for objects passing near the zenith. The Pleiades could be
well observed. They southed about 63-2/3° above the horizon in the year
2140 B.C. or thereabouts when they were on the equinoctial colure.[46]
But if I am right in taking the year 3300 B.C. when Alpha Centauri shone
down the smaller ascending passage in southing, the Pleiades were about
58° only above the horizon when southing, and therefore even more
favourably observable from the great meridional gallery.
In passing I may note that at this time, about 3300 years before our
era, the equinoctial point (that is, the point where the sun passes
north of the equator, and the year begins according to the old manner of
reckoning) was midway between the horns of the Bull. So that then, and
then alone, a poet might truly speak of spring as the time
"Candidus auratis aperit quum cornibus annum
Taurus."
as Virgil incorrectly did (repeating doubtless some old tradition) at a
later time. Even Professor Smyth notices the necessity that the pyramid
gallery should correspond in some degree with such a date. "For," says
he, "there have been traditions for long, whence arising I know not,
that the seven overlappings of the grand gallery, so impressively
described by Professor Greaves, had something to do with the Pleiades,
those proverbially seven stars of the primeval world," only that he
considers the pyramid related to _memorial_ not _observing_ astronomy,
"of an earlier date than Virgil's." The Pleiades also, it may be
remarked, were scarcely regarded in old times as belonging to the
constellation of the Bull, but formed a separate asterism.
The upper end of the great gallery lies very near the vertical axis of
the pyramid. It is equidistant, in fact, from the north and south edges
of the pyramid platform at this level, but lies somewhat to the east of
the true centre of this platform. One can recognise a certain
convenience in this arrangement, for the actual centre of the platform
would be required as a position from whence observation of the whole sky
could be made. Observers stationed there would have the cardinal points
and the points midway between them defined by the edges and angles of
the square platform, which would not be the case if they were displaced
from the centre. Stationed as they would be close to the mouth of the
gallery, they would hear the time signallings given forth by the
observers placed at various parts of the gallery; and no doubt one chief
end of the exact time-observations for which the gallery was manifestly
constructed, would be to enable the platform observers duly to record
the time when various phenomena were noticed in any part of the heavens.