Khufu's Pyramid

Historical drawings and surveys

 



John Greaves - pub. 1646

South wall of 'Queen's Chamber' (QC) on EW centre axis of pyramid - sarcophagus chamber more or less correctly placed to the south of centre axis:

 

  

 


Greaves description of the 'well-shaft,' shown in his drawing at the lower end of the 'Grand Gallery':

"At the end of it, on the right hand, is the well mentioned by Pliny; the which is circular, and not square, as the Arabian writers describe:  the diameter of it exceeds three feet;  the sides are lined with white marble, and the descent into it is by fastening the hands and feet in little open spaces cut in the sides within, opposite and answerable to one another, in a perpendicular.  (This well is described in Plate 2. Fig. 1.)..........but I return from the cisterns and wells there, to this in the Pyramid; which, in Pliny's calculation, is eighty-six cubits in depth; and it may be, was the passage to those secret vaults mentioned but not described by Herodotus, that were hewn out of the rock, over which this Pyramid is erected.  By my measure founding it with a line, it contains twenty feet in depth.  The reason of the difference between Pliny's observation and mine, I suppose to be this; that since his time it hath almost been dammed up, and choaked with rubbish; which I plainly discovered at the bottom, by throwing down some combustible matter set on fire."  (Greaves 1646: 118 - 119)  link




Pliny:  "In the interior of the largest pyramid there is a well, eighty-six cubits deep, which communicates with the river, it is thought."  (Pliny the Elder, 'The Natural History' Book 36, Chap. 17)  link

If Pliny's 86 cubit deep well refers to the well shaft connecting the lower end of the Grand Gallery with the descending passage, then the upper chambers and passages were accessible before the first known access c. 820 AD by Caliph Abdullah Al Mamun.

Greaves description of the 'well' as circular with a diameter of over 3 ft (~92 cm) is not an accurate description of the well shaft, as it has a square section with ~71 cm sides.  How he could mistake a square shaft for a circular one is a mystery.


J.S. Perring's description:  "The Well does not seem to have been a part of the original design, as the mouth of it was not regularly built in the masonry, but forced through after that part of the building had been completed.  This forced and broken appearance has induced people to believe that the natural rock rises nearly to the mouth of it.  The Grotto is in a bed of gravel which occurs in the rock, and the sides of the Well have in this place been lined with masonry to keep out the gravel, which some curious inquirer has excavated, and thus formed the Grotto, having previously removed part of the masonry in search of a passage supposed to be concealed by it.  The rock rises in the shaft to the height of 22 feet above the base, and it may be here observed, shews itself on the outside of the Pyramid, at the north-eastern corner 13 feet 4 inches above the base.  Mr. Davison, in 1764, had explored the well down to the point M, below which it was filled with rubbish, which was fully cleared out by Mr. Caviglia, in 1817."  (J.S. Perring 1839 (Part I) : 2)


Well shaft (J.S. Perring 1839 (Part I) Pl. II)



Frederik Norden - 1737

Both the sarcophagus chamber and QC are shown on the EW centre axis:




Detail:





Bonaparte's surveyors -  end of 18th century

The QC even further north from the pyramid's EW centre axis - sarcophagus chamber on EW centre line of pyramid:

 

 

 
'The Monuments of Egypt' The Napoleonic Edition, Vol V, Pl 14 

Coutelle explored the 'well' some distance beyond the 'grotto', but found it blocked with dirt and pebbles that appeared to have originated in the 'grotto'.  After clearing the shaft for a further 16 - 17 m, progressing to a level he wrongly believed was over 16m below the level of the Nile, military operations forced him to suspend the work.  According to Coutelle, the 'well' is ~65m deep, and the N/S cross sectional drawing through the pyramid shows the 'well' almost vertical but slightly veering to the south.

Maragioglio & Rinaldi's 1965 drawing is more accurate:



 

 

J.S. Perring - survey 1837 - 38

EW centre line of 'QC' directly beneath the edge of the 'great step', but ~3.35 m (~6.4 cubits) north of pyramid's EW centre axis:


 
The Pyramids of Gizeh, from actual survey and Admeasurement, by J.S. Perring, Esq. Civil Engineer.  Illustrated by Notes and References to the several plans, with sketches taken on the spot, by E.J. Andrews, Esq.  Part I, The Great Pyramid.  London: James Fraser,  M.DCCC.XXXIX.  Fig 1

 

Perring's drawing showing EW centre axis of pyramid ~5 m (~9.6 cubits) from north wall of sarcophagus chamber:

 


 




'Egypt's Place in Universal History' Vol. 2, C.C.J. Bunsen 1854 (based on Perring's drawing):



 

 

C. Piazzi Smyth - survey, January to April, 1865 - published results in his 'Life and Work at the Great Pyramid' in 1867.

His 'Vertical Meridian section of Great Pyramid' in Vol I, page 18, Pl. II, shows QC more or less directly beneath the 'great step', but north of EW centre axis of pyramid.

Smyth's survey compared to Petrie's - EW centre line of pyramid about 47 cm south of EW centre line of QC in Smyth's drawing: 

 

 

 

 

Smyth's engraving for the Royal Observatory Edinburgh, published between 1850 - 1880? (source), shows EW centre axis of pyramid aligned with south wall of 'Grand Gallery', and south wall of QC:

 

 

 

 

 

A more detailed drawing by Smyth.  South wall of QC, and south wall of 'Grand Gallery' are aligned with 'vertical axis' of pyramid:


   
'Our Inheritance in the Great Pyramid'  C. Piazzi Smyth 1874, Pl VII

 

 

Another drawing from the same book however, has QC and south wall of Grand Gallery centred on pyramid's EW centre line - subterranean chamber centered on pyramid's EW centre axis (his earlier drawing has it correctly shown to the south):


'Our Inheritance in the Great Pyramid'  C. Piazzi Smyth 1874

 

 

 

 W.M.F. Petrie - pub.  1883

QC and the edge of 'Great Step' centered on EW centre axis of pyramid:


'The Pyramids and Temples of Gizeh' W.M. Flinders Petrie 1883 Pl 9

 

 

"In the Queen's Chamber, it seems from the forgoing statement, that the ridge of the roof is exactly in the mid-place of the Pyramid, equidistant from the N. and S. sides;  it only varies from this plane by a less amount than the probable error of the determination."  (Petrie 1883: 66)


"At the upper end of the gallery, we have already stated the S. wall to be 61.7 ± .8 of the Pyramid centre; and hence the face of the great step at the head of the gallery (which descends behind both floor and ramps) is (61.7 – 61.3) = .4 ± .8 S. of the Pyramid centre. It may, therefore, be taken as intended that the face of this step, and the transition from sloping to horizontal surfaces, signalizes the transit from the Northern to the Southern half of the Pyramid. This same midplane of the Pyramid being also signalized by the midplane of the Queen's Chamber, which is measured as .3 ± .8 N. of the Pyramid centre."  (Petrie 1883: 74)

 

Assuming the sarcophagus was positioned so that it aligned with the NS centre line of the pyramid, and the EW centre line of the sarcophagus chamber, it was ~21 cubits (3 x 7) south of the EW centre line of the pyramid, and ~14 cubits (2 x 7) west of the centre line of the passage system.

 

 

 

A late 19th century Freemasonry publication also has QC centered on EW centre axis:


'Origin and Antiquity of Freemasonry, and its analogy to the eschatology of the Ancient Egyptians, as witnessed by the 'Book of the Dead', and by the Great Pyramid of Gizeh, the first Masonic Temple in the world'          A. Churchward 1898: 65

 



Maragioglio & Rinaldi Part IV 1965: Fig. 1 section S-M

The east / west centre line of the QC and the edge of the 'great step' are both on the east / west centre line of the pyramid:

 

 

  

Gantenbrink - survey 1992 - 3

 Important basic points within the passage / chamber system surveyed - his survey agrees with Petrie's, that has the QC and edge of the 'great step' aligned with pyramid's EW centre axis:


link

 

 

 

 Probable reason for discrepancy between Smyth's and Petrie's surveys:

 In April 1865, using a 500" (12.7 m) cord, Smyth attempted to measure the length of the sides of the pyramid, but was only able to measure the extent of the core-masonry  - each side was between 8900 - 9000 inches (226 - 228.6 m) long (Petrie:  9001.5" (228.638 m)).  At the end of April, a Mr Inglis,  cleared the corner 'sockets', and measured the length of the sides between the outer corners of the  'sockets':

Inglis (1865):

N = 9120" (231.648 m)

S = 9144" (232.258 m)

E = 9102" (231.191 m)

W = 9102" (231.191 m)

mean = 9110" (231.394 m)

 

Petrie (1870):

N = 9069.4" (230.363 m)

S = 9069.5" (230.365 m)

E = 9067.7" (230.320 m)

W = 9068.6" (230.342 m)

 mean = 9068.8" (230.347 m)

 

Inglis's mean length for the sides is 1.046 m longer than Petrie's, which explains why Smyth's QC, and 'great step' are ~50 cm north of EW centre axis of pyramid, whereas Petrie has them aligned with the centre axis.


note:  later, Smyth used a figure of 9140" (232.156 m).  He divided this figure by the number of days in a year:  9140 / 365.242 = 25.025" (0.636 m), which he calculated to be "the ten-millionth of the length of the earth's semi-axis of rotation...."  - in other words, a ten millionth part of the earth's polar radius:  6356800 m / 10,000,000 = 0.636 m. 

Smyth believed this to be a superior method of deriving a basic unit of linear measure related to the size of the earth, as its based on a straight line.  The metre 0n the other hand, was originally calculated to be a ten millionth part of the surface distance from the north pole to the equator - a problematic curve (the earth is not a perfect sphere), rather than a simple straight line.  Smyth quotes Sir John Hershel to support his idea:

 "So long as the human mind continues to be human, and retains a power of geometry, so long will the diameter be thought of more primary importance than the circumferance of a circle."

Both the metre and Smyth's 'Sacred Cubit' are based on a ten millionth part of an earth related distance.

 

 

Average length of side, and angle of incline from early surveys:

1638  Greaves, ~211.226 m (north side), height, 152.095 m; 55.224 degs

1801  Le Pere / Coutelle,  232.747 m;  51.317 degs

1801  Jomard, 230.902 m

1837-38  Perring, 232.867 m

1865  Inglis, 231.394 m  (Smyth 1874: 32)

1869  Royal Engineer surveyors, 231.902 m  (Smyth 1874: 32)

1880  Petrie, 230.347 m;  51.844 degs

1925  Cole, 230.364 m

 

 

The mean length of the sides according to Perring's 1837 - 38 survey, is 764 ft (9168" / 232.867 m), 2.520 m longer than Petrie's figure - this partly explains why his QC and 'great step' are ~3.350 m north of EW centre axis.

 

In 1925, J.H. Cole set out "to determine as accurately as possible the exact size, shape, and orientation of the original base of the Pyramid on the pavement."  The base of the pyramid was first cleared to the extent that it exposed the line of the bottom edge of the casing blocks that was extended to the corners.  On the north side for example, the original line of the bottom edge was found over a distance of 55 m - for 20 m, the casing blocks were still in position.  The remaining casing blocks on the north side had an angle of incline of ~51.9 degs.

Cole (1925):

N = 230.253 m

S = 230.454 m

E = 230.391 m

W = 230.357 m

mean = 230.364 m

mean height above sea level for bottom edge of casing stones on pavement: ∼60 m

60.416 m  (Giza Mapping Project:  59.63 m)

 

Cole's survey confirms the accuracy of Petrie's survey.

Cole's mean length of 230.364 m, differs from Petrie's 230.347 m, by only 17 mm.


Deviation from cardinality of the four sides of Khufu's pyramid (Nell and Ruggles 2006)

N - S direction: -0˚ 04.0'

E - W direction: -0˚ 02.4'

N side: -0˚03.6'

E side: -0˚03.4'

S side: -0˚00.5'

W side: -0˚03.7'

 

note:  

Cubit derived from the length of Khufu's sarcophagus chamber:  o,524 m (Petrie 1883: 178)

Cubit derived from the average side length of Khufu's pyramid:

Cole, 230.364 m / 440 = 0.52355 m

Petrie, 230.347 m / 440 = 0.52352 m

Cubit used in the design of Khufu's pyramid:   ~o.5237 m (20.62").

New Kingdom cubit rod of Amenhetep I (1525 - 1504) - 0.5235 m long, with 28 main divisions.  15 of these divisions are subdivided into 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, and 16 parts (measurements down to ~1 mm were possible)


 

 

Chris Tedder,  Autumn 2008