in latitude 30 deg., as closely as their means of observation permitted.
Let us consider what result they achieved, and the evidence thus afforded
respecting their skill and scientific attainments. In our own time, of
course, the astronomer has no difficulty in determining with great
exactness the position of any given latitude-parallel. But at the time
when the great pyramid was built it must have been a matter of very
serious difficulty to determine the position of any required
latitude-parallel with a great degree of exactitude. The most obvious
way of dealing with the difficulty would have been by observing the
length of shadows thrown by upright posts at noon in spring and autumn.
In latitude 30 deg. north, the sun at noon in spring (or, to speak
precisely, on the day of the vernal equinox) is just twice as far from
the horizon as he is from the point vertically overhead; and if a
pointed post were set exactly upright at true noon (supposed to occur at
the moment of the vernal or autumnal equinox), the shadow of the post
would be exactly half as long as a line drawn from the top of the pole
to the end of the shadow. But observations based on this principle would
have presented many difficulties to the architects of the pyramid. The
sun not being a point of light, but a globe, the shadow of a pointed rod
does not end in a well-defined point. The moment of true noon, which is
not the same as ordinary or civil noon, never does agree exactly with
the time of the vernal or autumnal equinox, and may be removed from it
by any interval of time not exceeding twelve hours. And there are many
other circumstances which would lead astronomers, like those who
doubtless presided over the scientific preparations for building the
great pyramid, to prefer a means of determining the latitude depending
on another principle. The stellar heavens would afford practically
unchanging indications for their purpose. The stars being all carried
round the pole of the heavens, as if they were fixed points in the
interior of a hollow revolving sphere, it becomes possible to determine
the position of the pole of the star sphere, even though no bright
conspicuous star actually occupies that point. Any bright star close by
the pole is seen to revolve in a very small circle, whose centre is the
pole itself. Such a star is our present so-called pole-star; and, though
in the days when the great pyramid was built, that star was not near the
pole, another, and probably a brighter star lay near enough to the
pole[17] to serve as a pole-star, and to indicate by its circling motion
the position of the actual pole of the heavens. This was at that time,
and for many subsequent centuries, the leading star of the great
constellation called the Dragon.
The pole of the heavens, we know, varies in position according to the
latitude of the observer. At the north pole it is exactly overhead; at
the equator the poles of the heavens are both on the horizon; and, as
the observer travels from the equator towards the north or south pole of
the earth, the corresponding pole of the heavens rises higher and higher
above the horizon. In latitude 30 deg. north, or one-third of the way from
the equator to the pole, the pole of the heavens is raised one-third of
the way from the horizon to the point vertically overhead; and when this
is the case the observer knows that he is in latitude 30 deg. The builders
of the great pyramid, with the almost constantly clear skies of Egypt,
may reasonably be supposed to have adopted this means of determining the
true position of that thirtieth parallel on which they appear to have
designed to place the great building they were about to erect.
It so happens that we have the means of forming an opinion on the
question whether they used one method or the other; whether they
employed the sun or the stars to guide them to the geographical position
they required. In fact, were it not for this circumstance, I should not
have thought it worth while to discuss the qualities of either method.
It will presently be seen that the discussion bears importantly on the
opinion we are to form of the skill and attainments of the pyramid
architects. Every celestial object is apparently raised somewhat above
its true position by the refractive power of our atmosphere, being most
raised when nearest the horizon and least when nearest the point
vertically overhead. This effect is, indeed, so marked on bodies close
to the horizon that if the astronomers of the pyramid times had observed
the sun, moon, and stars attentively when so placed, they could not have
failed to discover the peculiarity. Probably, however, though they noted
the time of rising and setting of the celestial bodies, they only made
instrumental observations upon them when these bodies were high in the
heavens. Thus they remained ignorant of the refractive powers of the
air.[18] Now, if they had determined the position of the thirtieth
parallel of latitude by observations of the noonday sun (in spring or
autumn), then since, owing to refraction, they would have judged the sun
to be higher than he really was, it follows that they would have
supposed the latitude of any station from which they observed to be
lower than it really was. For the lower the latitude the higher is the
noonday sun at any given season. Thus, when really in latitude 30 deg.
they would have supposed themselves in a latitude lower than 30 deg., and
would have travelled a little further north to find the proper place, as
they would have supposed, for erecting the great pyramid. On the other
hand, if they determined the place from observations of the movements of
stars near the pole of the heavens, they would make an error of a
precisely opposite nature. For the higher the latitude the higher is the
pole of the heavens; and refraction, therefore, which apparently raises
the pole of the heavens, gives to a station the appearance of being in
a higher latitude than it really is, so that the observer would consider
he was in latitude 30 north when in reality somewhat south of that
latitude. We have only then to inquire whether the great pyramid was set
north or south of latitude 30 deg., to ascertain whether the pyramid
architects observed the noonday sun or circumpolar stars to determine
their latitude; always assuming (as we reasonably may) that those
architects did propose to set the pyramid in that particular latitude,
and that they were able to make very accurate observations of the apparent
positions of the celestial bodies, but that they were not acquainted
with the refractive effects of the atmosphere. The answer comes in no
doubtful terms. The centre of the great pyramid's base lies about one
mile and a third _south_ of the thirtieth parallel of latitude; and from
this position the pole of the heavens, as raised by refraction, would
appear to be very near indeed to the required position. In fact, if the
pyramid had been set about half a mile still farther south the pole
would have _seemed_ just right.
Of course, such an explanation as I have here suggested appears
altogether heretical to the pyramidalists. According to them the pyramid
architects knew perfectly well where the true thirtieth parallel lay,
and knew also all that modern science has discovered about refraction;
but set the pyramid south of the true parallel and north of the position
where refraction would just have made the apparent elevation of the pole
correct, simply in order that the pyramid might correspond as nearly as
possible to each of two conditions, whereof both could not be fulfilled
at once. The pyramid would indeed, they say, have been set even more
closely midway between the true and the apparent parallels of 30 deg.
north, but that the Jeezeh hill on which it is set does not afford a rock
foundation any farther north. 'So very close,' says Professor Smyth,
'was the great pyramid placed to the northern brink of its hill, that
the edges of the cliff might have broken off under the terrible
pressure had not the builders banked up there most firmly the immense
mounds of rubbish which came from their work, and which Strabo looked so
particularly for 1800 years ago, but could not find. Here they were,
however, and still are, utilised in enabling the great pyramid to stand
on the very utmost verge of its commanding hill, within the limits of
the _two_ required latitudes, as well as over the centre of the land's
physical and radial formation, and at the same time on the sure and
proverbially wise foundation of rock.'
The next circumstance to be noted in the position of the great pyramid
(as of all the pyramids) is that the sides are carefully oriented. This,
like the approximation to a particular latitude, must be regarded as an
astronomical rather than a geographical relation. The accuracy with
which the orientation has been effected will serve to show how far the
builders had mastered the methods of astronomical observation by which
orientation was to be secured. The problem was not so simple as might be
supposed by those who are not acquainted with the way in which the
cardinal points are correctly determined. By solar observations, or
rather by the observations of shadows cast by vertical shafts before and
after noon, the direction of the meridian, or north and south line, can
theoretically be ascertained. But probably in this case, as in
determining the latitude, the builders took the stars for their guide.
The pole of the heavens would mark the true north; and equally the
pole-star, when below or above the pole, would give the true north, but,
of course, most conveniently when below the pole. Nor is it difficult to
see how the builders would make use of the pole-star for this purpose.
From the middle of the northern side of the intended base they would
bore a slant passage tending always from the position of the pole-star
at its lower meridional passage, that star at each successive return to
that position serving to direct their progress; while its small range,
east and west of the pole, would enable them most accurately to
determine the star's true mid-point below the pole; that is, the true
north. When they had thus obtained a slant tunnel pointing truly to the
meridian, and had carried it down to a point nearly below the middle of
the proposed square base, they could, from the middle of the base, bore
vertically downwards, until by rough calculation they were near the
lower end of the slant tunnel; or both tunnels could be made at the same
time. Then a subterranean chamber would be opened out from the slant
tunnel. The vertical boring, which need not be wider than necessary to
allow a plumb-line to be suspended down it, would enable the architects
to determine the point vertically below the point of suspension. The
slant tunnel would give the direction of the true north, either from
that point or from a point at some known small distance east or west of
that point.[19] Thus, a line from some ascertained point near the mouth
of the vertical boring to the mouth of the slant tunnel would lie due
north and south, and serve as the required guide for the orientation of
the pyramid's base. If this base extended beyond the opening of the
slant tunnel, then, by continuing this tunnelling through the base tiers
of the pyramid, the means would be obtained of correcting the
orientation.
This, I say, would be the course naturally suggested to astronomical
architects who had determined the latitude in the manner described
above. It may even be described as the only very accurate method
available before the telescope had been invented. So that if the
accuracy of the orientation appears to be greater than could be obtained
by the shadow method, the natural inference, even in the absence of
corroborative evidence, would be that the stellar method, and no other,
had been employed. Now, in 1779, Nouet, by refined observations, found
the error of orientation measured by less than 20 minutes of arc,
corresponding roughly to a displacement of the corners by about 37-1/2
inches from their true position, as supposed to be determined from the
centre; or to a displacement of a southern corner by 53 inches on an
east and west line from a point due south of the corresponding northern
corner. This error, for a base length of 9140 inches, would not be
serious, being only one inch in about five yards (when estimated in the
second way). Yet the result is not quite worthy of the praise given to
it by Professor Smyth. He himself, however, by much more exact
observations, with an excellent altazimuth, reduced the alleged error
from 20 minutes to only 4-1/2, or to 9-40ths of its formerly supposed
value. This made the total displacement of a southern corner from the
true meridian through the corresponding northern corner, almost exactly
one foot, or one inch in about twenty-one yards--a degree of accuracy
rendering it practically certain that some stellar method was used in
orienting the base.
Now there _is_ a slanting tunnel occupying precisely the position of the
tunnel which should, according to this view, have been formed in order
accurately to orient the pyramid's base, assuming that the time of the
building of the pyramid corresponded with one of the epochs when the
star Alpha Draconis was distant 3 deg. 42' from the pole of the heavens.
In other words, there is a slant tunnel directed northwards and upwards
from a point deep down below the middle of the pyramid's base, and
inclined 26 deg. 17' to the horizon, the elevation of Alpha Draconis at
its lower culmination when 3 deg. 42' from the pole. The last epoch when
the star was thus placed was _circiter_ 2160 B.C.; the epoch next before
that was 3440 B.C. Between these two we should have to choose, on the
hypothesis that the slant tunnel was really directed to that star when
the foundations of the pyramid were laid. For the next epoch before the
earlier of the two named was about 28,000 B.C., and the pyramid's date
cannot have been more remote than 4000 B.C.
The slant tunnel, while admirably fulfilling the requirements suggested,
seems altogether unsuited for any other. Its transverse height (that is,
its width in a direction perpendicular to its upper and lower faces) did
not amount to quite four feet; its breadth was not quite three feet and
a half. It was, therefore, not well fitted for an entrance passage to
the subterranean chamber immediately under the apex of the pyramid (with
which chamber it communicates in the manner suggested by the above
theory). It could not have been intended to be used for observing
meridian transits of the stars in order to determine sidereal time; for
close circumpolar stars, by reason of their slow motion, are the least
suited of all for such a purpose. As Professor Smyth says, in arguing
against this suggested use of the star, 'no observer in his senses, in
any existing observatory, when seeking to obtain the time, would observe
the transit of a circumpolar star for anything else than _to get the
direction of the meridian to adjust his instrument by_.' (The italics
are his.) It is precisely such a purpose (the adjustment, however, not
of an instrument, but of the entire structure of the pyramid itself),
that I have suggested for this remarkable passage--this 'cream-white,
stone-lined, long tube,' where it traverses the masonry of the pyramid,
and below that dug through the solid rock to a distance of more than 350
feet.
Let us next consider the dimensions of the square base thus carefully
placed in latitude 30 deg. north to the best of the builders' power, with
sides carefully oriented.
It seems highly probable that, whatever special purpose the pyramid was
intended to fulfil, a subordinate idea of the builders would have been
to represent symbolically in the proportions of the building such
mathematical and astronomical relations as they were acquainted with.
From what we know by tradition of the men of the remote time when the
pyramid was built, and what we can infer from the ideas of those who
inherited, however remotely, the modes of thought of the earliest
astronomers and mathematicians, we can well believe that they would look
with superstitious reverence on special figures, proportions, numbers,
and so forth. Apart from this, they may have had a quasi-scientific
desire to make a lasting record of their discoveries, and of the
collected knowledge of their time.
It seems altogether probable, then, that the smaller unit of measurement
used by the builders of the great Pyramid was intended, as Professor
Smyth thinks, to be equal to the 500,000,000th part of the earth's
diameter, determined from their geodetical observations. It was
perfectly within the power of mechanicians and mathematicians so
experienced as they undoubtedly were--the pyramid attests so much--to
measure with considerable accuracy the length of a degree of latitude.
They could not possibly (always setting aside the theory of divine
inspiration) have known anything about the compression of the earth's
globe, and therefore could not have intended, as Professor Smyth
supposes, to have had the 500,000,000th part of the earth's polar axis,
as distinguished from any other, for their unit of length. But if they
made observations in or near latitude 30 deg. north on the supposition
that the earth is a globe, their probable error would exceed the
difference even between the earth's polar and equatorial diameters. Both
differences are largely exceeded by the range of difference among the
estimates of the actual length of the sacred cubit, supposed to have
contained twenty-five of these smaller units. And, again, the length of
the pyramid base-side, on which Smyth bases his own estimate of the
sacred cubit, has been variously estimated, the largest measure being
9168 inches, and the lowest 9110 inches. The fundamental theory of the
pyramidalists, that the sacred cubit was exactly one 20,000,000th part
of the earth's polar diameter, and that the side of the base contained
as many cubits and parts of a cubit as there are days and parts of a day
in the tropical year (or year of seasons), requires that the length of
the side should be 9140 inches, lying between the limits indicated, but
still so widely removed from either that it would appear very unsafe to
base a theory on the supposition that the exact length is or was 9140
inches. If the measures 9168 inches and 9110 inches were inferior, and
several excellent measures made by practised observers ranged around the
length 9140 inches, the case would be different. But the best recent
measures gave respectively 9110 and 9130 inches; and Smyth exclaims
against the unfairness of Sir H. James in taking 9120 as 'therefore the
[probable] true length of the side of the great pyramid when perfect,'
calling this 'a dishonourable shelving of the honourable older observers
with their larger results.' The only other measures, besides these two,
are two by Colonel Howard Vyse and by the French _savants_, giving
respectively 9168 and 9163.44 inches. The pyramidalists consider 9140
inches a fair mean value from these four. The natural inference,
however, is, that the pyramid base is not now in a condition to be
satisfactorily measured; and assuredly no such reliance can be placed
on the mean value 9140 inches that, on the strength of it, we should
believe what otherwise would be utterly incredible, viz. that the
builders of the great pyramid knew 'both the size and shape of the earth
exactly.' 'Humanly, or by human science, finding it out in that age was,
of course, utterly impossible,' says Professor Smyth. But he is so
confident of the average value derived from widely conflicting base
measures as to assume that this value, not being humanly discoverable,
was of necessity 'attributable to God and to His Divine inspiration.' We
may agree, in fine, with Smyth, that the builders of the pyramid knew
the earth to be a globe; that they took for their measure of length the
sacred cubit, which, by their earth measures, they made very fairly
approximate to the 20,000,000th part of the earth's mean diameter; but
there seems no reason whatever for supposing (even if the supposition
were not antecedently of its very nature inadmissible) that they knew
anything about the compression of the earth, or that they had measured a
degree of latitude in their own place with very wonderful accuracy.[20]
But here a very singular coincidence may be noticed, or, rather, is
forced upon our notice by the pyramidalists, who strangely enough
recognise in it fresh evidence of design, while the unbeliever finds in
it proof that coincidences are no sure evidence of design. The side of
the pyramid containing 365-1/4 times the sacred cubit of 25 pyramid
inches, it follows that the diagonal of the base contains 12,912 such
inches, and the two diagonals together contain 25,824 pyramid inches, or
almost exactly as many inches as there are years in the great
precessional period. 'No one whatever amongst men,' says Professor Smyth
after recording various estimates of the precessional period, 'from his
own or school knowledge, knew anything about such a phenomenon, until
Hipparchus, some 1900 years after the great pyramid's foundation, had a
glimpse of the fact; and yet it had been ruling the heavens for ages,
and was recorded in Jeezeh's ancient structure.' To minds not moved to
most energetic forgetfulness by the spirit of faith, it would appear
that when a square base had been decided upon, and its dimensions fixed,
with reference to the earth's diameter and the year, the diagonals of
the square base were determined also; and, if it so chanced that they
corresponded with some other perfectly independent relation, the fact
was not to be credited to the architects. Moreover it is manifest that
the closeness of such a coincidence suggests grave doubts how far other
coincidences can be relied upon as evidence of design. It seems, for
instance, altogether likely that the architects of the pyramid took the
sacred cubit equal to one 20,000,000th part of the earth's diameter for
their chief unit of length, and intentionally assigned to the side of
the pyramid's square base a length of just so many cubits as there are
days in the year; and the closeness of the coincidence between the
measured length and that indicated by this theory strengthens the idea
that this was the builder's purpose. But when we find that an even
closer coincidence immediately presents itself, which manifestly is a
coincidence _only_, the force of the evidence before derived from mere
coincidence is _pro tanto_ shaken. For consider what this new
coincidence really means. Its nature may be thus indicated: Take the
number of days in the year, multiply that number by 50, and increase the
result in the same degree that the diagonal of a square exceeds the
side--then the resulting number represents very approximately the number
of years in the great precessional period. The error, according to the
best modern estimates, is about one 575th part of the true period. This
is, of course, a merely accidental coincidence, for there is no
connection whatever in nature between the earth's period of rotation,
the shape of a square, and the earth's period of gyration. Yet this
merely accidental coincidence is very much closer than the other
supposed to be designed could be proved to be. It is clear, then, that
mere coincidence is a very unsafe evidence of design.