ERECTION OF OBELISKS.
(35) The only reference the Egyptians have left us actually referring
to the erection of a monument is that given in the Papyrus Anastasi I
(for publication, see section 28). The monument to be erected is in
this case a colossus. The text gives (§ XIV): “It is said to thee:
_Empty the magazine that has been loaded with sand under the monument_
of thy Lord which has been brought from the Red Mountain. It makes 30
cubits stretched on the ground, and 20 cubits in breadth . . . . . -ed
with 100 (??) chambers filled with sand from the river-bank. The
. . . . . of its (?) chambers have a breadth of 44 (?) cubits and a
height of 50 cubits, all of them . . . . . in their . . . . . . . . .
Thou art commanded to find out what is before the Pharaoh (??). How
many men will it take to demolish (_ḫm_—also “remove” or “overturn”) it
in six hours—if (?) apt are their (?) minds (?), but small their desire
to demolish it without there coming a pause when thou givest a rest to
the soldiers, that they may take their meal—so that the monument may be
established in its place?”
Here the technical details are extremely obscure, as there are many
unknown words in the text.
In the same papyrus (§ XII), there is a reference to an embankment,
which may well have been intended for the erection of a monument,
perhaps an obelisk, as the problem immediately following concerns the
transport of an obelisk from the quarry. The scribe Ḥori puts the
problem: “There is made a ramp of 730 cubits, with a breadth of 55
cubits, consisting of 120 compartments (?) filled with reeds and beams
with a height of 60 cubits at its summit, its middle of 30 cubits, its
batter (?) 15 cubits, its base (?) of 5 cubits. The quantity of bricks
needed for it is asked of the commander of the army . . . . . . .
Answer us as to the quantity of bricks needed. Behold its measurements
(??) are before thee; each one of its compartments (?) is of 30 cubits
long and 7 cubits broad.”
Since the words translated by “compartment” and “base” are very
doubtful in meaning, it is difficult to obtain any definite idea as to
the internal construction of the ramp. Borchardt supposes the words
“the middle” to mean the space filled with rubbish in the inside of the
embankment as a means of economising the bricks.
The ‘compartments’ may refer to the longitudinal divisions in the
middle of the embankment, which can still be seen in the construction
ramp inside the South Ptolemaic (?) pylon at Karnak. Choisy, in his
_L’Art de bâtir chez les Égyptiens_, p. 86, gives rather a good
little sketch of this, apparently made when the ramp was newly
cleared. Borchardt, on the other hand, imagines the compartments to be
transverse divisions. It is certain, however, that there is a mistake
in the measurements given in the Anastasi papyrus, as it seems quite
impossible to {36} divide up the embankment according to the data, even
if we take ‘compartments’ to mean the sections or towers into which
nearly all brick enclosure walls and embankments were divided (see
SOMERS CLARKE, _J. Eg. Arch._, vol. VII, p. 77).
It seems to me that Borchardt is right as to the embankment being, as
it were, a brick box filled with earth; otherwise there is a great
redundance of data. Obviously, the only measurements necessary for an
embankment (built of plain brickwork or in towers like the great temple
walls), if solid, are: Horizontal length of ramp (L); highest part
(H); width at top (W); and the batter (B). Then the number of bricks
required will be, to a close approximation: ½ LH (W + B) divided by
the volume of one brick, plus a factor for waste bricks.
It may be remarked that if the Aswân obelisk were pulled up an
embankment of the slope given here, it would need (neglecting friction)
over 2000 men.
Classical authors tell us next to nothing; as an example I give Pliny’s
account of an erection done by the Egyptians. In his _Natural History_,
book XXXVI, chap. 14, he tells us: “Rhamsesis, who was reigning at
the time of the capture of Troy, erected one 140 cubits high (73
metres). Having left the spot where the palace of Mnevis stood, this
monarch erected another obelisk 120 cubits (63 metres) in height,
but of prodigious thickness, the sides being no less than 11 cubits
in breadth (5.77 metres). It is said that 120,000 men were employed
upon this work, and that the king, when it was on the point of being
elevated, being apprehensive that the machinery employed might not
prove sufficiently strong for the weight, and with a view of increasing
the peril that might be entailed by the want of precaution on the part
of the workmen, had his own son fastened to the summit, in order that
the safety of the prince might at the same time ensure the safety of
the mass of stone . . . . . ”
(36) Mediæval and modern writers have speculated freely on the ancient
method of erecting obelisks, their ideas ranging from fairly sound
theories to the assertion constantly made to me by the less responsible
spiritualists, that it was done by _levitation_!
Of modern theories two seem to be popular; the first suggests that the
obelisk was laid flat, with one side of its base just above the notch,
which in nearly all cases runs along one side of the pedestal, and that
it was gradually levered up, and at the same time banked from below,
being assisted when it had become sufficiently high by pulling with
head-ropes, and similarly checked by ropes when on the point of tilting
over on to its base. This with slight modifications, was the method
used for the erection of the obelisk of Seringapatam, and is described
by Gorringe in his _Egyptian Obelisks_ (p. 157), and by Commander
Barber, in _The Mechanical Triumphs of the Ancient Egyptians_ on page
102. It must be remembered, however, that the whole obelisk weighs only
about 35 tons. To assert that this method was that to be used for the
Aswân obelisk is not justifiable. The reasons against this method may
be summed up as follows:
(1) It would be almost impossible to lever up a large obelisk, close
to a pylon, on an ever-increasing earth slope, and it could not be
‘rocked’ up as it would slip out of the notch.
(2) Pulling by head-ropes, with or without the aid of a strut or
‘raising-lever’, would be useless until the obelisk was almost
upright, even if it was done from a high embankment. {37}
(3) It would not explain how Ḥatshepsôwet’s obelisks were introduced
into the middle of the court of Tuthmôsis I^{st}.
(4) Ropes would almost surely be inadequate to stop the obelisk from
rocking out of control after it had passed its dead centre. The New
York obelisk, when being pulled into a horizontal position about a
specially made trunnion, supposed to be at its centre of gravity, took
charge, snapped the cables and escaped breaking by a miracle.
(5) Ḥatshepsôwet’s standing obelisk has (apparently) jumped forward
nearly a foot in front of its notch. It can be seen, if one pulls
upright a foot-long alabaster obelisk (sold at the Cairo fancy-shops)
with cotton threads that it is impossible to make it jump forward
after passing its dead-centre. What it does, if the pulling is not
very even and square, is to pivot on one of its corners at the
beginning or end of its first rock, with what would be disastrous
results in a large obelisk.
(37) The more usual explanation as to how the erecting was performed is
that the obelisk was pulled on rollers up a long inclined embankment
until it was at a height well above the centre of gravity of the
obelisk. Having been rolled up base foremost, it was tilted over the
end of the embankment, and the earth gradually cut away from below
it until it settled down on to its pedestal, leaning against the
embankment; from thence it was pulled upright (see PETRIE, _Arts and
Crafts of Ancient Egypt_, p. 77, quoted in section 55).
This seems a far more probable method than the last, but from a
practical point of view it leaves a good deal unexplained. Anyone
who has seen, in _sabâkh_ work or elsewhere, earth being cut from
under a stone, or even being itself undercut, knows the way it has of
slipping sideways or any way but the expected—generally on the heads
of one’s workmen. With, say, a 500‐ton obelisk, the undercutting would
be a somewhat delicate business to make it settle down true on to the
pedestal.
The tendency to rock and pivot when being finally pulled upright is not
dealt with. Whatever method the Egyptians used, it was _sure_, and did
not depend on the skill of the men with the hoe and basket.
Before describing the method which I believe was used, it would be well
to consider what means the Egyptians had at their disposal.
(38) Levers must have surely been familiar to the Egyptians; the
constant import of tree-trunks from Syria would furnish them with
the material, and a hundred occurrences in every-day life, such as
extracting a stone with the point of a hoe would suggest to them the
application. The occurrence of a lever in the filling of a tomb at
El-Bersheh is published by M. Daressy in _Annales du Service_, vol. I,
p. 28, where he remarks: “On a retrouvé une branche d’acacia taillée en
biseau à une extrémité qui avait dû servir de ciseau et de levier pour
soulever le couvercle”.
In several of the temples in the Theban area and—Dr. Reisner informs
me—in the temple of the third pyramid at Gizeh, one may see large
blocks, undercut at various points along their length as if to take the
point of a lever. {38}
Rollers, too they must have known, even if they did not get the idea
from the Assyrians. We know that they used sleds running on sleepers—at
Lahun pyramid the tracks have actually been found—and it is incredible
that the greater ease in pulling, when a small sled ran over a stick,
should escape their notice. It might be asked why the statue of
Dḥutḥotpe was _not_ pulled along on rollers, instead of on a sled only
(cf. section 29). The reason seems to be that, given a moderate sized
block and plenty of men, the progress would be quicker, as the sled
does not need the constant adjustment and attention which is required
by rollers. As we have already remarked, the friction renders the use
of sleds alone impossible for a large obelisk (cf. section 31), so,
since it appears that obelisks must have been brought into the temple
precincts endways, there is no other means we know of other than
rollers.
Several pieces of wood, which were probably used as rollers, were found
in the débris round the Lahûn Pyramid, and are published in BRUNTON,
_Lahun I, the Treasure_, plate XX. They vary from a foot to about 8
inches in length, having diameters from 2 to 3 inches. The ends of
all the examples are rounded. It is strange that, in the quarry and
chip-heap cleared at El-Lahûn, so few workmen’s tools were found with
the exception of wooden mallets and sleepers.
Dr. G. A. Reisner, in reply to my question as to whether any rollers
had been found in the course of his excavations, has kindly sent me the
following note. “At Nuri (Ethiopia) we found two short thick granite
rollers in the chamber of Pyramid VIII, where there was a granite
coffin, weighing 7–8 tons, which may have been used for moving the
coffin from the foot of the stairs through rooms A and B to its place
in C. We actually used these rollers in moving the coffin out.” He
gives the date of these rollers as about 550 B. C.
(39) On the other hand, it appears that the capstan and the block and
tackle, arranged to give a large mechanical advantage, were quite
unknown until quite late times. No trace has been found of them in
the town-sites excavated in recent years, nor is there any trace
of their derivatives, such as the spoked well-drum in one case or
the application of the other for hauling up the sails of ships. In
the scene of the expedition to Punt in the time of Ḥatshepsôwet, an
examination of the sail halliards reveal nothing in the nature of a
block and tackle.
Sheers, gyns and derricks may well have been known in principle, but
for moving weights like those of obelisks, these are of no use except
in conjunction with the capstan and block and tackle. When the Luxor
obelisk was being lowered for removal, in spite of the elaborate
calculations of the stresses set up in the wooden sheers, and of the
good modern carpentry used in their construction and the steady pull
given by the capstans, the structure crushed and jammed, and it was
only by the use of screw-jacks that the necessary repairs could be
made. This was with a 227‐ton obelisk!
A method which may have been used, and which I should myself attempt if
I were entrusted with such a piece of work, is as follows:
(40) A square funnel is first built round and above the pedestal on
which the obelisk is to stand (see plate VIII), leaving a space about
half a metre high, and one and a half metre wide, clear over the edge
of the pedestal, to lead out to a tunnel. The sides of the funnel,
which are {39} of smooth masonry, are set at a slope so that the
obelisk on being lowered into it can lie against the wall of the slope
without passing its dead-centre and coming of itself to an upright
position. The sides of the funnel are continued upwards—perhaps in
brick, for economy—until the height of the funnel is well above the
centre of gravity of the obelisk; the higher, the better. Around the
funnel the brickwork would be brought out to form a square tower, with
the pylon wall for its revetement, perhaps, on one side. The tunnel
mentioned above leads from the pedestal to the further wall of the
tower.
A long sloping embankment (section 35) is made to lead up to the top of
the platform, and a gentle curve cut in the brick (A) to lead down to
the interior of the funnel. In the case of the obelisk of Ḥatshepsôwet,
the platform must have been at a high enough level to clear any
buildings in the way.
The obelisk is then pulled up on rollers, base foremost, until it just
overhangs the slope A. The funnel, previous to this, is filled with the
finest Aswân sand, which has very little cohesion in its particles,
banked high against the butt of the obelisk. The sand is then very
gradually removed from the tunnel, thus letting the obelisk slowly down
on to its pedestal. In this process, men would descend with the obelisk
until the masonry portion of the tunnel was reached. Precautions would
have to be taken, by banking the sand up before the butt of the obelisk
and, if necessary, by inserting wooden struts between the butt and the
wall B of the funnel, to prevent the obelisk jamming against it. After
the masonry is reached, there would be little fear of a jam.
There is fairly good proof that blocks and statues were lowered on to
their beds by emptying sand-bags which supported them. Choisy, in his
_L’Art de bâtir chez les Égyptiens_, takes it for granted that this
method must have been used for obelisks as well. His suggestion—or
rather description, for he might well have been there—of how the
Egyptians erected their obelisks, on page 124, is not to be taken
seriously, except perhaps for the smallest obelisks (see section 50).
If the method I suggest, or a modification of it, was that used for the
erection of the largest obelisks, sand-bags are not necessary at all.
As to the flow of fine blown sand, I can speak from personal experience
on the matter, as I have several times approached a big tomb-shaft
filled with blown sand from below, having entered by another tomb
breaking into it. The sand always lay sloping from the roof of the
chamber joining the shaft to the floor, at an angle of about 20
degrees. It can be easily and safely removed from below without
bringing down an avalanche. I am very sure that, at the end of the
tunnel, no constant flow will occur, even when the sand is being
pressed down by a 1168‐ton obelisk; it is more likely that men would
have to remove the sand from half-way along the tunnel.
The bottom of the funnel would have to be slightly larger than the base
of the obelisk, so as to be able to remove the sand, stones and brick
fragments which might have come down with it.
If all went well, the obelisk, when it touched the pedestal, would
lie against the near wall of the funnel with its base engaging in the
notch. Men would then enter through the tunnel, and clear out all
particles of sand from the surface of the pedestal and, if necessary,
from around the base of the obelisk. {40}
Before passing the proofs of the volume, but after plate VIII was
printed, I made a wooden model of a funnel of almost exactly the same
proportions as that shewn on the plate. The height of the end of the
embankment was 30 centimetres. This I tried with a 1/100 scale model of
the obelisk in limestone, using finely sifted Aswân sand.
The result was interesting, since it shews the great importance of
unsuspected details in this kind of undertaking.
In the model, I did not use a tunnel, but allowed the sand to escape at
any desired rate through an aperture in the stand on which the model
was placed. Since the model was not fixed to the stand, the position of
the aperture with regard to the bottom of the funnel could be varied.
I found that, if the aperture was on the side away from the embankment,
there was a decided tendency for the obelisk to jam against the
opposite wall of the funnel. If, on the other hand, the sand ran
out from the near side, the obelisk came down resting against the
embankment wall, with its edge where the slot should be. It seems
most likely that the sand was removed, not from the tunnel shewn on
plate VIII, but from one on the opposite side, leading out from under
the embankment. The tunnel shewn in the plate seems necessary for the
proper cleaning of the pedestal before the obelisk was pulled upright.
In a subsequent model, in which the side of the funnel was vertical and
made of glass, I was enabled to examine the base of the obelisk and the
levels of the sand during the descent. The results shewed no reason
for modifying the diagram on plate VIII except in the manner mentioned
above.
It is possible that the sand was removed from above until the obelisk
was low enough for there to be no fear of a jam; after that point had
been passed, it would not matter from which side of the pedestal the
sand was removed.
I realise that if the model were enlarged up to full-size, the grains
of sand would be at least one centimetre in diameter. It seems to me
that, using ordinary sand with a full sized obelisk, the flow would
be better than is the case in the model, as there would be less
skin-friction with the sides of the funnel. On the other hand, there
may well be factors, unforeseen by me, which might render the behaviour
of the full-sized obelisk different from that of the model, so I give
these results without insisting that they are a _proof_ that such a
method is possible for erecting obelisks.
Another point arises in connection with the funnel; this is the
possibility of the _side_ walls of the funnel having been constructed
vertically, the width of the funnel being only slightly greater
than the width of the base of the obelisk. The advantage of this
modification would be that if sand were piled on to the obelisk in
the initial stages of its descent, the weight of the sand would be a
great help in forcing the base down the funnel past the point where it
might be likely to jam. It would, however, make the examination of the
obelisk during its descent a difficult matter owing to lack of space.
Mr. Somers Clarke points out that, if the obelisk came down on to
its pedestal supported on one edge, that the strain would crush the
granite. It seems that the slot in the pedestal served a double
purpose, one to keep the obelisk from twisting, and the other to ensure
that the weight {41} is taken on the edge of the slot and not on the
edge of the obelisk (see fig. 8). Let us assume that the edge of the
slot crushes until there is 2 inches of supporting surface; then since
the obelisk is about 165 inches along its base, the bearing surface
will be 330 square inches and the resulting crushing stress about
3 ½ tons per square inch, which is not so very excessive. By putting
moderately soft wood in the slot, the weight could be borne both by the
edge of the obelisk and the edge of the slot, thus further reducing the
stress set up. In the case of the standing obelisk of Ḥatshepsôwet, it
has come down without engaging in the slot, with the result that the
corners have crushed considerably.
Figure 8 shews the position of this obelisk as it now stands on its
pedestal, the position taken up being CDEF instead of C′D′E′F′.
The corners E and F have split badly owing to the great weight and have
been rounded to cover up the defect. In this case the inner side of
the slot, AB, as far as can now be seen, is still sharp. In all the
other pedestals I have examined, where the obelisks have apparently
come down so as to bear on the inner edge of the slot, the edge is very
distinctly crushed.
[Illustration: Fig. 8.
Position of Ḥatshepsôwet’s obelisk on its pedestal.]
(41) Before the obelisk was pulled upright, the space in front of the
obelisk, and between it and the wall B, might well be filled up with
_halfa_ and reeds, to make a kind of cushion, and to damp any tendency
to rock backwards and forwards. The notch would prevent any twist
before it engaged with the reed cushion. If the obelisk twisted, it was
because the reed cushion was not sufficiently tightly packed, the twist
taking place after it had rocked over to its further edge.
If the obelisk was on a sledge, I should think that it was removed
before introducing it into the mouth of the funnel; the removal of the
rollers would be automatic.
The raising of the obelisk without the aid of an embankment is proposed
by Choisy in _L’Art de bâtir chez les Égyptiens_. He assumes that
the obelisk was raised by a series of levers used horizontally on a
fulcrum, and that it was heaved up simultaneously from both sides and
packed from below after each heave, the obelisk and levers rising
together till the obelisk was sufficiently high to lower on to the
pedestal (cf. section 50 and fig. 11).
Let us assume that this method was to be used for the Aswân obelisk. I
think that the largest levers practicable would be 15 metre tree-trunks
used with a mechanical advantage of 10 to 1. Not more than 30 levers
could be used on each side of the obelisk. The number of men required
to raise the obelisk can be found to be about 56 per lever, assuming
that they all heave at the end. I hardly see how such a number can
be put on a horizontal lever unless we assume that a cross-baulk is
attached along the ends of the levers and the whole loaded with stones.
The levers would have to be dismounted at each heave and the time taken
would be considerable. The method, however, is a possibility, so I
include it as an alternative to the embankment. {42}
(42) Before leaving this subject, it is as well to ascertain if the
obelisk is strong enough to bear the internal strain due to its own
weight when it is supported at its centre of gravity.
The volume of a truncated cone is given by the formula V = H/3 (A^2
+ A_a_ + _a_^2).
In the shaft of this obelisk, H is 37.25, A is 4.20 and _a_ is 2.50
metres. Substituting, we have: V = 37.25/3{(4.2)^2 + 4.2 × 2.5
+ (2.5)^2} from which we find that the volume of the shaft is 426 cubic
metres. Aswân granite weighs about 2.679 tons per cubic metre, which
makes the shaft weigh 1143 tons.
The weight of the pyramidion is {(base)^2 (height) (unit weight)}/3,
or (2.50)^2 (4.50) (2.679)/3 = 25 tons, so that the total weight of the
obelisk would have been 1143 + 25 = 1168 tons.
The distance of the centre of gravity of a tapering square-sectioned
solid from the butt is given by the formula: {¼ H (A^2 + 2A_a_
+ 3_a_^2)}/(A^2 + A_a_ + _a_^2).
Here H is 37.25 m.; A = 4.2 m.; _a_ = 2.5 m.
Substituting we get: (37.25/4) {[(4.20)^2 + 2 (2.50 × 4.20)
+ 3 (2.50)^2]/[(4.20)^2 + (2.50 × 4.20) + (2.50)^2]}.
That is, the distance of the C. G. from the butt, (LN on fig. 11), is
15.35 metres.
Taking the pyramidion by itself. Its height is 4.50 metres, so that its
C. G. must be one-fourth that distance from the base, which makes 1.12
metres.
If _x_ is the distance of the centre of gravity of the whole obelisk
from the butt, by taking moments about the butt we have: (Total weight)
× _x_ = (weight of pyramidion) × (1.12 + length of shaft) + (weight of
shaft) × 15.35, or 1168 _x_ = 25 × 38.37 + 1143 × 15.35, from which _x_
= 15.84. _That is, the distance of the centre of gravity of the whole
obelisk from the butt is 15.84 metres._
The breadth of the obelisk at its centre of gravity is 4.2
− (15.84/37.25) × (4.2 − 2.5) or 3.49 metres.
(43) Let us assume that the obelisk is balanced at its C. G., and
find the stresses due to bending. The weight on each side will be
equal. Taking the right hand half, its weight will act at its C. G.
Using the formula for the C. G. of a tapering square-sectioned
solid, quoted above, we get: (15.84/4) {[(4.20)^2 + 2 (4.20) (3.49)
+ 3 (3.49)^2]/[(4.20)^2 + (4.20) (3.49) + (3.49)^2]} = 7.43 metres,
which means that the centre of gravity of the right-hand half of the
obelisk will act at a distance of 7.43 metres from the butt, or 15.84
− 7.43 = 8.41 metres from the balancing point, or C. G. of the whole
obelisk.
The sum of the moments to the right of the C. G. of the whole obelisk
will be half the total weight multiplied by 8.41 = 584 × 8.41.
Then, if _s_ is the internal stress set up due to the bending of the
obelisk when supported at its C. G., we have:
(Section modulus) (stress) = sum of moments on one side of support.
The modulus of the square section is one sixth the cube of the depth,
so we have: {[(3.49 × 39.37)^3]/6} _s_ = 584 × 8.41 × 39.37 × 2240.
From which _s_ = 1001 pounds per square inch (39.37 being the reduction
of metres to inches). {43}
The modulus of rupture for granite from Aswân is given as 1500 pounds
per square inch, so it will be seen that the obelisk, if not converted
into a live load (by a jerk, for instance) can be supported at its
C. G. without breaking.
It is rather difficult to say how far the Egyptians were able to
carry their calculations. The erection could well have been rehearsed
by means of a scale-model, which could have been further used for
obtaining the weight and the position of the centre of gravity. I
do not think that they ever troubled about the bending-moment; at
any rate, their mathematics were not sufficiently advanced for its
determination. It may be that, since in all the obelisks we know
of, whose taper does not vary to any great extent, can be supported
anywhere, the Egyptians never had a case of such a monument breaking by
its own weight.
Another interesting point arises in connection with this, and that is,
since in obelisks (and all beams) of the same proportion, the bending
stress due to their own weight depends on the linear dimension, and
therefore the fact that a granite scale-model does not break will be
no indication that the monument itself will not break when similarly
supported. If the 108 cubit (56.70 metres) obelisk of Ḥatshepsôwet,
mentioned by Ṭḥutiy (section 3), does indeed apply to _one_ and not to
the _two_ placed butt to butt on the boat shewn in the Dêr el-Baḥari
sculpture, then, if the proportions are about the same as the Aswân
obelisk, the stress set up when supported at its centre of gravity (see
section 40) would be in the nature of 56.70 × 1001/41.75 = 1360 pounds
per square inch, which is perilously near the breaking stress of 1500
pounds per square inch.
It will be clearly seen that the obelisk, part of which is at
Constantinople, cannot have been part of the 108‐cubit obelisk, as it
would be much thinner than the one at Aswân and would certainly not
support its own weight either at the centre of gravity or at its ends.
When worked out, the internal stress set up in such an obelisk more
than doubles the ultimate strength of granite.
{45}