argue that, in the first place, it may have been by express design that
the period of the earth's rotation was made to bear this particular
relation to the period of gyration in the mighty precessional movement:
which is much as though one should say that by express design the height
of Monte Rosa contains as many feet as there are miles in the 6000th
part of the sun's distance.[21] Then, they urge, the architects were
not bound to have a square base for the pyramid; they might have had an
oblong or a triangular base, and so forth--all which accords very ill
with the enthusiastic language in which the selection of a square base
had on other accounts been applauded.
Next let us consider the height of the pyramid. According to the best
modern measurements, it would seem that the height when (if ever) the
pyramid terminated above in a pointed apex, must have been about 486
feet. And from the comparison of the best estimates of the base side
with the best estimates of the height, it seems very likely indeed that
the intention of the builders was to make the height bear to the
perimeter of the base the same ratio which the radius of a circle bears
to the circumference. Remembering the range of difference in the base
measures it might be supposed that the exactness of the approximation to
this ratio could not be determined very satisfactorily. But as certain
casing stones have been discovered which indicate with considerable
exactness the slope of the original plane-surfaces of the pyramid, the
ratio of the height to the side of the base may be regarded as much more
satisfactorily determined than the actual value of either dimension. Of
course the pyramidalists claim a degree of precision indicating a most
accurate knowledge of the ratio between the diameter and the
circumference of a circle; and the angle of the only casing stone
measured being diversely estimated at 51 deg. 50' and 51 deg. 52-1/4',
they consider 50 deg. 51' 14.3" the true value, and infer that the
builders regarded the ratio as 3.14159 to 1. The real fact is, that the
modern estimates of the dimensions of the casing stones (which, by the
way, ought to agree better if these stones are as well made as stated)
indicate the values 3.1439228 and 3.1396740 for the ratio; and all we
can say is, that the ratio really used lay _probably_ between these
limits, though it may have been outside either. Now the approximation of
either is not remarkably close. It requires no mathematical knowledge at
all to determine the circumference of a circle much more exactly. 'I
thought it very strange,' wrote a circle-squarer once to De Morgan
(_Budget of Paradoxes_, p. 389), 'that so many great scholars in all
ages should have failed in finding the true ratio, and have been
determined to try myself.' 'I have been informed,' proceeds De Morgan,
'that this trial makes the diameter to the circumference as 64 to 201,
giving the ratio equal to 3.1410625 exactly. The result was obtained by
the discoverer in three weeks after he first heard of the existence of
the difficulty. This quadrator has since published a little slip and
entered it at Stationers' Hall. He says he has done it by actual
measurement; and I hear from a private source that he uses a disc of
twelve inches diameter which he rolls upon a straight rail.' The
'rolling is a very creditable one; it is as much below the mark as
Archimedes was above it. Its performer is a joiner who evidently knows
well what he is about when he measures; he is not wrong by 1 in 3000.'
Such skilful mechanicians as the builders of the pyramid could have
obtained a closer approximation still by mere measurement. Besides, as
they were manifestly mathematicians, such an approximation as was
obtained by Archimedes must have been well within their power; and that
approximation lies well within the limits above indicated. Professor
Smyth remarks that the ratio was 'a quantity which men in general, and
all human science too, did not begin to trouble themselves about until
long, long ages, languages, and nations had passed away after the
building of the great pyramid; and after the sealing up, too, of that
grand primeval and prehistoric monument of the patriarchal age of the
earth according to Scripture.' I do not know where the Scripture records
the sealing up of the great pyramid; but it is all but certain that
during the very time when the pyramid was being built astronomical
observations were in progress which, for their interpretation, involved
of necessity a continual reference to the ratio in question. No one who
considers the wonderful accuracy with which, nearly two thousand years
before the Christian era, the Chaldaeans had determined the famous cycle
of the Saros, can doubt that they must have observed the heavenly bodies
for several centuries before they could have achieved such a success;
and the study of the motions of the celestial bodies compels 'men to
trouble themselves' about the famous ratio of the circumference to the
diameter.
We now come upon a new relation (contained in the dimensions of the
pyramid as thus determined) which, by a strange coincidence, causes the
height of the pyramid to appear to symbolise the distance of the sun.
There were 5813 pyramid inches, or 5819 British inches, in the height of
the pyramid according to the relations already indicated. Now, in the
sun's distance, according to an estimate recently adopted and freely
used,[22] there are 91,400,000 miles or 5791 thousand millions of
inches--that is, there are approximately as many thousand millions of
inches in the sun's distance as there are inches in the height of the
pyramid. If we take the relation as exact we should infer for the sun's
distance 5819 thousand millions of inches, or 91,840,000 miles--an
immense improvement on the estimate which for so many years occupied a
place of honour in our books of astronomy. Besides, there is strong
reason for believing that, when the results of recent observations are
worked out, the estimated sun distance will be much nearer this pyramid
value than even to the value 91,400,000 recently adopted. This result,
which one would have thought so damaging to faith in the evidence from
coincidence--nay, quite fatal after the other case in which a close
coincidence had appeared by merest accident--is regarded by the
pyramidalist as a perfect triumph for their faith.
They connect it with another coincidence, viz. that, assuming the height
determined in the way already indicated, then it so happens that the
height bears to half a diagonal of the base the ratio 9 to 10. Seeing
that the perimeter of the base symbolises the annual motion of the earth
round the sun, while the height represents the radius of a circle with
that perimeter, it follows that the height should symbolise the sun's
distance. 'That line, further,' says Professor Smyth (speaking on behalf
of Mr. W. Petrie, the discoverer of this relation), 'must represent'
this radius 'in the proportion of 1 to 1,000,000,000' (or _ten_ raised
to power _nine_), 'because amongst other reasons 10 to 9 is practically
the shape of the great pyramid.' For this building 'has such an angle at
the corners, that for every ten units its structure advances inwards on
the diagonal of the base, it practically rises upwards, or points to
sunshine' (_sic_) 'by _nine_. Nine, too, out of the ten characteristic
parts (viz. five angles and five sides) being the number of those parts
which the sun shines on in such a shaped pyramid, in such a latitude
near the equator, out of a high sky, or, as the Peruvians say, when the
sun sets on the pyramid with all its rays.' The coincidence itself on
which this perverse reasoning rests is a singular one--singular, that
is, as showing how close an accidental coincidence may run. It amounts
to this, that if the number of days in the year be multiplied by 100,
and a circle be drawn with a circumference containing 100 times as many
inches as there are days in the year, the radius of the circle will be
very nearly one 1,000,000,000th part of the sun's distance. Remembering
that the pyramid inch is assumed to be one 500,000,000th part of the
earth's diameter, we shall not be far from the truth in saying that, as
a matter of fact, the earth by her orbital motion traverses each day a
distance equal to two hundred times her own diameter. But, of course,
this relation is altogether accidental. It has no real cause in
nature.[23]
Such relations show that mere numerical coincidences, however close,
have little weight as evidence, except where they occur in series. Even
then they require to be very cautiously regarded, seeing that the
history of science records many instances where the apparent law of a
series has been found to be falsified when the theory has been extended.
Of course this reason is not quoted in order to throw doubt on the
supposition that the height of the pyramid was intended to symbolise the
sun's distance. That supposition is simply inadmissible if the
hypothesis, according to which the height was already independently
determined in another way, is admitted. Either hypothesis might be
admitted were we not certain that the sun's distance could not possibly
have been known to the builders of the pyramid; or both hypotheses may
be rejected: but to admit both is out of the question.
Considering the multitude of dimensions of length, surface, capacity,
and position, the great number of shapes, and the variety of material
existing within the pyramid, and considering, further, the enormous
number of relations (presented by modern science) from among which to
choose, can it be wondered at if fresh coincidences are being
continually recognised? If a dimension will not serve in one way, use
can be found for it in another; for instance, if some measure of length
does not correspond closely with any known dimension of the earth or of
the solar system (an unlikely supposition), then it can be understood to
typify an interval of time. If, even after trying all possible changes
of that kind, no coincidence shows itself (which is all but impossible),
then all that is needed to secure a coincidence is that the dimensions
should be manipulated a little.
Let a single instance suffice to show how the pyramidalists (with
perfect honesty of purpose) hunt down a coincidence. The slant tunnel
already described has a transverse height, once no doubt uniform, now
giving various measures from 47.14 pyramid inches to 47.32 inches, so
that the vertical height from the known inclination of the tunnel would
be estimated at somewhere between 52.64 inches and 52.85. Neither
dimension corresponds very obviously with any measured distance in the
earth or solar system. Nor when we try periods, areas, etc., does any
very satisfactory coincidence present itself. But the difficulty is
easily turned into a new proof of design. Putting all the observations
together (says Professor Smyth), 'I deduced 47.24 pyramid inches to be
the transverse height of the entrance passage; and computing from thence
with the observed angle of inclination the vertical height, that came
out 52.76 of the same inches. But the sum of those two heights, or the
height taken up and down, equals 100 inches, which length, as elsewhere
shown, is the general pyramid linear representation of a day of
twenty-four hours. And the mean of the two heights, or the height taken
one way only, and impartially to the middle point between them, equals
fifty inches; which quantity is, therefore, the general pyramid linear
representation of only half a day. In which case, let us ask what the
entrance passage has to do with half rather than a whole day?'
On relations such as these, which, if really intended by the architect,
would imply an utterly fatuous habit of concealing elaborately what he
desired to symbolise, the pyramidalists base their belief that 'a Mighty
Intelligence did both think out the plans for it, and compel unwilling
and ignorant idolators, in a primal age of the world, to work mightily
both for the future glory of the one true God of Revelation, and to
establish lasting prophetic testimony touching a further development,
still to take place, of the absolutely Divine Christian dispensation.'
III.
_THE MYSTERY OF THE PYRAMIDS._
Few subjects of inquiry have proved more perplexing than the question of
the purpose for which the pyramids of Egypt were built. Even in the
remotest ages of which we have historical record, nothing seems to have
been known certainly on this point. For some reason or other, the
builders of the pyramids concealed the object of these structures, and
this so successfully that not even a tradition has reached us which
purports to have been handed down from the epoch of the pyramids'
construction. We find, indeed, some explanations given by the earliest
historians; but they were professedly only hypothetical, like those
advanced in more recent times. Including ancient and modern theories, we
find a wide range of choice. Some have thought that these buildings were
associated with the religion of the early Egyptians; others have
suggested that they were tombs; others, that they combined the purposes
of tombs and temples, that they were astronomical observatories,
defences against the sands of the Great Desert, granaries like those
made under Joseph's direction, places of resort during excessive
overflows of the Nile; and many other uses have been suggested for them.
But none of these ideas are found on close examination to be tenable as
representing the sole purpose of the pyramids, and few of them have
strong claims to be regarded as presenting even a chief object of these
remarkable structures. The significant and perplexing history of the
three oldest pyramids--the Great Pyramid of Cheops, Shofo, or Suphis,
the pyramid of Chephren, and the pyramid of Mycerinus; and the most
remarkable of all the facts known respecting the pyramids generally,
viz., the circumstance that one pyramid after another was built as
though each had become useless soon after it was finished, are left
entirely unexplained by all the theories above mentioned, save one only,
the tomb theory, and that does not afford by any means a satisfactory
explanation of the circumstances.
I propose to give here a brief account of some of the most suggestive
facts known respecting the pyramids, and, after considering the
difficulties which beset the theories heretofore advanced, to indicate a
theory (new so far as I know) which seems to me to correspond better
with the facts than any heretofore advanced; I suggest it, however,
rather for consideration than because I regard it as very convincingly
supported by the evidence. In fact, to advance any theory at present
with confident assurance of its correctness, would be simply to indicate
a very limited acquaintance with the difficulties surrounding the
subject.
Let us first consider a few of the more striking facts recorded by
history or tradition, noting, as we proceed, whatever ideas they may
suggest as to the intended character of these structures.
It is hardly necessary to say, perhaps, that the history of the Great
Pyramid is of paramount importance in this inquiry. Whatever purpose
pyramids were originally intended to subserve, must have been conceived
by the builders of _that_ pyramid. New ideas may have been superadded by
the builders of later pyramids, but it is unlikely that the original
purpose can have been entirely abandoned. Some great purpose there was,
which the rulers of ancient Egypt proposed to fulfil by building very
massive pyramidal structures on a particular plan. It is by inquiring
into the history of the first and most massive of these structures, and
by examining its construction, that we shall have the best chance of
finding out what that great purpose was.
According to Herodotus, the kings who built the pyramids reigned not
more than twenty-eight centuries ago; but there can be little doubt that
Herodotus misunderstood the Egyptian priests from whom he derived his
information, and that the real antiquity of the pyramid-kings was far
greater. He tells us that, according to the Egyptian priests, Cheops 'on
ascending the throne plunged into all manner of wickedness. He closed
the temples, and forbade the Egyptians to offer sacrifice, compelling
them instead to labour one and all in his service, viz., in building the
Great Pyramid.' Still following his interpretation of the Egyptian
account, we learn that one hundred thousand men were employed for twenty
years in building the Great Pyramid, and that ten years were occupied in
constructing a causeway by which to convey the stones to the place and
in conveying them there. 'Cheops reigned fifty years; and was succeeded
by his brother Chephren, who imitated the conduct of his predecessor,
built a pyramid--but smaller than his brother's--and reigned fifty-six
years. Thus during one hundred and six years, the temples were shut and
never opened.' Moreover, Herodotus tells us that 'the Egyptians so
detested the memory of these kings, that they do not much like even to
mention their names. Hence they commonly call the pyramids after
Philition, a shepherd who at that time fed his flocks about the place.'
'After Chephren, Mycerinus, son of Cheops, ascended the throne, he
reopened the temples, and allowed the people to resume the practice of
sacrifice. He, too, left a pyramid, but much inferior in size to his
father's. It is built, for half of its height, of the stone of
Ethiopia,' or, as Professor Smyth (whose extracts from Rawlinson's
translation I have here followed) adds 'expensive red granite.' 'After
Mycerinus, Asychis ascended the throne. He built the eastern gateway of
the Temple of Vulcan (Phtha); and, being desirous of eclipsing all his
predecessors on the throne, left as a monument of his reign a pyramid of
brick.'
This account is so suggestive, as will presently be shown, that it may
be well to inquire whether it can be relied on. Now, although there can
be no doubt that Herodotus misunderstood the Egyptians in some matters,
and in particular as to the chronological order of the dynasties,
placing the pyramid kings far too late, yet in other respects he seems
not only to have understood them correctly, but also to have received a
correct account from them. The order of the kings above named
corresponds with the sequence given by Manetho, and also found in
monumental and hieroglyphic records. Manetho gives the names Suphis I.,
Suphis II., and Mencheres, instead of Cheops, Chephren, and Mycerinus;
while, according to the modern Egyptologists, Herodotus's Cheops was
Shofo, Shufu, or Koufou; Chephren was Shafre, while he was also called
Nou-Shofo or Noum-Shufu as the brother of Shofo; and Mycerinus was
Menhere or Menkerre. But the identity of these kings is not questioned.
As to the true dates there is much doubt, and it is probable that the
question will long continue open; but the determination of the exact
epochs when the several pyramids were built is not very important in
connection with our present inquiry. We may, on the whole, fairly take
the points quoted above from Herodotus, and proceed to consider the
significance of the narrative, with sufficient confidence that in all
essential respects it is trustworthy.
There are several very strange features in the account.
In the first place, it is manifest that Cheops (to call the first king
by the name most familiar to the general reader) attached great
importance to the building of his pyramid. It has been said, and perhaps
justly, that it would be more interesting to know the plan of the
architect who devised the pyramid than the purpose of the king who built
it. But the two things are closely connected. The architect must have
satisfied the king that some highly important purpose in which the king
himself was interested, would be subserved by the structure. Whether the
king was persuaded to undertake the work as a matter of duty, or only to
advance his own interests, may not be so clear. But that the king was
most thoroughly in earnest about the work is certain. A monarch in those
times would assuredly not have devoted an enormous amount of labour and
material to such a scheme unless he was thoroughly convinced of its
great importance. That the welfare of his people was not considered by
Cheops in building the Great Pyramid is almost equally certain. He
might, indeed, have had a scheme for their good which either he did not
care to explain to them or which they could not understand. But the most
natural inference from the narrative is that his purpose had no
reference whatever to their welfare. For though one could understand his
own subjects hating him while he was all the time working for their
good, it is obvious that his memory would not have been hated if some
important good had eventually been gained from his scheme. Many a
far-seeing ruler has been hated while living on account of the very work
for which his memory has been revered. But the memory of Cheops and his
successors was held in detestation.
May we, however, suppose that, though Cheops had not the welfare of his
own people in his thoughts, his purpose was nevertheless not selfish,
but intended in some way to promote the welfare of the human race? I say
his purpose, because, whoever originated the scheme, Cheops carried it
out; it was by means of his wealth and through his power that the
pyramid was built. This is the view adopted by Professor Piazzi Smyth
and others, in our own time, and first suggested by John Taylor.
'Whereas other writers,' says Smyth, 'have generally esteemed that the
mysterious persons who directed the building of the Great Pyramid (and
to whom the Egyptians, in their traditions, and for ages afterwards,
gave an immoral and even abominable character) must therefore have been
very bad indeed, so that the world at large has always been fond of
standing on, kicking, and insulting that dead lion, whom they really
knew not; he, Mr. John Taylor, seeing how religiously bad the Egyptians
themselves were, was led to conclude, on the contrary, that those _they_
hated (and could never sufficiently abuse) might, perhaps, have been
pre-eminently good; or were, at all events, of _different religious
faith_ from themselves.' 'Combining this with certain unmistakable
historical facts,' Mr. Taylor deduced reasons for believing that the
directors of the building designed to record in its proportions, and in
its interior features, certain important religious and scientific
truths, not for the people then living, but for men who were to come
4000 years or so after.