Chap. 18. Architectural Ideas of the Pyramid Builders
Pages 162 - 172
121. [p. 162] In this chapter the more general principles, common to all the pyramids, will be considered; leaving the points which are peculiar to the Great Pyramid, to be discussed in the History of the Great Pyramid and its design.
The characteristic Mastaba-angle, and the nature of Mastaba-Pyramids and true Pyramids, have been already stated (section 103). The design of the various slopes that are met with, appears to be always a simple relation of the vertical and horizontal distance. It is important to settle this, as it bears strongly on the whole planning of each building. And though the vertical and horizontal distances would seem to be the natural elements for setting out a slope, yet proof of this is necessary; for Ahmes, in his mathematical papyrus, defines pyramids by their sloping height up the arris edge, and their diagonal of the base beneath that line. Such a method of measurement would naturally be adopted, when the knowledge of the design was lost, as the arris height could be easiest measured; but it is very unlikely as a specification of design.
The angles of the various Pyramids, and so-called Pyramids, are as follow:—
By photographs of the inner casings they vary from 69º to 85º; averaging 70º 12'.
[p. 163] The angles determined by Perring for Colonel Vyse cannot be considered very satisfactory for comparison with theories, as they seem in one case to be distinctly in error (in the Second Pyramid angle); and some of the observations are so extremely near to theoretical angles, that they seem to have been modified by the observer. But taking those Pyramids of which I measured the angles repeatedly in many ways, the variations from the slopes which would result from integral amounts, is usually about half the probable error; and the variation only equals the probable error in the Third Pyramid, which is least accurately built. From these close coincidences it seems clear that the rule for slopes in designing, was to set back the face an integral number of cubits, on a height of an integral number. The use of angles of 4 on 3 (which has hypothenuse 5), and 20 on 21 (which has hypothenuse 29), seems to suggest that the square of the hypothenuse being equal to the squares of the two sides may have been known; particularly as we shall see that the use of squared quantities is strongly indicated in the Great Pyramid.
122. No discussion of the sizes of the Pyramids can lead us to the ideas involved in their design, unless it is first settled whether they were each completely planned at their beginnings, or each carried forward as far as the life of the builder permitted. This last idea, which may be called the "theory of accretion," would show that the size of each Pyramid was solely due to a series of accidental events; and that no foreseen design can be expected in the external dimensions, or in their relations to the inside. As several names have been associated with this theory, it will be best to avoid them all; and treat it on its own merits impersonally, like all other theories mentioned in this work
We will first, then, consider the questions that have been put forward on Pyramid building, and the applicability of the theory of accretion to each of them, and after that notice some of the other points bearing on this theory.
(1) How does it happen that the Pyramids are of such different sizes? The theory of accretion answers that each king continued building his Pyramid until his death, and hence the Pyramids differ in size because the reigns differed in length. When, however, we see that the lengths of the reigns are not in proportion to the bulk of the respective Pyramids, this apparent explanation merely resolves itself into saying, that because two quantities vary they must be connected. On comparing the lengths of the reigns with the sizes of those Pyramids whose builders we know, the disproportion is such that Khufu, for instance, must have built the Great Pyramid 15 times as fast as Raenuser built the Middle Pyramid of Abusir; or else Raenuser built for only 1/15th of his reign; either alternative prevents any conclusion being drawn as to inequalities in time producing inequalities in the sizes of the Pyramids.
(2) How could later kings be content with smaller Pyramids after Khufu and Khafra had built the two largest? This question the accretion theory [p. 164] cannot explain; for many of the later kings lived nearly as long as Khufu and Khafra (one even much longer), without producing anything comparable in size. When we look at the mournful declension in the designs of Pyramid building, from the beauty of the fourth down to the rubble and mud of the sixth dynasty, the falling off in size as well as quality is merely part of the same failure.
(3) How is the fact to be accounted for that an unfinished Pyramid is never met with? In the same work in which this question is asked, it is said of one of the Abusir Pyramids, that it "seems never to have been completed;" and of the South Stone Pyramid of Dahshur, "The whole pyramid was probably intended to have the same slope as the apex, but the lower part was never completed." This question is only another form of No. 5.
(4) How could Khufu have known that his reign would be long enough to enable him to carry out such a vast design? However this may be, he certainly worked far more quickly than any other king, and the arrangement of the interior of his Pyramid, as we shall see below, proves that it was all, or nearly all, designed at first.
(5) If a builder of a great pyramid had died early, how could his successor have finished the work, and built his own pyramid at the same time? First, we have no proof that a successor did not appropriate the work to himself, or share it with the founder; and, secondly, no other kings worked at a half, or perhaps a tenth, of the rate that Khufu and Khafra worked, or with anything like the same fineness; and hence any king might easily have had two pyramids on hand at once, his father's and his own.
The accretion theory, then, though not actually condemned by the application of these questions which are adduced in its support, is at least far from being the "one entirely satisfactory answer" to them, as it has been claimed to be. And the supposed proof of it, from the successive coats of the Mastaba-Pyramids of Medum and Sakkara, is, in the first place, brought from works that are not true Pyramids; and, in the second place, shows that the buildings quoted were completely finished and cased many times over, probably by successive kings, and not merely accreted in the rough, until the final casing was applied. A confirmation claimed for this theory is "the ascertained fact that the more nearly the interior of the pyramid is approached, the more careful does the construction become, while the outer crusts are more and more roughly and hastily executed." This is certainly not true in many, perhaps most, cases. The Pyramids of Sakkara, as far as they have been opened, show quite as fine work in the outer casing as anywhere else; and the rubble of the inside is equally bad throughout. The Great Pyramid of Gizeh shows far finer work in the outermost parts of the passage, casing, and pavement, than in most, or perhaps all, of the inside, and the Second Pyramid is similar. In a great part of the pyramids we [p. 165] know nothing of the comparative excellence of the work of different parts, comparing fine work with fine work, and core with core masonry.
123. Now, if the accretion theory were true, it ought to be of the greatest value when applied to the largest Pyramids; for these are the most difficult to account for, and their extraordinary size is the main feature appealed to in support of the theory.
Let it then be critically applied to the Great Pyramid of Gizeh, the largest known (see Pl. vii.). First, it must be noticed that the centre of the Pyramid cannot have been much shifted by accretion on one side of it, as all the chambers are near the middle; and if any shift of its axis were due to this, the accretion must have been on the N. side, as two chambers are S. of the middle. Trying, therefore, how small a Pyramid might have been begun, let it be taken at A: if a Pyramid existed of this size, it would be completely anomalous, and unlike anything known; it would have (j) a horizontal passage, (2) opening near the top of it; (3) a chamber close to the top of the Pyramid; and (4) an entrance to the lower chamber far outside the Pyramid. Each of these peculiarities condemn it as impossible. The next larger size that would not leave chambers half exposed on the outside of the building, would be at B. With this size there would be the anomalies of (I) two entrances on one face; (2) one sloping upwards; (3) a great hall and a chamber close to the outside, and near the top of the Pyramid. Each of these points condemn such a design as un-Egyptian, and unlike any other known pyramid, no matter how small. The least size, then, that could possibly be supposed to be the first design would be at C, as it is clear that any lesser design would leave impossible anomalies in the arrangements. Thus it is plain that the accretion theory breaks down in its application to any size under 600 feet for the Great Pyramid; and if we are thus compelled by its arrangements to acknowledge a primary design of a base of 600 feet (which is larger than nineteen-twentieths of the other pyramids), what need is there of a theory of accretion to account for its being 750 feet?
Next let this theory be applied to the Second Pyramid of Gizeh, which is only exceeded in size by that we have discussed above (see Pl. vii.). Here the chamber is practically central, and the axis of the Pyramid cannot therefore have been much shifted by one-sided accretion. Supposing that it was designed of any size less than A, there would then be the anomalous features of (i) an entrance on the ground level; and (2) a secondary entrance far out from the Pyramid. These features are unknown in any other pyramid, large or small, and the need of them thus condemns, as practically impossible, any design of less size than about 500 feet. Here then the accretion theory breaks down, as in the Great Pyramid design.
124. The summing up on this theory then is, that every argument brought forward in its support is either inconclusive, or false in examples; and that on [p. 166] applying it critically to the two cases in which it is most needed, and which have been mainly adduced to support it, it is completely contradicted by the essential formation of the pyramids. If we are then forced to accept the fact of gigantic primary designs for the largest pyramids, where is there any need of a theory to account for the far smaller designs, of very inferior workmanship, seen in the other pyramids? That some of the lesser and ruder pyramids (as the Third of Gizeh, which is ninth in order of size) may have been enlarged, is not unlikely; but such enlargement was an accident of increased ambition, and not a general law of construction; and it has nothing to do with the great designs, so magnificently carried out in the largest pyramids.
125. A theory which has obtained much belief, is that of the passages of each pyramid having been plugged up after the interment of the builder. But though this is often alluded to by some writers as even an undisputed fact, yet the evidence for it is not forthcoming. No doubt special parts were plugged up so as to conceal the openings of passages; and some disused passages might be blocked, more or less entirely; but, generally speaking, there is no evidence of a plugging of the entire passages.
In the Great Pyramid the entrance passage is often spoken of as having been plugged up; and the holes in the floor are adduced in proof, as showing where the destroyers got under the blocks to force them out. But these holes have been cut by a person standing in the clear passage below them, and picking at the stone from the southward; as is clearly seen on examining the cutting marks. Also the floor, being not only the most awkward part to work upon, but also the hardest stone, would certainly not be attacked to loosen any plugs; but the sides or roof would rather be chosen. Again, the holes are not deep enough to hold a man, though five or six feet long; and they only reach as far as Mamun's Hole, and not down to the subterranean parts. Moreover, if plug-blocks had been dragged out, or broken up in the passage, the walls and roof would inevitably have been bruised or broken where each block was attacked whereas, there is no trace of such injury visible; and the triangular stone covering the plug-blocks in the roof would have been broken loose before Arabic times. Besides these points, in the upper corners of the passage may be seen remains of the plaster, rubbed by the fingers into the angle; and this would have been displaced if any blocks that were cemented in had been dragged out.
There is, of course, no question but that the lower end of the ascending passage is plugged up with granite blocks, but it is very doubtful if there ever was much more plugging than is there at present. It is clear that the Arabs, on forcing the way by Mamun's Hole, ran along the side of the granite plugs, until they reached a higher point in the passage, where, owing to some reason, they could get into the passage more easily. And if the rest of the passage had [p. 167] been plugged, they would either have forced their way in the softer limestone alongside of the plugs, as they had already done; or else, if the plugs were removable they would have filled up the awkward hollow of Mamun's Hole with them, to avoid the labour of carrying them all out of the Pyramid. But there is not one known, out of the large number of such blocks that ought to be found if the whole passage had been plugged up.
The mouth of the passage to the Queen's Chamber was certainly blocked but no one has supposed that the whole of that passage, or that the gallery, was blocked.
Thus there is an absence of any trace of blocking of the passages, beyond the closing of the mouths of two passages, merely to prevent their being detected.
In the Second Pyramid the flaws in the passage are plastered up — sometimes over a large surface — and then tinted red; if; then, any blocks had been drawn out, this plastering would have been scraped, and at least the colouring rubbed off; on the sides of the passage are also projecting scraps of plaster .1 to .15 thick; and in the top corner of the E. side are some scraps 3/4 inch thick; these would have been rubbed off in removing any plugging. The evidence here, then, is decidedly against the main passage having been plugged. The lower passage from the pavement, as being a duplicate passage not required, was plugged up, like the duplicate and disused passage in the Third Pyramid.
In the Pyramids of Dahshur, the passages have been filled with desert pebbles, sand, and masons' chips; a filling which could not come in by accident, and would not be put in by design except by the builders. This, therefore, was a filling up to prevent casual access to the inside; but such as could be readily taken out if it was required to be opened. It shows that no stone plugging, or building up, was put in the entrance passage; although a duplicate passage in one of these Pyramids was plugged by blocks.
In the Pyramid of Pepi, and in another at Sakkara, the passages are lined with long and delicate inscriptions; which, at least in that of Pepi, do not show any mortar in the hollows. Indeed, it would not be likely that an inscription should be put where it was to be built over afterwards with plug-blocks.
Not only, then, is the evidence inconclusive that the main passages of the Pyramids were ever plugged throughout their length, but, on the contrary, there are incidental proofs that no general plugging was ever introduced or extracted.
126. The possibility of the Pyramids having had movable doors has been quite overlooked in modern times, owing to the general belief that the passages were plugged up. of course, if a passage was filled up solid there could not have been any door to it; but as we have seen that there is no evidence of [p. 168] such plugging, doors may have existed. And as we shall further see that there is very substantial evidence of the former existence of doors, we have, therefore, equally valid proofs of the non-existence of any plugging.
The traces of a stone flap door, or turning block, in the mouth of the South Pyramid of Dahshur, have been already described (section 109), as well as the signs of a wooden door behind that. Such a formation of the passage mouth is unmistakable in its purpose; but after drawing conclusions from that doorway, it was a most satisfactory proof of the generality of such doors, to observe the following passage from Strabo on the Great Pyramid. "The Greater (Pyramid), a little way up one side, has a stone that may be taken out , (εξαιρεσιμον, exemptilem) which being raised up (αρθεντος, sublato) there is a sloping passage to the foundations." This sentence is most singularly descriptive of opening a flap door; first, the stone is taken out, or lifted outwards from the face; and then, being thus raised up, the passage is opened. The two different words exactly express the change in the apparent motion, first outwards and then upwards; and they show remarkable accuracy and precision in their use. Besides this description, there is another statement that the Pyramids of Gizeh had doors, in an Arabic MS., quoted by Vyse; this was written in 850 A.D., and, therefore, only twenty or thirty years after Mamun had forced his way into the Great Pyramid, and thus re-discovered the real entrance.
The mechanical proofs of the existence of a door to the Great Pyramid are of some weight, though only circumstantial, and not direct evidence like that of the above authors. No one can doubt that the entrance must have been closed, and closed so as not to attract attention at the time when the Arabs made their forced passage, about a hundred feet long, through the solid masonry. Moreover, it is certain that the entrance was not covered then by rubbish: (i) because the Arabic hole is some way below it, and the ground-level at the time of the forcing is seen plainly in the rubbish heap; (2) because the rubbish heap, which is even now much below the original doorway, is composed of broken casing, and the casing was not yet broken up at the time of forcing the passage. Therefore the doorway must have been so finely closed that the various accidental chippings and weathering on all the general surface of the casing completely masked any wear or cracks that there might be around the entrance; and so invisible was the door then, that, standing on the heap from which they forced their hole, the Arabs could not see anything to excite their suspicion on the surface only 35 feet above them; they, therefore, plunged into the task of tearing out the stone piecemeal, in hopes of meeting with something in the inside. Yet we know from Strabo that the Romans had free access to the passage, though he says that it was kept a secret in his time. No extractable plug or block, weighing necessarily some tons, would have been [p. 169] replaced by every visitor until the Arab times, especially without there being any shelf or place to rest it on while it was removed.1
The restoration of a door shown in Pl. xi., would agree to these various historical requirements, and be in harmony with the arrangement at Dahshur; such a block would only need a pull of 2.5 cwt. on first taking it outwards, and 4 cwt. to lift it upwards to its final position; it would leave no external opening; it would also allow just half of the passage to be quite clear; and from the passage being halved in its height by two courses at the beginning, such an opening is the most likely. Though the general form is thus indicated, the details are of course conjectural.
To sum up. A self-replacing door, which left no external mark, is absolutely required by the fact of the Arabs having forced a passage. only a flap door, or a diagonal-sliding portcullis slab, can satisfy this requirement. A flap door is unequivocally shown to have been used at Dahshur. And Strabo's description of the entrance agrees with such a door, and with no other. Such is the evidence for the closing of the Pyramids by doors; equally proving also the absence of any plugging up of the entrance passages.
127. Reference has often been made in previous pages, to the varying character of the work of the Pyramids; both for its own interest, and for its historical value. Some connected remarks are therefore desirable, on the different architectural ideas of the builders, in their general style of construction and an attempt is here made to range the principal pyramids in the order of their excellence of workmanship.
The Great Pyramid at Gizeh (of Khufu, fourth dynasty) unquestionably takes the lead, in accuracy and in beauty of work, as well as in size. Not only is the fine work of it in the pavement, casing (section 26) King's (section 52) and Queen's Chambers (section 41), quite unexcelled; but the general character of the core masonry is better than that of any other pyramid in its solidity and regularity.
The small Pyramids by the (Great Pyramid of Khufu's family, fourth dynasty) are of very good work in their passages, and in the remains of their chambers they are also good in the core masonry (excepting one that has crumbled), and were well cased with fine limestone. Considering the internal work, and the apparent use of hard-stone edging of diorite and basalt in the quoins (section 101), these Pyramids may rank next to the Great Pyramid.
The Third Pyramid (of Menkaura, fourth dynasty), though not so accurate in its interior as some of the others, may nevertheless come next, by reason of [p. 170] the excellence of its core masonry. In this it equals the Great Pyramid, and is far better than any other.
The rank of the Pyramid of Abu Roash (of Menkaura, fourth dynasty?) is doubtful, owing to its ruined state. The design of the vast rock chamber, afterwards so massively lined, is very bold: its core masonry might rank almost as high as that of the following Pyramids; and the use of a very large amount of intractable red granite, both internally and externally, raises it character.
The Second Pyramid at Gizeh (of Khafra, fourth dynasty), would rank next to the Great Pyramid by its accuracy of work, both inside and outside; and even before the Great Pyramid in the work of its coffer. But the lamentably bad stone of its general core masonry, the rounded and carelessly shaped blocks, and the inferior quality of its casing stone, prevents its taking the second place.
The North Pyramid at Dahshur is about equal in general masonry to the Second of Gizeh; but inferior in the accuracy of its internal work. It is most of all like the Great Pyramid of Gizeh in its style of work, the fineness and whiteness of its casing, and the design of the overlapping roofs; but it is inferior to that Pyramid in every detail.
The South — or blunted — Pyramid at Dahshur is of good work; very good in the lower part of the core, but poorer in the upper parts, both in quality and working of the stones. There, is however, some very good work in the joints of the casing of it; flaws in the stone have been cut out, and filled in with sound pieces. It is only inferior to the preceding in the quality of the casing. The general impression received, from the work and design of these two large Pyramids of Dahshur, is that they are more archaic than the Great Pyramid of Gizeh; and the builders seem to be feeling their way, rather than falling off in copying existing models.
The Mastabat-el-Farun (of Unas, fifth dynasty) at Sakkara can scarcely be judged, without seeing either the casing or the inside; but by the general masonry, and the large size of the blocks used, it should rank close to the preceding buildings.
The Mastaba-Pyramid at Medum is of good work; the joints of its casing are fine and close, and the joint-surfaces are well dressed. The core masonry is passable; but it is inferior to those already mentioned in the size of the stones of all parts.
The Pyramids at Abusir (of Sahura and Raenuser, fifth dynasty) may, perhaps, take about this rank; for though good in their fine masonry, the general bulk of the core is poor, and begins to show the system of retaining walls filled in with rubble.
The Mastaba-Pyramid at Sakkara (or Great Step-Pyramid) is built of bad and small stones, often crumbling to dust: its casings are fairly good, though of [p. 171] small stones; but as they vary in angle, no accuracy seems to have been aimed at.
The other Pyramids of Sakkara (of end of fifth, and of sixth dynasty) as far as their construction is visible, appear to be all of the same type. They are made up of rude retaining walls, not even built continuously, but merely piecemeal; these walls are of rough broken small stones laid in mud; and they are filled in with loose stones, without even any mud. The outer casing was, however, of very good work, and consisted of large stones of fine quality; and the interiors are equally good. It was in the unseen mass of the masonry that deterioration took place.
The mud-brick Pyramids might, perhaps, stand before the generality of the rubble Pyramids just mentioned; as some skill is needed in the production of sound bricks of large size, that will bear at the present day being bowled down from top to bottom of the Pyramid, by the official excavators, without breaking. The casing of these Brick Pyramids was also of excellent white Mokattam limestone, where it has been seen.
Having thus pointed out a few of the reasons for assigning the above order of excellence to the Pyramids, it may be observed that (as far as is yet known absolutely) there is but slight exception to the rule of continuous decadence. The Third Pyramid of Gizeh is ranked next above the Second, and the Mastabat-el-Farun next above the Pyramids of Abusir; but otherwise the degeneration of design and work, so particularly seen in the hidden parts, follow the order of time. It is not likely that this is entirely the case if we knew the name of the builder of each Pyramid, but it is at least a general clue of value. And whether the Mastaba-Pyramids and those of Dahshur may prove to be the oldest examples or no, still, it would be almost impossible to assign a rubble Pyramid — so clearly a deteriorated type — to the age of the sound masonry of the fourth dynasty.
128. The use of plaster by the Egyptians is remarkable; and their skill in cementing joints is hard to understand. How, in the casing of the Great Pyramid, they could fill with cement a vertical joint about 5 X 7 feet in area, and only averaging 1/50 inch thick is a mystery; more especially as the joint could not be thinned by rubbing, owing to its being a vertical joint, and the block weighing about 16 tons. Yet this was the usual work over 13 acres of surface, with tens of thousands of casing stones, none less than a ton in weight.
The Egyptian notions about the use of plaster and stucco were very free; they never hesitated to use plaster in making good small defects in any place. In the monolith pillars of the Granite Temple, the flaws are filled by plaster, which is coloured red; the same is done on the roof of the King's Chamber, and the granite passage of the Second Pyramid. on limestone also plaster was freely used, especially in the faulty parts of the rock in the tombs. Often the rock has [p. 172] weathered away in powder, leaving the plaster with its hieroglyphs as sharp and fresh as when first laid on; this is well seen in the tomb of Khafra-ankh ("Tomb of Numbers"), and in tombs in the cutting round the Second Pyramid. Probably the continual use of plaster, to make good defects in building, was a habit which arose from the necessity of using it for flaws in the rock in the large number of excavated tombs; these are of the earliest time, the use of fine stone linings to the rock being a later method, not common till the fifth dynasty.
It is not usually known that the statues carved in diorite and alabaster were painted. Yet such seems certainly to have been the case. The fragments of diorite statues, that I found W. of the Second Pyramid, where all stuccoed on the outside, with a firm hard white coat; and the fragments of alabaster statues had bright green paint on the dress, and black on the plaited wig. Though it has long been known that the limestone statues were generally painted, and that those of granite were partially coloured; yet the concealing of the translucent alabaster, and of the polished and variegated diorite, by a coat which might merely hide limestone or plaster, seems to have escaped notice hitherto. This custom shows that the qualities of the stone were regarded more for preciousness than for beauty.
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