Pyramid

Pyramid, the name for a class of buildings, first taken from part of the structure,' and mistakenly applied to the whole of it by the Greeks, which has now so far acquired a more definite meaning in its geometrical sense that it is desirable to employ it in that sense alone. A pyramid therefore should be understood as meaning a building bounded by a polygonal base and plane triangular sides which meet in an apex. 2 Such a form of architecture is only known in Middle Egypt, and there only during the period from the IVth to the XIIth Dynasty (before 3000 B.C.) - having square bases and angles of about 50°. In other countries various modifications of the tumulus, barrow or burial-heap have arisen which have come near to this type; but these when formed of earth are usually circular, or if square have a flat top, and when built of stone are always in steps or terraces. The imitations of the true Egyptian pyramid at Thebes, Meroe and elsewhere are puny hybrids, being merely chambers with a pyramidal outside and porticos attached; and the structures found at Cenchreae, or the monument of Caius Sestius at Rome, are isolated and barren trials of a type which never could be revived: it had run its course in a country and a civilization to which alone it was suitable.

The origin of the pyramid type has been entirely explained by the discovery of the various stages of development of the tomb. In prehistoric times a square chamber was sunk in the ground, the dead placed in it, and a roof of poles and brushwood overlaid with sand covered the top. The Ist Dynasty kings developed a wooden lining to the chamber; then a wooden chamber free-standing in the pit, with a beam roof, then a stairway at the side to descend; then a pile of earth held in by a dwarf wall over it. By the IIIrd Dynasty this dwarf wall had expanded into a solid mass of brickwork, about 280 by 150 ft. and 33 ft. high. This was the mastaba type of tomb, with a long sloping passage descending to the chamber far below it. This pile of brickwork was then copied in stonework early in the IIIrd Dynasty (Saqqara). It was then enlarged by repeated heightening and successive coats of masonry. And lastly a smooth casing was put over the whole, and the first pyramid appeared (Medum).

It is certain that the pyramids were each begun with a definite design for their size and arrangement; at least this is plainly seen in the two largest, where continuous accretion (such as Lepsius and his followers propound) would be most likely to be met with. On looking at any section of these buildings it will be seen how impossible it would have been for the passages to have belonged to a smaller structure (Petrie, 165). The supposition that the designs were enlarged so long as the builder's life permitted was drawn from the compound mastabas of Saqqara and Medum; these are, however, quite distinct architecturally from true pyramids, and appear to have been enlarged at long intervals, being elaborately finished with fine casing at the close of each addition.

Around many of the pyramids peribolus walls may be seen, and it is probable that some enclosure originally existed around each of them. At the pyramids of Gizeh the temples attached to these mausolea may be still seen. As in the private tomb, the false door which represented the exit of the deceased person from this world, and towards which the offerings were made, was always on the west wall in the chamber, so the pyramid was placed on the west of the temple in which the deceased king was worshipped. The temple being entered from the east (as in the Jewish temples), the worshippers faced the west, looking towards the pyramid in which the king was buried. Priests of the various pyramids are continually mentioned during the old kingdom, and the religious endowments of many of the priesthoods of the early kings were revived under the Egyptian renaissance of the XXVIth Dynasty and continued during Ptolemaic times. A list of the hieroglyphic names of nineteen ' The vertical height was named by the Egyptians pir  (see E. Revillout, Rev. Eg., 2nd year, 305-309), hence the Greek form pyramis, pl. pyramides (Herod.), used unaltered in the English of Sandys (1615), from which the singular pyramid was formed.

For figures of geometrical pyramids see Crystallography, and for their mensuration see Mensuration.

of the pyramids which have been found mentioned on monuments (mostly in tombs of the priests) is given in Lieblein's Chronology, p. 32. The pyramid was never a family monument, put belonged - like all other Egyptian tombs - to one person, members of the royal family having sometimes lesser pyramids adjoining the king's (as at Khufu's); the essential idea of the sole use of a tomb was so strong that the hill of Gizeh is riddled with deep tomb-shafts for separate burials, often running side by side 60 or 80 ft. deep, with only a thin wall of rock between; and in one place a previous shaft has been partially blocked with masonry, so that a later shaft could be cut partly into it, macled with it like a twin-crystal.

The usual construction of pyramids is a mass of masonry composed of horizontal layers of rough-hewn blocks, with a small amount of mortar; and this mass in the later forms became more and more rubbly, until in the VIth Dynasty it was merely cellular system of retaining walls of rough stones and mud, filled up with loose chips, and in the XIIth Dynasty the bulk was of mud bricks. Whatever was the hidden material, however, there was always on the outside a casing of fine stone, elaborately finished, and very well jointed; and the inner chambers were of similarly good work. Indeed the construction was in all cases so far sound that, had it not been for the spite of enemies and the greed of later builders, it is probable that every pyramid would have been standing in good order at this day. The casings were not a mere " veneer " or " film," as they have been called, but were of massive blocks, usually greater in thickness than in height, and in some cases (as at South Dahshur) reminding the observer of horizontal leaves with sloping edges.

Inside of each pyramid, always low down, and usually below the ground level, was built a sepulchral chamber; this was reached in all cases by a passage from the north, sometimes beginning in the pyramid face, sometimes descending into the rock on which the pyramid was built in front of the north side. This chamber, if not cut in the rock altogether (as in Menkaura's), or a pit in the rock roofed with stone (as in Khafra's), was built between two immense walls which served for the east and west sides, and between which the north and south sides and roofing stood merely in contact, but unbonded. The gable roofing of the chambers was formed by great sloping cantilevers of stone, projecting from the north and south walls, on which they rested without pressing on each other along the central ridge; thus there was no thrust, nor were there any forces to disturb the building; and it was only after the most brutal treatment, by which these great masses of stone were cracked asunder, that the principle of thrust came into play, though it had been provided for in the sloping form of the roof, so as to delay so long as possible the collapse of the chamber. This is best seen is the pyramid of Pepi (Petrie), opened from the top right through the roof. See also the Abusir pyramids (Howard Vyse) and the king's and queen's chambers of the great pyramid (Howard Vyse, Piazzi Smyth, Petrie). The roofing is sometimes, perhaps usually, of more than one layer; in Pepi's pyramid it is of three layers of stone beams, each deeper than their breadth, resting one on another, the thirty stones weighing more than 30 tons each. In the king's chamber (Gizeh) successive horizontal roofs were interposed between the chamber and the final gable roof, and such may have been the case at Abu Roash (Howard Vyse).

The passages which led into the central chambers have usually some lesser chamber in their course, and are blocked once or oftener with massive stone portcullises. In all cases some part, and generally the greater part, of the passages slopes downwards, usually at an angle of about 26°, or i in 2. These passages appear to have been closed externally with stone doors turning on a horizontal pivot, as may be seen at South Dahshur, and as is described by Strabo and others (Petrie). This suggests that the interiors of the pyramids were accessible to the priests, probably for making offerings; the fact of many of them having been forcibly entered otherwise does not show that no practicable entrance existed, but merely that it was unknown, as, for instance, in the pyramids of Khufu and Khafra, both of which were regularly entered in classical times, but were forced by the ignorant Arabs.

The pyramids of nearly all the kings of the IVth, Vth and VIth Dynasties are mentioned in inscriptions, and also a few of later times. The first which can be definitely attributed is that of Khufu (or Cheops), called " the glorious," the great pyramid of FIG. I. - Pyramid of Medum (Meidoun).

Gizeh. Dad-ef-ra, who appears next to Khufu in the lists, had his pyramid at Abu Roash. Khafra rested in the pyramid now known as the second pyramid of Gizeh. Menkaura's pyramid was called Of the architectural peculiarities of some particular pyramids some notice must now be given. The pyramid of Medum (figs. 1, 2) was the first true pyramid. It was begun as a mastaba, AA, like other such tombs, such as that of King Neter-khet at Beyt Khalaf. This mastaba was then enlarged by heightening it and adding a coating, and this process, repeated seven times, resulted in a high stepped mass of masonry. Such had been made before, at the step pyramid of Saqqara; but for the first time it was now covered with one uniform slope of masonry from base to top, and a pyramid was the result. The chamber is peculiar for being entered by a vertical shaft in the floor. The great pyramid (fig. 3) of Gizeh (Khufu's) is very different in its internal arrangements from any other known. The pyramid covers upwards of 13 acres, and is about 150 ft. higher than St Paul's Cathedral. As compared with St Peter's, Rome, it covers an area which is as 29 to I I, or nearly three times as much, and it is 50 ft. higher. The greater number of passages and chambers, the high finish of parts of the work, and the accuracy of construction all distinguish it. The chamber which is most normal in its situation is the subterranean chamber; but this is quite unfinished, hardly more than begun. The upper chambers, called the " king's " and " queen's," were completely hidden, the ascending passage to them having been closed by plugging blocks, which concealed the point where it branched upwards out of the roof of the long descending passage. Another passage, which in its turn branches from the ascending passage to the queen's chamber, was also completely blocked up. The object of having two highly-finished chambers in the mass may have been to receive the king and his co-regent (of whom there is some historical evidence) and there is very credible testimony to a sarcophagus having existed in the queen's chamber, as well as in the king's chamber. On the details of construction in the great pyramid it is needless to enter here; but it may be stated that the accuracy of work is such that the four sides of the base have only a mean error of six-tenths of an inch in length and 12 seconds in angle from a perfect square.' '14/ A' ¦ z ,/ AA Mastaba. 100 -- - \--_  - ? s -- ? - FIG. 2. - Pyramid of Medum.

the upper," being at the highest level on the hill of Gizeh. The The second pyramid lesser pyramids of Gizeh, near the great and third pyramids, belong entrances (one in the respectively to the families of Khufu and Khafra (Howard Vyse). The pyramid of Aseskaf, called " the cool," is unknown, so also is that of Userkaf of the Vth Dynasty, called the " holiest of buildings." Sahura's pyramid, the north one of Abusir, was named " the rising soul," much as Neferarkara's at Abusir was named " of the soul." Raenuser's pyramid, " the firmest of buildings," is the middle pyramid of Abusir. The pyramid of Menkauhor, called " the most divine building," is somewhere at Saqqara. Assa's pyramid is unidentified; it was " the beautiful." Unas not only built the mastaba Farun, long supposed to be his pyramid, but had a pyramid called " the most beautiful of buildings " at Saqqara, which was opened in 1881 (see Recueil des travaux, by M. Maspero, iii., for those opened at Saqqara). In the VIth Dynasty the " pyramid of souls," built by Ati (Rauserka), is unknown. That of Teta, " the most stable of buildings," was opened at Saqqara in 1881, as well as that of Pepi (Rameri), " the firm and beautiful." The pyramids. of Rameren, " the beautiful rising," and of Neferarkara, " the firm life, " are unknown. Haremsaf's pyramid was opened at Saqqara in 1881. Of the last two kings of the VIth Dynasty we know of no pyramids. In the VIIth or VIIIth Dynasty most probably the brick pyramids of Dahshur were erected. In the XIth Dynasty the pyramid, " the most glorious building," of Mentuhotep II. is at Deir el Bahri, and the mud pyramid of one of the Antef kings is known at Thebes. In the XIIth Dynasty the pyramids, the " lofty and beautiful " of Amenemhat I. and " the bright " of Usertesen II., are known in inscriptions, while the pyramid of Senusert I. is at Lisht, that of Senusert II. is at Illahun, that of Senusert III. at Dahshur (N. brick), and the brick pyramid at Howara is of Amenemhat III., who built the adjoining temple.

of Gizeh, that of Khafra, has two separate side, the other in the pavement) and two From Vyse's Pyramids of Ghizeh.  FIG. 3. - Section of Great Pyramid.

1 With respect to the construction of this and other pyramids, see Howard Vyse; on measurements of the inside of the great pyramid and descriptions, see Piazzi Smyth; and on measurements in general mechanical means, and theories, see Petrie.

chambers (one roofed with slabs, the other all rock-hewn), these chambers, however, do not run into the masonry, the whole bulk of which is solid so far as is known. This pyramid has a part of the original casing on the top; and it is also interesting as having the workmen's barracks still remaining at a short distance on the west side, long chambers capable of housing about 4000 men. The great bulk of the rubbish from the work is laid on the south side, forming a flat terrace level with the base, and covering a steep rock escarpment which existed there. The waste heaps from the great pyramid were similarly tipped out over the cliff on its northern side. Thus the rubbish added to the broad platform which set off the appearance of the pyramids; and it has remained undisturbed in all ages, as there was nothing to be got out of it. The third pyramid, that of Menkaura, was cased around the base with red granite for the sixteen lowest courses. The design of it has been enlarged at one bound from a small pyramid (such as those of the family of Khufu) to one eight times the size, as it is at present, the passages needed therefore to be altered. But there is no sign of gradual steps of enlargement: the change was sudden, from a comparatively small design to a large one. The basalt sarcophagus of this pyramid was ornamented with the panel decoration found on early tombs, unlike the granite sarcophagi of the two previous pyramids, which are plain. Unhappily it was lost at sea in 1838.

An additional interest belongs to the third pyramid (of Menkaura) owing to its chamber being ceiled with a pointed arch (fig. 4). But it is not a true arch, the stones being merely cantilevers opposite to each other, with the underside cut to the above form (see fig. 5).

Farther south are the pyramids of Abusir, described in the work of Colonel Howard Vyse, and since excavated by the Germans. Next come those of Saqqara. The construction of 1 t the step-pyramid or cumulat ive mastaba has been noticed above; its passages are very peculiar and intricate, winding around the principal chamber, which is in the centre, cut in the rock, very high, and with a tombchamber built in the bottom of it, which is closed with a great plug of red granite, a circular stopper fitting into a neck in the chamber roof. A doorway faced with glazed tiles bearing the name of King Neter-khet of the IIIrd Dynasty existed here; the tiles were taken to Berlin by Lepsius. The other pyramids of Saqqara are those of Unas, Pepi, Haremsaf, &c. They are distinguished by the introduction of very long religious texts, covering the whole inside of the chambers and passages; these are carefully carved in small hieroglyphics, painted bright green, in the white limestone. Beyond these come the pyramids of Dahshur, which are in a simple and massive style, much like those of Gizeh. The north pyramid of Dahshur has chambers roofed like the gallery in the great pyramid by successive overlappings of stone, the roof rising to a great height, with no less than eleven projections on each side. The south From Vyse. pyramid of Dahshur has still the greater part FIG. 5. - Section of its casing remaining, and is remarkable for of Sepulchral Chambeing built at two different angles, the lower ber, Third Pyramid. part being at the usual pyramid angle, while the upper part is but 43. This pyramid is also remarkable for having a western passage to the chambers, which was carefully closed up. Beyond the Memphitic group are the scattered pyramids of Lisht (Senusert I.), Illahun (Senusert II.), and Howara (Amenemhat III.), and the earliest pyramid of Medum (Sneferu). Illahun is built with a framework of stone filled up with mud bricks, and Howara is built entirely of mud bricks, though cased with fine stone like the other pyramids.

The dimensions of the pyramids that are accurately known are in inches: The first two closely agree to the proportion of 7 high on II base, approximately the ratio of a radius to its circle. And on dividing the base at Medum by II the modulus is 515.64, and the base of Khufu = I 1 is 824.44. These moduli are 25 cubits of 20.625 and 40 cubits of 20.611; so it appears that the form was of the same type, but with moduli of 25 and 40 cubits respectively.

Beyond these already described there are no true pyramids, but we will briefly notice those later forms derived from the pyramid. At Thebes some small pyramids belong to the kings of the XIth Dynasty; the tomb-chamber is in the rock below. The size is under 50 ft. square. These are not oriented, and have a horizontal entrance, quite unlike the narrow pipe-like passages sloping down into the regular pyramids (see Mariette, in Bib. arch. trans. iv. 193). In Ethiopia, at Gebel Barkal, are other so-called pyramids of a very late date. They nearly all have porches; their simplicity is lost amid very dubious decorations; and they are not oriented. They are all very acute, and have flat tops as if to support some ornament. The sizes are but small, varying from 23 to 88 ft. square at Gebel Barkal and 17 to 63 ft. square at Meroe. The interior is solid throughout, the windows which appear on the sides being useless architectural members (see Hoskin's Ethiopia, 148, &c.). The structures sometimes called pyramids at Biahmu in the Fayum have no possible claim to such a name; they were two great enclosed courts with sloping sides, in the centres of which were two seated statues raised on pedestals high enough to be seen over the walls of the courts. This form would appear like a pyramid with a statue on the top; and a rather similar case in early construction is shown on the sculptures of the old kingdom. Obelisks then were single monuments (not in pairs) and stood in the midst of a great courtyard with sides sloping like a mastaba; such open courtyards on a small scale are found in the mastabas at Gizeh, and are probably copied from the domestic architecture of the time.

On the vexed question of inscriptions on the pyramids it will suffice to say that not one fragment of early inscription is known on the casing of any pyramid, either in situ or broken in pieces. Large quantities of travellers' " graffiti " doubtless existed, and some have been found on the casing of the great pyramid; these probably gave rise to the accounts of inscriptions, which are expressly said to have been in many different languages.

The mechanical means employed by the pyramid-builders have been partly ascertained. The hard stones, granite, diorite and basalt were in all fine work sawn into shape by bronze saws set with jewels (either corundum or diamond), hollows were made (as in sarcophagi) by tubular drilling with tools like our modern diamond rock-drills (which are but reinvented from ancient sources, see Engineering, xxxvii. 282). The details of the questions of transport and management of the large stones remain still to be explained.

See Colonel Howard Vyse, Operations at the Pyramids (1840); Professor C. Piazzi Smyth, Life and Work at the Great Pyramid  (1867); W. M. Flinders Petrie, Pyramids and Temples of Gizeh, (1883).

(W. M. F. P.)