Update: 29th August 2008, 13:00 UT

The Keys of Atlantis

A Study of Ancient Unified Numerical and Metrological Systems

by Peter Wakefield Sault

Copyright © Peter Wakefield Sault 1973-2008
All rights reserved worldwide


The Keys of Atlantis

Appendix C.

Principal Data of The Pyramids of Giza

Sections

1. Recent Developments
2. Names and Places
3. Prof. Sir William M. Flinders Petrie
4. J.H.Cole BA FRGS

Illustrations

1. Satellite Image of Giza
2. Satellite Image of Kheops
3. Satellite Image of Khephren
4. Satellite Image of Mykerinos
5. Map of the Pyramids (1953)
6. Map of the Pyramids (2006)

Tables

1. Names of the Pyramids
2. Petrie's Measurements of the Pyramids
3. Petrie's Measurements of the Centres
4. Cole's Measurements of Kheops
5. Cole's Means for Kheops
6. Cole's Comparisons to Petrie's Dimensions of Kheops
7. Cole's Comparisons to Petrie's Azimuths of Kheops


The Keys of Atlantis [C]

C-1. Recent Developments

4th January 2006

GOOGLE EARTH has just come online. With this tool it is possible to view satellite imagery of every place on Earth and, moreover, to obtain precise geographical coordinates of landmarks.

The images below were obtained from above a position somewhere northwest of Giza therefore in locating the place markers it has been necessary to correct for parallax and the markers have accordingly been placed at the intersections of the diagonals of the bases rather than at the apparent positions of the apices. In each of the images of single pyramids, the coordinates of the respective place marker is shown in the status bar beneath.


Figure C-1. Satellite Image of The Pyramids of Giza


Figure C-2. Satellite Image of Kheops


Figure C-3. Satellite Image of Khephren


Figure C-4. Satellite Image of Mykerinos


The Keys of Atlantis [C]

C-2. Names and Places

The Greek names, and modern revised spellings thereof, used throughout this work are those by which the three larger Giza Pyramids are commonly known to English speakers. Kheops is also known as the Great Pyramid.

Number Greek Egyptian
#1 Kheops Khufu
#2 Khephren Khafre
#3 Mykerinos Menkaure
Table C-1. Names of the Pyramids

There have been major obstacles to establishing the precise dimensions of the Giza Pyramids. Firstly that they were at one time severely vandalised — the white marble casings of Kheops stripped and the capstone lost and secondly that the bases were buried deep in sand and rubble. Nonetheless there have been at least two reputable surveys the results of which are given below.


Figure C-5. Map of The Pyramids of Giza (1953)

The grid lines shown in Figure C-5 are derived from the geographical coordinates, 29º58'51.06"N × 31º09'00"E, of the apex of Kheops given in 'The Authorship and Message of the Great Pyramid' by Julian T. Gray (1953). Contrast this with the map shown below in Figure C-6, which is based upon the Global Positioning System (GPS) coordinates returned by Google Earth. The earlier map (Figure C-5) has been retained to show the difference in precision that satellite observation makes.


Figure C-6. Map of The Pyramids of Giza (2006)


The Keys of Atlantis [C]

C-3. Prof. Sir William M. Flinders Petrie

W.M.F.Petrie commenced his survey in 1880, remaining at Giza until 1882.1 Dimensions in British Imperial Standard Long Inch.2

Pyramid Side Length
(Inches)
Difference
from Mean
Azimuth3 Difference
from Mean
Angle
             
Kheops N 9,069.4 +0.6 –0º03'20" +0º00'23" 51º50'40"
  E 9,067.7 –1.1 –0º03'57" –0º00'14"  
  S 9,069.5 +0.7 –0º03'41" +0º00'02" 51º57'30"
  W 9,068.6 –0.2 –0º03'54" –0º00'11"  
  Mean 9,068.8 0.65 –0º03'43" 0º00'12" 51º54'05"
             
Khephren N 8,471.9 –3.0 –0º05'31" –0º00'05"  
  E 8,475.2 +0.3 –0º06'13" –0º00'47"  
  S 8,476.9 +2.0 –0º05'40" –0º00'14"  
  W 8,475.5 +0.6 –0º04'21" +0º01'05"  
  Mean 8,474.9 1.5 –0º05'26" 0º00'33"  
             
Mykerinos N 4,153.5 –0.1 +0º16'48" +0º02'45"  
  E 4,149.2 –4.4 +0º12'23" –0º01'40"  
  S 4,157.8 +4.2 –0º12'57" –0º01'06"  
  W 4,153.9 +0.3      
  Mean 4,153.6 3.0 +0º14'03" 0º01'50"  
Table C-2. Petrie's Measurements of the Pyramids

Of the angle and elevation of Kheops, Petrie says “On the whole, we probably cannot do better than take 51º52' ± 2' as the nearest approximation to the mean angle of the Pyramid, allowing some weight to the South side. The mean base being 9,068.8 ± 0.5 inches, this yields a height of 5,776.0 ± 7.0 inches.”

Regarding the angle and elevation of Khephren — “53º10' ± 4' will be the best statement. Hence the height will be 5,664 ± 13 inches.”

There is more uncertainty about Mykerinos — “Considering the various sources of error: that the dressed granite in situ is very irregular; that the 1st course joint at S.S.W. may easily be estimated too far out; and that we have no guarantee in the moved granite blocks, or the limestone from the upper part, that the courses were horizontal (on the contrary, one granite block has two different joint surfaces, 1º40' different); the best conclusion seems to be 51º0' ± 10'. But from a consideration of the granite courses (see below), the angle would be 51º10'30" ± 1'20"; and this might well be adopted, as being close to the very uncertain result from the measured angles. Hence the height of the Pyramid would have been 2,564 ± 15; or 2,580.8 ± 2.0 by the granite courses.”

Petrie measured the distances of the centres of the Pyramids along parallels inclined at 5' W of true N. Dimensions in British inches.

Centres North East Direct Angle
Kheops-Khephren 13,931.6 13,165.8 19,168.4 43º22'52"
Kheops-Mykerinos 29,102.0 22,616.0 36,857.7 37º51'06"
Khephren-Mykerinos 15,170.4 9,450.2 17,873.2 34º10'11"
Table C-3. Petrie's Measurements of the Centres

1. The Pyramids and Temples of Gizeh (London, 1883).
2. British Imperial inch = 25.399978mm. Note: US inch = 25.400508001 mm.
3. azimuth n. The horizontal angle of the observer's bearing in surveying, measured clockwise from a referent direction, as from the north, or from a referent celestial body, usually Polaris. In trigonometrical surveying, it is customary to reckon the azimuth of a line from the south point of the horizon around by the west from 0º to 360º. Petrie says — “Azimuths, wherever stated, are written + or –, referring to positive or negative rotation, i.e., to E. or to W., from the North point as zero. Thus, azimuth –5', which often occurs, means 5' west of north. Where the deviation of a line running east and west is stated to be only a few minutes + or –, it, of course, refers to its normal or perpendicular, as being that amount from true north.”


The Keys of Atlantis [C]

C-4. J.H.Cole BA FRGS

For Kheops we have also the measurements of J.H.Cole.4 Dimensions in metres.

Side Length True Azimuth
North 230.253 89º57'32"
South 230.454 89º58'03"
East 230.391 359º54'30"
West 230.357 359º57'30"
NE-SW 325.699 44º56'45"
NW-SE 325.868 314º57'03"
Table C-4. Cole's Measurements of Kheops

From these measurements, Cole derived the following means:—

Central Axis Length Azimuth
North-South 230.374 359º56'00"
East-West 230.354 89º57'48"
General Mean 230.364 0º03'06"
Table C-5. Cole's Means for Kheops

Cole also provided comparisons to the results of W.M.F.Petrie. Dimensions in British inches.

Side Length
Petrie
1880
New
Determination
1925
Difference
North 9069.4 9065.1 –4.3
South 9069.5 9073.0 +3.5
East 9067.7 9070.5 +2.8
West 9068.6 9069.2 +0.6
Mean 9068.8 9069.4 +0.6
Table C-6. Cole's Comparisons to Petrie's Dimensions of Kheops


Side Azimuth
Petrie
Azimuth
Cole
Difference
North –3'20" –2'28" +0'52"
East –3'41" –1'57" +1'44"
South –3'57" –5'30" –1'33"
West –3'54" –2'30" +1'24"
Mean –3'43" –3'06" +0'37"
Table C-7. Cole's Comparisons to Petrie's Azimuths of Kheops

4. Determination of the Exact Size and Orientation of the Great Pyramid of Giza (Cairo, 1925).


The Keys of Atlantis

Copyright © Peter Wakefield Sault 1973-2008
All rights reserved worldwide