(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 (?m—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 ?ori 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?L??H?(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 ?atshepsÔwet’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) ?atshepsÔwet’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 D?ut?otpe 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 ?atshepsÔwet, 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 ?atshepsÔwet, 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 3½ 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 ?atshepsÔwet, 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 C?D?E?F 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, A?B, 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.

(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(A² +A?a +a²).

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: {¼H(A² +2?A?a +3?a²)}/(A² +A?a +a²).

Here H is 37.25m.; A =4.2m.; a =2.5m.

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, (L?N 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 1168x =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 ?atshepsÔwet, mentioned by ??utiy (section 3), does indeed apply to one and not to the two placed butt to butt on the boat shewn in the DÊr el-Ba?ari 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.