7/29/2019 badawy_jea_63_1977

1/11

THE JOURNAL OFEgyptian

ArchaeologyVOLUME 63

1 9 7 7

PUBLISHED BY

THE EGYPT EXPLORATION SOCIETY3 DOUGHTY MEWS, LONDON WC1N 2PG

Price to non-members 10-00ISSN 0307-5133

7/29/2019 badawy_jea_63_1977

2/11

T HE J O U R N A L O F

Egyptian ArchaeologyV O L U M E 6 3

P U B L I S H E D BYTH E EGYPT EXPLO RATION SOCIETY

3 D O U G H T Y M E W S , L O N D O N , W C i N 2 P G1977

7/29/2019 badawy_jea_63_1977

3/11

CONTENTSPAGE

EDITORIAL FOREWORD iFORGED DECORATION ON PREDYNASTIC POTS . . J . Crowfoot Payne, A . Kacz-

marczyk, and S. J. Fl eming . 5EXCAVATIONS AT THE MEMPHITE TOM B OF HOREMHEB

1976: PRELIMINARY REPORT . . . . . Geoffrey T . Martin . . 13THE SACRED ANIMAL NECROPOLIS, NORTH SAQQARA:1975/6 . . . . . . . . H . S. Smit h and D . G. Jeffreys 20Q ASR IBRIM, 1976 . . . . . . . J. Martin Plumley, W. Y. Adams,

and El izabeth Crowfoot . 29A BIBLIOGRAPHY OF ELISE JENNY BAUMGARTEL . . V. A. Donohue . . . 48THE PERIODIC SYSTEM OF BUILDING A PYRAMID . Alexander Badawy . . . 52THE IDENTIFICATION OF D

r

WjSMVI AND DC

W IN THEDECORATION OF THEIR TOM B AT DEIR EL-GEBRAWI . Naguib Kanawati . . . 59NEFERHOTEP AND H IS FRIENDS . . . . . William A. Ward . . . 63THE CONSTRUCTION OF AN ANCIENT EGYPTIAN WI G

(c. 1400 B.C .) IN THE BRITISH MUSEUM . . . J . Stevens Cox . . . 67A BUILDING OF AMENOPHIS I I I AT KO M EL- (ABD . Barry J. Kemp . . . 71ONCE AGAIN SOME MORE COMMEMORATIVE SCARABS OF

AMENOPHIS I I I . . . . . . . C. Blankenberg-van Delden . 83NEFERTITI'S REGALITY . . . . . . Julia Samson . . . . 88A BESET AMULET FROM THE AMARNA PERIOD . . Kate Bosse-Griffiths . . 98TUT

7/29/2019 badawy_jea_63_1977

4/11

iv C O N T E N T SREVIEWS PAGE

G. JANSSENS, Contribution to the Verbal System in OldEgyptian . . . . . . . . Reviewed by Mordechai Gilula . 1 8 2

T . G . A L L E N , The Book ofthe Dead or Goingforthby Day . R. 0. Faulkner 1 8 2D . LORTON , The Juridical Terminology of International

Relations in Egyptian Texts through Dyn. XVIII D . B. Redford 1 8 3E . EDEL , Die Felsgrdbernekropole der Oubbet el Hawa bei 1 8 3

Assuan. II. Abteilung . . . . . . K. A. Kitchen 1 8 4M. G ORG , Untersuchungen zur hieroglyphischen Wieder-

1 8 4gabe paldstinischer Ortsnamen. . . . . K. A. Kitchen 1 8 5

E . EDEL , Agyptische Arzte und dgyptische Medizin am 1 8 5hethitischen Kbnigshof . . . . . . K. A. Kitchen 1 8 6

M. L. BIERBRIER, The Late New Kingdom in Egypt (c.1300-664 B . C . ) . . . . . . . . Erik Hornung 1 8 6J . CERNY , A Community of Workmen at Thebes in the

Erik HornungRamesside Period . . . . . . M. L. Bierbrier 1 8 7

L . MANNICHE , Ancient Egyptian Musical Instruments . R. D. Anderson 1 8 9H. S. SMITH , A Visit to Ancient Egypt Alan B. Lloyd 1 9 0Other Books Received . . . . . . W . V . Davies 1 9 0

PLATES I - I I IPLATE I VPLATES V - V I I IPLATE I XPLATE XPLATES X I - X I IPLATES X I I I - X I VPLATES X V - X V IPLATES X V I I - X V I I IPLATE X I XPLATES X X - X X IPLATES X X I I - X X I I I APLATE X X I VPLATE X X VPLATE X X V IPLATE X X V I IPLATES X X V I I I - X X I X

LIST OF PLATES{at end)

The Memphite Tomb of HoremhebThe Sacred Animal Necropolis, North Saqqara, 1 9 7 5 - 6Qasr Ibrim, 1976Neferhotep and His FriendsThe Construction of an Ancient Egyptian WigA Building of Ameno phis II I at Kom el - (AbdAgain more Commemorative Scarabs of Amen oph is II IA Beset Amulet from the Amarna PeriodTu^ankhamun's Razor BoxHow Old was Tut cankhamun ?Medical Reinterpretation of Surgical PapyrusThree Acephalous StelaeMeryet-Amun on a Limestone Fragment in CambridgeShabtis of PedamenopePtolemaic Remains from Kalabsha TempleA Letter from the King of the Blemmyes to the King of the NoubadesMuseum Acquisitions

7/29/2019 badawy_jea_63_1977

5/11

(5*)

THE PERIODIC SYSTEM OF BUILDING A PYRAMIDBy ALEXANDER BADAWY

THE building of a pyramid involved special problems, among which are cosmic orientation, avoiding twist and maintaining the angle of incline. We know that buildingproceeded in horizontal courses whose height decreased toward th e top . A study ofthe cross-section shows a series of layers of equal wid th slanting at 75 aroun d acentral core.Some of the constructional problems common to other types of monuments wererende red m ore difficult on account of the natu re of the py ram id. T h e blocks were to beof a constant height th rou gh ou t one course, and of relatively large dimension s. Th e sizeof the pyramid set another problem, if one thinks that about 115,000 blocks averaging0 7 5 m etres in height were required for only the casing of Kh ufu's pyram id. Th e transpo rt of materials from the q uarries was in itself an achievement, even thou gh advantagewas taken of the flood waters that allowed one to sail closer to the quarries in the east,and to the pyram id sites in the west. Un like buildings located in the valley, the p yramids stood on the western desert plateau and the blocks transported on the river orcanal boats had to be hauled up from the water's edge by means of sleds made to slidealong a slippery ramp.Causeways of pyramids were certainly used at the start of the work as constructionalramps. At least two ramps rose to the east and south sides of the pyramid at Meydum,in addition to its causeway, though there could have been, according to Petrie, 1 onemore on the sou th and one or two more on the north, ' thus there were the needed fiveor six lines of approach for the materiaP. Co nstructional ram ps existed at Giza (K hufu,Kha

7/29/2019 badawy_jea_63_1977

6/11

T H E P E R I O D I C S Y S T E M O F B U I L D I N G A P Y R A M I D 53Before dealing with the problem of avoiding twist and maintaining the angle ofincline during the construction of a pyramid it is essential to examine the internalstructure. All pyramids of the Old Kingdom show a series of slanting layers laid out onconcentric squares around a prismatic core. Th ese layers slanted 75, the usual batter

for the faces of mastaba superstructures. The faces of these so-called 'accretion layers'were made of better stone and masonry than their internal core, even to be smoothlydressed as at Neterikhet and at M eydu m. C larke and Engelbach5 tentatively m entionedthat it was 'an aid to the stability of the structure', or was the result of 'intenseconservatism' or of a 'religious motive' . There is no way to investigate the internalstructu re of the three pyramids at Giza, bu t Borchardt dedu ced from the occurrence ofwell-dressed 'girdle-blocks' every ten cubits along the passage driven through existingmaso nry to the G reat G allery of Kh ufu tha t the system of accretion layers was followedthere. Against this theory Clarke and Engelbach6 raised, among other objections, thecloseness of the layers and the consistent superb masonry in successive faces. The firstargument loses much of its impact in view of the fact that Sekhemkhet's pyramidshowed thirteen accretion layers, restored by Lauer as twinned layers, ten cubits thickfor every layer. That the accretion layers were intended to enhance the stability of thepyramid is certainly true since forces within the structure are made to act toward thecore. In addition they formed datum planes from which the process of constructioncould be constantly checked for accuracy. At Meydum, however, an error of 2-6 metresout of the square was detected by Petrie.7

The problem of maintaining accuracy throughout the lengthy process of construction of a pyramid that could rise 220 courses high (Khufu) must have been a majorconcern with the ancient architects. Twist in the pyramid had to be avoided, perhapsthrough checking the diagonals of the square plan with reference to datum points onthe ground that would be projected on to the course.8 Another major concern wouldhave been to maintain the angle of incline. Two solutions were presented by Clarkeand Engelbach: calculating the square at every course and describing it accurately onthe masonry, or measurements by plumbing. The first method was seemingly not usedby the builders (Clarke and Engelbach). As to the second one, the only suggestedpossibility was horizontal measuring to build up the slope 11:14 from a plumb lineoutside the foothold emb ankm ent. It was essential, however, to carry out this m easurement over a considerable height, no less than 5 metres, and not on every courseseparately, to eliminate any cumu lative error. T hi rty shifts wo uld th en h ave sufficedfor the tallest pyramid. Clarke and Engelbach concluded with the assumption thatpits for plumb lines were built in the embankments. Lauer does not lend much attention to the problem, but mentions casually numerous large set squares, which wouldnot have reached higher than two or three courses at a time. Measuring from a plumbline exposed to the wind or even sheltered within a pit would have presented seriousdifficulties and never could have been foolproof.

5 Clarke and Engelbach, op. cit. 121.6 Ibid. 124.7 Medum (London, 1892), 6, 7. 8 Clarke and Engelbach, op. cit. 125, fig. 136.

7/29/2019 badawy_jea_63_1977

7/11

54 A L E X A N D E R B A D A W YSince the Fourth Dynasty, and probably even earlier, a sighting device was used tocontrol the batter of 75-76 0 or 1: 4 in walls. Petrie 9 found in a mastaba at Meydumtha t there w ere vertical corner walls standing at foundation level. A dou ble line markedin red sloped at 75 from the lower corner of each of the two inner faces. Th is in dicated

the trace of the plane of the battered face of the mastaba an d formed a dat um or guideline for sighting and stretching a cord between both ends of the wall under construction. Horizontal lines marked with inverted triangles the levels at cubit intervals, thusproviding at the points of intersection with the guide-line as many points as necessaryfor controlling the accuracy of batter during the progress of construction. This methodof sighting with guide-lines at the corners of enveloping walls was used at all periods,as for controlling the vertical profile of the foundation platform of the shrines at Tellel-Rub fa (Late Period).10Pyramid builders did not forget earlier methods or types of construction, since theyincorporated in the pyramid structure the massif, battered at 75 , characteristic of the

mastaba. It is most probable that they built this massif, at least in the earliest attem pt atM eyd um , with the help of enveloping corner walls. (See fig. 1.) T h e faces of the massifwere then well dressed. The process was repeated for every skin or accretion layer tothe designed height, keeping also control throu gh ou t against twist by checking diagonalsand axes of concentric squares. This process adapted to build the casing would haverequired corner walls inscribed with guide-lines sloping at 11:14 which could haveenabled one to sight along the outer face at each course level, before it would beembedded in the rising embankment. (See fig. 2.) Such corner walls would have beenof brick built on the embankment, tangent to the alignment of the casing or at somedistance, to allow handling the blocks from the front.Controlling the slope of the faces by sighting and measuring from corner wallswould have presented an immense advantage over measuring from a plumb line ina pit built as deep as 17 metres in the embankment, as tentatively suggested by Clarkeand Englebach.11 Moreover the same corner walls would have served again for thedressing of the face, as the embankment would be lowered and a wooden scaffoldingbuilt to the height of the corner walls. 12 An alternative method, less satisfactory thanthat using corner walls, but improving upon the sunken pit system would be to buildsuch a pit from the level of construction up. (See fig. 3.) From the guide-line markedon its walls horizontal measurements but no sighting could be made.The practice of dressing the accretion faces was discontinued after Neterikhet andSnefru, and this allowed the whole pyramid to be built course by course throughout.13T h e system of building in periods u p to th e levels of the accretion faces, if correct, wascertainly brought in conjunction with the corner walls corresponding to these levels.It was observed14 that the casing blocks of Khufu's pyramid show a periodic decreasein height, which was explained as resulting from the use of certain amounts of stonerenewed when exhausted according to a planned supply. It would be of interest to9 Architecture, 8, 29, fig. 10.1 0 D . P. H ansen, ' Th e Excavations at Te ll el Rub'a*, JARCE. 6 (1967), 7.11 Op. cit . 126-8. I 2 Ibid . 125. Ibi d. 121. * Ibid . 128.

7/29/2019 badawy_jea_63_1977

8/11

F I G . I

7/29/2019 badawy_jea_63_1977

9/11

F I G . 2

7/29/2019 badawy_jea_63_1977

10/11

T H E P E R I O D I C S Y S T E M O F B U I L D I N G A P Y R A M I D 57

F I G . 3investigate this periodic decrease in size, for there is strong presumption that it echoesthe system of periodic construction determined by the steps of accretion layers.Since the number of accretion layers seems to have been a determining factor in theperiodic construction of a pyramid, it would have been of importance to keep themas few as possible. This number averages between 5 (Zawyet el-*Aryan), 6 (Neterikhet,Sahure

7/29/2019 badawy_jea_63_1977

11/11

58 A L E X A N D E R B A D A W Yexamination of the section of Meydum pyramid shows that the heights of steps inaccretion layers, and consequently those of corresponding corner walls, were from thebottom: 14-5, 10, 10, 10, 10, 10, 8, 8 metres for a constant width of 5 metres to theaccretion layer. Building corner walls of such heig hts in b rick p resented no difficulty,for 10 me tres seems to have been the average height reached by brick girdle walls fromthe Second Dynasty (Abydos, Hierakonpolis) throughout later periods (fortresses atBuhen, Mi'am).Essentially structural as the purpose was to stabilize the huge mass and to providedatum planes during the process of constructing the accretion layers within the pyramid, the process could also have had, as hinted by Clarke and Engelbach,15 a religiousmotive. Left apparent in the earlier step pyramids (Zawyet el-*Aryan, Neterikhet,earliest Meydum), they formed a gigantic stairway which enabled the Pharaoh tomount up to the Imperishable Stars. In the Pyramid Texts this idea of a stellar destinyfollowing an ascent on a stairway is clearly expressed: 'A staircase to heaven is laid forhim that he may ascend on it to the sky' (no. 365). l6 This concept is found again inthe hieroglyph ^ sometimes described as a dou ble stairway, but mo re prob ablyrepresenting the profile of a step pyramid and determining the verb irr ' to ascend'.17The names of the pyramids of Snefru, Khufu, Dedefret, and Nebre< indicate clearlya stellar connotation while those of Sahure