Myths and Marvels of Astronomy
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