CAT2025CheopsPetrie
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Nov2025: CAT2025ChepsPetrie ¦ CAT2025Cheops ¦ Motif
¦ Sources ¦ History
¦ GoogleTextExamples
¦ BirdsallRef ¦ GoogleTextFlaws ¦ BirdsallPetrie
CAPACITIVE TRANSMISSION CheopsPetrie — CAT2025C
QueenMid ¦ Petrie
breaks the Enigmatic ice — TCA ¦ PetrieEntranceEquation ¦ Petrie19thCourse
¦
TheBreakTHROUGH
— Ai machine confirmation in AIV08
31Oct2025 ¦
• HOW PETRIE RETRIEVED THE FINAL PYRAMID BASE LENGTH
9068.80”
• Ronald Birdsall Petrie
Corrections
Jump directly to
the CheopsPetrie
only up to end of CHAPTER 7 section 64,
p.95, The Cheops Pyramid details
THE PYRAMIDS AND TEMPLES OF GIZEH, Flinders Petrie 1883
Full Text And
Numbers Searchable Flinders Petrie Cheops Pyramid Book (1881-83).
THE
PETRIE ORIGINAL TEXT DOCUMENT IN THIS DOMAIN UNIVERSE HISTORY MUST IN NO WAY —
OR BY NO NATURE WHAT SO EVER — BE USED FOR COMMERCIAL PURPOSES. IT IS ONLY FOR
SCIENTIFIC SHARING ALONE.
As recommended by Google in its foreword to its Petrie PDF
book scan copy
PetrieCH6 — BelowPave ¦ PetrieCh7
All
Petrie chapters with sections are here @Internet linked to on the form
..
CAT2025CheopsPetrie.htm.#C0s00
with
C0 from C0 (intro) to C7 and s00 from s01 to s64.
—
Calling these leads directly to this here presented version of Petrie’s
original book text.
PETRIE
TABLES:
• Where so has been appropriate:
—
Petrie Tables are often highly tight and typographically dense, often with
multiple headline text separated by inline column text, also vertical text.
—
Making these more accessible by direct text search, it has (sometimes) been
convenient to name the columns alphabetically, giving each column a separate
letter line below the Petrie table. That allows more access to the whole column
headline (also vertical parts) on a single line of text.
• We do not repeat this notification for
every occasion, but let it be known here.
Occasionally, we have image copied the
Petrie table, parallel to this Petrie book text copy for thorough inspection,
in certain cases.
Motif: CAT2025Cheops
While the
GoogleTextCopy of the Petrie book
THE PYRAMIDS AND
TEMPLES OF GIZEH, 1883
is a veritable
disaster in erasing the actual Petrie collected numerical figures,
but fairly, and
mostly, preserves the textual correctness, however with relatively few errors,
the
Petrie1883FullText.html copy is a havoc. Misspelt words in heaps, with
»a GoogleTextCopy Enhanced additional
flora» of character species, apparently partly hieroglyphic,
apparently also in a mutual battle of vandalizing the most of Petrie’s thorough
and high precision (1/1200 ”) instrumentally measured
Cheops Pyramid values. If that is Modern HiTech
OCR (illustrated), the conditions were certainly better year 1311.
— We had to do
something about that pretty much shredded excellent Petrie work. Especially as
an Ai machine recently has suggested in advertising a ”breakthrough”
in The Cheops Pyramid Story and history. So .. a safe, open, public and totally
free, no profit ideas, just for scientific sharing, searchable Petrie text copy
must be available for scrutinized inspection and comparison on the actual
Petrie measured values. It is all about high precision construction math.
Apparently at present Nov2025 beyond the direct scope of Google.
The already existent excellent Ronald
Birdsall Petrie web page, its precise Petrie given chapters
and sections (and corrections) and Petrie Plate illustrations, will certainly
be an excellent fully certified complement to this full text Petrie book
searchable production: both text and numbers in full — however for starters
only in concern of the Cheops Pyramid chapters, the Petrie book from its
beginning CheopsPetrie up to page 95.
Sources: Motif
It is recommended
that the interested (critical) reader has the full Goggle Stanford Library PDF
scanned picture copy (or other original) of the 1883 Petrie book in a parallel
view to this production for exact comparison. The Petrie page PDF-copy page
number is 24 higher than the actual Petrie book number (PetriePage 50 = PDF
page 74, the Stanford copy).
SOURCES
AND REFERENCES:
Our Petrie book PDF scanned
picture copy (Nov2025)
INTERNET
ARCHIVE
The
GOOGLE copy: from STANFORD UNIVERSITY LIBRARY (1969), base to this production
https://archive.org/details/the-pyramids-and-temples-of-egypt
The
most prominent; the PDF copy, and its (as noted above bad) FULL TEXT
Pressing
Ctrl+F on the GoogleCopy — takes about 5 minutes (W11 Samsung Computer) to
complete a text searchable version
(which
then can be copied to a text editor: Alt+ A marks the entire whole, Ctrl + C
copies it, and Ctrl + V pastes it into whatever appropriate).
Additional PDF source version
INTERNET
ARCHIVE
Petrie
PDF source scanned copy from CORNELL UNIVERSITY LIBRARY
https://archive.org/details/cu31924012038927
• It has a direct searchable text function —
but only
by text, no numbers.
In
this production, the entire Petrie text (from the book’s beginning to end of
Chapter 7, p95),
with all the numeric trimmings, is searchable in every detail, in to the last
Petrie prick. No offense.
BIRDSALL’S
PETRIE WEB SITE IS RECOMMENDED
Note that also the Petrie
printed book version has some ERRATA (»unfortunate errors»), having also been scrutinized by the Birdsall
Petrie website on different locations — with specified references. As comparing
calculations on the Petrie measures have been made, it is recommended that the
Reader strictly holds on to the Birdsall commented corrections — which also
will be marked in this production for proper communication — on establishing a
the most reliable information (»Natural
Project Development» .. provided zero flaws).
BE
CAREFUL IN CONSULTING PETRIE BOOK ELECTRONICALLY SCANNED TEXT COPIES
MEANING:
there are several Petrie book Copies @Internet, with following PDF copies —
perhaps not referring the Birdsall corrections (so a certain care must be taken
in comparing whatever the text says ..).
—
However, we have no idea here what these other Petrie scanned text versions tell
or not tell.
History: Sources
How this copy of the Petrie book
on Cheops Pyramid was produced;
An
Oct2025 Cooperation inquiry with an Ai machine in The BreakTHROUGH explains all the
details why this document (now finally) has been launched (quoteClickConnects):
We
have spent the years 2017-2024 in reckoning through all the foremost Petrie
measure data in the light of this confirmed (simple,
for starters) Breakthrough math — so we need
precise referring Petrie data, all of them exacted to the last prick, for a check on the
conforming results:
—
As observed (Nov2025): any as present DIRECT GoogleTextCopy of the Petrie book
would destroy such an inquiry most effectively.
People
in general do have a certain (A27.1)
right to share any significance in scientific progress, and as far as such can
be shown to hold. So .. we decided to give it a shot — along with the already
excellent Petrie documentation in the Ronald Birdsall
(partly much more sophisticated) Petrie
text linkings — especially on the Cheops Pyramid subject.
How it came along: Nov2025
• A free PDF edition of Petrie’s 142 year old
book is available @Internet;
• The Petrie book exists as a digital copy
with a GOOGLE foreword;
• the Petrie book can be used freely for
non-commercial purposes as its copyright has expired;
• Google can transfer (OCR) the scanned book
pages to (ASCII, UNICODE) characters, and so we can receive the book text as a
Google PDF-OCR scan supported copy — as if directly written on a computer.
• However:
—
The
Google OCR scan has deep issues — »battling» (as illustrated) the Content
of Petrie’s book:
GoogleTextExamples:
History
Some
featuring examples in Swedish:
Alla
felställen i den följande textkopian från Petries bok som GoogleCopyText visar
— felaktiga eller utelämnade tecken — har markerats
med färg typ . .
COLOR:
R G B : 230 230 255 ¦ HEX: E6 E6 FF = DEC 151324415 — »fairly weak» not
to destroy the over all text impression.
(mot Googles ” ’ ”) — och det är många ställen
det: Bokens typografi använder · för decimalkomma (vårt normala Engelska . )
samt ett teckensnitt av typen ( Constantia ) 
; mera av regel än undantag visar GoogleCopy talvärden där 6-9
ingår — med det sanna värdet roterat (!) 180°:
Googles
textkopia presenterar det på typformen 
:
Google
läser 119.69 som 69.611 (samt inte
sällan 1 som I och 0 som O eller O| [eller o]), även tillsammans med andra
siffror .. ± ofta som + .. eller inte alls .. Petries decimalkomma tolkas av
Googles textkopia som tecknet för bågminut ’ , vilket sker på en uppsjö av
ställen (»tusental») i Googles textkopia. Alla sådana ställen är här justerade
till Petries original med färgmarkeringar som ovan, med Petries korrekt angivna
värden och uttryck.
Boktexten
gör även skillnad mellan avstavningstecken -, minustecken – och tankestreck —,
som Google omformar till enbart - ( - ) [även sektionssluten :— som Google
omformar konsekvent till :- . Alla dessa (om inte färgmarkerade) har ersatts
utan särskild markering. Dessa GoogleGrepp skulle göra originalets
textläsning svåröverskådlig och inte alls enligt boktryckets intentioner. Nu
har vi rymt ifrån det fängelset (eller rättare, befriat Planeten från Det).
Tack så mycket.
Boken
använder också förkortade bråkvärden typ
(font: MS Reference 2) — som Google kopian helt och hållet
struntar i. Dessa ställen är speciellt lätta att hitta i Petrie’s boktext, också
dessa har här justerats och markerats med färg på den mera sökbara enkla formen
Täljare/Nämnare typ 1/1200. Så
blir, om vi inte har missat något, hela Petries textkopia perfekt sökbar (med viss
reservation för några få av Petries tabeller med dennes vertikalt inlagda
förklaringstexter: vi har angivit dessa i separata partier, typexempel se VertTEXTex).
—
Samma markeringsfärg som ovan har också använts i omskrivningen av
Petrietabellernas REPETERANDE ”-tecken: kolumnrader i referens till samma
kolumnrubrik, på rader under, skrivs i Petrietabellerna ofta med ”-tecken under
kolumnrubriken. Med samma färgmarkering som ovan har dessa avsnitt fyllts ut
med hela kolumntexten färgmarkerad, där utrymmen så medgetts.
(Petrietabeller med vertikaltext: texten har här
angivits separat i anslutning till aktuell tabell, så att samtlig Petries text
kan sökas på).
(Kolumnrubriker
i Petrietabeller med särskilt utrymmeskrävande kolumntext, i Petrietabellerna
ofta med ett rubrikord per rad, har omformats med typen A B C .. med
specificering av A B C kolumnernas Petrietext under tabellen).
—
Det kan tyckas oförskämt. Men på det hela taget blir (Nov2025) Googles
textkopia av Petries bokoriginal ett patetiskt uppvisat skämt. Hela
bokoriginalets spjutspets — de noggranna, ytterst avancerat instrumentellt
uppmätta mätvärdena från hela Petriegruppens mätningar på Cheopspyramiden
1881-83 — fungerar i GoogleKopian som vägdammet efter en långtradare. Med andra
ord, inte alls. Rena dammet. Helt meningslöst. Fullständigt oanvändbart.
—
Vi försöker fullständiga arbetet löpande med att komplettera på ev. missade
förekomster.
— Särskilt framträdande stycken i Petries
boktext har markerats med särskild (ljus) bakgrundsfärg: QueenMid ¦ The19thCourse ¦ PetrieEnigmaBreak ¦ BasaltPavement ¦ PetrieAdmiresStonePrecision ¦ PyramidSockets ¦
PyramidBaseOrigin ¦ SecondPyramidParallel
¦ CasingSearch ¦ TheMysteriousGraniteEntranceStone ¦ PetrieExplainsTheMeasuringWork ¦
BirdsallRef: GTEx
Exempel
på en seriöst genuint framhävd kopia av Petries boktext ges (också) av Ronald
Birdsall. @Internet; https://ronaldbirdsall.com/gizeh/petrie/
Hans webbsida visar Petries hela textverk i noggrant uppställda tabeller
med Petries alla talvärden: Birdsall markerar också olika smärre observerade
tryckfel i Petries boktext (med ljusrosa).
Dessa ställen kommer också att redovisas här (med särskild
färg och länkar [som
förhoppningsvis ska koppla genuint @Internet direkt till Birdsalls ställen] så att vi vet säkert att vi kommunicerar på
samma frekvens och våglängd .. smärtfritt)
i den följande textkopian av Petries bokoriginal (CheopsPetrie).
GoogleTextFlaws: BR
FROM GOOGLE:s EXTRACTED TEXT:
304 pages in some 5 minutes (Samsung W1, Nov2025)
Attempting
to SEARCH IN TEXT from the Google scanned Petrie copy will take some time ..
before ready ..
• A Petrie book copy of The GoogleTextScan
presents (estimated) 10-50 character errors on each Petrie data specified page
• So .. as a genuine Petrie Data Reference
Digital Copy of the Stanford University Library book TEXT, the Google OCR
scanned text version as a stand alone artifact is completely useless.
So the reader must be
»Google-warned» ..:
In
the Petrie original text, all the original book printed quotient types
(font: MS Reference 2)
have,
in this production, been replaced by a searchable normal type fraction form
N/D, type
1/1200
and all the occurring other quotient types.
From Google’s foreword:
”
This is a reproduction of a library book .. to preserve the information in
books and make it universally accessible”.
— Yes. A great
initiative — when the Instrument for Scanning An Original becomes Well
Developed.
— At present: it
is not. (The
conditions were better year 1311, illustrated).
It is a
disaster. A havoc report. And this is it.
(We
have the original GoogleTEXTcopy, safely locked in, in a safe box, so it won’t
get out, preserved for proof, if anybody stresses a questioning ..).
(..
you know .. ”enhanced experience” ..
and stuff like that .. Google 2015+ .. ).
(..
Google and Microsoft does not cooperate with individual humans ..).
(..
Neither did Mississippi 1850 ..). (.. rounded corners .. 700 million users ..
Windows 11 .. 2024 .. must not change .. no squares any more .. no
free will ..).
BirdsallPetrie: GTF
We also
recommend the fine Ronald Birdsall Petrie compilation (as
a second index to answers) on the Petrie book and its collected data (in [much]
more sophisticated order than here). Birdsall gives special notes to the Petrie
edition. The Birdsall Web site gives remarks on missed numbers, and others,
which remarks certainly will be added here [in color with links] for most
complete overview.
The Birdsall web page was from the
beginning here in UH the only one precision informing source consulted on the
Cheops Pyramid — in explicit from 1Nov2017.
Editor11Nov2025
¦19Nov2025
CAT2025ChepsPetrie ¦ Nov2025
¦ CAT2025Cheops ¦ Motif
¦ Sources ¦ History
¦ GoogleTextExamples
¦ BirdsallRef ¦ GoogleTextFlaws ¦ BirdsallPetrie ¦
CheopsPetrie: CAT2025Cheops
CONTENTS ¦ ContentOUTSIDE
Cheops Pyramid ¦ ContentINSIDE
Cheops Pyramid ¦
Add 24 to land
on the actual Petrie book page in the PDF Stanford Library copy,
Type:
PetrieBookPage 38 = PDFpage 62.
----------------
From a GOOGLE scanned Stanford
Library PDF book original COPY 10Nov2025
Windows
11 exposes »CON» keyboard and copying issues
that seem to point out that the programmers cannot handle computers.
IT
MUST BE EMPHASIZED, AS IT HAS MADE THIS TRANSFER MORE COMPLICATED THAN
NECESSARY.
AFTER
SOME WRITING, THE KEYBOARD GOES BAZOOKA: Question sign becomes _ and that one
becomes ? .. And so on.
The
only way to abort is to Log Out — meaning all sessional writ becomes erased.
From GOOGLE:s foreword [[‡]]:
"
This is a digital copy of a book that was preserved for generations on library
shelves before it was carefully scanned by
Google as part of a project
to make the world’s books discoverable online.”,
“
It has survived long enough for the copyright to expire and the book to enter
the public domain.".
----------------
.............................................
The actual Petrie book is picture
scanned from:
.............................................
STANFORD
UNIVERSITY LIBRARY
1969
———————————————————
STANFORD
UNIVERSITY LIBRARIES
STANFORD
AUXILIARY LIBRARY
STANFORD,
CALIFORNIA 94305-6004
[415]
723-9201
All
books may be recalled after 7 days
———————————————————
-------------------------------------------------------------------------------------------------------------------------
STANFORD
UNIVERSITY
—
The library from where the Google scan was extracted —
“
For general university inquiries,
contact Stanford University Media Relations:
“.
-------------------------------------------------------------------------------------------------------------------------
THE
PYRAMIDS AND TEMPLES
OF GIZEH.
————————
THE PYRAMIDS AND TEMPLES OF
GIZEH.
BY
W. M. FLINDERS PETRIE,
Author of "Inductive Metrology," " Stonehenge," &.c.
——————————
LONDON:
FIELD
& TUER, YE LEADENHALLE PRESSE; SIMPKIN, MARSHALL & CO., STATIONERS'
HALL
COURT; HAMILTON, ADAMS & CO., PATERNOSTER ROW.
NEW
YORK: SCRIBNER & WELFORD, 743 BROADWAY
——————
PUBLISHED
WITH THE ASSISTANCE OF A VOTE OF
ONE
HUNDRED POUNDS
FROM
THE GOVERNMENT-GRANT COMMITTEE
OF
THE ROYAL SOCIETY.
1883.
............................
Contents: CheopsPetrie
CONTENTS.
—————
SECTION. PAGE
INTRODUCTION.
I Methods
employed … ... xiii
2 Scope of
the present work xiv
3 Use of
expressions ... xiv
CHAP.
I.-OBJECTS AND MEANS.
4 Need of
fresh measurements 1
5 Outline of
work demanded 3
6 Stay at
Gizeh ... 6
7 Assistance
obtained 7
CHAP.
11.-INSTRUMENTS.
SECTION. PAGE
8 List of
instruments ... 10
9 Details of
lineal instruments ... ... 11
10 Details
of angular instruments... 15
CHAP.
III.-METHODS OF MEASUREMENT.
11 Lineal
measures 22
12 Angular
measures 23
CHAP.
IV.-EXCAVATIONS.
13 Inside
Great Pyramid ... ... ... 27
14 Casing,
&c., of Great Pyramid 29
15 Second
Pyramid, casing, &c. ... 30
16 Third
Pyramid, casing, &c. ... 31
17 Workmen
... ... … 32
————————————————————
CHAP.
V.-CO-ORDINATES.
18 Station
marks 34
19 Table of
co-ordinates... … 34
CHAP.
VI.-OUTSIDE OF GREAT PYRAMID.
SECTION. PAGE
20 Relation
of sockets to casing.... 37
21 Length of
sides of casing ...... 39
22 Levels
and positions of sockets … 40
23 Levels up
the Pyramid ... … 41
24 Angle of
the Pyramid... ... 42
25 Form of
top of the Pyramid... … 43
26 Casing of
the Pyramid ... … 43
27 Pavement
of the Pyramid ...... 44
28 Basalt
pavement ... ... 46
29 Rock
trenches... … 47
30 Trial
passages ... ... 50
31
Connection of inside and outside . 51
32 Original
position of entrance ... 51
33 Mouths of
air-channels ... ... ... 52
34 Blocks
above entrance.. ...... 53
CHAP
VII.-INSIDE OF GREAT PYRAMID.
SECTION. PAGE
35 Entrance passage,
length 55
36 Entrance passage, azimuth and angle 58
37
Subterranean chamber, &c. ...... 59
38 Ascending
passage, length ... 61
39 Ascending passage, azimuth and angle 64
40 Passage
to Queen's Chamber ..... 65
41 Queen's
Chamber, plan ... ... 66
42 Queen's Chamber,height ...... 67
43 Queen's Chamber, niche... 69
44 Queen's Chamber, channels 70
viii CONTENTS.
SECTION. PAGE
45 Gallery, length and angles ... 71
46 roof and walls ... ...... 72
47 Antechamber and passages ... 75
48 dimensions ...... 76
49 details of walls ... 77
50 granite leaf ... 78
51 King's Chamber, walls ... 79
52 plan .. 80
53 roof ... 81
54 floor
.. 82
55 working ...... 82
56 channels 83
57 Coffer, character ... ... 84
58 position ... ... 84
59 offsets to surfaces ...... 85
60 calipering... ... 89
61 volumes...... ...... 90
62 Chambers of construction 19
63 details ... 92
64 Summary of interior positions ... 95
THIS PETRIE BOOK TEXT COPY ENDS HERE
The following indexing
below is (yet) of a pure ordely interest.
CHAPTER 7 ends the Cheops
Pyramid Petrie description in this document.
not included in this document:
SECTION. PAGE
CHAP.
VIII.-OUTSIDE OF SECOND PYRAMID.
65 Relation of rock to casing ... 96
66 Length of sides of casing ... 97
67 Angle of Pyramid, and height... 97
68 Courses of the Pyramid 98
69 Pavement ... ... 99
70 Levelled site ... 99
71 Peribolus walls ... 100
72 Barracks of workmen ... 101
CHAP.
IX.-INSIDF OF SECOND PYRAMID.
73 Entrance passage... ... 104
74 Horizontal passage ... 104
75 Great chamber ... 105
76 Coffer, character ... ... 106
77 dimensions ... 107
78 Lower chamber, and passage ... 108
CHAP.
X.-OUTSIDE OF THIRD PYRAMID.
79 Nature of the casing ... 111
80 Length of the sides... 110
SECTION. PAGE
81 Angle and height of Pyramid 112
82 Courses ...... 112
83 Peribolus walls and temple ... 114
СHAP.
XI.-INSIDE OF THIRD PYRAMID.
84 Entrance passage... ... 117
85 First chamber ... ... 117
86 Second chamber ... ... 118
87 Granite chamber... ... 118
88 Loculus chamber... ... 119
89 Original entrance passage ... ... 120
CHAP.
XII.-LESSER PYRAMIDS OF GIZEH.
90 Northern small Pyramid ... 121
91 Middle small Pyramid ... 123
CHAP.
XIII.-PoSITIONS AND ORIENTATION OF THE PYRAMIDS.
92 Relative positions of Pyramids ... 125
93 Orientation of large Pyramids... ... 125
94 Change of earth's axis ... ... 126
СHAP.
ХIV.-THE GRANITE TEMPLE, &C.
95 Position of Granite Temple ... 128
96 Description of T'emple... ... 129
97 Workmanship of Temple ... 132
98 Original appearance of T'emple ... 133
99 Date of Temple ...... ... 133
100 Constructions near Great l'yramid. 134
101 Basalt and diorite casings ... 135
102 Diorite at (Gizeh... ... 135
СHAP.
ХV.-ТомBS OF GIZEH.
103 Angles of Mastabas... ... ... 138
104 Campbell's tomb ... 138
105
Abu Roash, Pyramid of Men.....ra ...
140
CHAP.
XVI.-NOTES ON OTHER PYRAMIS.
106 Sakkara, Pyramid of Pepi...... 142
CONTENTS. ix
SECTION. PAGE
107 Dahshur, Great Pyramid ...... 144
108 Dahshur, South Pyramid .…. ... 144
109 Dahshur,"" door...... 145
110 Mastaba-Pyramids, Sakkara & Medum 146
CHAP.
XVII.-HISTORICAL NOTES.
FACTS.
111 Climate of early times ... ... 149
112 Men.....ra of Abu Roash 151
113 Khufu and Khnumu-Khufu ... 152
114 Ratatef 152
115 Khafra ... 153
116 Menkaura, and the Third Pyramid ... 153
117 Brick Pyramids ... ... 155
118 Petukhanu's tablet of Khufu ... 156
119 Destruction of buildings ... 157
120 Accuracy of Greek historians ... ... 159
121 Angles of the Pyramids 162
122 The Accretion Theory of building... 163
123 Application of it to the large Pyramids 165
124 Inapplicability of the theory ... 165
125 Plugging of the Pyramid passages ... 166
126 Doors of the Pyramids... ...... 167
127 Relative workmanship of Pyramids ... 169
128 Use of Plaster.. ...... 171
CHAP.
XIX.-MECHANICAL METHODS OF THE PYRAMID BUILDERS.
129 Nature of tools employed on hard stone 173
130 Examples of sawing ... 174
131 Examples of tubular drilling ...... 175
132 Examples of turning ... 176
133 Rate of working ... ... 177
134 Tools not actually found ... 177
135 References on other details ... 177
СHАР.
ХX.-VALUES OF THE CUBIT AND DIGIT.
136
The cubit in the Great Pyramid... 178
137
The cubit in other buildings ...... 179
138 Divisions
of lists in the tombs... ... 179
139
Decimal
division of cubit 180
140
Values
of the digit ... 180
141
Comparison with
previous results ... 181
SECTION.
PAGE
CHAP.
XXI.-THEORIES COMPARED WITH
142
The comparisons based
on the facts ... 182
143
The
Great Pyramid base ... 182
144
height
... 183
145
angle
... 184
146
courses
... 184
147
Rock trenches
by Great Pyramid ... 185
148
Positions
of the chambers ... 186
149
Lengths
of the passages ... 187
150
Dimensions
of the passages ... 189
151
Angles of the passages... ... 190
152
Subterranean Chamber... ... 191
СHAP.
XVIII.-ARCHITECTURAL IDEAS OF THE
PYRAMID BUILDERS.
153
Queen's Chamber ... 191
154
Antechamber ... 193
155
King's Chamber... 194
156
Coffer ... 195
157
Synopsis of Great Pyramid theories
... 198
158
The Tombic theory ... 200
159
Second Pyramid, outside ... 201
160
inside 99 19 ... 202
161
coffer... ... 203
162
Third Pyramid ...... ... 204
163
Comparison of previous surveys... 205
СHAP.
ХXII.-HıSTORY OF THE GREAT PYRAMID, AND ITS DESIGN.
164
Nature of the site ... 208
165
Source of the stone ... 209
166
Organization of the labour ... 210
167
Preparation of the site ... 211
168
Planning of the courses ... 212
169
Raising the stones ... 212
170
Tools and chips... ... 212
171
Deterioration of the work ... 213
172
Plans altered... ... 214
173
Closing of the Pyramid... ...... 215
174
A second coffer ...... ... 216
175
Violation of the Pyramid ...... 217
176
Inscriptions on the Pyramid... ... 217
177
Destruction of the Pyramid ... 219
178
Summary of probable theories ... 220
X CONTENTS.
SECTION. PAGE
APPENDICES.
1.—ON THE ARRANGEMENT OF A TRIANGULATION.
179 Nature of survey of short distances ... 223
180 Distribution of the observations... 223
181 Order of observations ... ... 224
II.—THE
REJECTION OF DISCORDANT OBSERVATIONS.
182 Continual and occasional errors... 226
183 Discrimination of occasional errors ... 227
184 Weighting observations by their
divergence... ...
185 Application of the law of distribution 228
186 Practical elimination of occasional errors
... 230
SECTION. PAGE
187 Probable error, a factor, not a term ... 231
188 Plus and minus errors always possible 232
189 Secondary probable errors ... 233
190 Applicability of approximate formulæ 235
191 Testing the normal distribution 236
III.—GRAPHIC REDUCTION OF TRIANGULATION.
192 The need of a graphic method ... 238
193 Old and new methods of graphic reduction 239
194 The practice of graphic reduction ... 239
195 Delineation of the traces ... 241
196 Accuracy in the present survey ... 241
197 Applicability of graphic reduction ... 243
INDEX 245
LIST OF
PLATES. xi
[ The actual plates in the Petrie List of Plates are not
given here. They are very well represented in the Ronald Birdsall Petrie book
edition, see BirdsallRef].
[See also Petrie’s own
clarification on the origin of these plates here in PlateRef];
[In explicit as observed:
there is an inaccuracy of the vertical, not the horizontal, scaling in
the copy of Petrie’s PLATE.9, Petries
ritning PLATE.9]:
[While the horizontal x-scaling in PLATE.9 (Plate.ix) matches Petrie’s values perfectly, the vertical scaling
does not: the error grows with height];
[Which suggests a
perspective y-plane optical scan issue, given the Petrie PlateRef ];
[The (scanned) original Plate9 is NOT 2D y-SCREEN
PLANE CORRECT: the y-scaling error growing
with pyramid height would certainly not be one PlateRef Petrie’s own credit, but rather
a less precise photoscan of Petrie’s thorough drawing — its horizontal
scaling matches perfectly with the Petrie’s values, but not the vertical.
• However we don’t know
this for sure here until someone responsible for or familiar with the PLATE.9 copying will clarify
the observed differences].
LIST OF
PLATES.
FRONTISPIECE-THE
NINE PYRAMIDS OF GIZEH, FROM THE SOUTH.
I. PLAN OF TRIANGULATION OF THE PYRAMIDS,
EТС.
II. BASALT PAVEMENT AND TRENCHES, ON EAST OF
GREAT PYRAMID.
III. ENDS OF THE ROCK TRENCHES; SECTION OF
TRIAL PASSAGES.
IV. WALLS AND BARRACKS AROUND THE SECOND PYRAMID.
V. WALLS ARQUND THE THIRD PYRAMID.
VI. PLAN OF THE GRANITE TEMPLE.
VII. SECTIONS OF THE GREAT AND SECOND PYRAMIDS,
AND MASTAВАPYRAMIDS.
VIII. COURSES OF THE GREAT PYRAMID MASONRY.
IX. PASSAGES OF THE GREAT PYRAMID.
X. SOCKETS AND CASING OF GREAT PYRAMID.
XI. MOUTHS OF PASSAGES AND CHANNELS; AND
CASING OF GREAT PYRAMID.
XII. CASING OF PYRAMIDS; BOSSES: DECORATION,
ETC.
XIII. WALLS OF THE KING'S CHAMBER.
XIV. SPECIMENS OF SAWING, DRILLING, AND TURNING;
FROM GIZEH, ETС.
XV. INSTRUMENTS EMPLOYED, OF NEW TYPES.
XVI. TRACES OF THE OBSERVATIONS, AROUND THE
GREAT PYRAMID.
ERRATA.
Page 30 line
7 f(e)r
oonsider read consider.
38 1 case core.
41 2
othe thers the others.
41 43
+. +
.1
42 33
0.9 .09
43 13
measurement re-measurement.
50
28 .24' 24'
65 34
± 3. ± .3
157 12 dozen
dozens.
212
1 tweve
twelve.
218 10 Ibr
Ibn.
Plate xiv., Fig. 7, the lithographer has drawn the lines
wavy,
whereas they
really form a true spiral, as described p. 174, and in
Anthropoligical Journal.
[A specially observed,
apparently, typographically book print accident (The Stanford University
Library book copy):]
[ 
restoration,
PetrieBookPage 51 *-addition — seems like a PDF scan error .. or a broken typo .. ]
[We image copied 
the res’oration from
the Petrie book, duplicated it, removed oration, isolating the t in tion, inserting that t in the res’oration: perfect assembly:
Conclusion: most likely a broken typo (the
actual book printed physical letter type)].
INTRODUCTION.
1. THE nature of
the present work is such that perhaps few students will
find
interest in each part of it alike. The ends and the means appeal to
separate
classes: the antiquarian, whose are the ends, will look askance at the
means,
involving co-ordinates, probable errors, and arguments based on purely
mechanical considerations;
the surveyor and geodetist, whose are the means,
will
scarcely care for their application to such remote times; the practical man
who may
follow the instrumental details, may consider the discussion of
historical
problems to be outside his province; while only those familiar with
mechanical
work will fully realize the questions of workmanship and tools here
explained.
An investigation thus based on such
different subjects is not only at a
disadvantage
in its reception, but also in its production. And if in one part or
another,
specialists may object to some result or suggestion, the plea must be
the
difficulty of making certain how much is known, and what is believed, on
subjects so
far apart and so much debated.
The combination of two is often
most fertile apparently distinct subjects,
in results;
and the mathematical and mechanical study of antiquities promises
a full measure of success. It is sometimes said, or
supposed, that it must be
useless to apply
accuracy to remains which are inaccurate; that fallacies are
sure to
result, and that the products of such a method rather originate with the
modern
investigator than express the design of the ancient constructor. But
when we look
to other branches of historical inquiry, we see how the most
refined
methods of research are eagerly followed : how philology does not
confine
itself to the philological ideas of the ancient writers, but analyzes their
speech so as
to see facts of which they were wholly unconscious; how chemistry
does not
study the chemical ideas, but the chemical processes and products of
the
ancients; how anthropology examines the bodies and customs of men to
whom such
inquiries were completely foreign. Hence there is nothing
unprecedented,
and nothing impracticable, in applying mathematical methods
in the study
of mechanical remains of ancient times, since the object is to get
behind the
workers, and to see not only their work, but their mistakes, their
xiv
INTRODUCTION.
amounts of error,
the limits of their ideas; in fine, to skirt the borders of their
knowledge
and abilities, so as to find their range by means of using more
comprehensive
methods. Modern inquiry should never rest content with saying
that
anything was "exact;" but always show what error in fact or in work
was
tolerated by
the ancient worker, and was considered by him as his allowable
error.
2. The materials
of the present volume have been selected from the results
of two
winters' work in Egypt. Many of the points that were examined, and
some
questions that occupied a considerable share of the time, have not been
touched on
here, as this account is limited to the buildings of the fourth dynasty
at Gizeh,
with such examples of later remains as were necessary for the
discussion
of the subject. All the inscriptions copied were sent over to Dr.
Birch, who
has published some in full, and extracted what seemed of interest in
others; Dr.
Weidemann has also had some of them; and they do not need,
therefore,
further attention on my part. Papers on other subjects, including the
Domestic
Remains, Brickwork, Pottery, and travellers graffiti, each of which
were
examined with special reference to their periods, are in course of publication
by the Royal
Archæological Institute. The mechanical methods and tools
employed by
the Egyptians were discussed at the Anthropological Institute,
and are more
summarily noticed here. A large mass of accurate measurements
of remains
of various ages were collected; and these, when examined, will
probably
yield many examples of the cubits employed by the constructors. Of
photographs,
over five hundred were taken, on 1/4
size dry plates, mainly of
architectural
points, and to show typical features. Volumes of prints of these
may be
examined on application to me, and copies can be ordered from a
London
photographer. The lesser subjects being thus disposed of, this volume
only treats
of one place, and that only during one period, which was the main
object of
research. The mass of the actual numerical observations and
reductions
would be too bulky to publish, and also unnecessary; the details of
the
processes are, in fact, only given so far as may prove useful for comparison
with the
results obtained by other observers.
Though, in describing various
features, reference has often been made to the
publications
of Colonel Howard Vyse* (for whom Mr. Perring, C.E., acted as
superintendent),
and of Professor C. Piazzi Smyth,† yet it must not be supposed
that this
account professes at all to cover the same ground, and to give all the
details that
are to be found in those works. They are only referred to where
necessary to
connect or to explain particular points; and those volumes must
be consulted
by any one wishing to fully comprehend all that is known ofthe
Pyramids.
This work is, in fact, only supplementary to the previous descriptions,
*Operatio as at the Pyramids," 3 vols. 1840.
†"Life
and Work at the Great Pyramid," 3 vols. 1867.
INTRODUCTION. XV
as giving fuller
and more accurate information about the principal parts of the
Pyramids,
with just as much general account as may be necessary to make it
intelligible,
and to enable the reader to judge of the discussions and conclusions
arrived at
on the subject, without needing to refer to other works. Colonel
Vyse's
volumes are most required for an account of the arrangements of the
Second and
smaller Pyramids, of the chambers in the Great Pyramid over the
King's
Chamber, of the negative results of excavations in the masonry, and of
various
mechanical details. Professor Smyth's vol. ii. is required for the
measurements
and description of the interior of the Great Pyramid. While the
scope of the
present account includes the more exact measurement of the whole
of the Great
Pyramid, of the outsides and chambers of the Second and
Third
Pyramids, of the Granite Temple, and of various lesser works; also the
comparison
of the details of some of the later Pyramids with those at Gizeh,
and various
conclusions, mainly based on mechanical grounds.
The reader's knowledge of the
general popular information on the subject,
has been
taken for granted; as that the Pyramids of Gizeh belong to the first
three kings
of the fourth dynasty, called Khufu, Khafra, and Menkaura, by
themselves,
and Cheops, Chephren, and Mycerinus, by Greek-loving Englishmen;
that their
epoch is variously stated by chronologers as being in the third, fourth,
or fifth
millennium B.C.; that the buildings are in their bulk composed of blocks
of
limestone, such as is found in the neighbouring districts; that the granite
used in
parts of the insides and outsides was brought from Syene, now Assouan;
and that the
buildings were erected near the edge of the limestone desert,
bordering the
west side of the Nile valley, about 150 feet above the inundated
plain, and
about 8 miles from the modern Cairo.
3. One or two
technical usages should be defined here. All measures
stated in
this volume are in Imperial British inches, unless expressed otherwise;
and it has
not been thought necessary to repeat this every time an amount is
stated; so
that in all such cases inches must be understood as the medium of
description.
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 probable error of all important
measurements is stated with the sign
± prefixed to it as usual. A full description of this
will be found in any modern
treatise on
probabilities; and a brief account of it was given in "Inductive
Metrology,"
pp. 24–30. Some technical details about
it will be found here in
the Appendix
on "The Rejection of Erroneous Observations"; and I will only
add a short
definition of it as follows:—The
probable error is an amount on
xvi
INTRODUCTION.
each side of
the stated mean, within the limits of which there is as much chance
of the truth
lying, as beyond it; i,e., it is
1 in 2 that the true result is not
further
from the
stated mean than the amount of the probable error. Or, if any one
prefers to
regard the limits beyond which it is practically impossible for the true
result to
be, it is 22 to I against the truth being 3 times the amount of the
probable error
from the mean, 144 to I against its being 4 times, or 1,380 to 1
against its
being as far as 5 times the amount of the probable error from the
mean result
stated. Thus, any extent of improbability that any one may choose
to regard as
practical impossibility, they may select; and remember that 4 or 5
times the
probable error will mean to them the limit of possibility. Practically,
it is best
to state it as it always is stated, as the amount of variation which there
is an equal
chance of the truth exceeding or not; and any one can then consider
what
improbability there is in any case on hand, of the truth differing from the
statement to
any given extent.
It should be
mentioned that the plans are all photolithographed from my
drawings,
in order to avoid inaccuracy or errors of copying; and thence comes
any
lack of technical style observable in the lettering.
As to the results of the whole
investigation, perhaps many theorists will
agree with
an American, who was a warm believer in Pyramid theories when he
came to
Gizeh. I had the pleasure of his company there for a couple of days,
and at our
last meal together he said to me in a saddened tone,—"Well, sir! I
feel as if I
had been to a funeral." By all means let the old theories have a
decent
burial; though we should take care that in our haste none of the wounded
ones are
buried alive.
THE PYRAMIDS
AND TEMPLES OF GIZEН.
CHAPTER I.
OBJECTS AND
MEANS.
4. THE small piece of desert plateau opposite
the village of Gizeh, though
less than a
mile across, may well claim to be the inost remarkable piece of
ground in
the world. There may be seen the very beginning of architecture, the
most
enormous piles of building ever raised, the most accurate constructions
known, the
finest masonry, and the employment of the most ingenious tools;
whilst among
all the sculpture that we know, the largest figure—the
Sphinx—and also
the finest
example of technical skill with artistic expression—the Statue
of Khafra—both belong to Gizeh. We shall look in vain
for a more wonderful
assemblage
than the vast masses of the Pyramids, the ruddy walls and pillars of
the granite
temple, the titanic head of the Sphinx, the hundreds of tombs, and
the
shattered outlines of causeways, pavements, and walls, that cover this earliest
field of
man's labours.
But these
remains have an additional, though passing, interest in the
present day,
owing to the many attempts that have been made to theorise on
the motives
of their origin and construction. The Great Pyramid has lent its
name as a
sort of by-word for paradoxes; and, as moths to a candle, so are
theorisers
attracted to it. The very fact that the subject was so generally
familiar,
and yet so little was accurately known about it, made it the more
enticing;
there were plenty of descriptions from which to choose, and yet most
of them were
so hazy that their support could be claimed for many varying
theories.
Here, then, was a field which
called for the resources of the present time for
B
2 OBJECTS
AND MEANS. [Chap, i
its due
investigation; a field in which measurement and research were greatly
needed, and
have now been largely rewarded by the disclosures of the skill of the
ancients,
and the mistakes of the moderns. The labours of the French Expedition,
of Colonel
Howard Vyse, of the Prussian Expedition, and of Professor
Smyth, in
this field are so well known that it is unnecessary to refer to them,
except to
explain how it happens that any further work was still needed.
Though the
French were active explorers, they were far from realising the
accuracy of
ancient work; and they had no idea of testing the errors of the
ancients by
outdoing them in precision. Hence they rather explored than
investigated.
Col. Vyse's work, carried on by Mr. Perring, was of the same
nature, and
no accurate measurement or triangulation was attempted by these
energetic
blasters and borers; their discoverics were most valuable, but their
researches
were always of a rough-and-ready character. The Prussian Expedition
sought with
ardour for inscriptions, but did not advance our knowledge of
technical
skill, work, or accuracy, though we owe to it the best topographical
map of
Gizeh. When Professor Smyth went to Gizeh he introduced different
and
scientific methods of inquiry in his extensive measurements, afterwards
receiving
the gold medal of the Royal Society of Edinburgh in recognition of his
labours. But
he did not attempt the heaviest work of accurate triangulation.
Mr. Waynman
Dixon, C.E., followed in his steps, in taking further measurements
of the
inside of the Great Pyramid. Mr. Gill—now
Astronomer Royal at the
Cape—when engaged in Egypt in the Transit
Expedition of 1874, made the next
step, by
beginning a survey of the Great Pyramid base, in true geodetic style.
This far
surpassed all previous work in its accuracy, and was a noble result of the
three days'
labour that he and Professor Watson were able to spare for it. When
I was
engaged in reducing this triangulation for Mr. Gill in 1879, he impressed on
me the need
of completing it if I could, by continuing it round the whole
pyramid, as
two of the corners were only just reached by it without any check.
When, after
preparations extending over some years, I settled at Gizeh
during
1880-2, I took with me, therefore, instruments of the fullest accuracy
needed for
the work; probably as fine as any private instruments of the kind.
The
triangulation was with these performed quite independently of previous
work; it was
of a larger extent, including the whole hill; and it comprised an
abundance of
checks. The necessary excavations were carried out to discover
the fiducial
points of the buildings, unseen for thousands of years. The measurements
previously
taken were nearly all checked, by repeating them with greater
accuracy,
and, in most cases, more frequency; and fresh and more refined
methods of
measurement were adopted. The tombs around the pyramids were
all
measured, where they had any regularity and were accessible. The methods
of
workmanship were investigated, and materials were found illustrating the
tools
employed and the modes of using them.
Sect. 5.]
OUTLINE OF WORK DEMANDED. 3
5. For a detailed
statement of what was urgently wanted on these subjects,
I cannot do
better than quote from a paper by Professor Smyth,* entitled, "Of
the
Practical Work still necessary for the Recovery of the Great Pyramid's
ancient,
from its modern, dimensions"; and add marginal notes of what has
now been
accomplished.
*As my measures referred chiefly to
the interior of the
structure,
and as there the original surfaces have not been much
broken, the
virtual restoration of that part has been by no means unsuccessful;
and requires
merely in certain places—places which
can only be
recognised from time to time as the theory of the building shall
advance—still more minutely exact measures than
any which I
was able to make, but which will be comparatively
easy to a
scientific man going there in future with that one special
object
formally in view."
Notes of work, 1880-2. [Book’s right margin note:]
The
whole interior now re-examined and much remeasured, more accurately.
"The exterior, however, of the
Great building, is exceedingly
dilapidated,
and I have few or no measures of my own to set forth
for its
elucidation. That subject is, therefore, still "to let"; and
as it is too
vast for any private individual to undertake at his own
cost, I may
as well explain here the state of the case, so that either
Societies or
Governments may see the propriety of their taking up
the grand
architectural and historical problem, and prosecuting it earnestly until a
successful
solution of all its parts shall have been
arrived
at."
Notes of work, 1880-2. [Book’s right margin note:]
Total
cost of present work £300.
"Size and Shape, then, of the
ancient exterior of the Great
Pyramid, are
the first desiderata to be determined."
(A statement of the various
measurements of the base here
follows.)
"As preparatory, then, to an
efficient remeasurement of the
length of the
Base-sides of the Great Pyramid, itself an essential preliminary to almost all
other
Pyramidological researches, I beg
to submit
the following local particulars."
"(1.) The outer corners of
four shallow sockets, cut in the
levelled surface
of the earth-fast rock outside the present dilapidated
corners of
the built Great Pyramid, are supposed to be the points
to be
measured between horizontally in order to obtain the original
length of
each external, finished, 'casing-stone' base-side."
Notes of work, 1880-2. [Book’s right margin note:]
Sockets
are not corners of base-side.
"(2.) Previous to any such
measurement being commenced,
the present
outer corners of those sockets must be reduced to their
ancient
corners, as the sockets have suffered, it is feared, much
dilapidation
and injury, even since 1865; owing to having been
then
imperfectly covered over, on leaving them, by the parties who
at that time
opened them."
Notes of work, 1880-2. [Book’s right margin note:]
Sockets
are apparently quite uninjured.
"(3.) The said sockets must be
proved to have been the sockets
originally
holding the corner stones of the casing; or showing how
far they
overlapped, and therefore and thereby not defining the
ancient base
of the Great Pyramid to the amount so overlapped.
Notes of work, 1880-2. [Book’s right margin note:]
By
form of core, and by casing lines lying within the sockets, noothers are
possible.
* Edinburgh
Astronomical Observations, vol. xiii., p. 3.
[These below
additions appear in the book as narrow marginal columns, adopted to the book's
organized paragraphs]
[To approach
a similar copy, each of the below should be reorganized to be added to that
paragraph, not done here]
4 OBJECTS
AND MEANS. [Chap. i.
. . . . the
ground should be cleared far and wide about each
corner to
see if there are any other sockets in the neighbourhood."
"(4.) Whether any more rival
sockets claiming to be the true
corner
sockets of the ancient base are, or are not, then and in that
manner,
found,—the usually known or selected
ones should further
be tested,
by being compared with any other remaining indications
of where the
line of each base-side stood in former days. Some
particular
and most positive indications of this kind we know were
found by
Col. Howard Vyse in the middle of the Northern side;
and there is
no reason why as good markings should not be discovered,
if properly
looked for, along the other three sides; and
they are so vitally
important to a due understanding of the case, that
their
ascertainment should precede any expense being incurred
on the
measurement of lengths from socket to socket.'
Notes of work, 1880-2. [Book’s left margin note:]
Casing
now found on all sides, and completely fixed.
"(5.) Col. H. Vyse found those
invaluable markings of the
line of the
North base-side, or part of the very base-side itself, by
accomplishing
the heavy work of digging down by a cross cut, through
the middle
of the heap of rubbish, near 50 feet high, on
that side.
But he has published no records of how those markings,
or that
actual portion of the base-side, agree, either in level or in
azimuth with
the sockets. Indeed, he left the ground in such a
state of hillock
and hole, that no measures can, or ever will, be
taken with
creditable accuracy until a longitudinal cut through the
rubbish heap
shall be driven from East to West and all along
between the
two N.E. and N.W. sockets."
Notes of work, 1880-2. [Book’s left margin note:]
Messures
having been taken by triangulation, no extensive cuttings were needed,
"(6.) The making of such a
long and laborious cut, and then
the 'lining'
and levelling' of the bases of the Colonel's casing
stones in
situ (or their remains, for they are said to have been
mischievously
broken up since then), and their comparison with the
sockets or
their joining lines by appropriate and powerful surveying
instruments,
should be the first operation of the new measurers, to
whom, it is
fervently to be hoped, an intelligent Government
will grant
the due means for effecting it satisfactorily."
Notes of work, 1880-2. [Book’s left margin note:]
Casing-stones
are not broken up, and the cutting is not necessary.
"(7.)
A similar longitudinal cut, and similar comparisons are
to be made
in the other base-side hills of rubbish, together with a
wider
clearing away of the rubbish outside, in order to determine
the form and
proportion of the 'pavement' which is believed to
have
anciently surrounded the Pyramid; but of which the only
positive
information which we have, is based on the little bit of it
which Col.
H. Vyse cut down to near the middle of the North side."
Notes of work, 1880-2. [Book’s left margin note:]
Sides
now found by pits, and fixed by triangulation. Pavement traced on each side.
"This work might cost from
£12,000 to £14,000; for the
material to
be cut through is not only extensive but so hard and
concreted
that it turns and bends the hoes or picks employed in (a)
Nile
cultivation, and which are the only tools the Arabs know of. [The Stanford Library scan copy shows a tight
margin .. some end characters may be lost]
Notes of work, 1880-2. [Book’s left margin note:]
Cuts,
if wanted, might be made for a tenth
of this sum.
But besides
the theoretical value of such an operation for distinguishing
and
identifying the base to be measured, it would certainly yield
practically
abundant
fragments of casing stones,
and perhaps
settle the oft-mooted questions of ancient inscriptions
on the outer
surface of the Pyramid."
Notes of work, 1880-2. [Book’s left margin note:]
Inscribed
casing found, Greek.
Sect. 5.]
OUTLINE OF WORK DEMANDED.
"(8.) When the four sides of
the base, and the corresponding
sides of the
pavement are exposed to view,—a new
fixation of the
exact
original places of the precise outer corners of the now Done
dilapidated
and rather expanded corner sockets may be required;
and then,
from and between such newly fixed points, there must be
Notes of work, 1880-2. [Book’s right margin note:]
Done.
A. Linear
measures of distance taken with first-rate Done.
accuracy.
Notes of work, 1880-2. [Book’s right margin note:]
Done.
B.
Levellings. Done.
Notes of work, 1880-2. [Book’s right margin note:]
Done.
C.
Horizontal angles, to test the squareness of the base. Done.
Notes of work, 1880-2. [Book’s right margin note:]
Done.
D.
Astronomical measures to test the orientation of each of
the base
sides. Done.
Notes of work, 1880-2. [Book’s right margin note:]
E. Angular
and linear measures combined to obtain both Done.
the vertical
slope of the ancient Pyramid flanks, and
the distance
of certain of the present joints of the
entrance
passage from the ancient external surface
of the
Pyramid in the direction of that passage produced—a
matter
which is at
present very doubtful,
but a new
and good determination of which is essential
to utilize
fully the numerous internal observations contained in this
and other books."
Notes of work, 1880-2. [Book’s right margin note:]
Done.
"(9.) When all the above works
shall have been carefully accomplished,
the men who
have performed them will doubtless
have become
the most competent advisers as to what should be
undertaken
next; whether in search of the fourth chamber, concerning whose
existence
there is a growing feeling amongst those
who have
studied certain laws of area and cubic contents which
prevail
among the presently known chambers and passages; or
for the more
exact measurement of certain portions of the building
which shall
then be recognised by the theory as of fiducial character and importance."
Notes of work, 1880-2. [Book’s right margin note:]
Much
of the interior now remeasured, with higher exactitude.
"(10.) Should the next
remeasurement unfortunately not be
under
sufficiently favourable auspices or powerful patronage
enough to
attempt all that has been sketched out above—I
would
suggest to
those employed upon it the importance of endeavouring
to operate in
that manner on at least the north side of the Great Pyramid alone,
where much
of the work has been already performed, and where traces of the old
base-side
are known to exist,
or did
certainly exist 34 years ago."
Notes of work, 1880-2. [Book’s right margin note:]
All
results obtained without patronage.
"(11.) The levels as well as
temperatures of water in the wells
of the plain
close to the Pyramid, and in the Nile in the distance,
should also
be measured through a full twelvemonth interval. A
meteorological
journal should likewise be kept for the same period
at the base
of the Pyramid, and the corrections ascertained to
reduce it
either to the summit or King's chamber levels above,
or to the
plain level below; while no efforts should be spared
to re-open
the ventilating channels of the King's chamber and to
prevent the
Arabs from filling them up again."
Notes of work, 1880-2. [Book’s right margin note:]
Channels
filled by wind, not by Arabs.
"(12.) An examination should
be made of the apparent Pyramid
in the
desert almost west of the Great Pyramid; likewise of the
Notes of work, 1880-2. [Book’s right margin note:]
Done.
6 OBJECTS
AND MEANS. [Chap. i.
northern
coasts of Egypt, where they are cut by the Great
Pyramid's
several meridian and diagonal lines produced; also
of the fourth dynasty remains in the
Sinaitic Peninsula; and of
any
monuments whatever, whether in Egypt or the neighbouring
countries
for which any older date than that of the Great Pyramid
can reasonably be assigned;
including also a fuller account than
any yet
published of King Shafre's Tomb and its bearings with,
or upon, the
origin, education, labours and life of the first of the
Pyramid
builders."
Notes of work, 1880-2. [Book’s left margin note:]
N.W.diagonal done. Done
partly. Done.
6. To carry out,
therefore, the work sketched in the above outline, and to
investigate
several collateral points, I settled at Gizeh in December, 1880, and
lived there
till the end of May, 1881; I returned thither in the middle of October
that year,
and (excepting two months up the Nile, and a fortnight elsewhere),
lived on
there till the end of April, 1882; thus spending nine months at Gizeh.
Excellent
accommodation was to be had in a rock-hewn tomb, or rather three
tombs joined
together, formerly used by Mr. Waynman Dixon, C.E.; his door
and shutters
I strengthened; and fitting up shelves and a hammock bedstead, I
found the
place as convenient as anything that could be wished. The tombs
were
sheltered from the strong and hot south-west winds, and preserved an
admirably
uniform temperature; not varying beyond 58° to 64° F. during the
winter, and
only reaching 80° during three days of hot wind, which was at 96°
to 100° outside.
I was happy in having Ali Gabri,* the
faithful servant of Prof. Smyth, Mr.
Dixon, and
Mr. Gill; his knowledge of all that has been done at Gizeh during
his lifetime
is invaluable; and his recollections begin with working at four years
old, as a
tiny basket carrier, for Howard Vyse in 1837. He was a greater help
in measuring
than many a European would have been; and the unmechanical
Arab mind
had, by intelligence and training, been raised in his case far above
that of his
neighbours. In out-door work where I needed two pair of hands, he
helped me
very effectually; but the domestic cares of my narrow home rested
on my own
shoulders. The usual course of a day's work was much as follows:
—Lighting my
petroleum stove, the kettle boiled up while I had my bath; then
breakfast
time was a reception hour, and as I sat with the tomb door open, men
and children
used to look in as they passed; often a friend would stop for
a chat,
while I hastily brewed some extra cups of coffee in his honour, on the
little stove
behind the door; Ali also generally came up, and sat doubled up in
the doorway,
as only an Arab can fold together. After this, starting out about
nine
o'clock, with Ali carrying part of the instruments, I went to work on the
triangulation
or measurements; if triangulating, it was Ali's business to hold an
* Called Ali Dobree by Prof. Smyth.
G is universally pronounced hard by Egyptians,
soft by
Arabs; thus either Gabri or Jabri, Gizeh or Jizeh, General or Jeneral, Gaz or
Jaz
(petroleum).
Sect. 7. ASSISTANCE
OBTAINED.
umbrella so
as to shade the theodolite from the sun all day-the observer took his
chance; if
measuring, I generally did not require assistance, and worked alone,
and I always
had to get on as well as I could during Ali's dinner hour. At dusk
I collected
the things and packed up; often the taking in of the triangulation
signals was
finished by moonlight, or in the dark. Then, when all was safely
housed in my
tomb, Ali was dismissed to his home, and about six or seven
o'clock I
lit my stove, and sat down to reduce observations. Dinner then began
when the
kettle boiled, and was spun out over an hour or two, cooking and
feeding
going on together. Brown ship-biscuit, tinned soups, tomatoes (excellent
in Egypt),
tapioca, and chocolate, were found to be practically the most convenient
and
sustaining articles; after ten hours' work without food or drink,
heavy food
is not suitable; and the great interruption of moving instruments,
and breaking
up work for a midday meal was not admissible, Then, after
washing up
the dishes (for Arab ideas of cleanliness cannot be trusted), I sat
down again
to reducing observations, writing, &c., till about midnight. Ali's
slave,
Muhammed the negro, and his nephew, little Muhammed, used to come up
about nine o'clock,
and settle in the next tomb to sleep as guards, safely locked
in. Having a
supply of candle provided for them, they solaced themselves with
indescribable
tunes on reed pipes; often joining in duets with Abdallah, the
village
guard, who used to come up for a musical evening before beginning his
rounds. Very
often the course of work was different; sometimes all out-door
work was
impossible, owing to densely sand-laden winds, which blew the grit
into
everything—eyes, nose, ears, mouth,
pockets, and watches. During the
excavations
I turned out earlier—about sunrise; and
after setting out the men's
work,
returned for breakfast later on in the morning. On other occasions, when
working
inside the Great Pyramid, I always began in the evening, after the
travellers
were clean away, and then went on till midnight, with Ali nodding, or
even till
eight o'clock next morning; thus occasionally working twenty-four
hours at a
stretch, when particular opportunities presented themselves. The
tomb I left
furnished, as I inhabited it, in charge of Ali Gabri, and not having
been looted
in the late revolt, it will, I hope, be useful to any one wishing
to carry on
researches there, and applying to Dr. Grant Bey for permission to
use the
furniture.
7. My best thanks
are due to M. Maspero, the Director of Antiquities, for
the
facilities he accorded to me in all the excavations I required, kindly
permitting
me to work
under his firman; and also for information on many points.
It is much
to be hoped that the liberal and European policy he has introduced
may
flourish, and that it may overcome the old Oriental traditions and ways
that clogged
the Department of Antiquities. Excepting Arab help, I worked
almost
entirely single-handed; but I had for a time the pleasure of the society
of two
artists: Mr. Arthur Melville, staying with me for a week in May, 1881, and
8 OBJECTS
AND MEANS. [Chap. i.
kindly
helping in a preliminary measure of my survey base, and in an accurate
levelling up
to the Great Pyramid entrance; and Mr. Tristram Ellis, staying
with me for
a fortnight in March and April, 1882, and giving me most valuable
help in
points where accuracy was needed, laying aside the brush to recall his
former skill
with theodolite and measure. Thus working together, we measured
the base of
survey (reading to 1/100 th inch) five
times, in early dawn, to avoid the
sunshine; we
levelled up the Great Pyramid, and down again (reading to 1/100 th
inch); took the
dip of the entrance passage to the bottom of it, and gauged its
straightness
throughout; took the azimuth of the ascending passages round
Mamun's
hole; callipered the sides of the coffer all over, at every 6 inches, and
raised the
coffer (weighing about 3 tons), by means of a couple of crowbars, to
8 inches
above the floor, in order to measure the bottom of it. For the instrumental
readings, in
these cases, Mr. Ellis preferred, however, that I should be
responsible,
excepting where simultaneous readings were needed, as for the base
length, and
in Mamun's hole. To Mr. Ellis I am also indebted for the novel
view of the
Pyramids, showing the nine at once, which forms the frontispiece of
this work.
To Dr. Grant Bey I owe much, both
for occasional help at the Pyramid,
in visiting
the chambers of construction, the well, &c.; and also for his unvarying
kindness
both in health and sickness, realizing the conventional Arab
phrase,
"My house is thy house." Further, I should mention the kind interest
and advice of
General Stone Pasha, who gave me many hints from his intimate
knowledge of
the country; and also the very friendly assistance of our ViceConsul,
Mr. Raph.
Borg, both in procuring an order for my residence and
protection
at Gizeh, and in prosecuting an inquiry into a serious robbery and
assault on
me, committed by the unruly soldiery in October, 1881; unhappily,
this inquiry
was a fruitless task apparently, as the military influence was too
strong in
the examination.
And now I must not forget my old friend
Shekh Omar, of the Pyramid
village,
shrewd, sharp, and handsome; nor how anxious he was to impress on
me that
though some people of base and grovelling notions worked for money,
and not for
their "good name," he wished to work for fame alone; and as he
had no doubt
I should make a big book, he hoped that I should contract with
him for
excavations, and give him a good name. I gratified him with one
contract,
but finding that it cost many times as much as hiring labourers
directly,
and was not sufficiently under control, the arrangement was not
repeated;
but I will say that I found him the most respectable man to deal
with on the
Pyramid hill, excepting, of course, my servant Ali Gabri, who was
equally
anxious about his good name, though too true a gentleman to talk
much about
it. The venerable Abu Talib and the loquacious Ibrahim, shekhs
of the
Pyramid guides, also conducted themselves properly, and Ibrahim seemed
Sect. 7.]
ASSISTANCE OBTAINED. 9
honestly genial
and right-minded in his words and acts, and knew what so few
Arabs do
know—how not to obtrude. The rank and
file of the guides—so
familiar,
with their little stocks of antikas in the corners of old red
handkerchief—sreckoned that I was free of the place,
having Ali for my servant; they
never gave
me the least trouble, or even whispered the omnipresent word
bakhshish,
but were as friendly as possible on all occasions, many claiming a
hand-shaking
and a hearty greeting. My impression of a year's sojourn with
Arabs is
favourable to them; only it is necessary to keep the upper hand, to
resist
imposition with unwearied patience, to be fair, and occasionally liberal
in dealings,
and to put aside Western reserve, and treat them with the same
familiarity to
which they are accustomed between different classes. With such
intercourse
I have found them a cheerful, warm-hearted, and confiding people.
C
10
INSTRUMENTS. [Chap. it.
CHAPTER II.
INSTRUMENTS.
8. THE list of
instruments employed was as follows :
A* Standard scale, steel 100 inches long,
divided to 1 inch.
B* Steel tape 1,200 50
C Steel chain 1,000 20
D Pine poles, a pair I inch diameter 140
10
E* Pine rods, a pair I x 2 inches 100 1
F* Pine rods, 10 of ½x1 60 1
(Jointing together into two lengths
of 250 each.)
G* Pine rods 3 of ½ x 2 inches 60 1
for levelling 2 of ½ x 1 60 1
H* Pine rods, 2,of ½ x 1 40 and 20
J Box on mahogany rods, 2 of 1× 1 25 1/10
K Boxwood scale, 1.25 ×
.13 12 1/50
L Steel scale, 1.07 × .04 12 1/10
M* Ivory scales, 2 of 1.18 x .08 10 1/50
N* Boxwood
scale, 1.18 x .08 10 1/50
O* Gun metal scale, 1.06 x .09 6 1/50
P* Ivory scale, 1.0 x .08 1 1/100
(The
divisions of those marked * are all known to within 1/1000 inch).
Q Double calipers, 72 inches long.
R Supports for catenary measurement by
tape and chain.
S 10
thermometers for scale temperatures.
a Theodolite 10 inch circle, divisions
5', vernier 3" telescopе x 35.
by Gambay 7 inch circle, 10,
10" telescopе x 35.
b Theodolite 5 inch circle, 30', 1'
telescope x б.
by King 5 semicircle, 30', 1' telescope x б.
c Theodolite 4 inch circle, 30', 1' telescope x 8.
by Troughton 4 semicircle, 30', 1 telescope
x 8.
d Box sextant
by Troughton 1.64 inch radius, division 30', vernier 1'.
e Hand level in brass case.
f Gun metal protractor, by Troughton, 5.9 diam., divisions 30'.
g Mahogany
goniometer, 11 and 9 inch limbs.
h Queen's chamber air channel
goniometer.
j Sheet steel square, 35 and 45 inches
in the sides.
k Folding wooden tripod stand, old
pattern.
Sect. 9.]
DETAILS OF LINEAL INSTRUMENTS. 11
l Rigid
tripod stand, 30 inches high, octahedral.
m Rigid tripod stand, 16 inches high, octahedral.
n Rigid
iron tripod, 12 inches high, octahedral.
o 12
signals, with plumb bobs.
The above
were all used, most of them continually; a few other instruments
were also
taken out, but were not needed.
9. Several of
these instruments were of new or unusual patterns, which—as
well as
various fittings adapted to them—require
some explanation. The
dimensions
are all in inches.
A. The steel standard and
straight-edge was on a new principle, employing
the
stiffness of a tube to maintain the straightness of a strip. It was skilfully
executed by
Mr. Munroe, of King's Cross. A steel tube, 102 inches long,
2.0 diam., and .06
thick (see Fig. I, Pl. xv.) was supported at the two neu ral
points, 20.8 per cent. from the ends, resting on two
feet at one point and one at
the other.
This tube carried a series of 15 flat beds, all dressed exactly to
straight
line when the tube rested on its supports. These beds supported the
actual
standard, which was formed of three independent strips of steel, each
34 inches
long, 2.0 wide, and .1 thick, butting end to end. These strips
bore on
the upper
face, along the front edge, very fine graduations, the lines being about
1/1000 wide. To ascertain the mean temperature throughout
the whole length of
the
standard, a rod of zinc was screwed tightly to one end of the standard, and
bore a scale
divided to 1/200 ths at the other end;
the scale rising through a slot in
the
standard. The value of the divisions for various temperatures was carefully
ascertained.
As this standard was also a straight-edge, the edges of the three
strips were
all true straight lines, with a mean error of 1/1200
th inch; and the
edges were
brought into one continuous straight line by adjusting screws set in
the
supporting beds, at the ends of the back edge of each strip. The object of
having three
separate strips was that they could be dismounted for independent
use in
measuring or drawing, and for testing each other's straightness; that
unequal
heating of one edge should not cause as much distortion, in length or
straightness,
as if it were in one continuous piece; and that the weight should not
be too great
for the rigidity, in handling it when detached from the supports. The
principle of
separating the stiff part from the actual scale was adopted in order
to use the
regular drawn weldless steel tube, which is the stiffest thing for its weight
that can be
had, and also to prevent any unequal heating warping the straightness,
as the tube
was boxed in by a thin wooden sheath, and so was sheltered far more
than the
scale could be. The minor details were that strips were held down
by screws
with countersunk heads, bearing on steel spring washers; and they
were pressed
home against each other's ends, and also against the back adjusting
screws, by
diagonally acting springs. Along the front of the tube were projecting
screws,
nutted on and adjusted to form a right angle with the face of the strip ;
so that the
standard could be applied to any surface exactly at right angles.
12
INSTRUMENTS. (Chap. ii.
The value of the divisions was
ascertained by comparison with a brasS
standard
scale. This scale was tested by Capt. Kater in 1820, 1824, 1830, and
1831; and by
the Standards Department in 1875 (see a report on it in the
Report of the
Warden of the Standards, 1875, Appendix x., pp. 36–41):
as the
steel
standard was sufficient for comparisons, this scale was not taken to Egypt
for fear of
injury. The form of this brass standard is a bar, 42.14 long.
1.58 wide, .17
thick; bearing a scale of 41 inches in length, divided to .1 inch,
with a
vernier of 1/1000 ths, and also bearing
a metre divided to millimetres.
The steel
standard was ascertained, by means of this brass standard, to be exact
at 19.6°
cent.; and the mean error of graduation and reading combined was
0002, the
greatest error being 0005. By the intermediary of a steel tape, the
steel
standard was further compared with the public Trafalgar Square standard;
and
according to that it was I in 60,000 longer, or true length at 17.8° cent., or
a difference
of .021 on the length of the public
standard, after allowing for the
published
error of .019 inch. This is a guarantee
that the length of the tapе,
which was
used to transfer from the steel standard to the public standard, has
no greater
error than this; and, on the whole, I should place as much, or rather
more,
confidence in the series of comparisons between the Imperial, the brass,
the steel
standard, and the steel tape, made under the best circumstances indoors,
rather than
in comparisons between the steel tape, the Trafalgar Square
standard,
and certain steel rod measures, made in the open air, with wind and
varying
temperature. The difference in any case is immaterial, in regard to any
of the
points measured, in the present inquiry.
B. The steel tape was over 100 feet
long, .37 inch wide, and .008 thick, and
weighed just
over a pound. It was coiled on an unusually large drum (4.2 diam.),
to avoid any
chance of permanent distortion. Etched divisions, in the ordinary
style, being
too ill-defined, I had an unmarked length of tape, and divided it
by fine cut
lines at every 50 inches; the position of each line was shown by
heating the
steel to brown oxidation, and marking the number out of the brown
by acid. It
was found on trial that such lines did not weaken apiece of tape,
even when it
was violently twisted and wrenched; and that the steel, being hard
drawn and
not tempered, nothing under red heat softened it. The cuts were
not put on with
any special care, as their exact value was to be ascertained; but
the worst
error throughout was .0098, the mean
error .0039 inch, and the total
length true
at 19.8° cent. This comparison was made
when the tape was lying
unstretched,
on a flat surface, as ascertained by measuring successive 100-inch
lengths on
the steel standard. It stretched .0127
per lb. on the whole length of
1,200
inches.
C. The steel chain of 1,000 inches
I made on an entirely new pattern; and
it proved,
both in Egypt, and, some years before, at Stonehenge, to be very handy
in use. The
links are cach 20 inches long, made of wire 092 diam., this being
Sect. 9.
DETAILS OF LINEAL INSTRUMENTS. 13
as thin as
can be used with fair care. The eyes (see Fig. 3, Pl. xv.) are wide
enough to
fold up one in the other, without any intermediate rings. They are
rhomboidal,
so that they cannot hitch one on the other, but will always slip down
when pulled;
and the internal curvature of the end of the eye is only just greater
than that of
the section of the wire, so that the linkage is sure when in use to
come to its
maximum length.* The junction of the eye is made with a long
lapping
piece, cut one-third away, and tinned to the stem. The whole was tested
with 100
lbs. pull, to bring it to its bearings, before marking the divisions. The
exact length
of the links is unimportant, as, after the chain was made and
stretched, a
narrow collar of sheet copper was soldered about the middle of each
link, the
collars being adjusted to exactly 20 inches apart. Besides this, each
link bore
its own number, marked by a broad collar of copper for each 100, and
a narrow
collar for each 20 inches or link; thus, at 340 inches there were three
broad and
two narrow collars by the side of the central dividing mark on the
link. These
collars were put towards one end of the link, apart from the dividing
mark, and
counted from each end up to the middle, as usual. The central eye
of the chain
was not tinned up, but was held by a slip clutch; thus the chain
could be
separated into two 500-inch lengths if needed, each complete in itself,
as for base
lines for offsets. The handles were kept separately, hooking into
any link at
which accurate readings under tension might be needed. They were
of the same
wire as the chain, with wooden cross-bars. One of them included an
inverted
spring (see Fig. 2, Pl. xv.), so that the pull compressed the spring.
When the
pull reached 10 lbs., a small catch (not shown in the Figure) sprang
out from the
stem, and caught the coils. This left only a very small amount of
play; and
hence, when using it, the regulation of the tension did not require to
be looked
at, but was felt by the finger when at 1o lbs. pull.
The advantages of this pattern are:
(1) Great lightness and compactness of
the chain,
as it only weighs 2½ lbs., and forms a
sheaf 1½ inch diam.; (2) consequent
small error
by catenary curves, and ease of carrying it clear of the
ground by its
two ends; (3) accuracy of the divisions; (4) freedom from errors
in the
linkage; (5) that no counting of the links is required, each being numbered;
and (6) that
standard tension can be maintained by touch, while the eyes are
used on
reading the chain length. The worst error of division was .03, the
average
error .01, and the total length, with
10 lbs. tension, true at 15.8° cent.;
the
stretching 'O1 per lb. on the 1,000-inch total length.
D. The pine poles were only used
for common purposes, being correct to
about .02.
E. F. G. H. All these rods were divided
from the standard scale. I made
*This is
preferable to the type of the standard chain of the Standards Department, as
that
has such a
flat curve at the end of the eye that it is not certain to pull to the maximum
length;
and in a
light thin chain such a form would be liable to bend.
14
INSTRUMENTS. [Chap. ii.
a
right-angled triangle of sheet steel and stout brass tube, to slide along the
edge
of the standard.
It was 13' in its bearing length, with a straight edge 4.3 long
at right
angles, for ruling by. It carried a fine line on inlaid German silver, by
which it was
adjusted (with a magnifier) to successive inches of the standard, for
the
successive cuts to be made. Altogether I divided 80 feet of rods into 1-inch
spaces by
this, with an average error of .0015
inch.
The jointing rods were connected by
a slip joint (see Fig. 4, Pl. xv.); a
screw on
each rod slipping through a hole in the other, and then sliding in a slot
until the
rod butted against the stop, S. Both the butt and rod ends were made
by a screw
in the end, sunk up to its head, the screw being screwed in until only
slightly in
excess, and then ground down to a true length, with a radius equal
the length
of the rod. The levelling rods I made with similar jointing and
fitrings. A
base-rod of 60 inches stood on the ground, having a flange against
which the
upper rods could be slid up or down by hand. It had also a block
the side, carrying
a circular level, by which its verticality could be observed.
The mode of
work was for the staff-holder to hold the base-rod vertical, and slide
the upper
rods up or down, till a finely-divided scale at the top was in the field
of the
telescope; then setting the rods, so that one of the inch cuts on them
should agree
with the zero line on the base-rod, the fractions of an inch were
read by the
level telescope, and the whole inches reported by the staff-holder.
This method
enables a larger scale to be used for reading on than if there were
similar
divisions all down the rods; and yet it takes but little time for adjustment,
as that is
only done to the nearest whole inch or two, and it does not
sacrifice
any accuracу.
The other scales do not need any
remark.
Q. The calipers (see Fig. 5, Pl.
xv.) were made for gauging the thickness
of the
coffer sides; the arms were of equal length, so that variations were read on
the scale of
their actual value at the other end. The scale was the gun-metal
scale, O,
screwed temporarily on to the projection at the top, and read by a line
on a brass
plate, underlapping it, on the opposite limb. The zero of the scale
was
repeatedly read, during the series of measurements, by putting an iron bar
of known
length (±.0002 inch) and parallel ends,
between the steel points at the
bottom, in
place of the side of the coffer. The limbs I made of pine, 71 x 4 x [unclear right margin scan copy] 
.. ,
71 × 4 × 1,
lightened by
holes cut through them. The hinge was of steel plates, with copper
foil washers
between them to prevent friction, and closely fitting on a stout iron
pin. The
readings of the scale value corresponding to the gauge-piece were
four times 5.77, and once 5.76,
showing that there was no appreciable shake or
flexure in
the instrument as used.
R. As the steel tape and chain were
often used, suspended in catenary
curves, two
terminal supports were made to hold the ends six inches from
the ground.
One support was simply a wedge-shaped stand with a hook on it
Sect. 10.]
the other
DETAILS OF
ANGULAR INSTRUMENTS. 15
support
carried a lever arm, weighted so that it balanced with
10 lbs.
horizontal pull from the point where the tape was attached; hence
the stand
was drawn back until the arm swung freely, and then there was
10 lbs.
tension on the tape. But transferring apparatus was needed, to transfer
down from
the marks on the tape to the station mark; and to be able to read
as
instantaneously as if the tape lay on the station mark, for simultaneous
readings at
each end. After several experiments I adopted a horizontal
mirror,
levelled in the direction of the tape length, and supported at half the
height of
the tape. The edge of this mirror being placed just beneath the tape,
the reflection
of the tape marks could be seen side by side with the station
mark; both
marks being at the same virtual distance from the eye, and therefore
both in
focus together. Motion of the eye does not affect the coincidence,
except when
the mirror is not level, or not at half the height of the tape; and
even then
only if large variations occur together. The mirror, its stand, and
level, I
arranged to pack inside the wedge-shaped terminal support.
S. The thermometers were common
mercurial and spirit tubes. I
graduated
them by freezing point, and a hot bath with a fine chemical
thermometer
in it. Divisions are most easily and visibly marked on the
tubes by
coating one side with whiting and a trace of gum, then scratching
the lines
through that with a point; and then fixing, by dipping the tube
in thick
varnish. The tubes were mounted with the divisions placed behind,
and thus
much spread out from side to side, as seen through the tube. The
wooden
frames were thick enough to protect the whole bulb and tube sunk
in them; and
the numbering could be safely trusted to the frame, though
the accuracy
of the divisions was secured on the tube. This plan of seeing
the scale
through the tube, might be improved on by instrument makers
flashing a
thin coat of opaque white glass down the back of the tube, and
then etching
out the divisions through it.
10. a. The
principal angular was a splendid theodolite
Gambay, said
to have been used by the French in their share of the
AngloFrench triangulation.
It was of a very unusual form, the support of the
upper parts
and altitude circle being a pillar formed of the cone axis of the
lower or
azimuth circle; and the 10-inch or altitude circle being set on
horizontal
axis parallel to the plane of it, so that it could be turned over
horizontal,
as an azimuth circle, with its centre over the axis of the fixed or
7-inch
horizontal circle. This was a bold device for making available the full
accuracy of the
finest of the circles for either altitudes or azimuths, and it
was quite
successful, as I could never detect the least shake in the converting
axis, even
though this was taken apart every time the instrument was packed
The total
weight was so small—being only 37 lbs.—that I could freely carry
it, as set
up for work, from station to station; but to avoid straining it in
16
INSTRUMENTS. Chaf
travelling,
and to carry it easier over rough ground, it was usually packed
in three
boxes : one for the 7-inch circle and feet, one for the 10-inch circle,
and one for
the telescope, levels, and counterpoise. Its original case was
ludicrously
clumsy, heavy, and dangerous—a sort of
thing to need two stout
sappers to
haul it about, and to take care that it never was turned over.
The 10-inch circle was very finely
graduated on silver to 5', the lines
being so
close as to show diffraction spectra. It was read by four very long
verniers of
100 divisions each, one division equal to 3". The magnifying
power
originally provided was quite inefficient,*
being but single lenses of
1½ inch focus. One of these I retained for
index reading, and then fitted four
microscopes
of (1/4)-inch equivalent focus (or
magnifying 20 diams. on 5-inch
standard, or
40 diams., as opticians are pleased to magnify it): with these
the reading
was excellent, the average error of a single reading and graduation
being only .4"; or, combined with errors of
parallax, by the planes of the
circles
being about 1/100 inch different, it
was .7". The circle errors were
determined
by repeating the quadrants of the verniers around it many times,
and then
going round the circle by stepping the length of each vernier; thus
each
quadrant was divided up by the mean stepping of four vernier lengths
of 8(1/4)° each. These four values were mapped in
curves, and a mean curve
was drawn
through them; this mean curve was ever after used (along with
corrections
for level, &c.) in correcting all the observations of each vernier
independently,
so as to detect any extraordinary error or reading. The
instrumental
errors were all small: the eccentricity of the circles was in the
10-inch=4.8", in the 7-inch=15.5"; the difference of axes of inner and
outer
cones of
repeating motion=5.2"; the
difference between the two ends of the
transit
level-bearing and the steel pivots sunk in them=6.6";
the difference of
the
diameters of the pivots, and their errors of circularity, inappreciable. The
runs of the
four verniers were .42", .92", .25,
and .12" on 5' or 300". Of
course,
in field
work, the errors of pointing, of vibration of the instrument, and personal
errors due
to wind, sand, heat, glare, and constrained positions, increased the
mean error
of reading; and, on the average, it is 1.1"
for a single observation.
The 7-inch circle was scarcely ever
used; the long cone of it was so finely
ground that,
on being set on an ordinary table (soon after I had thoroughly
cleaned it),
the whole of the upper part of the instrument (about 18 lbs. weight)
was seen to
be slowly revolving in azimuth, without any apparent cause. On
* Instrument makers seem to ignore
the fact that there is a definite law for the power nf
reading
microscopes; the angular width to the eye of a minute as seen in the telescope
should
equal the
width of a minute as seen in the microscopes, else there must be a waste of
accuraсу
somewhere.
The formula is—focal length of
object-glass : radius of circle :: focal distance of
eye-piece;
focal distance of microscope. Of course, in compound eyepieces and microscopes
the
equivalent focal distance must be employed, inversely to that deceptive term
"magnifying
power."
Sect. 10.]
DETAILS OF ANGULAR INSTRUMENTS. 17
examining
it, it was found that, not being quite level, and the counterpoise of
5 lbs. not
being put on it, its centre of gravity was not at the lowest point
attainable;
hence the rotation. The telescope was equal in character to the
rest of the
instrument, the object-glass being 1.66
diam., and 16(1/4) inches focal
length, and
the eye-piece of high power and large field; thus it magnified 35
diameters.
The form of the slow motions was far superior to that of English
instruments
; all the tangent screws had a steel ball on the shank, which
worked
between two circular holes, in plates which were clamped together by
a fixed
screw; the nuts were also spherical, cut into two separate halves, and
also clamped
between circular holes. Thus there was practically perfect
absence of
shake, and great working smoothness, even when stiffly clamped.
Another
excellent device was the use of spring steel washers to all screws
whose
tension was in question; the screws were all made to run dead home on
a seat, and
to produce pressure through a curved washer, which they flattened,
either for
fixed tension, or for rotation of an axis. Thus a slight loosening of a
screw made
no difference or shake, and no delicate tightening up was needed; if
the pressure
had to be altered, the washer was taken out and bent accordingly.
The three levels of the theodolite
were suitably delicate, the value of one
division
being 2.47" (altitude), 4.92" (transit), and 12.8" (cross
level). For
these and
every other level used, I adopted a distinctive system of numbering.
Every level
had a different number for the mean position of the bubble end,
and the
divisions were numbered uniformly in one direction, and not simply on
each side of
the mean. Thus the ranges were respectively from 5 to 15, 16 to
24, 28 to
32, 40 to 60, &c., on the levels called No. 10, No. 20, No. 30, No. 50,
&c.; and
when once a number was recorded (the mean of the two ends was
always taken
mentally),it showed which level was read, and in which direction,
with any
doubt, or further note.
Other adjuncts that I provided for
this, and also for the other theodolites,
were slit
caps (see Figs. 6, 7, 8, Pl. xv.). It is manifest that objects seen through
a fine hole
are always in equally good focus, no matter what may be the distance;
hence, if an
object-glass is limited to a small hole, it does not need focusing.
But
definition is commonly required in only one direction at once, either
vertically
or horizontally; hence a slit—which
admits more light—will be as
effective as
a hole. When a line is quite invisible, by being out of focus, placing
a slit cap
over the object-glass, parallel with the line, will make it clear; and
it will be
well defined in proportion to the fineness of the slit. Each of the
theodolites
were therefore fitted with two movable slit caps, fine and wide, to
cover the
object-glasses. As focusing is always
liable to introduce small errors,
by shake of
the tubes in each other, these slit caps were adopted to avoid the
need of
changing focus continually from near to distant objects; they also serve
to bring
near points in view, at only a foot or two from the glass. To be able to
D
18
INSTRUMENTS. [Chap. ii.
place the
slit-cap on the end of the telescope, without shaking it, was essential.
This I did
by making the slit of thin steel spring; soldered to brass clutches, so
as to grip
the telescope by three points; provided also with a projecting tongue
above, and
another below it, whereby to bend it open for clipping it on (see
Figs. 6, 7,
8, Pl. xv.). The smaller theodolites were also fitted with diagonal
mirrors
clipping on to the object-glass; these enabled the instruments to be
very
accurately centred without a plumb-line.
b. The 5-inch
theodolite, by King, was an old one, and was obtained for
rough work;
but it had never been adjusted, so I had to take it in hand; and
on finding
its errors, after correction, to be even less than those of the 4-inch
Troughton, I
generally used it for all small work. I corrected it in the
rectangularity
of cones to the circles, of transit axis to the cones, and of cradle
axis to
transit axis; also in adjustment of verniers for run. The telescope was
of long
focussing-range when I got it, and I increased the range from infinite
down to 5½ feet focus, which made it very useful in
near levelling, as in
buildings;
also I did away with the mere fit of sliding tubes for focussing; and
made the
inner tube run on four points, slightly punched up in the outer tube,
and pressed
in contact with them by a spring on the opposite side of it. The
old level I
replaced by a good one of Baker's, running 41.5"
to .1 inch.
Microscopes
of (1/4)-inch equivalent focus were
fitted to two arms, which were
slipped
together when required for use, and rode round on the compass-boх;
with these
the average error of reading on the 1'
verniers was 7".
The spider lines in this, and the
next theodolite, were somewhat different to
the usual
pattern. When either a single vertical line, or a diagonal cross, is
used, it
blocks out any very small signal; and I have even heard of an engineer
hunting in
vain for his signal, because the line exactly hid it. To ensure greater
accuracy, I
therefore put in two parallel lines, crossed by one horizontal (needed
for
levelling); the lines being about 1/400
inch apart; if closer they may cling
together if
vibrated, and it is awkward to separate them while in the field.
Thus the
interval of the vertical lines was about 1',
and signals could be very
accurately
centred between them.*
c. The 4-inch
theodolite by Troughton was not often used, except where
lightness
was important; I fitted it with two microscopes, similarly to the
5-inch; and
its mean error of reading was about 8" on the 1' vernier.
Though
neither of these were transit theodolites,yet in practice I used
them as such
for all accurate work. By reversing the telescope, end for end,
and upside
down, and turning the circle 180º, all the errors are compensated as
*
Spider line from webs is useless, as it is covered with sticky globules
to catch small flies;
the path-threads
of the spider are clean, but thick; so that the best way of all is to catch a
very
small
spider, and make it spin to reach the ground, winding up the thread as fast as
it spins it
out,
dangling in mid-air
Sect. 10.] DETAILS
OF ANGULAR INSTRUMENTS. 19
in a
transiting instrument; the only extra source of error is irregularity in the
form of the
rings, which can be tested by revolving the telescope in its cradle.
h. For
ascertaining the angles of the Queen's Chamber air channels I needed
to measure
as long a length of slope as possible, at about 8 feet inside a
passage
which was only 8 inches square. For this I pivoted an arm on the
end of a
long rod (see Fig. 9, Pl. xv.), and passed it into the passage in the
dotted position
at A; on reaching the slope it turned itself up to the angle by
pressure,
the main rod touching the passage roof. The arm carried an index,
which
touched a scale attached to the main rod. This scale was divided by
actual
trial, by applying a protractor to the limbs and marking the scale. Тo
read it, a
candle was carried on an arm, which shaded the direct light from the
eye; and the
scale was inspected by a short-focus telescope. Thus the readings
were made
without needing to withdraw the goniometer from the narrow
channel, and
hence the arm of it could be much longer than would be otherwise
possible.
j. A large
square, 35 and 45 inches in the sides, of sheet steel strips, 2 inches
wide, and
tinned together, I made for testing angles; it was not exactly
adjusted to
squareness, but its angles were very carefully fixed, by triangulating
a system of
fine punched dots on the face of it ; and the edges werc
adjusted
straight within about .003 throughout
their length. It could be used
for the
absolute value of slopes of about 51° 50' and 26° 20', by means of a
rider level
placed on one edge of it, and reading by means of a divided head
screw at one
end. To render the square stiff enough sideways, it was screwed
down (with round
projecting screw heads, not countersunk) to a frame of
wooden bars,
2 x 1 inch in section. I generally
found, however, that it was best
to measure a
slope by theodolite and offsets.
k. l.
m. n. These stands were used for the theodolites. Generally
the 10-inch
theodolite
could be placed directly on the rock, or on a stone; but when a
stand was
needed I used one about 30 inches high, that I made of 1 x 1 pine rod;
the top was
stouter and about 12 inches triangle, and the feet about 30 inches
apart,
connected by cross bars. Thus it was of the octahedral pattern, a triangular
face at the
top, another at the base, and six faces around; this being the
only form
absolutely free from racking. The screw feet of the theodolite rested
on leaden
trays on the top of the stand, which allowed free sliding for adjusting
its
centring. A similar octahedral stand about 16 high, was made of ½ x 1
inch
pine, for
the 5-inch theodolite; in order to stand it in chambers or on stones.
The instrument was clamped on to
the stand by a screw from beneath, passing
through a
plate under the triangular top of the stand, and screwing into the base
plate of the
theodolite, which rested upon the top of the stand. Thus it could
be slid
about on the stand, to adjust its centring, and then clamped tight afterwards.
The iron
stand was of just the same pattern, but made of 1/4
inch iron
20
INSTRUMENTS. Chap. ii
rod; the
rods were bent parallel where joined, and passed into sections of iron
tube, the
whole filled up with tinning. These small stands would stand on the
top of the
large one when required.
o. For
signals in the triangulation, to show the places of the station marks,
I made a
number of short wooden cylinders, 1(1/4)
diam., painted white, and standing
on three legs
of wire (see Fig. 10, Pl. xv). In order to enable these to be centred
over the
station marks by a plumb-bob, the cylinder was cut in two across
the middle;
a diaphragm of thin card was then put in it, with a hole truly
centred by adjusting
a circle on the card to the outline of the cylinder; and the
two halves
of the cylinder were pegged together again. Then, having a plumbbob
hanging by a
silk thread through the hole, at whatever angle the cylinder
could stand
the bob would be always beneath its centre. The bob was fixed to
hang at the
right height, according to the irregularities of the rock, by drawing
the thread
through the hole, and pressing it down on a dab of wax on the top of
the
cylinder.
The plumb-bobs are all of a new pattern
(see Fig. 11, Pl. xv). The point
of
suspension is generally too near to the centre of gravity, so that a slight
shift
in it would
move the position of the lower end a good deal more. Hence the
suspension
and the end of the bob are here made equidistant from the middle.
To avoid the
complication of screw plugs to each bob, there was a large horizontal
hole through
the neck, to hold the knot; and a smaller vertical hole in
the axis of
the bob for the thread to pass.
The finest white silk fishing line
was found to be the best thread for plumblines, or
for
stretching for offset measures; it does not tend to untwist, or to
spin the
bob; it is only inch diam., well defined and clean, and very visible.
Wax is
invaluable for hanging plumb-lines in any position; and a piece of wooр
an inch
square, well waxed, if pressed against a stone warmed by a candle, will
hold up
several pounds weight.
For station marks on rocks or
stones, I entirely discarded the bronze and lead
forms. They
may be very good in a law-abiding country, but I found that half
of those put
down by Mr. Gill, in 1874, were stolen or damaged in 1880. The
neat
triangular stones in which they were sunk also attracted attention. I therefore
uniformly
used holes drilled in the rock, and filled up with blue-tinted plaster;
they are
easily seen when looked for, but are not attractive. To further protect
them, I
madethe real station mark a small hole .15
diam.; and, to find it easier,
and yet draw
attention from it if seen, I put two ½-inch
holes, one on each side
of it;
usually 5 inches from it, N.E. and S.W. Thus, if an Arab picked out the
plaster
(which would not be easy, as the holes are 1
to 1½ inches deep) he would
be sure to
attack a large hole, which is unimportant. Where special definition
was wanted,
as in the main points round the Great Pyramid, a pencil lead was set
in the
middle of the plaster. This cannot be pulled out, like a bit of wire, but
Sect. 10.] DETAILS OF ANGULAR INSTRUMENTS. 21
crumbles
away if broken; and yet it is imperishable by weathering. To clean the
surface of
the marks, if they become indistinct, a thin shaving can be taken off the
rock,
plaster, and central graphite altogether. Where I had to place a stone for a
station
mark, I sunk it in the ground; and for the base terminals I took large
pieces of
basalt, and sunk them beneath the surface; thus a couple of inches of
sand usually
covers them, and they cannot be found without directions.
On reading this description of the
instruments, it might be asked what need
there
could be for doing so much in adjustment, alteration, and manufacture,
with
my own hands. But no one who has experienced the delays, mistakes,
expense,
and general trouble of getting any new work done for them, will
wonder
at such a course. Beside this, it often happens that a fitting has to be
practically
experimented on, and trials made of it, before its form can be settled.
And,
further, for the instinctive knowledge of instruments that grows from
handling,
cleaning, and altering them, and for the sense of their capabilities and
defects,
the more an observer has to do with his own instruments the better for
him
and for them.
22 METHODS
OF MEASUREMENT. [Chap, iii.
CHAPTER III.
METHODS OF
MEASUREMENT.
11. FOR the
general questions of the principles of the arrangement of a
triangulation,
and of the reduction of the observations, we must refer to the two
appendices
on these subjects. They are so purely technical, and uninteresting
to any but a
specialist, that they are therefore omitted from the general course
of this
account. We begin here with lineal measure, and then proceed to
angular
measure, including theodolite work in general.
For lineal dimensions, I always
used the system of a pair of rods butting
end to end,
and laid down alternately, instead of making marks at each rod
length. In
testing measures, the value of the sum of two rods can also be
obtained
more accurately than the exact butt length of either of them alone.
But for the
more important points, the direct measurement of a space by a rod
has been
often abandoned for the more accurate method of referring all parts to
horizontal
and vertical planes of known position. This is a necessary refinement
when
precision is needed, and it specifies a form in every element of size, angle,
and place.
In the passages, where the use of horizontal planes was impracticable,
a plane at a
given angle was adopted, and the roof and floor were referred
to that.
In the Great Pyramid, the King's
Chamber was measured by hanging a
plumb-line
from the roof in each corner of the room; and measuring the offsets
from the
lines to the top and bottom of each course on each side of the corner.
Then the
distances of the plumb-lines apart were measured by the steel tape on
the floor. The
heights of the courses were read on a rod placed in each corner.
For the
levels, the 5-inch theodolite was placed just about the level of the first
course; then
at 24 points round the side a rod was rested on the floor, and the
level and
the first course read on the rod.
The coffer was measured by means of
a frame of wood, slightly larger than
the top,
resting upon it; with threads stretched just beyond the edges of the
wood, around
the four sides. The threads gave true straight lines, whose
distances and
diagonals were measured. Then offsets were taken to the coffer
Sect. 12.]
ANGULAR MEASURES. 23
sides from a
plumb-line hung at intervals over the edge of the wood; its distance
from the
straight stretched thread, being added to the offsets, thus gave the
distances of
the coffer sides from true vertical planes of known relation to each
other, at
various points all over the sides. Similarly, the inside was measured
by a frame,
slightly smaller inside it than the coffer. The bottom was measured
by raising
the coffer 8 or 9 inches; the theodolite was placed to sight under it,
and offsets
were thus read off to the outside bottom from a level plane, also
reading the
height of the plane of sight on a vertical rod; then the theodolite
was raised
so as to sight over the top of the coffer, the height of its plane on the
same fixed
rod was read off to give its change of level, and then long offsets
were taken
to points on the inside bottom of the coffer. Thus the thickness of
the bottom
is determined by the differences of level of the theodolite, minus the
two offsets.
Besides this, a check on the sides was taken by a direct measurement
of their
thickness with the pair of calipers already described.
The antechamber was measured in the
common way; but the granite leaf
in it had a
bar placed across the top of it, with a plumb-line at each end of the
bar, ie.,
N. and S. of the leaf. The distances of the lines apart were taken below
the leaf,
and offsets were taken all up the leaf on each side; this was done at
each end and
in the middle of the leaf.
In the Queen's Chamber two
plumb-lines were hung from the ends of the
roof-ridge,
their distance apart observed, and offsets taken to the side walls and
to the ends.
Offsets were also taken to the niche, which was, beside this, gauged
with rods
between its surfaces all over. The heights of the courses were also
measured in
each corner. The angles of the air channels were read by the
goniometer
already described.
The subterranean chamber was
measured in the common way, with rods
along the
sides, but the irregularity of the floor, and the encumbrance of stones
left by
Perring made it very difficult to measure.
12. Turning next
to measurements made with the theodolite, these generally
included
some determination of angular as well as lineal quantities. The
straightness
of the sloping passages was uniformly observed by clamping a
theodolite
in azimuth, pointing along the passage, and having a scale held as
an offset
against the wall at marked intervals; thus variations in azimuth of the
passage were
read. On reaching the end, the assistant holding the scale
stopped, the
theodolite was clamped in altitude instead of in azimuth, and
the
assistant returned, holding the offset scale to the floor or roof; thus
variations
in slope of the passage were read. The whole length of the entrance
passage, and
the ascending passage and gallery in one length, were thus
measured.
For the air channels on the outer face, where the floor is unbroken,
a slip of
board carrying a perpendicular mirror was let down the channel by a
string, in
lengths of 10 feet at a time; and the dip to the reflection in the
24 METHODS
OF MEASUREMENT. [Chap, iii.
mirror was noted
by a theodolite at the mouth. It is then a matter of mere
reduction to
obtain the variations from a straight mean axis.
The horizontal measurements outside
the Pyramid were entirely performed
by
triangulation; and this included in a single system the bases of the
three larger
Pyramids, the pavement of the Great Pyramid, the trenches and
basalt
pavement on the E. side of the Great Pyramid, and the walls around the
Second and
Third Pyramids. The Great Pyramid was comprised in a single
triangle.
This triangulation by means of the 10-inch
theodolite occupied some
months in
all; some angles being read 14 times, and the fixed stations being
about 50 in
number, besides about as many points fixed without permanent marks.
The
first-class points were fixed with an average probable error of 06 inch; and
the least
accurate points, such as those on the rough stone walls, were fixed
within 1 or 2 inches. For fixing the points
uncovered by excavation, a rod
was placed
across the top of the hole, and a plumb-line dropped from it to
the point to
be fixed. A theodolite was then placed near it, and was fixed in
the
triangulation by reference to known stations; the distance of the plumb-line
from the
theodolite, was then measured by the angle subtended by divisions
on the horizontal
rod which supported it.
For connecting together the inside
and outside measurements of the Great
Pyramid, a
station of the external triangulation was fixed on the end of the
entrance
passage floor, thus fixing the position of the passage on the side of the
Pyramid.
From this station the azimuth down the passage was observed ;
thus fixing
the direction of the passage. And levelling was also carried up
from the
pavement and casing stones of the N. face to this station; thus
fixing the
level of the passage, and hence that of all the interior of the Pyramid.
The
positions of the passages of the Second and Third Pyramids, on their faces,
were also
fixed in the triangulation.
The base of the survey was thrice
measured, with a probable error of
± .03 inch (or 1/260000
of the whole) by the steel tape. To avoid the need of
a truly
levelled base line, a series of blocks of stone was put between the
terminals of
the base, which are 659 feet apart; a stone was placed at each
tape length
(1,200 inches), and at each chain length (1,000 inches); and a
sufficient
number of stones were placed also between these, as to support the
chain or
tape in catenary curves throughout, with the usual 10 lbs. tension.
The stones
thus varied from 140 to 393 inches apart. Then, the distances and
levels of
the stones being known, the reduction to be applied to the tape as it
lay on them
to ascertain its horizontal length, were easily applied. No attempt
was made to
place a mark at exactly each tape length on the stones; but
a scale of (1/50)ths of an inch was fixed temporarily on
each stone at which the
tape lengths
joined; then the two ends of the tape were read simultaneously on
the scales
several times over, slightly shifting the tape each time in order to
Sect. 12.] ANGULAR
MEASURES. 25
equalize the
friction of its support : thus the distances of the zeros of the scales
placed all
along the base were ascertained, and hence the total length of the base.
For the height of the Great Pyramid
a line of levelling was run up the
S.W. corner,
across the top, and down the N.E. corner, stepping 15 to 20 feet
at each
shift. Separate lines of level were twice run round the Pyramid,
(including
the basalt pavement, &c.), and the differences were under inch,
both between
them and from the levels of Mr. Inglis, excepting his S.E. socket.
Thus a
complete chain, from N.E. to S.E., to S.W., to top, across top, and
to N.E. was
made; and the difference was only 1/4
inch on the return, the
total run being
3,000 feet distance, and 900 feet height. Besides this, an
independent
measurement by rods had been carried up each of the four corners
of the
Pyramid to the top; generally two, and sometimes three or four, steps
were taken
in one length, and levelled to the nearest, 1/10
inch, from the upright
rod to the
upper step, by a reversible horizontal rod with level attached.
The
intermediate courses in each length were also mcasured off. This gives
all the
course heights, and is regulated at every 10 or 20 courses by the
accurate
levelling on the N.E. and S.W. The same point was always used on
each step,
both in the measuring and the levelling, so as to avoid errors of
levelling
and dressing in the steps ; and each tenth course has a cross scored on
the stone,
at the point used in the levelling. The Third Pyramid was only
measured by
rods up the courses.
The angles of the ascending
passages were not retaken, as Professor Smyth
had already
done that work fully; but the angle to the bottom of the entrance
was observed
by the 10-inch theodolite, placed on a shelf across the mouth of
the passage.
The levels of the horizontal passages were taken with the 5-inch
theodolite,
placed in the middle, and reading on both ends. The level from the
entrance
passage to the ascending passage was read off on a single vertical
rod placed
in Mamun's Hole; a theodolite being put first in the lower and then
in the upper
passage to read on it.
As a general principle, in
observing down a passage with a theodolite, no
dependence
was placed on measuring the position of the theodolite, which was
usually
outside the passage in question; but in all cases a signal was fixed in
the passage
near the theodolite, as well as one at the farthest point to te
observed,
and the azimuths of both were noted; the distances being roughly
known, the
minute corrections to be applied to the azimuth of the further signal
could be
readily determined. The azimuth observations of Polaris always
included a
greatest elongation. For the dip of the entrance passage the 10-inch
theodolite
was clamped in altitude, at closely the true angle; an offset was
taken to the
roof at the bottom, and the theodolite was reversed and re-read as
usual to get
the dip, reading level at the same time. Offsets were then read to
points all
up the roof, keeping the telcscope clamped in its second position; thus
E
26 METHODS
OF MEASUREMENT. [Chap. iii.
it was not
necessary to know the exact height of the plane of the roof above the
theodolite.
The azimuth of the entrance passage was determined down to
Mamun's
Hole, by connection with the triangulation, whose azimuth is otherwise
known; and
it was also determined down to the bottom by Polaris' observations.
The azimuths
of the horizontal subterranean passages were read by the
5-inch
theodolite, placed at the bottom of the entrance passage, and reading on a
signal at
the top, and on candles placed in the passages;* the S. end of the S.
passage
being invisible from the theodolite, its candle was sighted on in line with
its N. end
candle, and the line measured off in the chamber. The azimuth of
the
ascending passages was measured by three theodolites used together; all
of the
telescopes were set to infinite focus, so as to see each other's cross wires
plainly when
a candle was held behind the telescope observed on. The 10-inch
was put in
the entrance passage, reading on a signal at top, and on the 5-inch; the
latter was
placed on the rubbish in Mamun's Hole, reading on the 10-inch and
4-inch; and
this last was placed just above the granite plug blocks, reading on
the 5-inch
and on a signal at the top of the ascending passage. Thus a chain of
angles was
formed from signal to signal, quite free from any errors of centring
the theodolites
or station marks. For the angle of the Great Pyramid casing
stones in
situ, the 10-inch theodolite was placed on the steps above; the dip was
read to
points on the top of the casing stones, and on the pavement in front of
them; and then
offsets were measured from these points to the face of the stone.
The Second
and Third Pyramid casing was measured by goniometer and
protractor.
Thus it will be seen that several
fresh methods of observation have been
introduced,
in order to obtain greater accuracy and more information: in particular
the methods
of plumb-lines and optical theodolite-planes, with offsets from
these, have
yielded good results. A fresh feature in the discussion of observations
is the
introduction of "concentrated errors;" on the principle of showing
all the
divergences from regularity on their natural scale, while reducing the
distances of
the parts so that they may readily be compared together. This
is the
essential basis of the method of graphic reduction, described in the
Appendix
(shown in Traces of Observations, Pl. xvi); and it renders possible the
use of
graphic methods in work of any delicacy; it is also exemplified in the
diagrams of
the King's Chamber walls (Pl. xiii), and of the relation of the casing
and pavement
(Pl. x).
*
Naked candles are good objects for observing on, where there is no wind;
the spot of
flame, the
white candle, or the thin wick, serving at different distances; offset
measurements
can also be
taken accurately to the wick. Lanterns were only used for outside work.
Sect. 13.]
INSIDE GREAT PYRAMID. 27
CHAPTER IV.
EXCAVATIONS.
13. IN Egypt all
excavations are forbidden, and a special permission is
required for
any such researches, the law of treasure-trove being the same as in
England.
Having in 1880-1 done all the triangulation of my station marks, it
was
requisite in 1881-2 to connect them with the ancient points of construction.
For this,
therefore, I needed permission to excavate, and applied to M. Maspero,
the
courteous and friendly director of the Department for the Conservation of
Antiquities;
Dr. Birch kindly favouring my request. In order to save delay and
needless
formalities, M. Maspero at once said that he would permit me to work
under his
firman, on all the points that I had indicated to him in writing; the
Bulak Museum
being formally represented by a reis, who would observe if anything
of portable
value should accidentally be discovered, though such was very
unlikely and
unsought for. Under this arrangement, then, I carried on
excavations
for about six weeks, having during most of the time about 20 men
and boys
engaged. The total expense was only about £18, or £22 including
the reis of
the Museum. He was a son of old Reis Atweh, who worked for
Prof. Smyth;
a very polite man, who quite understood that his presence was a
formality.*
The first work that needed to be
done (and that quickly, before the
travellers'
season set in) was to open the entrance passage of the Great Pyramid
again to the
lower chamber. The rubbish that had accumulated from out of
Mamun's Hole
was carried out of the Pyramid by a chain of five or six men in
the passage.
In all the work I left the men to use their familiar tools, baskets
and hoes, as
much as they liked, merely providing a
couple of shovels, of picks,
and of
crow-bars for any who liked to use them. I much doubt whether more
work could
be done for the same expense and time, by trying to force them into
using
Western tools without a good training. Crowbars were general favourites,
the chisel
ends wedging up and loosening the compact rubbish very easily; but
a shovel and
pickaxe need a much wider hole to work them in than a basket
* A notice of these excavations
appeared at the time in the Academy of 17th
December,1881.
28 EXCAVATIONS.
[Chap. iv
and hoe
require; hence the picks were fitted with short handles, and the shovels
were
only used for loose sand. In the passage we soon came down on the big
granite
stone which stopped Prof. Smyth when he was trying to clear the
passage, and
also sundry blocks of limestone appeared. The limestone was
easily
smashed then and there, and carried out piecemeal; and as it had nо
worked
surfaces it was of no consequence. But the granite was not only tough,
but
interesting, and I would not let the skilful hammer-man cleave it up slice by
slice as he
longed to do; it was therefore blocked up in its place, with a stout
board across
the passage, to prevent it being started into a downward rush. It
was a slab
20.6 thick, worked on both faces, and
one end, but rough broken
around the
other three sides; and as it lay flat on the floor, it left us 27 inches
of
height to pass down the passage over it. Where it came from is a complete
puzzle;
no granite is known in the Pyramid, except the King's Chamber, the
Antechamber,
and the plug blocks in the ascending passage. Of these sites the
Antechamber
seems to be the only place whence it could have come; and Maillet
mentions
having seen a large block (6 feet by 4) lying in the Antechamber,
which is not
to be found there now. This slab is 32 inches wide to the broken
sides, 45
long to a broken end, and 20.6 thick;
and, strangely, on one side edge
is part of a
drill hole, which ran through the 20.6
thickness, and the side of which
is 27.3 from the worked end. This might be said to
be a modern hole, made for
smashing it
up, wherever it was in situ; but it is such a hole as none but an
ancient
Egyptian would have made, drilled out with a jewelled tubular drill in
the regular
style of the 4th dynasty; and to attribute it to any mere smashers
and looters
of any period is inadmissible. What if it came out of the grooves in
the
Antechamber, and was placed like the granite leaf across that chambeт?
The grooves
are an inch wider, it is true; but then the groove of the leaf is an
inch wider
than the leaf. If it was then in this least unlikely place, what could be
the use of a
4-inch hole right through the slab? It shows that something has
been
destroyed, of which we have, at present, no idea.
Soon after passing this granite, we
got into the lower part of the entrance
passage,
which was clear nearly to the bottom. Here a quantity of mud had
been washed
in by the rains, from the decayed limestone of the outside of the
Pyramid,
thus filling the last 30 feet of the slope. This was dug out and spread
on the
passage floor, to save having to carry it out up the long 300 feet of the
narrow
passage; no truck arrangement could be easily worked, owing to the
granite block
lying in the passage. Work down at the bottom, with two
lanterns and
six men, in the narrow airless passage, was not pleasant; and my
visits were
only twice a day, until they cut through to the chamber. Here I
had the rest
of the earth piled up, clear of the walls, and also of the well, and
so
re-established access to these lower parts.
In the well leading from the
gallery to the subterranean passages, there is
Sect. 14.]
CASING, ETC., OF GREAT PYRAMID. 29
a part
(often called the "Grotto") cased round with small hewn stones. These
were built
in to keep back the loose gravel that fills a fissure in the rock,
through
which the passage passes. These stones had been broken through,
and much of the
gravel removed; on one side, however, there was a part of the
rock which,
it was suggested, might belong to a passage. I therefore had some
of the
gravel taken from under it, and heaped up elsewhere, and it was then
plainly seen
to be only a natural part of the water-worn fissure. This well is
not at all
difficult to visit; but the dust should be stirred as little as possible.
One may even
go up and down with both hands full, by using elbows and
toes against
the sides and the slight foot-holes.
14. The next
business was to find the casing and pavement of the Great
Pyramid, in
other parts beside that on the N. face discovered by Vyse: the
latter part
had been uncovered, just when I required it, in 1881, by a contractor,
who took the
chips of casing from the heaps on the N. face to mend the road.
Thus the
tourists to the Pyramid actually drive over the smashed-up casing
on their way. On the three other sides the Arabs had
some years ago cut
away a large
part of the heaps of casing chips, in search of pieces which would
do for village building. Thus the heaps were reduced
from about 35 to only 20
feet in
depth, over the middle of the base sides of the Pyramid ; though
they were
not touched at their highest parts, about 40 or 50 feet up the sloping
side of the
Pyramid.
The shafts for finding the casing
were then sunk first of all about 100 feet
from the
corners of the Pyramid; and then, finding nothing there but rock
(and that
below the pavement level), places further along the sides were tried;
until at
last the highest parts, in the very middle of the sides, were opened.
There
the casing and pavement were found on every side, never seen since the
rest
of the casing was destroyed a thousand years ago. Thus for the North
casing four
shafts were tried; but no casing was found, except where known
by Vyse. On
the East side four shafts were sunk, finding casing in the middle
one. On the
South four shafts were sunk, finding badly preserved casing in
one, and
good casing in another, entirely eaten away, however,
just at the
base (see
Pl. xii.). On the West side five shafts were tried, finding casing
in one of
them, and pavement within the casing line at the N.W. The East
and South
casing was seriously weathered away; on the East it was only
defined by
the pavement being worn away outside its ancient edge; and on
the South it
was found to be even hollowed out (Pl. xii.), probably by the
action of
sand whirled up against the base, and scooping it out like sea-worn
caves. The
shafts were cut as small as possible, to avoid crumbling of the
sides; and
they were steined with the larger blocks where the rubbish was
loose:
ledges were left at each six feet down, for the men to stand on for
handing up
the baskets and larger stones. The Arabs never would clear away
30 EXCAVATIONS.
[Chap. iv.
the loose
stuff from around the shafts, without having special directions; and
often there
was a long slope of 15 feet high of rubbish, just at the angle of
rest, over
one side of a shaft: this needed to be cut away and walled back.
Both the
excavators and myself had narrow escapes from tons of stuff suddenly
slipping in,
sometimes just after I or they had been at the bottom of the
shaft: the
deep Southern shaft no one but Negroes would work in at the
last. As I
did not uncover the casing on the North side, I did not consider
it incumbent
on me to cover it over again; and the casing down the shafts
is safe from
damage, as it is too troublesome and dangerous for the Arabs
to try to
break it or carry it off: it would be far easier for them to work out
more loose
pieces from the rubbish.
Besides these shafts, many pits and
trenches were dug to uncover the
outer edge
of the pavement. For the basalt pavement, the edge of the
rock bed of it
was traced on N.E. and S.; but no edge could be found on
the West. It
was cleared at the centre, where the trenches converge, and was
there found
to be all torn up and lying in confusion, along with many wrought
blocks of
red granite. Further out from the Pyramid it was perfect in some
parts, as
when first laid. The trenches were cleared at the ends, where
necessary;
the North trench was dug into as far as nine feet below the sand
at present
filling it, or about eighteen feet below the rock around it, but
nothing but
sand was found; the E.N.E. trench was cleared by cuttings
across and
along it, so as to find the bottom of each part, and make certain
that no
passage led out of it; the N.N.E. trench was cleared by pits along
it, and
traced right up to the basalt pavement. The trench near the N.E.
corner of
the Pyramid was cleared in most parts, and the rock cuttings around it
were also
cleared, but re-filled, as the carriage road runs over them. Thus
altogether
85 shafts, pits, or trenches were excavated around the Great
Pyramid.
15. At the Second
Pyramid it was not so necessary to find actual casing,
as it was
arranged differently: the bottom course of casing had an upright
foot 10 or
12 inches high, at the bottom of its slope, not ending in a sharp
edge, like
the Great Pyramid casing, which was very liable to injury. The
end of the
slope being thus raised up already some way, the pavement was
built
against the upright face, and to get depth enough for the paving blocks,
the
rock outside the casing was cut away. Thus the casing actually stood
on
a raised square of rock, some few inches above the
rock outside it (see
Pl. xii.),
and the edge of this raised square was further signalized by having
holes along
it (5 to 10 inches long and about half as wide), to receive the
ends of the
levers by which the blocks were moved. This arrangement is
very clearly
shown near the W. end of the S. side, where a block of casing
remains, but
slightly shifted; and therefore, where this raised edge was
Sect. 16.]
THIRD PYRAMID, CASING, ETC. 31
found in
other parts, it was accepted as being equivalent in position to
the foot of
the casing slope, without needing to find actual casing in each
place.
At the N.E. corner the raised edge
was found, scarcely covered over. On
the E. side
two pits were sunk, and the edge was found in one at the S. end.
The edge was
cleared at the S.E. corner. On the S. side the edge was found
at the E.
end, and the casing in situ cleared at the W. end. The S.W. corner of
the edge was
cleared. On the W. side the edge was found at the N. end. The
N.W. corner
was cleared, but no edge was found there. On the N. side the
edge was
found at the W. end. Thus the raised edge was found and fixed at
eleven
points around the Pyramid. The joints of the platform of huge blocks on
the E. of it
were partly cleaned to show the sizes of the stones. Three pits
were tried
on the N.W. of the Pyramid, and the edge of the rock bed of the
pavement was
found in two of them. Two trenches were made to examine the
edge of the
great rock cutting on the N. side of the Pyramid.
Twenty-three trenches and
sixty-seven pits were dug to uncover parts of
the great
peribolus walls of this Pyramid. Thus it was found that all the heaps
and ridges,
hitherto called " lines of stone
rubbish," were built walls of unhewn
stone, mud
plastered, with ends of squared stone, like antae. The great
barracks,
consisting of a mile and a half length of galleries, was thus opened.
Many
fragments of early statues in diorite, alabaster, and quartzite, were found,
as well as
early pottery, in the galleries; though not a five-hundredth of their
whole extent
was uncovered. The great hewnstone wall, built of enormous
blocks, on
the N. side of the Pyramid, was examined by pits; and quarry marks
were found
on the S. sides of the blocks. Two retaining walls of unhewn stone,
like those
of the galleries, were found in the large heap of chips, which is banked
against the
great N. wall. These retaining walls contained waste pieces of
granite and
basalt. The great platform of chips, tipped out by the builders
beyond the
S. peribolus wall, was cut into in two places. Some early pottery
was found;
and it was evident, from the regular stratification, that it had been
undisturbed
since it was shot there in the time of Khafra. Altogether, 108 pits
and trenches
were opened around the Second Pyramid.
16. At the Third
Pyramid it was necessary to clear the casing at the base
level; and
this was a more troublesome place to work on than any other.
Howard Vyse
reports that he abandoned his work here on account of the great
difficulty
and danger of it. The material to be removed consists entirely of
large blocks
of granite weighing a ton and upwards, which lie embedded in
loose sand;
hence, whenever the sand was removed in digging a hole, it ran
down from
the sides, and so let one of the large blocks drop into the hole. The
most successful
way of getting through it was to bring up other stones and
place them
so as to form a ring of blocks wedged together around the hole, and
32
EXCAVATIONS. [Chap, iv.
thus
supporting one another. As there is no clear setting for the casing here
as there is
in the Second Pyramid, and as the substratum had been removed at
the eastern
corners, it was necessary to find the casing foot near each end of
the sides,
and not to trust to the corners. There was no difficulty in finding
casing stones,
as the casing still remains above the rubbish heaps on every side;
the work was
to get down to the foot of it. This was done at the E. end of the
N. side, at
both ends of the E. side, at both ends of the S. side, and at the S.
end of the
W. side. The N.W. corner was very deeply buried, and several trials
were made to
get down, but without finding any place sufficiently clear of the
great
granite blocks; here, therefore, I had to be content with fixing the edge of
the fifth
course of casing, which stood above ground, and projecting this down
at the
observed angle by calculation. Seven points in all were thus fixed, of
the intended
finished surface of the original casing at the bottom course.
Besides
this, eighty-four pits were made along the peribolus walls of this Pyramid;
these holes
showed that the walls were all built like those of the Second
Pyramid, but
less carefully. Ninety-one pits in all were made around the Third
Pyramid.
This makes a total of 284 shafts, pits, or trenches, sunk in the hill of
Gizeh; and
in almost every case the objects sought were found.
17. Some few
details may be useful to future explorers. The tools used were
the ordinary
native forms, with a few English tools for special purposes, as have
been
described. Of supervision the Arabs require a good deal to prevent their
lounging,
and Ali Gabri looked well after them, proving zealous and careful in
the work: I,
also, went out with them every morning, allotting their work for the
day; then
visiting them generally just before noon; and again before they left
off, in the
afternoon. Going thus round to six or eight places some way apart,
and often
stopping to direct and help the men, occupied most of the day. It is
particularly
necessary never to put more men on a spot than are absolutely needed
to work
together; generally each isolated party was only a man and one or two
boys; thus
there was no shirking of the individual responsibility of each man to
get through
his work. Every man was told what his party had to do, and
if they were
lazy, they were separated and allotted with good workers,
where they
would be closely watched. The men were allowed to choose thcir
work
somewhat, according to their strength and capabilities; and if any man
grumbled he was
changed to different work, or dismissed. A very friendly
spirit, with
a good deal of zeal to get through tough jobs, was kept up all the
time by
personal attention to each man, and without any extra stimulus of
bakhshish,
either during or after the work. The wages I offered, and freely
obtained
labour for, were rather above what excavators are required to work for
by the
Museum; but were far less than what had been paid there before by
Europeans.
For ordinary work the rate was 10d. a
day, and 6d. for boys; for
work inside
the Pyramid, 1s. a day, and 7½d. for
boys. The men were paid
Sect. 17.]
WORKMEN. 33
weekly, and
no attempts were made to impose, as I kept a daily register of the
number employed.
Ali received what I always paid him while I was living
there, £1 a
week, and 4s. for his slave and nephew sleeping in the next tomb as
guards; for
this he was always at my disposal for work (though I did not
occupy half
of his time), and he made all purchases and arrangements with the
neighbours,
besides keeping me quite free from molestation or black-mailing by
the other
Arabs.
34
CO-ORDINATES OF STATION MARKS AT THE PYRAMIDS. [Chap. v.
CHAPTER V.
CO-ORDINATES
OF STATION MARKS AT THE PYRAMIDS.
18. THE station
marks of the triangulation consist of holes drilled in the
rock or
stone, and filled with blue-tinted plaster, as already described
(sec. 10).
Where great accuracy was needed a graphite pencil lead was put
vertically into
the plaster. Thus the mark may be scraped clean, if bruised or
defaced,
without destroying the mark. To enable the station-mark holes of
about (1/6)-inch diameter to be readily found, and
at the same time to draw off
attention
from them, two ½-inch holes, similarly
filled, are drilled, in most cases
one on each
side of each station mark, at 5 inches from it, to the N.E. and S.W.
I also
utilized some few of Mr. Gill's bronze station marks, that had escaped the
attention of
the Arabs. The less important stations, of the rock trenches,
are merely
marked by a single ½-inch hole, filled
with blue plaster. The
general
position of the station marks are shown in the plan of the triangulation
on Pl. i.
19. The
co-ordinates of the station marks, &c., are reckoned from a line
beyond the
N. side of the whole area, and from a line beyond the E. side of the
area: thus
there are no minus quantities. The azimuth of true North on the
system of
co-ordinates is East of the approximate North of the system, or the
azimuth of
its Eastern boundary, by
+ 1° 12' 22"±
6"
and the
value of the unit of co-ordinates in British inches is
.00508256±.00000003
log. .7060853±.0000017
or the
number of units in the inch
196.750±.001 log. .2939147±.0000017
Sect. 19.] TABLE
OF CO-ORDINATES. 35
TABLE OF
CO-ORDINATES OF MARKED STATIONS.
[error Marked
GoogleTextCopy color = color ]
Place. Letter From North. From
East.
S.W. corner
of the 9th Pyramid. A
3 987 140 0 935 234
N. side of
2nd Pyramid Temple B
5 393 798 3 411 980
N. side of
3rd Pyramid Temple C
8 382 255 5 839 239
Top block of
5th Pyramid D
9 143 054 6 836 560
N. side of
3rd Pyramid E
8 072 225 6 840 249
Rock of
hill, W. of Ist Pyramid F
4 246 813 8 132 966
Tomb, No.
17, Lepsius G 3 000 000 6 000 000
Hillock S.E.
of 3rd Pyramid H 10 092 621 5 571 047
Top of large
building E. of 3rd Pyramid J 7
828 554 1 491 863
Pile of
slabs N.E. of Ist Pyramid K
1
300 292 1 425 399 → GOOGLE READS
“ I ” for 1
Slab in ground
N. of entrance of Ist Pyramid
(Gill) L
908 159 2 242 158
Tomb N.W. of
N.W. corner Ist Pyramid M 1 483 587 3 431 388
Tomb W.
of (Gill)
Ist Pyramid N I 848 869 4 136 068
N.W. socket
of (Gill) Ist Pyramid Ο I
844 679 3 173 572
Edge of
floor of passage of Ist Pyramid P
I 993 386 2 221 893
N.E. socket
of 9 (Gil) Ist Pyramid Q 1
880 871 1 381 354
Staff on top
of Ist Pyramid R
2 756 484 2 298 662
W. side of
7th Pyramid S
3 007 571 0 915
729
E. side rubbish
heap of Ist Pyramid (Gill) T 2 706 202 1 477 899
S.E. socket
of (Gill) Ist Pyramid
U 3
672 518 1 417 048
S. side on
masonry of Ist Pyramid V
3 523 071 2 369 777
S.W. socket
of Ist Pyramid W
3 634 188 3 206 895
W. side
rubbish heap of (Gill) Ist Pyramid X
2 745 956 3 073 389
Tomb, No.
44, Lepsius (Gill) Ist Pyramid Y
2 926 171 3 863 947
E. end of
base line, on block of basalt Z
4 415 043 1 704
140
W. end of base line, on block of basalt α 4 30б 415 3
255 538
Masonry
above,
and W. of,
door, 2nd Pyramid β
4 732 762 4 900 971 — OO: this line changes TABS, when
lower TAB lines changes during edit .. W11
N.W.corner
of rock
cutting round 2nd Pyramid γ 4
146 945 5 968 245
N.W. corner 2nd Pyramid δ 4
592109 5 758 968
N.E. corner 2nd Pyramid ε
4 632 817 4 092 173
S.E. corner
(on masonry) 2nd Pyramid ζ 6
251 313 4 157 284
S.W. corner 2nd Pyramid η 6
262 182 5 785 021
W. side of
rock cutting round 2nd Pyramid θ
5 950 148 6 000 994
Wall W. of
3rd Pyramid i 7
563 291 8 109 839
N. side of
4th Pyramid κ 9
054 182 7 586 701
N.W. corner
of masonry of 3rd Pyramid λ
8 035 816 7 200 134
S.W. corner of
masonry of 3rd Pyramid μ
8 761 575 7 230 130
S.E. corner of
masonry of 3rd Pyramid ν 8
786 405 6 488 386
N.E. corner of
masonry of 3rd Pyramid ξ 8
038 0б9 6 485 183
Masonry
below door, Ist Pyramid π 935
512 2 249 041
N. end of
North Trench ρ 2
082 608 1 180 207
S. end of North
Trench σ
2 514 650? 1
175 360?
36
CO-ORDINATES OF STATION MARKS AT THE PYRAMIDS. [Chap. v.
[Manually,
direct from the Petrie book; GoogleCopy, the numbers]
TABLE OF
CO-ORDINATES OF MARKED STATIONS.
Place. Letter From North. From
East.
N. end of
South Trench r 3 051 826 1 184 632
S. end of South Trench υ 3 463 988 1 180 826
W. end of
E.N.E.Trench ϕ 2
678 581 881 168
E. end
of E.N.E.Trench χ 2 648 862 568 721
S. end of
Trial passages ψ 2 549 708 721 984
N. end of Trial passages ω 2
350 481 718 038
——————————————————————————————
RESULTING
CO-ORDINATES OF POINTS OF ANCIENT CONSTRUCTION.
Ex¦Casing
edge on N. side of 1st Pyramid 1 866 612 2
281 355
is ¦Casing
edge on N. side of 1st Pyramid 2 671 090 1 401
430
ti ¦Casing
edge on S. side of 1st Pyramid 3 646 300 2 515
643
ng¦Casing edge on W. side
of 1st Pyramid 2 664 836 3 185 923
N.E corner
of casing of side of 1st Pyramid 1 884 598 1
385 776
S.E. 3
668 168 1 421 276
S.W. 3
632 521 3 205 195
N.W. 1 848 772 3
169 668
Centre
of casing
1st Pyramid 2 758 515 2 295 478
NE. corner
of casing of 2nd Pyramid 4 630
771 4 089 656
S.E. 6
297 958 4 121 664
S.W. 6
265 598 5 789 181
N.W. 4
598 359 5 756 193
Centre
of casing
of 2nd Pyramid 5 448 171 4 939 173
N.E. corner
of casing of 3rd Pyramid 7 998 215 6 437 758
S.E. 8
814 325 6 457 924
SW. 8
793 987 7 275 727
N.W. 7
976 980 7 255 56о?
Centre
of casing
of 3rd Pyramid 8 395 877 6 856 742
Sect. 20.
RELATION OF SOCKETS TO CASING. 37
CHAPTER VI.
OUTSIDE OF
GREAT PYRAMID.
20. THE materials
available for a discussion of the original size of the base
the Great
Pyramid are:—(1) the casing in situ upon the pavement, in the
middle of
each face; (2) the rock-cut sockets at each corner; (3) the levels of
the pavement
and sockets; and (4) the mean planes of the present core
masonry.
Since the time of the first
discovery of some of the sockets in 1801, it has
always
been supposed that they defined the original extent of the Pyramid, and
various
observers have measured from corner to corner of them, and thereby
obtained
a dimension which was—without further
inquiry—put down as the
length
of the base of the Pyramid. But, inasmuch as the sockets are on different
levels, it
was assumed that the faces of the stones placed in them rose up
vertically
from the edge of the bottom, until they reached the pavement
(whatever
level that might be) from which the sloping face started upwards. Hence
it was concluded that the distances of the socket
corners were equal to the
lengths of
the Pyramid sides upon the pavement.
Therefore, when reducing my observations, after the first winter, I found
that
the casing
on the North side (the only site of it then known) lay about 30 inches
inside
the line joining the sockets, I searched again and again for any flaw in
the
calculations. But there were certain check measures, beside the regular
checked
triangulation, which agreed in the same story; another clue, however,
explained
it, as we shall see.
The form of the present rough core
masonry of the Pyramid is capable of
being very
closely estimated. By looking across a face of the Pyramid, either
up an edge,
across the middle of the face, or even along near the base, the mean
optical
plane which would touch the most prominent points of all the stones,
may be found
with an average variation at different times of only 1.0 inch. I
therefore
carefully fixed, by nine observations at each corner of each face,
where the
mean plane of each face would fall on the socket floors; using
a straight
rod as a guide to the eye in estimating. On reducing these observations
to give the
mean form of the core planes at the
pavement level, it
came out
thus :—
38 OUTSIDE
OF GREAT PYRAMID.
Case Plane
Sides. Azimuths. Socket Sides. Azimuths.
N. 9002.3 – 4' 35" 9129.8 – 3' 20"
E. 8999.4 – 5' 26" 9130.8 – 5' 21"
S. 9001.7 – 5' 23" 9123.9 +1'
15" ¦ CPS GoogleTextCopy: “4.1006” .. ?
W. 9002.5 – 5' 39" 9119.2 – 7'
33" ¦ Soc GoogleTextCopy: “2.6116” .. ?
.. changes .. alters ..
Mean 9001.5 – 5'16" 9125.9
–
3' 45" ¦ CPS GoogleTextCopy:
“5.1006” .. ? ..
Mean
Difference 1.0 20"
4.4 2'
42"
[Chap, vi.
Here, then,
was another apparently unaccountable fact, namely, that the
core masonry
was far more accurate in its form than the socket square. It is,
in fact,
four times as accurate in length, and eight times as accurate in angle.
This forced
me to the conclusion that the socket lines cannot show the finished
base of the
Pyramid.
The clue which explains all these
difficulties is—that the socket corners
vary from a
true square in proportion to their depth below the pavement, the
sockets
nearer the centre being higher.
This means that the sockets were
cut to receive the foot of the sloping face,
which was
continued right down to their floors, beneath the pavement. (See
Pl. xi.)
Hence the sockets only show the
size of the Pyramid, where it was started
from
varying levels, which were all under the pavement; and its true base upon
the
pavement is therefore 20 or 30 inches inside the lines of the sockets.
This exactly explains the position
of the casing found on the N. side, as it
was found to
be inside the line of the sockets.
The test, then, of this
explanation, was to find the casing on the other sides,
fix its
position, and see if it was likewise within the lines of the sockets. The
shafts were
accordingly sunk through the rubbish, two or three feet inside the
socket
lines; and the casing was found on each side, just in the expected alignment.
Without this
clue, the narrow shafts might easily have missed the casing
altogether,
by being sunk too far out from the Pyramid.
Now having found the casing foot on
each side of the Pyramid, it is settled
that the
faces must have passed through these fixed points, and when the casing
was duly
projected down at its angle of slope to the socket floors, it was found
to fall on
an average 4 inches inside the edges of the socket corners. This is
what might
be expected, as the socket sides are neither straight nor square; so
that this
margin would be much less at a minimum than it is at their corners ;
and it would
be natural to allow some free space, in which to adjust the
stone.
Sect. 21.]
LENGTH OF SIDES OF CASING. 39
21. Having, then,
four lines passing through the middles of the sides, what
is to define
the junctions of those lines at the corners? Or, in other words,
what defines
their azimuth? Was each side made equidistant (1) from its
socket's
sides? or, (2) from the core side at
each of its ends? Or was a corner
made
equidistant (3) from the sides of its socket corner? or, (4) from the sides
of its core corner? The core may be put out of the question; for if the sides
followed it
exactly in any way, they would run outside of the sockets in some
parts. Which,
then, is most likely: that the sockets were placed with an equal
amount of
margin allowed on the two ends of one side, or with an equal margin
allowed at
both sides of one corner? The latter, certainly, is most likely; it
would be too
strange to allow, say, 6 inches margin on one side of a socket, and
only
2 inches on its adjacent side. It seems, then, that we are shut up to the
idea
that the socket corners lie in the diagonals of the Pyramid casing.
But there is another test of this
arrangement, which it ought to satisfy.
Given four
diagonals, as defined by the socket corners; and given four points
near the
middles of the sides of the Pyramid, as defined by the existing casing : if
we start
from one diagonal, say N.E.; draw a line through the E. casing to
S.E.
diagonal; from that through the S. casing, to the S.W. diagonal; and so
on, round to
the N.E. diagonal again; there is no necessity that the line should
on its
return fall on the same point as that from which we started : it might as
easily, apart
from special design, fall by chance anywhere else. The chances
are greatly
against its exactly completing its circuit thus, unless it was so
planned
before by the diagonals of the socket corners being identical with those
of the
square of the casing.
On applying this test to the
diagonals of the sockets, we find that the
circuit
unites, on being carried round through these points, to within .1 inch;
far
closer, in fact, than the diagonals of the sockets and the line of the casing
can
be estimated.
This is, then, a conclusive test;
and we only need to compute a square that
shall pass
through the points of the casing found on each side, and having also
its corners
lying on the diagonals of the sockets.
This square, of the original base
of the Great Pyramid casing on the
platform, is
of these dimensions :—
Difference
Length. from Mean. Azimuth.
Difference from Mean.
—— ———— —————— ———— ———————————
N. 9069.4 +
.6 –3' 20" +
23”
E. 9067.7 – 1.1 –3' 57" – 14”
S. 9069.5 +
.7 –3' 41" +
2”
W. 9068.6
–
.2 –3 54 – 11”
—— ———— ——————————— ————
———————————
Mean 9068. 8
.65 –3' 43" 12”
[ W. Length:
GoogleTextCopy makes a 180 rotated
“6.8609” , also others, more by rule than exception .. ]
[GoogleCopy definitely
vandalizes all the Petrie values to totally useless information,
rotates 6.. 9 to a 180°
species, prints ‘ for Petrie’s decimal ·, ..
and .. I for 1 .. O for 0 ..]
[GoogleTextCopy .. Who are
you?]
[The reader of this should
have the Petrie book open, to verify all this here stated Google (unproclaimed)
Forgery ..]
[Corrections
of the GoogleCopy are marked with this color
(and occasionally this color) type . in “±.04”,
GoogleCopy shows ±04,
where
GoogleCopy also often is replacing the ± with a single + (or sometimes .. not
at all ..)]
40 OUTSIDE
OF GREAT PYRAMID. Chap, vi.
Thus the finished base of the
Pyramid had only two-thirds of the
irregularity
of the core masonry, the mean difference of which was 1.0 inch
and
20"; this is what would be expected from a final adjustment of the work,
after the
rougher part was finished.
But it must always be remembered
that this very small mean error of
.65 inch and 12" is that of the sockets, and not
that of the casing stones; these
latter we can
hardly doubt would be adjusted more carefully than the cutting
of the
sockets with their free margin.
Also it must be remembered that
this result includes the errors of survey.
Now the
probable errors of fixing the plumb-lines in the triangulation were
about .2 on E. side, .2
on S. side, .1 on W. side, and the
casing .1 on N. side;
the probable
errors of the triangulation of the points of reference is in general
much less
than this; we may then say ±.3 for the
absolute places of the plumblines.
The exact
amount of this is not of so much consequence, because the
errors of
estimating the original points of construction are larger. They are, on
the N., ±.04; on the E., ±.2; but another less satisfactory estimate differed 1.1:
on the S., ±.2; on the W., ±.5,
taking the mean of two points that differed 1.1
inches.
Besides this, the estimation of the socket diagonals cannot be put
under ±.5 by the bad definition of the edges and
want of straightness and
orientation
of the sides. If we then allow that the probable errors from all
sources of
our knowledge, of each of the original sides of the Pyramid amount
to ±.6, we shall not over-estimate them. Hence it
is scarcely to be expected
that our
determinations of the sides should agree closer than 65 inch, as they do
on an
average.
So we must say that the mean errors
of the base of the Great Pyramid were
somewhat
less than .6 inch, and 12" of
angle.
22. In computing
the above quantities, I have used my final determination
of the
socket levels below the pavement; these, with the first approximate
results, and
Inglis's figures, stand thus:—
Accurate in 1882. Approximate in 1881. Inglis in 1865.
—— ———————— —————————— ———————
N.E. – 28.5 – 28.7
– 28.6
S.E. – 39.9 – 39.9 – 42.2
S.W. – 23.0 – 22.9
– 23.0
N.W. – 32.8 – 32.6
– 32.8
the level of
the pavement being zero. The approximation was very roughly
done, and it
is strange that it should agree as well with the accurate determination
as it does.
From Inglis's measures I have subtracted 28.6,
in order to
reckon them
from the pavement level; by the exact agreement of my two
Sect. 23-]
LEVELS UP THE PYRAMID. 41
levellings
at the S.E. (which was taken second in the series each time, and hence
is checked
by othe thers), I conclude that Inglis is there in error by a couple of
inches; and
his other work, in measuring the steps, contains much larger
errors than
this.
The relations, then, of the core
masonry, the base of the casing on the pavement,
the edge of the
casing in the sockets, and the socket edges, are shown in
Pl. x., to a
scale of 1/50. The position of the
station marks is also entered. The
inclinations
of the various sides of sockets and casing are stated; and it is
noticeable
that the core masonry has a twist in the same direction on each side,
showing that
the orientation of the Pyramid was slightly altered between fixing
the sockets
and the core. The mean skew of the core to the base is 1' 33", and
its mean
azimuth – 5' 16" to true North.
The diagram also shows graphically how
much
deformed is the square of the socket lines; and how the highest socket
(S.W.) is
nearest to the centre of the Pyramid; and the lowest socket (S.E.) is
furthest out
from the centre of the socket diagonals, and also from the mean
planes of
the core.
23. For
ascertaining the height of the Pyramid, we have accurate levels of
the courses
up the N.E. and S.W. corners ; and also hand measurements up all
four
corners. The levels were all read to inch, to avoid cumulative errors;
but in
stating them in Pl. viii., I have not entered more than tenths of an inch,
having due
regard to the irregularities of the surfaces.* The discrepancy of .2
inch in the
chain of levels (carried from the N.E. to S.E., to S.W., on the ground,
thence to
the top, across top, and down to N.E. again), I have put all together
at the
junction of levelling at the 2nd course of the S.W., as I considered that
the least
certain point. It may very likely, however, be distributed throughout
the whole
chain, as it only amounts to 1.8"
on the whole run.
These levels, though important for
the heights of particular courses, have
scarcely any
bearing on the question of the total height of the original peak of
the casing
of the pyramid; because we have no certain knowledge of the thickness
of the
casing on the upper parts.
The zero of levels that I have
adopted, is a considerable flat-dressed surface
of rock at
the N.E. corner, which is evidently intended to be at the level of the
pavement; it
has the advantage of being always accessible, and almost indestructible.
From this
the levels around the Pyramid stand thus:—
[GOOGLEs copy of this below table is horrible .. we have to rearrange it
as the book shows it ..]
[Google copy sometimes, mostly, confuses ArcMinute ' with Decimal point
. in the book typography]
N.E. E. S.E S. S.W W.
W.N.W N.W N.
———————— ————— ————— ————— —— ———— —— ———— ———— ————
2nd Course +
107.7 .. + 105.5 .. + 111.2.
.. .. +
106.6 + 107.4
Ist Course
+ 58.6 .. .. .. + 57.6 .. .. +
58.0 + 58.9
Levelled
rock 0 E.N.E.
.. .. .. .. .. .. ..
Levelled rock – .15 N.N.E. .. .. .. .. .. .. ..
Pavement – .6? -5.5? +
1.1? –
1.2? +.
Socket – 28.5
.. – 39.9 .. – 23.0
.. .. 32.8 .. ..
* Owing to mistaking (in a photograph) the rock bed of the pavement for
the pavement
———————————————————————————————————————————
G
42 OUTSIDE
OF GREAT PYRAMID. [Chap. vi.
The pavement
levels, excepting that on the N. side below the entrance, are not
of the same
accuracy as the other quantities; they were taken without an assist.
ant, merely
for the purpose of showing that it really was the pavement on which
the casing
was found to rest on each side. The differences of the ist course
levels,
probably show most truly the real errors of level of the base of the
Pyramid.
24. To obtain the
original height of the Pyramid, we must depend on the
observations
of its angle. For this there are several data, as follows; the
method by
which the passage and air channels determine it being explained in
detail
further on, when the internal parts are discussed:—
Weight.
Casing
stones, in situ, N. side, by theodolite.. 51°
46' 45"
± 2'
7" 7
(To three
points on top and three on base.)
To three points on top
, by
goniometer and level 51°
49' 1'
2
by steel
square and level 51º
44' 11” 23" 0
To three 5 overthrown by goniometer 51° 52' 2' 0
To three 18 fragments, all sides, 51° 53'
4' 0
To (All above 2 inches in shortest length.)
N. face, by
entrance passage mouth 51°
53' 20"
1' 10
N. face, by
air channel mouth 51°
51' 30"
20” 5
—————————————————————
N. face,
weighted mean 51°
50' 40"
1' 5"
S. face, by
air channel mouth 51°
57'
30" 20”
[Without these corrected data from a direct manual read of the book,
the Google copy renders perfectly
useless].
In assigning the weights to these different
data, the reason that no weight
is given to
the angles of shifted casing stones is that there is no proof that the
courses did
not dip inwards somewhat; on the contrary, I continually observed
that the
courses of the core had dips of as much as ½°
to 1º; so that it is not at
all certain
that the courses of the casing were truly level to 5' or 10', and
occasional
specimens showed angles up to 54°. The angle by means of the
large steel
square was vitiated by the concretion on the faces of the stones being
thicker
below than above, I inch of difference making an error of 6'. The
small
goniometer was applied to the clear patches of the stone, selected in nine
different
parts. These three casing stones in situ have not as much weight
assigned to
them as they would otherwise have, owing to their irregularities.
One of them
is 0.9 in front of the other at the
top, though flush at the base—a
difference
of 4'. The datum from the air channel, though far more accurate
than that by
the passage mouth (being on a longer length), is not so certainly
intentional,
and is therefore not worth as much. (See sections 32 and 33 for
———————————————————————————————————————————
itself, Prof. Smyth has entered all the levels in his works (both of his
own measures and
those of others) from a datum 20
inches below the true pavement level. This has led him to
reckon the first course as two; hence all his course numbers must have
one subtracted, and all
his levels about zo inches subtracted, to reduce them to a true start from
the pavement surface.
Sect. 26.]
CASING OF THE PYRAMID. 43
details.)
From all these considerations the above weighting was adopted. It
is clear
that the South face should not be included with the North, in taking
the mean, as
we have no guarantee that the Pyramid was equiangular, and
vertical in
its axis.
25. The staff
which was set up by the Transit of Venus party in 1874
on the top
of the Pyramid, was included in my triangulation; and its place is
known within
± ½ inch. From this staff, the
distances to the mean planes of
the core
masonry of the Pyramid sides, were determined by sighting over their
prominent
edges, just as the positions of the mean planes were fixed at the
lower
corners of the faces. Hence we know the relation of the present top of
the core
masonry to the base of the Pyramid. The top is, rather strangely, not
square,
although it is so near to the original apex. This was verified carefully
by an entire
measurement as follows:—
Centre of
Pyramid base Mean of four Mean of three
horizontally
to the readings,
1881. readings, 1882. Mean of all.
---------------------------- ———————— ———————— —————
N. side 226.0 ±
.5 223.7 ± 2 224.5 ± .7
E. side 214'4
.4 213.8 .6 214'1 .3
¦ Seems GoogleCopy confuses .9 with .6 and
vice versa ..
S. side 215.0 .6
215.0 .4 215.0 .4
W. side 216.4 .5 218.7 .5 217.6 1.0
----------------------------
Now, at the level of these
measurements, 5407.9 at N.E., or 5409.2 at S.W.,
above the
base, the edges of the casing (by the angles of the N. and S. side
found above)
will be 285.3 ± 2.7 on the North, and 3016 on the South side,
from the
vertical axis of the centre. Thus there would remain for the casing
thickness 60.8 ± 3 on the N., and 86.6 on the S.; with 77.6 for the mean of E.
and W. Or,
if the angle on the S. side were the same as on the N., the casing
thickness
would be 69.2 on the S. This,
therefore, seems to make it more likely
that the
South side had about the same angle as the North.
On the whole, we probably cannot do
better than take 51° 52' ± 2' as the
nearest
approximation to the mean angle of the Pyramid, allowing some weight
to the South
side.
The mean base being 9068.8 ± .5
inches, this yields a height of 5776.0±
7.0
inches.
26. With regard
to the casing, at the top it must—by
the above data—
average
about 71 ± 5 inches in thickness from the back to the top edge of each
stone. Now
the remaining casing stones on the N. base are of an unusual
height, and therefore
we may expect that their thickness on the top would be
rather less,
and on the bottom rather more, than the mean of all. Their top
thickness
averages 62 ± 8 (the bottom being 108 ±8), and it thus agrees very
fairly with 71
± 5 inches. At the corners, however, the casing was thinner,
averaging
but 33.7 (difference of core plane and
casing on pavement); and this
is explained
by the faces of the core masonry being very distinctly hollowed.
44 OUTSIDE
OF GREAT PYRAMID. [Chap, vi.
This
hollowing is a striking feature; and beside the general curve of the face,
each side
has a sort of groove specially down the middle of the face, showing
that there
must have been a sudden increase of the casing thickness down the
mid-line.
The whole of the hollowing was estimated at 37 on the N. face; and
adding this
to the casing thickness at the corners, we have 707, which just
agrees with
the result from the top (71±5), and the remaining stones (62 ±8).
The object
of such an extra thickness down the mid-line of each face might be
to puta
specially fine line of casing, carefully adjusted to the required angle on
each side;
and then afterwards setting all the remainder by reference to that
line and the
base.
Several measures were taken of the
thickness of the joints of the casing
stones. The
eastern joint of the northern casing stones is on the top .020,
.002, .045
wide; and on the face .012, .022, .013,
and .040 wide. The next joint
is on the
face .011 and .014 wide. Hence the mean thickness of the joints there
is 020; and,
therefore, the mean variation of the cutting of the stone from a
straight
line and from a true square, is but .01
on length of 75 inches up the
face, an
amount of accuracy equal to most modern opticians' straight-edges of
such a
length. These joints, with an area of some 35 square feet each, were not
only
worked as finely as this, but cemented throughout. Though the stones
were
brought as close as 1/500 inch, or, in
fact, into contact, and the mean opening
of
the joint was but 1/50 inch, yet the
builders managed to fill the joint with cement,
despite
the great area of it, and the weight of the stone to be moved—some 16
tons.
To merely place such stones in exact contact at the sides would be
careful
work; but to do so with cement in the joint seems almost impossible
The casing
is remarkably well levelled at the base; the readings on the
stones of
the North side, and the pavement by them being thus:—
W. End. Middle. E.End. Pavement
by Casing. Core 40 ft. E. of Casing.
Front +58.83 +58.84
+58.90 –.01 .. ..
Casing
Back +58.84 .. +58.85 –.03 .. ..
Core +.02 +58.87
Pavement [–.56] [–.30] [–.05] .00 .. ..
The pavement
levels in brackets are on decidedly worn parts, and hence below
the normal
level, as shown in the fourth column. The average variation of
the casing
from a level plane of +58.85 is but .02; and the difference to the core
level, at
the farthest part accessible in that excavation, does not exceed this.
The
difference of pavement level out to the rock at the N.E. corner is but
.17 on a distance of 4,200 inches, or 8" of angle.
27. The works
around the Pyramid, that are connected with it, are—(1) The
limestone
pavement surrounding it; (2) the basalt pavement on the E. side;
and (3) the
rock trenches and cuttings on the E. side, and at the N.E, corner.
Sect. 27.]
PAVEMENT OF THE PYRAMID. 45
The
limestone pavement was found on the N. side first by Howard Vyse,
having a maximum
remaining width of 402 inches; but the edge of this part is
broken and
irregular, and there is mortar on the rock beyond it, showing that
it has
extended further. On examination I found the edge of the rock-cut bed
in which it
was laid, and was able to trace it in many parts. At no part has
the paving
been found complete up to the edge of its bed or socket, and it
is not
certain, therefore, how closely it fitted into it; perhaps there was а
margin, as
around the casing stones in the corner sockets. The distances of
the edge of
this rock-cut bed, from the edge of the finished casing on the
pavement
(square of 9068.8) were fixed by triangulation as follows:—
N.N.W. 6169 near the corner; corner itself
not found, nor any W.N.W. side.
6159 at 570 E.
of probable N.W. corner of pavement.
6187 at 670 E. of probable N.W. corner of pavement
6162 at 890 E. of probable N.W. corner of pavement
N. side {
564 to 568 } very rough and irregular, opposite entrance.
N.N.E. 5290 at
N.E. corner, N. side of it.
—
E.N.E. 5388, at N.E. corner E. side of it.
5339 at 586
from N.E. corner.
—
No cutting
found at S.E. corner.
5365 at 846 from S.W.
corner.
533'0 at 520 from S.W. corner
534'6 at 206 from S.W. corner
S.S.W. 5296 at
S.W. corner, S. side of it.
—
W.S.W. 536.0 at S.W. corner, W. side of it.
627.9
at 751 from S.W. corner.
From these
measures it appears that there is no regularity in the width of the
cutting; the
distance from the casing varying 99 inches, and altering rapidly
even on a single
side. The fine paving may possibly have been regular, with a
filling of
rougher stone beyond it in parts; but if so, it cannot have exceeded
529 in
width.
The levels of the various works
around the Pyramid are as follow, taken
from
the pavement as zero :—
Flat
rock-bed of pavement W. of N.W.
socket – 23.7
beside
N.W. – 21.6
N.
of N.W. – 17.0
N.E.
of N.W. – 15.9 ¦ GoogleCopy
"6.51"
before
entrance – 27.1
Basalt
pavement, E. side of it – 26.9
inner
end of E.N.E. trench + 2.0
W. side,
in excavation +
2.0
46 OUTSIDE
OF GREAT PYRAMID. [Chap. vi.
The Pyramid
pavement must then have varied from 17 to 27 inches in thickness;
it was
measured as 21 inches where found by Vyse.
28. The basalt
pavement is a magnificent work, which covered more
than
a third of an acre. The blocks of basalt are all sawn and fitted
together;
they are laid upon a bed of limestone, which is of such a fine
quality
that the Arabs lately destroyed a large part of the work to extract
the
limestone for burning. I was assured that the limestone invariably
occurs under
every block, even though in only a thin layer. Only about a
quarter of
this pavement remains in situ, and none of it around the edges;
the position
of it can therefore only be settled by the edge of the rock-cut
bed of it.
This bed was traced by excavating around its N., E., and S. sides;
but on the
inner side, next to the Pyramid, no edge could be found; and
considering
how near it approached to the normal edge of the limestone
pavement,
and that it is within two inches of the same level as that, it seems
most
probable that it joined it, and hence the lack of any termination of its bed.
Referring,
then, to the E. side of the Pyramid, and a central line at right
angles to
that (see Pl. ii.), the dimensions of the rock bed of the basalt
paving are
thus:—
NORTH
TO SOUTH.
From
mid-line of Pyramid . . 1046.0
to N.E. . 1061.9 to N.W.
1077.7
to S.E. . 1062.8 to S.W.
Total length
. . .
. . 2123.7 E. side. . 2124.7 W. side.
S. corner of
opening on E. side . . 321.0
to mid. . 756.7 to S.E.
N. . . . . . 693.3 . 352.7
to N.E.
EAST
TO WEST.
Width traced
. . .
. . . . . 1006.6
+ x
E. side,
from Pyramid base . . .
. . 2153.0 N. end.
E. side, from Pyramid base .
. . . . 2148.0
S. end.
S. corner of
opening on E. side to base . . .
2169.0
N. . .
. . . . .
. 2160.0
Next,
referring this pavement to the trench lines:—
NORTH
TO SOUTH.
N. trench,
inner end from basalt . . .
. 318.1
S. trench,
inner end from basalt . . .
. 327.9
EAST
TO WEST.
N.E, corner
to N. trench axis . . .
. . 1073.2
N. trench
axis there, to Pyramid . . .
. 1079.8
S.E. corner
to S. trench axis . . .
. . 1022.6
S. trench
axis there, to Pyramid . . .
. 1125.8
S.E. corner
to N. trench axis, continued .
. . 1075.0
N. trench
axis there, to Pyramid . . .
. 1073.0
[COMMENT ON LANDING ON
THE FINAL Petrie book original TABBING ..]
[W11: GoogleCopyText
→ OpenOfficeWrite → Microsoft WORD looses tabbing and spaces ..
so one has to redo it
all over again in a final Word edited htm-document .. I guess few people
would have the time for
such a demanding and tiering work .. however .. it is quite stimulating ..
once we have »got the
hang of» it .. as the Hours are seen
flying by .. we had some 24h shifts ..]
Sect. 29.
ROCK TRENCHES. 47
Hence the
plan of the basalt pavement seems to be two adjacent squares of
about 1,060
inches in the side; the N. trench axis being the boundary of
them, and
there being a similar distance between that and the Pyramid.
The outer
side of the paving was laid off tolerably parallel to the Pyramid
base; but
the angles are bad, running 15 inches skew.*
29. Next,
referring to the rock-hewn trenches alone, the dimensions of
the three
deep ones are as follow :—
NORTH
TO SOUTH.
N. trench,
outer end, to central line . . . 3510.2
axial length . . . . 2130.2
inner end,
to central line . . . . 1380.0
S. trench, . . . . . . . 1390.7
axial length . . . . 2093.7
outer end to central line . . 3430.4
E.N.E.
trench, outer end of axis N. of central line .
848.3
axis cuts N.
trench axis N. of central line . . 68.5
EAST
TO WEST.
N. trench
axis, outer end to base . . . 1085.5
inner . . . . . 1080.6
S. trench
axis, inner end to base . . . 1125.4
outer . . . . . 1122.9
E. of N. trench axis,
at centre . . 49.7
E.N.E.
trench, outer end of axis to base . . 4213.2
axial length from N. trench axis . 3231.1
from
actual bed of basalt 2112.6
from
straight edge . 2124.7
The slighter
trenches are three in number :—
NORTH
TO SOUTH.
N.N.E.
trench axis cuts N. trench axis N. of central line 116.0
Trench by
N.E. socket, end of axis from N. side of casing 643.3
on the
axis, from N. side of casing 1630.8
1563.3
Trench by
trial passages, ends of axis N. of central line
1274.4
EAST
TO WEST.
N.N.E.
trench, axis cuts pavement, from N.E. corner. 647.2
Trench by
N.E. socket, end of axis from E. side of casing 203.2
on the
axis, from E. side of casing 434.1
3161.6
Trench by
trial passages, ends of axis E. of Pyramid base
3167.6
———————————————————————————————————————
*
The broken blocks of basalt, which border a track down the hill side E.
of the
Pyramid, are
almost certainly from this pavement; they are of exactly the same stone, and
have many
worked faces remaining like those of the pavement. Their placing is quite
rude, and
looks as if done by some barbarian destroyers.
48 OUTSIDE
OF GREAT PYRAMID.[Chap. vi
The
subterranean passages are in one group :—
NORTH
TO SOUTH.
2233.6
Trial
passages axis, N. of central line, at the station marks
1220.8
EAST
TO WEST.
3446.7
Trial
passages axis, E. of central line, at the station marks
3441.2
Hence it
seems that the axial length of the E.N.E. trench outside the basalt
paving is
intended to be the same as the axial length of the North and
South
trenches.
The angles of the axes of these
trenches are as follow :—
To
E. Face of Pyramid. To true North.
N. trench + 7'
53'' + 3'
56''
S. trench + 4'
9'' +
12''
E.N.E.
trench + 75° 2'
26'' +
75° 58' 23''
N.N.E.
trench +
24° 25' 34''
+ 24° 21' 37"
Trench by
N.E. socket + 13° 9'
38" + 13° 5' 41"
Trench by
trial passages – 1°
11' –
1° 15'
Trial
passages + 18' 40" + 14' 43"
-----------------------
Actual image copy
needed to show this:
The Book has the actual end form table as (above top right) .. but in this
shape:
.. 56. Some possible ERRATA:
the numbers are columned as arcseconds, '';
.. 12.
.. 23' Columned as arcseconds ( “ ), noted as arcminute ( ‘ ).
There is no remark on this part (page 48) in the Petrie ERRATA section.
.......................
When cleaning up the GoogleCopy mess in OpenOffice (OO) Writer, OO has,
sometimes, a tendency to
CHANGE THE TABS ALREADY WRITTEN ABOVE — WHEN CHANGES ARE MADE TO tabs
BELOW.
— So ..There are all kinds of fuckups in our universe .. no offense.
(They were made explicitly for us to practice on .. oh my ..).
— And if nobody tells about it .. nobody knows about it
..
Remarks above for Page 48.
+++++++++++
Thus the angles
between the trenches are: S. trench to E.N.E. trench,
104° 1' 43" (or 2 x 52° 0' 52"); and E.N.E. to N.N.E. trench,
51° 36' 52''.
With regard to the details of these
rock cuttings, the forms of the ends
of the N.
and S. trenches were plotted from accurate offsets (see Pl. iii.); and
there is
little of exact detail in the cutting to be stated. The axes at the
ends were
estimated by means of the plans here given, but on double this
scale; and
the rock is so roughly cut in most parts that nothing nearer than
an inch need
be considered. The position of the inner end of the N. trench
is not very
exactly fixed, an omission in measurement affecting it, mainly
from N. to
S. In this trench I excavated to 110 below the present surface
of the sand,
or about 220 below the rock surface, without finding any bottom.
The S.
trench is more regular than the N. trench; at the outer end its width
is 205 to
206, and at the inner end 134.2: it has
a curious ledge around the
inner end at
25 below the top surface. At the outer end the rock is cut,
clearly to
receive stones, and some plaster remains there; also some stones
remain
fitted in the rock on the W. side of this trench. Built stones also
occur in the
N., E.N.E, and N.N.E. trenches. From the inner end of the
S. trench, a
narrow groove is cut in the rock, leading into the rock-cut bed
of the
basalt pavement; this groove was filled for a short way near the end
of the
trench by stone mortared in. It was evidently in process of being
cut, as the
hollows in the sides of it were the regular course of rock-cutting.
The rock
beside the trenches is dressed flat, particularly on the E. of the
Sect. 29.]
ROCK TRENCHES. 49
N. trench,
and the W. of the S. trench, where the built stones occur. There
is a short sort
of trench, on the E. side of the S. trench (not in plan); it is
about 25
wide, 70 long, and 50 deep, with a rounded bottom; the length
E. and W.
The E.N.E. trench is very different
to the others; it has a broad ledge
at the outer
end, and this ledge runs along the sides of the trench, dipping
downwards
until it reaches the bottom towards the inner end: the bottom
sloping
upwards to the surface at the inner end. There are stones let into
this ledge,
and .mortared in place, and marks of many other stones with
mortared
beds, all intended apparently to make good the ledge as a smooth
bed for some
construction to lie upon. The bottom of this trench I traced
all over, by
excavations across and along it; looking from the outer end, there
first came
two ledges—the lower one merely a
remainder of uncut rock, with
grooves left
for quarrying it—then the bottoin was
found about 200 inches below
ground
level; from this it sloped down at about 20° for about 200 inches; then
ran flat for
300 or 400; and then sloped up for 300 or 400; then rose vertically,
for some
way; and then, from about 120 below ground level, it went up a
uniform
slope to near the surface, where it was lost at the inner end under
high heaps
of chips. At the outer end the width near the top is 152.8, and
at 25 down
148.2; the lower space between the
sides of the ledge widens
rapidly to
the middle, from the end where it is 43.0
wide above and 35.0
below.
Towards the inner end the rock is very well cut; it has a row of
very rough
holes, about 6 diam., in the dressed rock along the N. edge of
the trench,
near the inner end. This dressed side of the trench ends sharply,
turning to
N. at 1603.6 from outer end of the trench axis; the width here
is 170.1, or 172.3 at a small step back in S. side,
a little E. of this point. The
trench had
not been clear for a long time, as many rudely-buried common
mummies were
cut through in clearing it; they were lying only just beneath
the sand and
rubbish in the bottom.
The N.N.E. trench was traced by excavations
along the whole length of
2,840
inches, up to where it is covered by the enclosure wall of the kiosk. It
is fairly
straight, varying from the mean axis 2.1,
on an average of five points
fixed along
it. The depth varies from 14 to 20 inches below the gencral
surface. It
is 38, 40, 39.2, and 36 in width, from
the outer end up to a
point 740
along it from the basalt pavement; here it contracts roughly and
irregularly,
and reaches a narrow part 18.2 wide at
644 from the pavement.
The sides
are built about here, and deeply covered with broken stones. Hence
it runs on,
till, close to the edge of the basalt pavement, it branches in two, and
narrows yet
more; one line runs W., and another turning nearly due S.,
emerges on
the pavement edge at 629.8 to 633.4 from the N.E. corner of
the
pavement, being there only 3.6 wide.
From this remarkable forking, it
II
50 OUTSIDE
OF GREAT PYRAMID. (Chap, vi.
is evident
that the trench cannot have been made with any ideas of sighting
along it, or
of its marking out a direction or azimuth; and, starting as it
does, from
the basalt pavement (or from any building which stood there),
and running
with a steady fall to the nearest point of the cliff edge, it seems
exactly as
if intended for a drain; the more so as there is plainly a gooр
deal of
water-wearing at a point where it falls sharply, at its enlargement. The
forking of
the inner end is not cut in the rock, but in a large block of
limestone.
The trench by the N.E. socket is
just like the N.N.E. trench in its
cutting and
size; and it also narrows at the inner end, though only for about
20 inches
length. It has a steady fall like the N.N.E. trench; falling from
the S. end
5'5 at 50, 85 at 100, 14'3 at 190, 210 at 300, and 270 at 400 inches.
The inner end
is turned parallel to the Pyramid, the sides curving slightly
to fit it.
The rock cuttings by it are
evidently the half-finished remains of a general
dressing
down of the rock; the hollows are from 3 to 6 inches deep, and so very
irregular
that they do not need any description beside the plan (Pl. ii.).
The trench beside the trial
passages is slight, being but 6 deep at N. and
17 at S.; it
is 29.0 wide at N., 26.5 in middle, and 27.9 at S. Its length is 289,
with square ends.
The sides are vertical at the N., narrowing 3.5
to bottom
at S.; ends
shortening 3.0 to bottom. The bottom
dips slightly to the S.,the
levels from
the N. running 0, — 1.7,
— 2.2,
— 3.2, and — 5.8.
30. The trial passages
(see Pl. iii.) are a wholly different class of works to
the
preceding, being a model of the Great Pyramid passages, shortened in
length, but
of full size in width and height. Their mean dimensions—and mean
differences
from those dimensions—as against the
similar parts of the Great
Pyramid,
are:—
26°32 mean difference 24 Pyramid
passage angle 26°27' mean
diff. .4'
41.46 mean difference .09 Pyramid passage widths 41.53 mean diff. .07
47.37 mean difference .13 Pyramid passage heights 47.24 mean diff. .05
23.60 mean difference .08 Pyramid ramp heights 23.86
mean
diff. .32
81.2 mean difference .6 Pyramid
gallery widths 82.42 mean diff. .44
28.63 mean
difference .54 Pyramid well widths
28.2 mean diff. .3
The details
of the measurements of each part are all entered on the section
(Pl. iii.).
The vertical shaft here is only analogous in size, and not in position, to
the well in
the Pyramid galiery; and it is the only feature which is not an exact
copy of the
Great Pyramid passages, as far as we know them. The resemblance
in all other
respects is striking, even around the beginning of the Queen's
Chamber
passage, and at the contraction to hold the plug-blocks in the
ascending passage
of the Pyramid (see section 38). The upper part of the vertical
shaft is
filled with hardened stone chips; but on clearing the ground over it, I
Sect. 32.]
CONNECTION OF INSIDE AND OUTSIDE. 51
found the
square mouth on the surface. The whole of these passages are very
smoothly and
truly cut, the mean differences in the dimensions being but little
more than in
the finely finished Pyramid masonry. The part similar to the
gallery is the
worst executed part; and in no place are the corners worked quite
sharp,
generally being left with radius about .15.
The N. end is cut in steps for
fitting
masonry on to it; and I was told that it was as recently as 1877 that the
built part
of it was broken away by Arabs, and it appeared to have been
recently
disturbed; in Vyse's section, however, the roof is of the present length,
so the
removal must have been from the floor. By theodolite observations the
plane of the
passage is straight and vertical within 5' or less.
31. Having thus
finished the statement of the outside of the Pyramid and
the works
surrounding it, the next subject is the connection of the outside and
inside of
the building.
To determine the exact place of the
passages and chambers in relation to
the
whole Pyramid, a station of the triangulation was fixed in a hollow just on
the
end of the entrance passage floor; and this was thoroughly connected with
three
main stations. Levelling was also carried up from the casing and pavcment
below,
to this station, and to the courses near it. Thus the inside, as far as
Mamun's
Hole, is completely connected with the outside; and in the ascending
passages
beyond that, there is only 2' of azimuth in doubt.
32. The original
length of the entrance passage has not hitherto been
known,
except by a rough allowance for the lost casing. But after seeing the
entrances
of the Third Pyramid, the South Pyramid of Dahshur, and the
Pyramid
of Medum, all of which retain their casing, there seemed scarcely a
question
but that the rule was for the doorway of a Pyramid to occupy the
height
of exactly one or two courses on the outside. That the casing courses
were
on the same levels as the present core courses, is not to be doubted, as they
are
so in the other Pyramids which retain their casing, and at the foot of the
Great
Pyramid.* The next step is to see if there is a course equal to the
vertical
height of the doorway; and, if so, where such a course occurs. Now
the vertical
height of the doorway on the sloping face of the Pyramid (or
difference
of level of its top and base) would be 37.95, if the passage mouth was
the same
height as the present end, or 37.78 if the passage was exactly the same
as the very
carefully wrought courses of the King's Chamber, with which it is
————————————————————————————————————————————
* The awkward
restoration of
the casing that Prof. Smyth adopted (Life and Work, iii., Pl. 3) was
forced on
him by his mistaken assumption of the pavement level 20 inches under the truth
(L. and W. ii. 137);
hence by
Vyse's casing stone measures he made the casing break joint with the core, in
defiance of Vyse's
explicit
drawing of its position; and was obliged to reduce the pavement to 5 or 10
inches, in place of the
21 inches
recorded by Vyse. The drawing of "backing stones," at the foot of Pl.
1., vol. iii., L. and W.,
is equally
at fault; the casing stones which remain in the middle of the side, ending
directly against the
core masonry;
and the core at the corners only leaving 34 inches for the casing thickness. No
backing
stones exist
behind the casing of the Third Pyramid or the cased Dahshur Pyramid.
52 OUTSIDE
OF GREAT PYRAMID. [Chap. vi.
clearly
intended to be identical. On looking to the diagram of courses (Pl. viii.)
it is seen
that at the 19th course is a sudden increase of thickness, none being so
large for 11
courses before it and 14 after it. And this specially enlarged course
is of
exactly the required height of the doorway, its measures running thus:—
By levelling
at entrance 37.67, by measuring ¦ mean.
¦
37.95 or
¦ doorway
courses 37.8; by N.E. 38.1,
S.E. 37.6, ¦ 37.94
¦
37.78
¦ height
N.W. 37.5, S.W. 39.1.
¦ ± .17 ¦
The19thCourse:
Here
the agreement is so exact that it is far within the small uncertainties of
the
two dimensions. Hence, if the passage emerged at the 19th course it would
exactly
occupy its height (see Pl. xi.).* Besides this, it will be observed that there
are two
unusually small courses next over this, being the smallest that occur till
reaching the
77th course. The explanation of these is clear, if the doorway came
out in the
19th course; an unusually thick lintel course was needed, so two
thinner
courses were put in, that they might be united for obtaining extra thickness,
as is done
over the King's Chamber doorway. These two courses are also
occasionally
united in the core masonry.
The crucial test then is, supposing
the passage prolonged outwards till it
intersects
this course, how will its end, and the face of the casing, stand to the
casing
stones at the foot of the Pyramid? The answer has been already given
in
the list
of determinations of the casing angle. It requires an angle
of slope
of
51° 53' 20" ± 1'; and this is so
close to the angle shown by other remains
that
it conclusively clenches the result to which we are led by the exact equality
of
the abnormal course height with the doorway height.
The data for calculating the result
are: (1) levels of the 19th course by
entrance
668.30 and 705.97; (2) floor of passage at station mark, level 611.2
(3)
which is inside the edge of the base of the casing horizontally, 638.4;
(4)
entrance passage angle at mouth 26° 29' ± 1';
(5) entrance passage
height
47.26.
33. By a similar
method the air channels give a determination of the
angle of the
faces. It is true that the channels did not occupy a whole course
like the entrance;
but as they are uniformly cut out as an inverted trough in
the under
side of a block which is laid on a broad bed, it is almost certain that
they
similarly continued to the outside, through the one—or perhaps two—stones
now stripped
off; and also that their floors thus started at a course level
(sce Pl.
xi.).† If this, then, were the case (as the N. channel cannot by its posi-
———————————————————————————————————————
* It should be explained that this
is called the 20th course by Prof. Smyth, owing to his
error about
the Ist course and pavement level. His measure of it is 38 inches, and the two
French
measures give it as 37 and 38 inches.
†
In the section of the S. air channel mouth published by Prof Smyth,
certainly"the
joints are not
put in from any measure," nor is any other feature of it. The passage, its
bed.
and top, are
all about half of their true size, and the form of it is unlike anything that
has
been there,
at least since Vyse's time.
Sect. 34.
BLOCKS ABOVE ENTRANCE. 53
tion have
come out in any but the 103rd course on the face, and the S. channel
in any but
the 104th), they would show that the casing rose on the N. face at
51° 51'
30", and on the S. face at 51° 57' 30", as before stated. The various
data
are entered
on the diagram of the channel mouths. The levels were fixed by
measuring
several courses above and below the present mouths, and thus
connecting
them to the course levelling at the corners of the Pyramid. With
regard to
the main part of these air channels, the details are given further on
in the
measures of the King's Chamber (section 56); and it is disappointing that
they vary so
much in azimuth and altitude, that they are useless for connecting
the measures
of the inside and outside of the Pyramid.
34. The sloping
blocks over the entrance to the Pyramid, and the space
below them,
were examined (partly by means of a ladder), and measured; but
the details
are not worth producing here, as the work of them is so rough. The
large blocks
are as follows, in general size :—
E. upper. W. upper. E. lower. W.
lower.
Length on
top [185] [194] 151+x 167.7
Length below
117½ 121 84+x 107.6
Breadth 80.0 to 91½ 88.3 82.6
81.6
Height of
mid-line. . [114] . . . 91
Lean of face
20' to 2° in 2° 20' in 20' to 30' out 25'
to 30' in
Angle on
top. 35° 40' to 39° 50' mean
40° 38° 45' to 50' 39° 30'
on base. 38° 45' to 50' 39°
30' 39° 20' to 50' 39° 30' to 55'
on butment 49° 50' to 50° 10' 50° 40' hidden
50° 30'
The measures
in brackets are deduced from the angles and other measures.
These blocks
are much like a slice of the side of a casing stone in their angle;
but their
breadth and length are about half as large again as any of the casing
stones.
Their mean angle from 12 measures is 50° 28' ± 5'. The thickness of
these blocks
is only 33 inches, and there are no others exactly behind them, as I
could see
the horizontal joints of the stones running on behind them for some
inches. On
the faces of these blocks are many traces of the mortaring which
joined to
the sloping blocks next in front of them. These were placed some
70 inches
lower at the top, and were not so deep vertically. By the fragment
left on the
E. side, the faces of these blocks were vertical. In front of these
came the
third pair, similar, but leaning some 7½°
or 8° inwards on the face,
judging by a
remaining fragment. Probably a fourth and fifth pair were also
placed here
(see Pl. ix.); and the abutment of the fiſth pair shows an angle of
70½° or 73° in place of 50°. The successive
lowering of the tops, leaning the
faces in,
and flattening the angle of slope of the stones as they approach the
outside,
being apparently to prevent their coming too close to the casing.
These
sloping blocks were probably not all stripped away, as at present, until
recently, as
there is a graffito, dated 1476 (half destroyed by the mock-antique
Prussian
inscription) on the face of the remaining block where it is now
54 OUTSIDE
OF GREAT PYRAMID. [Chap. vi.
inaccessible,
but just above where the next pair of blocks were placed. The
sloping
blocks are of remarkably soft fine-grained limestone, about the best
that
I have seen, much like that of the roofing of the chamber in Pepi's
Pyramid;
and it is peculiar for weathering very quickly to the brown tint, proper
to
the fine Mokattam I'mestone, darkening completely in about twenty ycars, to
judge
by the modern-dated graffiti.
Sect. 35.]
ENTRANCE PASSAGE, LENGTH. 55
CHAPTER VII.
THE INSIDE OF
THE GREAT PYRAMID.
35. HAVING, then,
fixed the original position of the doorway of the
Pyramid, we
may state that it was at 668.2 ± .1 above the pavement of the
Pyramid; 524.1 ± .3
horizontally inside (or S. of) the N. edge of the Pyramid
casing; and its
middle 287.0 ± 8 E. of the centre* of
the Pyramid; or 3723.6
from E.
side, and 4297.6 from W. side, at its level; the probable error being
that of
fixing the length of the sides. Thus we have the following positions in
he entrance
passage, reducing all to the true beginning of the floor :—
W.
Floor. W. Wall W. Wall
Base.
Top. W. Roof. E. Roof. E. Wall Top.
Doorway,
original 0 ± .3 0
± .3
End of
"basement sheet" 124.2
Station mark
127.90
1 178.75
2 226.46
1 276.63
3 285.29
2 331.79
4 340.56
2 348.10
5 406.04
3 414.21
6 465.46
4 474.02
Scored line 481.59
5 516.26
7 531.67
6 551.66
8 584.15
7 606.87
ANGIVEN
VERTIKALTEXT VÄNSTER MELLAN Station
mark och Scored
line:
“Prof.
Smyth's joint numbers”; PDF-kopians sidnummer 79.
* Whenever any point is
described as E. of the centre of the Pyramid, it is uniformly
meant that
it is that amount E. of a vertical plane, parallel to the mean of the Pyramid's
E. and
W. sides,
and which passes through the centre of the Pyramid. Similarly of similar
descriptions
N., S., and
W.
56 THE
INSIDE OF THE GREAT PYRAMID. [Chap. vii.
W.
Floor. W. Wall W. Wall
Base.
Top. W. Roof. E. Roof. E. Wall Top.
8 651.91
9 686.98
10 700.28
11 736 28
10 763.70
12 776.39
11 806.14
13 827.16
12 865.32
14 878.58
13 891.79
15 915.09
14 926.69
16 963.61
15 967.14
16 996.27
17 1003.69
18 1028:59
17 1056.78
19 1063.82
18 1106.13
Floor
Ascending
Passage 1110.64
20 1127.71
19 1136.06
21 1174.22 . . . . . . . . 1163.6
20 . . . 1177.14
1177.7
1188.1
. . . . . . . . . . . 1192.4
. . . . . . . . . . . . . 1207.1
. . . . . . . 1232.1
. . . . . . . . . . . 1243.7
. . . . . . . . . . . . . 1262.3
. . . . . . . . . . . 1296.1
. . . . . . . 1318.5
. . . . . . . Rock.
1340.1
. . . . . . . . . Rock.
. . . 1347.5
. . . . . . . . . . . 1350.7 Rock.
. . . . . . . . . . . Rock.
The above measures were taken by
rods from 124.2 to 285.29 (the rods
jointing
together with butt ends), by steel tape from 276.63
to 1177.14, and by
rods from
1163.6 to the rock; all duly corrected for temperature. On comparing
them with
Professor Smyth's measures, it will be found that his measures
make the
passage length about an inch shorter on an average; this is fairly
accounted
for (1) by his being all piece-meal measures added together, (2) by
the rude
method of making scratches with a screw-driver to mark the lengths of
Sect. 35.]
ENTRANCE PASSAGE, LENGTH. 57
rod on the
stone (L. and W. ii., 46), and (3) by there being "always a certain
amount of
risk as to the measuring rod slipping on the inclined floor" (L. and
W. ii., 35).
All these errors would make the reading of the length shorter than
it should
be; and all were avoided by the use of a steel tape lying on the side
of the
floor. Nevertheless, I tested again, by rod measure, some of the points
where the
difference of Professor Smyth's measures were greatest from the steel
tape, and
they come out thus :—
Between Joints. By Steel Tape. Again
by Rods. By Prof. Smyth.
5 to 6 on Floor 59.42 59.45 59.2
7 on Wall to 8 on Floor 22.72 22.72 22.2
14 on Wall
to 15 on Floor 11.60 11.58
10.9
14 on Wall
to 16 on Floor 36.92 36.93 37.6
15 on Wall
to 16 on Floor 3.53 3.47 2.9
These will practically show what
errors may creep in, by not using a continuous
measure like
a steel tape. The object of measuring the joints, as well
as the total
length, by steel tape, is sufficiently illustrated by this comparison.
One source of error may arise from
following the coarsely-scratched
prolongations
of the anciently drawn lines, and of the ascending passage floor
and roof.
These have been made by modern measurers; and they were always
rejected,
and a more accurate method employed.
The measures from the steel tape
onwards, by rods, down to the end of the
built
passage, where it rests on the rock, are not of the same accuracy as the
others; the
broken parts of the passage sides, and the awkwardness of
measuring
over the large block of granite, without any flat surface even to hold
the rods
against, prevented my taking more care over a point where accuracy
is probably
not of importance.
For the total length of the
entrance passage, down to the subterranean
rock-cut
part, only a rough measurement by the 140-inch poles was made,
owing to the
encumbered condition of it. The poles were laid on the rubbish
over the
floor, and where any great difference of position was required, the ends
were plumbed
one over the other, and the result is probably only true within
two or three
inches. The points noted down the course of the passage,
reckoning
from the original entrance (i.e., the beginning of the rock on the E.
side of the
roof being 1350.7), are the following:—
E. W.
Beginning of
inserted stones, filling a fissure. 1,569
1,555
Joint in
these stones 1,595
None.
End of these
inserted stones 1,629
1,595
Sides of
passage much scaled,
1 or 2 inches off, beyond here 2,750
Fissure in
rock 3,086
3,066
. . . . .
to 3,116 3.096
Mouth of
passage to gallery 3,825
. . . . .
to 3,856
End of
sloping roof (4,137 Vyse,
corrected
for casing). . . . 4,143
I
58 THE
INSIDE OF THE GREAT PYRAMID. [Chap. vii.
36. The azimuth and
straightness of the passage were carefully measured.
The azimuth
down the built part was taken by reference to the triangulation,
which in its
turn was fixed by six observations of Polaris at elongation, from a
favourable
station (G). The azimuth to the bottom of the rock-cut passage was
observed
independently, by five observations of Polaris at elongation. The
observations
of the straightness throughout gives a check by combining these
two methods,
and they are thus found to agree within 19", or just the sum of
their probable
errors, equal to only .09 inch lineally
on the azimuth of the built
part. The
results are:—
Azimuth. Altitude.
Mean axis of
whole length –3'44" ± 10" 26° 31' 23" ± 5"?
Mean axis of
built part alone –5'49"
± 7”
Same, by offsets
from 3'44" axis –5'28" ± 12" 26° 26' 42" ± 20"?
(Same by
Prof. Smyth,
two days. – 4' 27" and –5'34"
26° 26' 43" ± 60")
The
observations of the straightness of the walls, floor, and roof of the
passage,
when all reduced to offsets from its mean axis of the whole length
stand thus:—
Distance
from From – 3' 44"'azim. From 26° 31' 23" alt.
original
entrance. W. Mid. E.
Roof. Mid. Floor.
460 21.1 .3 W. 20.5 23.2 – .4 – 24.1
710 20.9 .2
W. 20.6
23.4
– .2
– 23.9
990 20.7 0 20.8 24.1 +.4 – 23.3
1,110 – 23.4
1,291 21.1? .1 E.
21.3
1,505 20.5 .2 E. 21.0 23.8
1,741 20.4 .4 E. 21.1 23.6
– .1
– 23.9
2,069 20.8 .2 E. 21.1 23.4 – .4 – 24.2
2,481 21.6 .3 W. 20.9
23.4
2,971 21.0 0
21.0
3,711 21.3 .4 W. 20.5 24.3 0
–
24.3
4,113? 21.3 .4 W. 20.5 236
– .6?
– 24.9?
4,140 20.8 23.9
——
——
Mean error .23 .30
(Floor at
1,110 interpolated from clinometer curve.)
But the passage
in the built part, and indeed for some 40 feet below that, is far
straighter
in azimuth than the lower part; taking this upper (2/5)
ths of it alone, it
has a mean
axis of — 5'49" ±7" in
azimuth, and varies thus:—
W.
Mid. E.
At 460
20.86
.06 W. 20.77
710 20.78
0 20.77
990 20.70
.05 E. 20.80
1,291 21.23 0 21.22
1,505 20.75 0 20.75
1,741 20.76 .01 W. 20.74
———
Mean Error .02
Sect. 37.]
SUBTERRANEAN CHAMBER, ETC. 59
These offsets
only being read to 1/20 inch (the 1/100 ths merely resulting from computation)
it is
remarkable that the errors of the mid-line of the passage are so
minute; and
it shows that in this particular we have not yet gone within the
builder's
accuracy; readings too 1/100 th inch or
to I" on the longer distances, are
now
required.
The absolute position, then, of the
middle of the S. end of the entrance
passage
floor will be, in level, 668.2—(4140 × sin. 26° 31' 23") – .8 difference of
floor
offsets, = – 1181 ± 1 ?; in distance
from N. base of pyramid 524.1+
3704.3= 4228 ± 2? or 306 N. from mid-plane; and
in distance E. from the
mid-plane
287.0—[sin.
(3'55" – 3' 44") x 3704] – .4 difference of offsets =286.4
± 10.
37. The
Subterranean chambers and passages are all cut roughly in the
rock. The
entrance passage has a flat end, square with its axis (within at least
1º), and out
of this end a smaller horizontal passage proceeds, leaving a margin
of the flat
end along the top and two sides. This margin is 4.5
wide at E., 3.2
at W., and 5.4 to 6.0
from E. to W. along the top. The dimensions and
distances
are as follow, from the S. end of the floor of the entrance passage (as
deduced from
the roof, which is better preserved); and the axial positions and
levels are
by theodolite observations:—
A
B C D
E F G
H
Top.
Base E.
W.
Beginning of
Horizontal 0 306 N. 40.8 .4 W. 286.4
48.5 0
– 1181 floor
passage 20 32.9 I.0 W. 285.8 Top+
38.3 –
1143 roof
Fissure 76 W. 91 E.
In Passage 121 32.3 32.4
N. Door of
Side Chamber. 218 88 N. 31.6 32.7
S. Door of Side Chamber 291 15 N. 31.9 33.0
N. Door of Large Chamber 346* 40 S. 32.0 33.3
.5
W. 286.3
35.5
36.0
Top+ 38.9 – 1142 roof
S. Door of Large Chamber 672 366 s. 29.5 29.5
1.9
W. 284.9
31+x† Top
– 6.6 – 1188 roof
In S.
Passage 760 29.6 27.3
In S. Passage 900
26.7 26.7
26.3 26.0
In S. Passage 1040
28.1 29.0 28.6 27.0
In S. Passage 1180
30.1 30.0 29.5 29.3
In S. Passage End 1318
1012 S. 26.0 9.7 W. 277.1 Top
– 2.6 – 1184 roof
Large
chamber, E. wall 325.9; at 100 from W.
wall 329.6?; N. wall 553.5; S. wall 554.1
Top+125.3‡ – 1056 roof
Side chamber
W. wall 69½ to 70½; N. wall 70.3;
S. wall 72.3 Top
+ 40 – 1137 roof
to + 48
A Distance from End of E.
P. Floor
B Distance fromMid. Plane
of Pyramid
C Width E. to W. Top.
Base
D Mid. from Entrance
Axis, continued
E Mid. E. from Mid. Line
of Pyramid
F Height E. W.
G Level above End of E.
P. floor
H Level below Pyramid
Pavement
[Avoiding complicated tab settings (the Petrie more tight type demands
more memory ..):]
[This
Petrie originally typographical dense table
has here been rearranged with A-H rows explaining the Petrie (A-H) columns]
The large
chamber walls are therefore distant from the Pyramid central
axis, 302.9 E. at N. wall; 299.6 E. at S. wall; 250.6
W. at N. wall; 254.5 W. at
S. wall; 40
S. and 366 S. The central axis thus not passing through the chamber, but 40
inches inside the rock of the N. side.
* E. side of
door-sill is at 351, and W. side 347, the wall not being fully dressed down
there.
† This doorway rounds off at
the top, rising 1½ inches in the 10 inches.
‡The top is + 124.3 at N. doorway, 125.4 to 127.6 at S.
doorway; the roof being cut away higher, just in the corner.
60 THE
INSIDE OF THE GREAT PYRAMID. [Chap, vil.
The side chamber is an enlargement
of the passage, westward and upward,
as are all the
chambers of the Pyramid; it is very rough and uneven, and
encumbered
now with large blocks of stone. The large chamber is most clearly
unfinished,
both in the dressing of the walls, and more especially in the
excavation
for the floor. The walls have an average irregularity estimated at
± .7, and projecting lumps of rock are left untouched in
some parts. The roof
is more
irregular, estimated average variation ± .3.
The floor is most irregular,
at the W.
end it rises at the highest to only to inches from the roof; and over
all the
western half of the chamber it is irregularly trenched with the
cuttings
made by workmen to dislodge blocks of the rock. It is, in fact, an
interesting
specimen of quarrying, but unfortunately now completely choked up,
by Perring
having stowed away there all the pieces of limestone taken out of his
shaft in the
floor. After dislodging several blocks, I crawled in over the knobs
and ridges
of rock, until jammed tight from chest to back in one place; and
thence I
pushed about one 140-inch rod, by means of the other, so as to measure
the length
up to the Western end. To measure along the W. side is impossible,
without
clearing away a large quantity of stones; and as there is no place to
stack them
safely without their going down the shaft, I could only measure the
width at 10o
from the W. end, perhaps somewhat askew. The lower-easternpart
of the
floor, 140 below the roof, which is comparatively flat, is, nevertheless,
very
irregular and roughly trenched, quite unfinished. The best worked floor
surface is
just around the square shaft, 198 below the roof, and about 40 below
the main
part of the floor, which is 155 below roof on a knob of rock beside the
shaft. The
square shaft is not parallel to the chamber, but is placed nearly
diagonally.
Its distances to the walls are, N.W. corner 135 to N. wall; N.E.
corner 60 to
E. wall; S.E. corner 9o to S. wall. Its sides are, N.E. 68 to 75?
S.E. 82½; S.W. 8o; N.W. 70 above, 79 below (the N.
corner being rounded
above); N. to
S. diagonal 100. The S.E. and S.W. sides stop at 67 deep, or
265 below
roof, or 1,321 under pavement; leaving a ledge about 20 inches wide
a second or
deeper part of the shaft goes downwards, the N.E. and N.W. sides
being
continuous with those of the upper part; it is, in fact, a smaller shaft
descending
out of the N. corner of the larger. The sides of the smaller shaft
are, N.E.
57? S.E. 53? S.W. 6o, N.W. 56. The original depth of the smaller
shaft I could
not see, it was apparently about 40 inches according to Vyse,
when Perring
sunk his round shaft down in the bottom of the ancient square
shaft. This
hole in the dimly-lighted chamber, about 30 feet deep (with water
in it after
heavy rains have rushed down the entrance passage), and with a very
irregular
and wide opening, makes measurement about here somewhat unpleasant.
I avoided
filling the shaft with the earth removed from the passage, or with the
stones which
Perring excavated from it, in case anyone should afterwards wish
* Like the shaft of the tomb
chamber of Ti at Sakkara; an unusual plan.
Sect. 38.]
ASCENDING PASSAGE, LENGTH. 61
to excavate
farther at the bottom. The southern passage is very rough,
apparently
merely a first drift-way, only just large enough to work in, intended
to be
aſterwards enlarged, and smoothed; its sides wind 6 or 8 inches in
and out.
38. The Ascending
passage from the entrance passage is somewhat
troublesome
to measure, owing to the large plugs of granite that fill some 15
feet of its
lower part; and also to the irregular way in which much of its floor
is broken
up.
For connecting it with the entrance
passage, we must first settle the most
probable value
of its angle, in order to carry on the projection of its floor; and
to complete
it over the plugging and breakage, which prevent direct measurement.
The angle of
the whole passage will be discussed further on; it will
suffice to
say here that the mean angle is 26° 2' 30"; and there is therefore a
presumption
that the plugged part is about the same angle, and not the 26½° of
the entrance
passage. This is confirmed by direct plumb-line measure of the
angle of the
plug-blocks at their lower end, giving 26° 7' (± 2'?); and noting
that the end
is square with the portion of passage beyond it to within 5'. Also
the actual
angle of the plug-blocks may be computed from Prof. Smyth's sloping
measures,
combined with my levelling between the floors of the passages, and
plumbing up
to the lower end of the plugs.* This gives 26° 12½'
for the angle of
the lower
300 inches of the passage; and 5' of variation would require a difference
of .4 inch vertical on .9 sloping. Hence the other data confirm this so
far, that it
had better be adopted as the angle through the plugged part;
until some
one shall improve on Prof. Smyth's sloping measure, or on my
levelling.
The junction of the passages was
not projected over the broken part uncertainly,
as had been done
before; but a plumb-line was hung from the W. side
of the
Ascending passage roof, in front of the plug-blocks ; and measures vertical,
perpendicular,
and sloping, were taken to the plugs, the fragments of the
ascending,
and the top and bottom of the entrance passage. Thus the whole
was knit
together to a true vertical line, the place of which was fixed on the
entrance
floor. From the mean of these measures, and 26° 12½'
as the ascending
angle, with
26° 21' as the descending angle at that spot (by Prof. Smyth), the
Ascending
passage roof starts vertically over 1110.90
on the sloping floor of the
*
The elements in question are (1) Prof. Smyth's plumb-line 48.5 on slope below his zero in
Ascending
passage; and (2) 180.5 on slope of
entrance passage, below beginning of Ascending
roof. (3) My
level in A.P., 71.3 on slope above C.P.S.'s zero in A.P. (4) My level in E.P.
1015.0 on slope below C.P.S.'s E.P. zero. (5)
Difference of my A.P. and E.P. level marks
156.2 vertically. (6) My plumb-line on E.P. foor
1027.3 on slope below C.P.S.'s E.P. zero.
(7) Height
on my pluunb to floor of A.P. 37.0. (8)
height of plug-blocks 47.3, and angle
of end
26° 7'. (9)
Angle of E.P. at junction 26° 21'. From these measures we get 125.1 tan. θ
+142.9 sin. θ
=124.7; :. θ = 26° 12½'.
62 THE
INSIDE OF THE GREAT PYRAMID. [Chap. vii.
entrance,
reckoning from the casing face; and the floor cuts the entrance floor
at 111064
from the same, both probably ±1.
Further, the
lower end of the plug-block is 74'19 from the intersection of
the floors;
and the upper end 5076 from the intersection of the roofs. Having
thus fixed
the beginning of the Ascending passage, by the point where its floor
produced
onwards intersects the floor of the entrance passage, we can proceed
up the
Ascending passage from this as a starting point. The distance past the
plug-blocks
being determined as above described, and that from the plug-blocks
to the S.
end of the passage, by steel tape measure on the E. side of the floor;
then, the
tape being corrected for temperature and tension, the results are thus,
on the
sloping floor:—
Floor,
E. side Base of E. wall.
Junction of
passage floors 0 0
Beginning of
actual floor . ·. 59.8
Base of plug-blocks
74.2
Top of
plug-blocks, present 252.7
Top of plug-blocks, ancient 277?
Joint numbers. Floor, E. side Base of E. wall.
Smyth's Dixon's.
1 27 298.2 298.2
(Petrie's
levelling mark 324.0)
2 26
about 333.6 333.6
25
374.9
6 23
496.6 496.6
7 22
552.3 552.3
21 593.3
8 604.4
20 637.9
19 690.3
10 18 716.1 716.1
11 17 749.0 748.9
12 799.1
16 812.1
14 848.1
13 854.2
15 13 922.4 922.2
16 12 955.0 955.3
11 1006.9
17 1008.0
10 1044.9
19 1080.3
9 1095.0
20 8 1130.0 1129.9
21 7 1161.5 1161.5
22 1202.4
6 1214'2
23 1255.4
Sect. 38.] ASCENDING
PASSAGE, LENGTH. 63
Joint numbers. Floor, E. side Base of E. wall.
Smyth's Dixon's.
5 1273.2
25 4 1337.9 1337.9
26 1368.6
3 1377.7
27 1427.1
28 1488.7
2 1515.5
Gallery,
plumb from wall over door 1546.5
29 Floor joint 1546.8
Wall joint
And edge
over door 1 1547.0
On comparing these measures with
Prof. Smyth's, it will be seen that he
makes the
passage about 3 inches shorter; and that this difference mainly
occurs in
the lower part, where the floor is much broken. Several lengths were
therefore
measured as tests, just as in the entrance passage, and the results are :—
Ist
measure 2nd measure Prof. Smyth,
by
tape. by tape. by one rod.
Mark (1) to
mark (2) 50.0 50.1
Mark (1) to
22 (Dixon) 56.3 56.3
22 Dixon to
21 Dixon 40.9 ¦ 41.0 ¦
¦
52.1 ¦ 52.1 49.7
21 Dixon to
8 Smyth 11.2 ¦
11.1
¦
8 Smyth to
20 Dixon 33.3 33.5
20 Dixon to
mark (3) 8.3 8.2
by
rods.
11 Smyth to
12 Smyth 50.1 50.2
50.2
12 Smyth to
16 Dixon 13.0 ¦
13.3 ¦
16 Dixon to
14 Dixon 36.0 ¦55.1 55.3 ¦
55.1 55.3
14 Dixon to
13 Smyth 6.1 ¦
5.7 ¦
13 Smyth to
15 Smyth 68.2 68.4
67.7
[The three
verticals ¦ are represented in Petrie’s book as one large vertical } ]
The close agreement of these two
series of measures, particularly in those
parts twice
measured by tape, will show (as in the entrance passage) that the
error is
certainly in the rod measures, and due to the same causes as the error
in the
entrance passage, i.e.,
slipping, irregular placing on broken floor, and the
marking off
of each length.
The result therefore is that from
the intersections of entrance and ascending
passage floors,
to the floor joint at the E. side of the grand gallery doorway,
is 1546.8 on the slope.*
The granite plugs are kept back
from slipping down by the narrowing of
the lower
end of the passage, to which contraction they fit. Thus at the lower,
or N. end,
the plug is but 38.2 wide in place of
41.6 at the upper end: the
height,
however, is unaltered, being at lower end 47.30 E., 47.15 mid, 47.26 W.;
and at
upper, or S. end 47.3. In the trial
passages the breadth is contracted
*
On the W. side this joint is 1.2
N. of the side joint of doorway.
64 THE
INSIDE OF THE GREAT PYRAMID. [Chap, vil
from 41.6 to
380 and 37.5 like this, but the height
is also contracted there from
47.3 to 42.3.
These plug-blocks are cut out of boulder stones of red granite, and
have not the
faces cut sufficiently to remove the rounded outer surfaces at the
corners:
also the faces next each other are never very flat, being wavy about
± .3. These particulars I was able to see, by putting my
head in between the
rounded
edges of the 2nd and 3rd blocks from the top, which are not in contact;
the 2nd
having jammed tight 4 inches above the 3rd. The present top one is
not the
original end; it is roughly broken, and there is a bit of granite still
cemented to
the floor some way farther South of it. From appearances there I
estimated
that originally the plug was 24 inches beyond its present end.
It has been a favourite idea with
some, that two horizontal joints in the
passage roof
just south of the plugs, were the beginning of a concealed passage:
I therefore
carefully examined them. They are 60.5
(or 60.1 second measure)
apart
vertically, and therefore quite different to the passages of the Pyramid,
which are 47
perpendicularly or 52 vertically. Further, there is no possibility of
the blocking
up of a passage existing there, as the stone of the roof is continuous,
all in one
with the sides; the three roof-blocks between the two
horizontal
joints are all girdle-blocks, either wholly round the passage, or
partially
so; and the block N. of these is a long one, over 125 inches from
E. to W.,
and continuous into both walls. These vertical girdle-blocks are a
most curious
feature of this passage (first observed and measured by Mr.
Waynman
Dixon, C.E.), and occur at intervals of 10 cubits (206.3 to 208.9
inches) in
the passage measuring along the slope. All the stones that can be
examined
round the plugs are partial girdle-blocks, evidently to prevent the
plugs
forcing the masonry apart, by being wedged into the contracted passage.
Many of the
stones about the blocks in Mamun's Hole are over 10 or 11 feet
long; the
ends are invisible, but probably they are about 15 feet over all.
39. For the angle
of the passage, and its straightness, it will be well to
consider it
all in one with the gallery floor, as they were gauged together all in
one length.
The angle of slope I did not observe, as I considered that that had
been settled
by Prof. Smyth; but the azimuth was observed, by a chain of three
theodolites,
round from the entrance passage. The straightness was observed
by offsets
to floor and side all along it, read from a telescope at the upper end of
the
plug-blocks. When I came to plot the results, I found that there were
no measures
taken at the point where Prof. Smyth's theodolite was set up. The
sloping
floor is nowhere, having been entirely cut away at the beginning of the
gallery; and
the top of the ramp (to which the theodolite had been referred)
was not
offsetted by me, nor was its slope measured by Prof. Smyth's clinometer
for 300
inches from the place. Hence we cannot say exactly what direct
relation the
theodolite bore to the passage; but we can obtain the angle of slope
very
satisfactorily, by taking the angles observed to signal at bottoin of ascend-
Sect. 40.]
PASSAGE TO QUEEN'S CHAMBER. 65
ing passage,
and to signal at top of gallery, and then (knowing the distances of
these
signals) calculate the angle of slope from signal to signal. This, when
corrected
for lower signal being .3 too high,
gives 26° 12' 50" for mean angle of
both passage
and gallery together. Hence, from my offsets to the places of
these
signals, the absolute angle, and the variations from it, can be obtained for
either part
independently. Thus we have the form and direction of the ascending
passage,
reckoning from the beginning of its floor on the entrance passage floor,
with its
variations, as follows :—
From From
– 4' ±
3' azimuth. From 26°
2' 30" altitude.
beginning W. mid.
E. roof.
mid. E.
floor
69 23.1 –.5 24.1
260 20.8 0 20.7 23.6
0
23.6
520 21.6
23.5
650 20.9
22.4
700 20.7
840 21.4 23.3
1,045 21.3 23.7
1,220 21.9 24.1
1,365 21.2 23.9
1,540 21.0
0
21.1
23.9 + .1 23.6
The surfaces
are so much decayed and exfoliated, that it is only just at the
ends that
two original faces can be found opposite to one another; hence the
width and height
cannot be measured, and the offsets can only be stated to one
surface.
From of the the this altitude, the
sloping length passage being 1546.8,
horizontal
length will be 1389.5, and the vertical
height 679.7, both being
corrected
for difference in the offsets of the ends. The determination of the
azimuth has,
unhappily, a large probable error, ± 3' (owing to bad foundation for
the
theodolite in Mamun's Hole); and its direction, –
4', is so close to that of
the Pyramid
side, that it may be assumed parallel to that ±
3'. This, on the
passage
length, =1.2 inches for the probable
error of the place of the upper end
of the
passage, in E. to W. direction in the Pyramid.
These, added to previous amounts,
give for the absolute place of the floor
end at the latitude
of the E. wall of the gallery (172.9+679.7)=852.6±.3 level
above
pavement; (1517.8+1389.5)=2907.3±.6
horizontally from N. edge of
Pyramid, or
1626.8±.8 northwards from centre; and
287±1.5 for middle of
passage
eastward from centre of Pyramid.
40. The
horizontal passage leading to the Queen's Chamber is the next
part to be
considered. This was measured with steel tape all along, and the
levels of it
taken with theodolite. The results for its length and levels are
thus, reckoning
from the mean door of the gallery at 1546.8
from beginning of
ascending
passage:—
K
[ERRATA p.65
l.34: ± 3'. → ± .3' ]
66 THE
INSIDE OF THE GREAT PYRAMID. [Chap, vii
Distance
Northward from .·.Roof
from
door. Pyramid centre. Floor level. level
Mean doorway
on floor 0
1626.8±8 852.6±3
On flat
floor 52 1575
858.4
Floor joint,
No. 8, Smyth 312.0
1314.8 † 857.4 ‡ 903.8
No. 16, 623.0 1003.8 † 856.1 ‡ 902.3
No. 21, 870.2 756.6
†
On floor 1000 627 † 856.2 ‡ 902.4
Floor joint,
No. 25, Smyth 1177.7 449.1 †
Step in
floor 1307.0 319.8 † ¦854.6 ‡ 901.0
¦834.9
‡
Chamber ¦ top of door 1523.9 102.9
N. wall ¦ side of door 1524.8
102.0
Floor joint,
No. 30, Smyth 1527.0 99.8
Niche, N.
side 1620.7 6.1 834.4
Niche, first
lapping 901.3
Chamber, E.
apex 1626.5 .3 1080.1
[Separat
vertikaltext i Petrietabellens original:
PETRIES TEXT, PDF-kopians sida 90:
† : All these are ±.8
‡ : All these are ±.3 ]
[De bägge vertikala ¦ motsvarar boktextens endA { ].
The is
azimuth of this passage was not measured, but the beginning of it
287±1.5 E. of the middle of the Pyramid; then for
the axis of it at the end we
may say the
same, or 287±3, since the gallery above it only differs about two
inches from
that quantity. In the above measures of length there is a steadily
accumulating
difference of about 1 in 300 between Prof. Smyth's measures and
these, for
which it seems difficult to account; but as in the other passages, I
have always
found on retesting the measures, that such differences are due to
errors in
the cumulative single rod measures, and not in my steel tape (which
was always
verified at the starting point after measuring), it seems unlikely that
the steel
tape should be in error here. Hence I should adopt these measures
without
alteration.
41. In the Queen's Chamber it seems, from the foregoing statement,
that
the
ridge of the roof is exactly in the mid-place of the Pyramid, equidistant
from N. and
S. sides; it only varies from this plane by a less amount than the
probable
error of the determination.
The size of the chamber (after allowing
suitably in each part for the incrustation
of salt) is
on an average 205.85 wide, and 226.47 long, 184.47
high on N.
and S.
walls, and 245.1 high to the top of the
roof ridge on E. and W. walls,
The
variations of the horizontal quantities in detail are as follows, from the
mean
dimensions.
Sect. 42.]
QUEEN'S CHAMBER, HEIGHT. 67
From below Apex, E.
Wall. From below Apex, W.
Wall. Below Ridge of Roof.
——————————— ——————————— ———————————
Above To N. (Sum.)
To S. To
S. (Sum.) To N. W. to
E. Wall.
Floor. Wall. (Sum.) Wall
Wall. (Sum.)
Wall. Wall.
to
E.
Wall.
—— —— ——— ——— ——
——— ——— —— —— ———
Mean
of all 102.92 205.68 102.76
. 102.67 206.02 103.35
. . 226.47
240 . . . . . . . . –.46
225.51 –.50
210 . . . . . . . . –.31
225.79 –.37
180 +.16 205.67 –.17 . –.14 broken
. –.24 226.12 –.11
156 +.06 205.60 –.14
127 +.10 205.72
. –.16 206.15 +.29 . 0
226.37 –.10
99 +.02 205.79 +.09
76 . +.09
205.68 –.25 . +.24
67 –.32
205.63 +.27 . +.27 226.91 +.17
8 . . . . +.37
206 29 . –.06
0 . . . . . . . . +45
227.47 +.55
For example,
to take the first entries, at 180 inches over the floor, on the
E. wall, the
N. wall is (102.92 +.16) = 103.08 from a vertical line below the
apex of the
roof; and the S. wall is (102.76–.17) = 102.59 from the same apex
line : the
sum of these quantities, or the total width, being 205.67. Thus the
mean
distances of the N. and S. walls from the apex on the E. and W. walls is
given at the
top of each column; and beneath that the small variations from
those mean
vertical wall faces. In the last division are given the distances of
the E. and
W. walls apart, below their apices; both the mean dimension, the
variations from
it, and the total at each point. It will be observed that the E.
and W. walls
have both a uniform tilt inwards; if we allow 14' for this as
an average,
the mean from a straight line inclined that amount is .057 on E.
and .025 on W.; a remarkably small amount of
error, comparable to the
extremely
fine work and close joints of the stones themselves. Also the ridge
of the roof
is not exactly over the middle of the chamber at either end. Beside
the above
resulting length of the middle of the chamber on the floor, separate
measures
were taken on the two walls; these give N. 227.41,
middle (from
above) 227.47, S. 227.61; mean of all 227.50 for floor
length.
42. In the matter
of height, the courses vary a good deal; and far more
care was spent
on the closeness, than on the regularity of the joints. For a
starting
point in measurement, the general floor is hopelessly irregular, consisting
plainly of
rough core masonry; and furthermore, it has been built over with
similar
rough masonry, which was afterwards stripped down to insert the chamber
walls. This
is proved by there being no fewer than eight edges of sunken spaces
upon it,
made (according to the universal habit of pyramid builders) to let in
the
inequalities of the upper course into the surface of the course below it.
These sunken
edges are well seen in other parts of the core masonry, and their
68 THE
INSIDE OF THE GREAT PYRAMID. [Chap,
meaning here
is unequivocal. But all round the chamber, and the lower part of
the passage
leading to it, is a footing of fine stone, at the rough floor level; this
projects 1
to 4 inches from the base of the walls, apparently as if intended as a
support for
flooring blocks, which have never been introduced. It is to this
footing or
ledge that we must refer as the starting point ; though what floor
was ever
intended to have been inserted (like the floor of the King's Chamber,
which is
inserted between its walls) we cannot now say. Certainly, a floor at
the level of
the higher part of the passage, would not reconcile everything; as
that higher
floor is also not a finished surface, but has sundry large round holes
in it, like
those in the chamber floor and elsewhere; intended, apparently, for
use in
process of building. Starting, however, from this footing at the base of
the walls,
the mean elevation of each course above the floor is as follows, with the
variation +
or – from the mean scale, at eleven
points around the chamber:—
Mean of N.W. Corner. N.E. Corner. E. Side,
Niche. S.E Corner S.W. Corner W. Side.
Corners. W. N.
N. E. Mid. Niche
E. S.
S. W. Mid.
¦N.+1.0 ¦S.
– .5
245.1 ¦ ¦
¦S.
– .1 ¦N.
– .6
214:35 + 2:05
– 2:05
184:47 –:37
–:18 –
.47 –.47 –.01 +.55
– .67
179.09 +.67 –.73 –.39 +.45
156.07 +.23
–.05
+.67
–.09
+.33
+.29
+.01
–.35
–.49
–.01
– .17
127.13 –.23
–.11
–.03
+.12
+.17 +.28 +.50 +.31 –.41 –.20 – .33
99.13 +.01
–.17
–.13
+.05
–.03
+.05
+.32
–.11
–.09. +.08 – .13
67.44 +.28
+.06
–.23 0 +.09
–.12
+.06
–.22
–.05
+.09
– .05
34.13 +.01
–.24
door 0 +.17
–.01
+.22
+.02
+3.08
+3.38
– .19
0 –.18
+.20 –.2
+.42
encumbered – .26
[The three verticals
¦: the book’s single larger vertical { ]
[
.. an entire line missing in GoogleTextCopy .. unless we missed something .. ]
The mean
course thicknesses, and their mean differences being—from the base
upwards—thus:—34.13 m.d. 19, 33.31
m.d. 18, 31.69 m.d, 14, 28.00 m.d. .21,
28.94 m.d. .27,
28.40 m.d. .48 to top of N. and S. walls. In the first column
above, 245.1 is the apex of the E. and W. walls, where
the sloping roof stones
end at their
junction; and the differences entered here, N. and S., are due to the
N. and S.
slabs not ending at the same level, one having fallen a little below
the other in
building; the highest shows, therefore, probably the intended point,
and this is
108.1 above the pavement. 214.35, in the first column, refers to the
topmost
joint on the E. and W. walls. 184.47 is
the top of the N. and S. walls,
and a joint
on the E. and W. walls. 179.09 is a
joint that occurs at each
side of the
E. and W. walls, but which does not run far, being soon
shifted
upward to the 184 level. 156.07, 127.13, 99.13,
are all joint levels
around the
chamber. 67.44 is a joint level,
signalized by the top of the doorway
and of the
channel mouths in N. and S. walls. 34.13
is a course around the
Sect. 43.]
QUEEN'S CHAMBER, NICНЕ. 69
chamber.
Ando is the fine stone footing of the walls, which is about the level
of the
variable and rough floor of the chamber. It must be remembered that
the above
figures only give differences from a mean scale, and do not profess
to be
levels; the columns, in fact, being only rigidly connected at the two sides
of any one
corner, which hence have no dividing line between them in the table.
Assuming,
however, that the above series of heights of E. and W. walls are
pretty
closely adjusted to the heights in the corners next to each, we have
for the
sloping roof block, the following figures, calculating from the above
quantities:—
E.
end, N. side. W. end, N. side. E. end, S. side. W. end, S. side.
Sloping
length 120.00 119.96 119.12
118.59
Angle 30° 48' 30°14' 30°33' 30°10
[Google-Copy-shifts (rotates 180°) 6¦9 (practically always); EX
GoogleCopied: "96.611", book shows: 119.96]
[Internet has to do something about The Google Corporation .. this is outrageous .. ”better experience ..” .. design ..]
These roof
blocks are seen—where Howard Vyse
excavated beneath one at the
N.W. corner—to go back 121.6 on slope, behind the wall
face; this, coupled
with the
thickness of these blocks (which is certain, by similar examples
elsewhere,
to be considerable) throws the centre of gravity of each of the slabs
well behind
the wall face,* so that they could be placed in position without
pressing one
on another. Hence there is never any arch thrust so long as the
blocks are
intact; they act solely as cantilevers, with the capability of yielding
arched
support in case they should be broken.
The projection on the western side
of the doorway, mentioned by Professor
Smyth, is really
a surplus left on both sides of the corner; in order to protect
the stone in
transit and in course of building. This undressed part in the
chamber, is
cut away down to the true surface at the top and at the middle
joint, in
order to show the workman exactly to where it needed to be dressed in
finishing it
off. The excess in the chamber begins 1.3
below joint at top of
doorway, and
thence projects 1.4, with a width of 5.5; it is dressed away for
1.05 at the middle joint, and then continues
sloping away rather thinner down
to the
floor. The projection into the passage is 1.5
maximum at base,
usually .8; and it is 5.5
maximum width, or usually 4.5.
43. The niche in
the eastern wall of this chamber, from its supposed
connection with
a standard of measure, was very closely examined. Its original
depth back
was certainly only 41 inches at every part from the bottom upwards.
The surface
that might be supposed to belong to the side of a deeper part, is only
that of a
joint of masonry, one stone of which has been broken up and removed;
this is
evident as there is mortar sticking to it, and as it is pick-dressed, quite
different to
the fine surfaces of the niche sides; beside this, it is not flush with
the side, or
any of the overlappings of the niche; and moreover, all down the
niche sides
are the traces of the edge of the back, at 41 from the front, where
it has been
broken away.
* As at
Sakkara, in the Pyramid of Pepi.
70 THE
INSIDE OF THE GREAT PYRAMID. [Chap, vif.
The general
form of the niche was a recess 41 inches (2 cubits) deep back;
62 inches (3
cubits) wide at base, and diminishing its width by four successive
overlappings
of the sides (at each wall course), each of 1/4
cubit wide, until at 156
high it was only
20 (I cubit) wide, and was finally roofed across at 184 high.
Thus, of the
3 cubits width of the base, one cubit was absorbed on each side by
the
overlappings, leaving one cubit width at the top. This cubit is the regular
cubit of
20'6 inches, and there is no evidence of a cubit of 25 inches here. The
exact
dimensions of every part are as follow, giving the mean dimensions, and
the
variations of each part, + or –, from
the mean. All corrected for the salt
exudation on
the two lower laps, as estimated at each point; there is no salt on
the upper
three laps :—
Excen-
Height of Laps of
Sides. From plum-line below Depth
tricity
Level —————————————— apex of roof Width from
from
above Mean Front.
Back. 10 10 10 —————————————— back to sides of
floor of All. N.
S. N. S. N. side. Mid. S side. Mean.
Front. Mid.
Back. front. chamber
183.80 15.20
S. 25.08 34.95
S. –.55 –.02 +.23
40.72 25.32
170. 27.70 –.02 –.01
+.02 +.10 20.30
–029 -.11
+.33
–.17
+.15 +.26
156.10 ——————————————————————————————————————————————————————————————————
10.21
S. 25.21 40.22 S. –.42 –.08 +.23 41.06 25.39
142. 28.94 +.08 –.06
+.16 –.22 30.43
–.25 –.11
+.25
–.02
+.06 +.35
127.16 ——————————————————————————————————————————————————————————————————
mid 4.55
S. 25.28 46.02 S. –.36 –0.13 +.07
41.20 25.44
113. 28.23 –.01 +.01
–.01 +.02
41.83
–.20 +
.05 +.19
–.10
+.17 +.31
98.93 ———————————————————————————————————————————————————————————————————
mid
.88 N. 25.16 51.02
S. –.66 –.04
+.19 41.15 25.20
83. 31.79 –.08
+.24 –.04 –.14 52.74 –.46 +.10 +.34
–.12
+.23 +.36
67.14 ———————————————————————————————————————————————————————————————————
5.41
N. 25.31 56.03
S. –.30 –.10 +.21
41.10 25.10
33.70 64.14 –.22 +.23
61.74
–.28 0
+.26
0 –.32
+.19 +.31 41.32
——————————————————————————————————————————————————————————————————————
Means .08 .13 .06
.12 25.19 41.41
–.30 +.04
+.26 41.07
25.29
--------------------------------------
[We
can see the (possible) reason for the explicit typographic font type:
— Petrie
exchanges our normal decimal comma — . — with our normal raised point — · — in
securing a mistaken sentence point — . —];
[As
the »GoogeTEXTCopy»
has not adopted, it mostly interprets the Petrie decimal comma as an arc minute
character — ' — .
— And so we
have to adjust all these BadGoogle occasions in the actual number
specifications — without which the Petrie data goes bazooka].
--------------------------------------
44. The channels
leading from this chamber were measured by the goniometer
already
described (h, section 10); they
are exactly like the air channels in
the King's
Chamber in their appearance, but were covered over the mouth by a
plate of
stone, left not cut through in the chamber wall; no outer end has yet
been found
for either of them, though searched for by Mr. Waynman Dixon,
C.E., who
first discovered them, and also by myself on the N. face of the
Pyramid.
The N. channel is 8.6 high, and about 8 wide in the chamber
wall, running
horizontally
for 76 inches, and then turning upwards. The S. channel is 8.8
high, and
runs 80.0 to its turn upwards. The mean
angles, measured between
the
horizontal part and the ascending slope of the channels, are thus:—
Sect. 45.]
GALLERY, LENGTH AND ANGLES. 71
N. Channel. S. Channel.
W. Mid. E.
Mean. W. Mid. E.
Mean.
37° 33' 37° 25' 37° 25' 37°
28' 38° 28' 38° 20 38°
35' 38° 28'
each
statement being the mean of two observations, which never differed more
than 6'.
Hence, if these channels were
continued to the outside of the Pyramid, their
floors would
end on the Pyramid faces at 2641.3 above the base, and 24608 from
the centre
of the Pyramid on the N. face; and at 2679.1
above the base, and
2431.2 from the centre on the S. face. I observed
something like the mouth of
a hole in
the 85th course on the S. face, scanning it with a telescope from below ;
but I was
hindered from examining it closely.
45. Returning now
to the gallery from which we diverged to the Queen's
Chamber, the
length of the gallery was measured like the other passages, with
the steel
tape, but not many joints were measured, and those were on the E.
ramp, on
which the tape was laid at 6 inches from the edge. The offsets to the
floor and E.
ramp were also read, in continuation of the series of the ascending
passage, as
explained before (section 39). The results are as follow, starting from
the N. wall
of the gallery, at 1546.8 from beginning of ascending passage.
Variations
from Mean Axis of Variations
from Mean
Distance
on + 1'
20" azimuth. Axis of 26°
16' 40" altitude.
Slope.
W. Mid. E. Ramp Top.
Floor.
N. wall 0 [1.6 22.3]
At 30 20.9 .1
Ε. 21.2
First joint,
vertical. 44.6
At 150
20.7 .2
W. 20.3
Joint at
"cut off"vertical 223.2
Face of "cut off" 223.7
Second "cut off" 263.8
Joint 264.1 20.9
0
20.9 2.0 22.9
At 400
21.0 .2 E. 21.4 2.3 23.1
At 700
20.8 .4 E. 21.6 2.6
23.6
Joint 912.4
At 1,000 21.1 0 21.0 1.5 23.4
Joint,
broken to next 1087.0
Joint 1186.5
At 1,300
21.5 .3 W.
20.8 2.3
23.3
Joint 1454.6
At 1,600
21.2 .1 E. 21.4 2.1 22.2
Ramp End 1815.5 21.3
0
21.2
1.8
22.1
S. wall, in
same line 1883.6
In the
variations in altitude, the height of the axis above the ramp top is
stated, as
well as its height over the floor. The axis, though different in azimuth
and altitude
from that of the ascending passage, is reckoned to start from the
end of it; hence
the offsets are a continuous series, though measured from a line
72 THE
INSIDE OF THE GREAT PYRAMID. [Chap, vii
which is
bent on passing from the passage to the gallery. The first-stated floor
offset here (in
brackets) is not what the continuation of the floor of the ascending
passage
actually is at the point; but it is the virtual floor of the gallery, ie.,
where it
would come if the trend of the rest of the gallery was continued, and
also
(judging by the altitude observations of Prof. Smyth) where it would come
if continued
parallel to the ramp top.
By successive rod measures, Prof.
Smyth made the gallery .8 shorter than
it appears
by this continuous measure; but the continuous measure is certainly
better in
principle and also in practice, as we have seen in the other passages.
The steel
tape of 1,200 inches required to be shifted in order to measure from
one end to
the other of the gallery, and three points were common to both tape
lengths; the
distances between these points were 305.5
by first, 305.6 by second
measure, and
480.2 by both first and second
measures, showing the same
accuracy in
this as in the taping of the other passages. The difference between
Prof.
Smyth's measures and the taping occurs almost entirely from the N. wall
to the cut
out in the floor, and is probably due to want of straightness and
squareness
in one or other of those surfaces.
Hence the floor of the gallery
intersects the S. wall at 1689.0 ± .5 above
the
pavement; at 61.7± .8 S. of the Pyramid
centre; and its middle is 284.4 ±
2.8 E. of the Pyramid centre; reckoning the
measures of length and angle
continuously
through from the plug-blocks upwards, so as to avoid all uncertainties
of
connection at the beginning of the gallery, and duly correcting for
difference
in offsets.
46. The holes cut
in the ramps or benches, along the sides of the gallery
(see section
of them in Pl. ix.), the blocks inserted in the wall over each, and the
rough
chopping out of a groove across each block—all
these features are as yet
inexplicable.
One remarkable point is that the holes are alternately long and
short, on
both sides of the gallery; the mean of the long holes is 23.32, with an
average
variation of .73, and the mean of the
short holes is 20.51, with average
variation .40. Thus the horizontal length of a long
hole is equal to the sloping
length of a
short hole, both being one cubit. This relation is true within less
than half
their average variations.
The roof of the gallery and its
walls are not well known, owing to the
difficulty
of reaching them. By means of ladders, that I made jointing together,
I was able
to thoroughly examine both ends and parts of the sides of the
gallery. The
roof stones are set each at a steeper slope than the passage, in
order that
the lower edge of each stone should hitch like a paul into a ratchetcut in
the top of
the walls; hence no stone can press on the one below it, so as
to cause a
cumulative pressure all down the roof; and each stone is separately
upheld by the
side walls across which it lies. The depth of two ofthese ratchetcuts,
at the S.
end, I measured as 1.0 and 1.9 to 2.0;
and the angles of the two
Sect. 46.]
GALLERY, LENGTH AND ANGLES. 73
slabs there
28° 0' to 28° 18',and 27° 56' to 28°
30', mean 28° 11'; which on a mean
slab 52.2 from N. to S., would differ 1.74 inches from the passage slope. The
edge of the
southernmost slab is 14.5 from the S.
wall; the next slab is 47.4
from N. to
S.
The verticality of the ends of the
gallery was measured from a plumb-line;
and the
horizontal distances of the top and bottom of each of the laps of stone
from the
ends of the roof are thus :—
[Manually (mostly) directly from the Petrie book — the GoogleCopy cannot
easily be extracted due to is line-row mixing and charcter errors ..]
Laps. N. End. Lean out. S. End. Lean in. Hiigh on
S. End. Lap on W side.
8 0 (?) 0 33.6
top 3.0 2.9 2.3
7 0 2.82
–.08 33.7
base 3.0
h
top 6.2 5.8
3.1
6 +.2
0 33.0
base 6.0 5.8
s
top 9.1 9.00
3.0
5 +.6
0 34.0
base 8.5 9.00
h
top 11.9 12.08
2.9
4 –.2
+.10 33.8
base 12.1 12.18
h
top 15.1 15.08
3 +.1
+.10
base 15.0 15.18
s
top 19.7 18.10
2 +.1
+.45
base 19.5 18.55
top 19.6 21.5
1 +.4
21.7 –.25
base 19.2 —— 21.25 ——
+1.2
+.32
The letters h and s in the column
of the N. end show the under edge of the
lap of stone
to be either horizontal or sloping; on the S. end it is always
horizontal.
The width of the top of the gallery is 40.9
at N., and 41.3 at S. end.
The
remarkable groove in the lower part of the third lap, along the whole length
of the
sides, was measured thus, perpendicularly:—
N.W. N.E. S.W. S.E. mean.
11.7 11.8 11.2 11.0
11.4
Groove
upwards
–6.1
from lap
edge
to 5.4 5.7 5.1 5.1 5.3
At the S.W.
it is cut to a depth of .8 inch, at the
S.E. to .6 (?); the upper
edge of it
is often ill-defined and sloping. According to Prof. Smyth the mean
L
[The
GoogleCopy most often loses the ±, writes only a "+"]
p74:
74 THE
INSIDE OF THE GREAT PYRAMID. [Chap, vii.
height of this
lap above the gallery floor is 166.2 ± .8
vertically; hence the
groove is at
172.1 to 179.0 vertically over the floor, and its lower edge is therefore
at half the
height of the gallery, that varying from 167 to 172. The
pickmarks in
the groove on the S. end of the W. side are horizontal, and not
along the
groove, showing that it was cut out after the walls were built, which
agrees with
its rough appearance. It belongs to the same curious class of rough
alterations
as the blocks inserted in the sides ofthe gallery and the rude grooves
cut away
across them.
At the top of the N. end is a large
forced hole, cut by Vyse in 1837, and
still quite
fresh-looking. The whole of the top lap of stone is so entirely cut
away there
that I could not decide to where it had come, and only suppose it to
project 3
inches, like the others.
From this the length of the roof of
the gallery is 1688.9 – 40.45 = 1648.4
horizontal,
or 1838.6 sloping.
By plumb-line measure at the S.
end, the roof on the E. side is inside the
floor edge
(or overhangs) 20.50, and on the W.
side 20.40. On the S. end
(eliminating
the lean) the projection is 209, and on N. 20.4;
mean of all, 20.55,
for the sum
of the seven projections of the laps, or one cubit, the laps being
then one
palm each in breadth. Thus the laps overhang the ramps along the
gallery
sides, and the space between the ramps (2 cubits), is equal to the space
between the
walls at the top.
The remarkable shaft, or
"well," that leads away from the lower end of the
gallery down
to the subterranean passage, was fully measured about its mouth;
but it
appears to be so rough and so evidently utilitarian (for the exit of workmen)
that it is
not worth while to publish more complete measures than those
of Prof.
Smyth. As, however, the position of its mouth has been supposed to
have a
meaning, it should be stated that the opening is from 21.8 to 49.0
horizontally
from N. wall of gallery on floor, 21.8
to 48.7 near its top, and 21.9
to 48.9 by the sloping distance reduced. Thus the
middle of it is at 35.40
35.25, oг 35.37
by different methods. The part of the shaft that passes through
a rock
fissure filled with gravel (often called the "grotto") has been
steined with
10 courses
of small stones, varying from 7(1/4) to
8 inches in height.
At the upper end of the gallery, we
have already stated the S. wall to be
61.7 ± .8
S. 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 mid-plane of the Pyramid being also signalized by the
mid-plane of
the Queen's Chamber, which is measured as .3
± .8 N. of the
Pyramid
centre.
Sect. 47.]
ANTECHAMBER
AND PASSAGES. 75
The
ramps along the sides, where they join this great step, are very
irregular.
Their top surfaces slope away downwards toward the side walls;
thus the E.
ramp top varies from 13.20 to 12.18
below the step from E. to W.,
and the W.
ramp top from 12.82 to 12.2 (?) from W. to E. At present, moreover,
the ends of
the ramps are parted away from the face of the step by
.30 on E. and .44
on W., an amount which has been duly subtracted from my
length
measures of the gallery. Beside this, the top of the step itself, though,
straight, is
far from level, the W. side being about 1.0
higher than the E. side.
And the
sloping floor seems to be also out of level by an equal amount in the
opposite
direction; since on the half width of the step (i.e, between the ramps)
the height
of the step face is 34.92 or 35.0 on E., and 35.80
or 35.85 on W.
The length
of the step from N. to S. is: on E. side 61.0,
and on W. 61.5. All
these
measurements are very carefully taken with elimination of wear, fractures,
and shifting
of the stones at the joints. Hence, at the line along which I
measured, 6
inches from the edge of the ramp, the step will be 61.1 long; and
this at the
angle 26° 12' 50" (by which the end of the gallery was calculated from
the
plug-blocks) will be 30.08 vertically,
for the virtual* above the actual floor
end. Then
the top of the step will (by above measures) be here 34.88 above
actual floor
end, and the step dips about .64 to the
S. wall at this part; so the
top of the
step at the S. wall is 34.88—.64—30.08=4.16 (say ±.2)
above the
virtual
floor end at the line of taping. And as the virtual floor end is at
1989.0±.5,
the step surface at the E. side of the S. doorway is 1693.2 ±.6 over
the
pavement.
47. The Antechamber
and its passages were measured both by steel tape
and rods, in
one length, from the step to the King's Chamber; and the joints
and floor
levels are as follow :—
A B C D
———— ———— ——————— —————————
Face of step – 61.32 .4
E. 4.7 E. 5.6
W. 1693.7
to 1694.6
S. wall of
gallery 0 61.7 4.2 E.
N. end of
Antechamber 52.02 113.7 1693.2
¦3.6 1692.6
Joint,
granite begins. 64.90 126.6 {
¦3.9 1692.9
Granite of
wall begins 75.26 137.0
Edge of wall
groove 91.79 153.5
¦3.7 1692.7
Joint of
floor 112.15 173.8
{
¦3.2 1692.3
Edge of wall
groove 113.48 175.2
Edge of wall groove 119.26 181.0
A Along Floor on E. side.
B Southward from centre of Pyramid ± .9.
C Level over virtual end of gallery ± .2.
D Level over pavement. ± .6.
Image Copy of the actual Petrie book Stanford Library scan, for
comparison
* The virtual floor end is where
the general floor slope, if carried on through the step,
would intersect
the plane of the S. wall.
76 THE
INSIDE OF THE GREAT PYRAMID. [Chap, vif.
A B C D
Joint of
wall 134'17 195.9
S. end of
Antechamber 168.10 229.8
2.9 1691.9
Joint of
floor 198.41 260.1 {
2.8 1691.8
Base of
King's Ch. wall 268.9 330.6
– .5
1688.5
End of
passage floor 269.04 330'7 3.0 1692.0
Raised
floor, King's Ch. 269.17 330.9
3.8 1692.8
A Along Floor on E. side.
B Southward from centre of Pyramid ± .9.
C Level over virtual end of gallery ± .2.
D Level over pavement. ± .6.
These measures vary somewhat from
those of Professor Smyth in 1865;
and,
comparing the greatest differences, they stand thus:—
A B C
N. end
Antechamber to joint S. of it 12.88 12.88
13.6
Next joint
to S. end Antechamber 55.95 55.73 and 55.80 55.5
A Steel tape, 1882.
B Rods, 188o.
C Rods, 1865.
So here, as
elsewhere, the measures in 1880-2 by steel tape and rods, entirely
independent of
each other, agree fairly together, and suggest that the 1865
rod measures
were somewhat in error. This is due generally to the latter
starting
from different points on different occasions, and to their different series
being
insufficiently locked together. Hence I adopt the steel tape measures as
the most
satisfactoryу.
48. Taking the
Antechamber alone, we may say that its dimensions above
the granite
wainscot of the sides, are as follow :—
Length, N. to S. Breadth, E. to W.
—————— —————————————————————————— ——————————————
A B C D E F G H I
147 116.85 116.22 116.05 115.65 64.80 64.48 64.96 64.76
129 117.00 116.18 116.03 115.37 64.72 64.98 65.26 65.25
114 117.00 116.11 115.73
114.07 65.06 65.00 65.48 65.21
95 116.55 115.91
70 116.58 115.93
45 115.91 116.12
133.5 at 2 from ceiling 133.14
Diagonals
N.W. to S.E. { } N.E. to S.W
133.07 over wainscot 132'98
A Height above floor.
B 2 from W.
C Middle.
D 12 from E.
E E. side.
F 2 from N.
G 40 from N.
H 76 from N.
I 2 from S.
The height
was measured as follows:—
Near N,
wall. 14 from N. 59 from N. 61 from N. S.
wall.
At E. side 149.47 149.09 149.17 149.62 149.63
Middle. 149.53 149.64 149.64
At W. side 149.32 149.01 149.10 149.65 149.57
Mean 149.44 149.05 149.13 149.64 149.61
Above
gallery end. 153.04 152.95 152.83 152.84 152.61
Sect. 49.]
ANTECHAMBER, DIMENSIONS. 77
The mean length is thus 116.30 (by the
two series from top to base), breadth
65.00, and
height 149.35 ; or the ceiling over the
virtual end of the gallery floor,
15285 ± .2, and 1841.8± .6 оver the pavement.
49. Coming now to
details of the walls, the rough and coarse workmanship
is astonishing,
in comparison with the exquisite masonry of the casing and
entrance of
the Pyramid; and the main object in giving the following details is
to show how
badly pyramid masons could work. The great variation in the
foregoing
measures illustrates this.
The N. wall is all rough picked
work, with .2 variation commonly; there
is
a great
irregular flaw, and a piece broken out of the stone about the level of the
top of the
leaf, as much as 1 inch deep. The E.
wall has the granite by the
side of the
leaf wavy and winding, and bulbous at the base, projecting 1.4. On
the wainscot
block at the S. end of this wall, which is all in one with the S. end
of the
chamber, are two conjoined deep scores or scrapes nearly vertical, much
like the
beginning of a regular groove; their distance from the S. wall is 3.6 to
7.2 at 90, and 2.6
to 6.4 at 52 from floor, where they
end; they are .48 deep at
maximum. The
S. wall has all up the E. side of it, over the wainscot, a
projection,
just equal in width to the wainscot, and varying in thickness from
.31 at top to 1.7
half-way down, and thence fading off down to the top of the
wainscot. On
the W. side of the S. wall the granite has been daubed over for
2 to 6
inches in breadth, with a thin coat of cement; this, at 1 inch from the
side is .35 thick; also at 13 from the W. side is a
slight sinking of the granite,
from .34 to .60
in depth, all quite ill-defined. The W. wall has the top of the
granite
wainscot uneven, rising toward the front, and there sinking suddenly .35
at 1'4 from
the front edge. The southern of the three semicircular hollows on the
top of this
wainscot (see Pl. xii.)*has the granite defective at the back of it, and is
backed with
rough limestone there. The southernmost stone over the wainscot
is dressed
very flat and true, but rough, + or – .03.
The next block has a
raised edge
to it on the S. side (figured by Prof. Smyth), and along the base of
it, which
consists of granite left rough, not dressed away in finishing; about
4 inches
wide, and 4 projection along the lower edge of the block; and 2 wide
and 1.2 maximum projection at the side. Theother
edges of this block were
marked out
by saw-cuts in the granite, about .2
deep, to guide the workmen in
dressing the
face.
The various courses and stones of the
chamber were measured, but the only
points of
interest are the following.
The south wall has four vertical
grooves all up it, which have been hitherto
supposed to
have extended down to the top of the passage to the King's
Chamber.
This was not the case, however; for, though much broken away, it is
still clear
that they became shallower as they neared the bottom, and probably
* The forms of the curves are plotted
from offsets taken at every inch along them.
78 THE
INSIDE OF THE GREAT PYRAMID. [Chap. vii.
ended
leaving an unbroken flat surface over the doorway. Their depths (as
well as the
forms of their sides) show this, as follows:—
Height above
door. E. groove. 2nd 3rd
W. groove.
at 10 2.8 Much Slight 2.8 at 8
at 7 2.5 broken. curve. 2.5 at 7
at 5 1.75 2.0 at 5½
50. The granite
leaf which stretches across the chamber, resting in grooves
cut in the
granite wainscots, must be somewhat less in width than the breadth
between the
grooves, ie., 48.46 to 48.76. Its
other dimensions were carefully
ascertained,
as much theoretic importance had been attached to them; though
to anyone
looking at the object itself, the roughness and irregularity of it would
put any
accuracy of workmanship out of the question. The thickness of the two
stones that
form it was gauged by means of plumb-lines at 33 points; it varies
from 15.16 to 16.20,
but the details are scarcely worth printing. This leaf is not
simply a
flat slab of granite, but on both its upper and lower parts it has a
projection
on its N. side, about 1 inch thick, where it is included in the side
grooves. The
edge of this projection down the W. side has been marked out by
a saw cut;
and the whole of the granite on the inner side of this cut has been
dressed away
all over the face of the leaf, leaving only one patch or boss of the
original
surface of the block.
This boss, of which so much has
been made by theorists, is merely a very
rough
projection, like innumerable others that may be seen; left originally for
the purpose
of lifting the blocks. When a building was finished these bosses
were knocked
away (I picked up a loose one among waste heaps at Gizeh)
and the part
was dressed down and polished like the rest of the stone. It is
only in
unimportant parts that they are left entire. This boss on the leaf is
very
ill-defined, being anything between 4.7
and 5.2 wide, and between 3.3 and
3.5 high on its outer face; at its junction
with the block it is still less defined,
and might be
reckoned anything between 7.2 and 8.2 wide, and 5.6
to 6.6 high. It
projects .94 to 1.10
from the block, according to the irregularities of the rough
hammer-dressing.
Anything more absurdly unsuited for a standard of measure
it would be
difficult to conceive. I write these remarks with a sharp plaster
cast of it
before me that I took in 1881. Traces of another boss remain
on the W.
wall of the Antechamber, above the wainscot; here there has been
a boss 12
inches wide and 9 high, which has been knocked away, and the surface
rough
dressed, though the rest of the face of the stone is ground down elsewhere.
The block
has been turned in building, so that the flat under-edge of the boss is
toward the
N. Remains of another boss may be seen on a block in the passage
to the
King's Chamber; remains of 15 or 16 others in the King's Chamber ;
5 others
complete in the spaces above that; and many on the casing of the
Third
Pyramid and elsewhere (see Pl. xii.). The E. to W. breadth of the leaf
Sect. 51.] KINGS
CHAMBER. 79
between its
side ledges in the grooves, varies from 40.6
to 41.2 at different
heights up
the middles of the ledges; but furthermore, the edges are not
square, and
we may say that 40 to 42 will about represent its irregularity.
Yet this was
another so-called "standard of measure" of the theorists. The top
of the upper
block of the leaf is a mere natural surface of the granite boulder
out of which
it was cut, utterly rough and irregular; and not materially broken
away as it
dips down deeply into the grooves, and is there plastered over. It
varies from
51.24 to 59.0, and perhaps more, below the ceiling. Yet the cubic
volume of
this block was eagerly worked out by the theorists.
51. The King's
Chamber was more completely measured than any other
part of the
Pyramid; the distances of the walls apart, their verticality in each
corner, the
course heights, and the levels were completely observed ; and the
results are
given in Plate xiii., in which all variations from the mean amounts
are shown on
their actual size. The principle of concentrated errors enables the
eye to grasp
at once the character of the variations in workmanship, in a way
that no
table of figures could show it.
For example, the N. wall is on an
average 412.59 inches long (see bottom
of
Pl. xiii.);
but the "face of West end" (see left hand of plate) is at the top .18
outside the
mean vertical line, and the "face of East end" is .42 inside the mean
vertical;
hence at the top the length is actually (.42
– .18) shorter than the mean,
i.e.,
it is 412.35. The line of the ceiling
on the W. edge of the N. wall will be
seen to be
18 over the mean level of the course, marked " 5 " at each side of
the
sheet; and
the ceiling line at the E. edge is as much as 1.00
over the same
mean level; hence
the ceiling slopes .82 on its length
along the N. side.
Referring
now to the floor or to the Ist course, where the mean levels are
marked by
continuous straight lines all across the diagram, it will be seen how
far the
variable lines of the "Actual First course" or "Actual
Floor" fluctuate up
and down, in
relation to their mean level; the first course, beginning at the
N.W., is at .23 over its mean level (marked I at the
edge), and runs upward
until it is
1.03 over its mean level at the N.E.,
then down to below mean level at
the S.E.,
then still further down along the S. wall, turning a little up to the
S.W. corner,
and then rapidly rising to above its mean level again at the N.W.
corner,
whence we started. Only the first course and floor were directly levelled
all round;
the upper courses were connected by vertical measures in each
corner,
hence their fluctuations along the sides were not measured, and they are
only marked
by broken lines. On looking down, say, the "Face of West-end,"
from joint 5
to 4, it is seen that the line bends out, showing the stone to be
slightly
hollowed;* but on the average it is about square with the course line;
and any
error seen in squareness of angle in the diagram, represents only 1/50 of
* The middle of the course was
only thus offsetted on the top course; the other courses
were read on
at the top and base of each, to give their errors of cutting and of placing.
80 THE
INSIDE OF THE GREAT PYRAMID. [Chap. vii.
the actual angular
error, or 5° equals 6’. Then, below that, it is seen that the line
from joint 4
to 3 begins very slightly outside the line from joint 5 to 4; showing
that the
stone of the 4th course is set back by that amount, owing to error in
placing it.
Similarly the squareness of faces, and truth of setting of the stones,
is shown for
all the other courses in each corner. In fact, a paper model,
showing all
the errors on the actual scale, might be made by cutting out four
sides, following
the outlines of the faces of the walls as here marked, and
bending each
side to make it fit to the irregular edge of its adjacent side.
This diagram will represent with
quite sufficient accuracy, without numerical
tables, the
small errors of this chamber; especially as it must be remembered
that this
shows its actual state, and not precisely its original form. On every side
the joints
of the stones have separated, and the whole chamber is shaken larger.
By examining
the joints all round the 2nd course, the sum of the estimated
openings is,
3 joints opened on N. side, total = .19;
1 joint on E. = .14; 5 joints
on S. = .41; 2 joints on W. = .38. And these quantities must be deducted from
the
measures, in order to get the true original lengths of the chamber. I also
observed, in
measuring the top near the W., that the width from N. to S. is
lengthened .3 by a crack at the S. side.
These openings or cracks are but
the milder signs of the great injury that
the whole
chamber has sustained, probably by an earthquake, when every roof
beam was
broken across near the South side; and since which the whole of the
granite
ceiling (weighing some 400 tons), is upheld solely by sticking and
thrusting.
Not only has this wreck overtaken the chamber itself, but in every
one of the
spaces above it are the massive roof-beams either cracked across or
torn out of
the wall, more or less, at the South side; and the great Eastern and
Western
walls of limestone, between, and independent of which, the whole of
these
construction chambers are built, have sunk bodily. All these motions are
yet but
small—only a matter of an inch or two—but enough to wreck the
theoretical
strength and stability of these chambers, and to make their downfall
a mere
question of time and earthquakes.
52. Applying,
then, these corrections of the opened joints to the lengths of
the lower
course—and also, as being the most likely correction, to the upper
parts as
well—we have the following values for the original lengths of the
chamber, and
for the error of squareness of the present corner angles.
N. N.E.
E. S.E.
S. S.W. W. N.W.
Top 412.14
+ 4” 206.30 –
35" 411.88 +1’ 35”
206.04 – 1'
4"
Mean 412.40 –2 57” 206.29 +2’ 20" 412.11 – 1’
2” 205.97 +1’ 39"
Base 412.78 –4 54” 206.43 +4’ 40”
412.53 – 4’
5” 206.16
+4’ 19"
Now it will be observed that though
the lengths can be corrected by the
sum of the
openings, the angles cannot be so corrected, as we do not know
Sect. 53.]
KINGS CHAMBER, ROOF. 81
which angle the
change of length has affected. Hence the present angles are
entered
above, with the reservation that the sides having altered about I in 1,000
of their
length, the original angles may have easily been 3' or 4’ different; and,
therefore,
all that we can say about the angles is, that the builders were probably
not 5' in
error, and very possibly less than that; also that the errors change
sign from
base to top, so that each course must be a true right angle at some
level up it.
Probably the base of the chamber
was the part most carefully adjusted and
set out; and
hence the original value of the cubit used can be most accurately
recovered
from that part. The four sides there yield a mean value of 20.632 ±
.004, and this is certainly the best determination of
the cubit that we can hope
for from the
Great Pyramid.
The top course of both the E. and
W. walls consists of a single stone; on
the N. and
S. walls the joints of it were measured thus :—N. wall, E. end o,
joints 62.1, 248.8;
S. wall, E. end o, joint 189.2.
The average variation of the
thickness of the courses from their mean is
.051, the mean being 47.045
between similar joints, or including the top course,
which was
necessarily measured in a different way, 47.040 ± .013.
53. The roof of the
chamber is formed of nine granite beams, of the
following
breadths, the two side beams partly resting on the ends of the
chamber:—
Along N. Side. Along S. Side.
Skew.
Stones. Total. Stones.
Total. Differencе of End Widths.
0 – x 0 – x
E. 22.4
+ x 17.8
+ x
22.4
17.8 – 4.6
45.5
45.8
+ .3
67.9 63.6 – 4.3
52.5
53.0 + .5
120.4 116.6
– 3.8
49.1
51.0 – 1.9
169.5 167.6 – 1.9
53.9
55.4 +1.5
223.4 223.0 – .4
44.8 45.8 +1.0
268.2 268.8 + .6
58.1 59.3 +1.2
326.3 328.1 +1.8
62.7 60.8 – 1.9
389.0 388.9
– .1
23.3
+ x 23.4 + x
W. 412.3 + x 412.3 + x
M
82 THE
INSIDE OF THE GREAT PYRAMID. [Chap, vii.
The column of "skew "
shows the difference in the position of the joints on
the opposite
sides of the chamber; and the "difference of end widths" the
variation
between the two ends of the same beam. From this table it seems
probable
that the roofing in of the chamber was begun at the W. end, as the
skew of the
beams increases up to the E. end; and also as the largest beams,
which would
be most likely to be first used, are at the W. end. The numbering
of the slabs
in the top space above the King's Chamber also begins at the W.
end. Vyse,
however, states that these "chambers of construction" were begun
at the E.
end.
These roofing-beams are not of
"polished granite," as they have been
described;
on the contrary, they have rough-dressed surfaces, very fair and true
so far as
they go, but without any pretence to polish. Round the S.E. corner,
for about
five feet on each side, the joint is all daubed up with cement laid on
by fingers.
The crack across the Eastern roof-beam has been also daubed with
cement,
looking, therefore, as if it had cracked before the chamber was finished.
At the S.W.
corner, plaster is freely spread over the granite, covering about a
square foot
altogether.
54. The floor of
the chamber, as is well known, is quite disconnected from
the walls,
and stands somewhat above the base of the lowest course. It is very
irregular in
its level, not only absolutely, but even in relation to the courses; its
depth below
the first course joint varying 2.29, from
42.94 to 40.65. This
variation
has been attributed to the sinking caused by excavation beneath it,
but this is
not the case; it has been only undermined at the W. end beneath the
coffer,* and
yet the floor over this undermined part is 1½
inches higher in relation
to the first
course, than it is at the S.E. corner; and along the S. side where it
has not been
mined it varies 1½ inches in relation
to the first course. In these
cases I
refer to the first course line, as that was the builder's conception of level
in the
chamber, to which they would certainly refer; but if we refer instead to
absolute
level, the anomalies are as great and the argument is unaffected.
It appears, then, that the floor
never was plane or regular; and that, in
this
respect, it shared the character of the very variable floor of the passage that
led to the
chamber, no two stones of which are on the same level. The passage
floor, even
out to the great step in the gallery, is also inserted between the walls,
like the
floor of the chamber.
55. Among
peculiarities of work still remaining, are the traces of 15 bosses
or lugs on
the faces of the granite blocks, all on the lower course. Those best
seen are two
on the fourth block of the N. wall, counting from the door; they
have been
about 12 inches wide and the same high, 14 inches apart, and their
flat bottom
edges 3 inches from the base of the block (see Pl. xii.). They may
be very
plainly seen by holding a candle close to the wall below them; this
* I know the hole well, having been
down into it more than once.
Sect. 56.]
KINGS CHAMBER, CHANNELS. 83
shows up the
grinding around them, and the slight projection and very much
less perfect
grinding of the sites of the bosses. There is a remarkable diagonal
drafted line
across the immense block of granite over the doorway; it appears
not to run
quite to the lower corner on the E, side; but this is doubtless due to
the amount
by which the block is built into the E. wall, thus cutting off the end
of the
diagonal line. This sunken band across the stone appears to have been
a true
drafted straight line cut in process of working, in order to avoid any
twist or
wind in the dressing of the face; this method being needful as the block
was too
large to test by the true planes otherwise used (see section 135).
The position of the King's Chamber
in the Pyramid is defined thus: N.
wall at base
330.6 ± .8
S. of centre of Pyramid ; S. wall 537.0 ± .8
from centre;
E. wall (284.4 ± 20.7)
= 305.1 ± 3.0 E. of centre; W. wall 107.7 ± 3.0
W. of
centre. Base
of walls 1686.3 to 1688.5 ± .6
above pavement; actual floor 1691.4
to 1693.7 ± .6
above pavement; ceiling 1921.6 to
1923.7 ± .6 above
pavement.
56. The air
channels leading from this chamber have been already mentioned
(see section
24) and reference has been made to Pl. xi. for the positions of
their outer
ends. The angles of them had not yet been accurately measured,
and
therefore I carefully observed them by a sliding signal and a theodolite.
The angles
on the floors of them at different distances from the theodolite
station at
the present outer ends are thus :—
N. Channel. | S. Channel.
|
At 84 to 180 32° 4' 45" |
At 0 to 120 45° 25'
6"
180 to 300 31° 37' 15" | 120
to 240 45° 30 7"
300 to 372 30° 43’ 15" | 240
to 360 45°
25' 57"
————— | 360
to 480 45° 25' 14"
Mean 31° 33' | 480
to 600 45°
15' 19"
| 600 to 720 45° 7’ 42"
| 720 to 840 44° 26' 18"
| —————
| Mean 45° 13'
40"
For example,
on the floor of the N. channel, the angle on the part from 180 to
300 inches
from the mouth averages 31° 37' 15"; this is, of course, quite apart
from
whatever the dip may be from the passage mouth to those points; and it is
reduced from
the actually observed quantities. The above list of angles are just
equivalent
to observations by a clinometer, sliding to different parts of the
passage. It
is striking that the slope of both passages continuously increases
up to the
outside (except just at the mouth of the S. channel); hence these
quantities,
which only extend over a part of either passage, cannot give the true
mean slope;
probably on the whole length the means would not be greater
angles than
31° and 44½° respectively.
The N. channel has been forced open
as a working passage for some way
84 THE
INSIDE OF THE GREAT PYRAMID. [Chap, vii.
inwards,
only leaving the floor and W. side perfect. The channel is now blocked,
just below
the end of the enlarged part, and on working a rod 4½ feet into the
sand, it ran
against limestone. The sand in the hole has blown in during gales,
which sweep
up sand like mist. The remains of the original channel show it to
have varied
from 8.9 to 9.2 (mean 9'o) in width, and to have been 8.72 and 8.74
in height.
The S. channel is blocked by sand
at 76 feet down. It is not straight in
the clear
length, curving more than its own width to the east; and the sides
often shift
a few tenths of an inch in passing from one stone to another. These
details were
seen by examining it with a telescope on Feb. 8, and by photographing
it on Nov.
2, 1881; these being the days on which the sun shines
down it at
noon. Its width at the top is 8.35 and
8.65, and its height 8.7 to 8.9.
57. The coffer in
the King's Chamber is of the usual form of the earliest
Egyptian
sarcophagi, an approximately flat-sided box of red granite. It has
the usual
under-cut groove to hold the edge of a lid along the inside of the N.,
Е.,
and S.
sides; the W. side being cut away as low as the groove for the lid to
slide over
it; and having three pin-holes cut in it for the pins to fall into out of
similar
holes in the lid, when the lid was put on. It is not finely wrought, and
cannot in
this respect rival the coffer in the Second Pyramid. On the outer
sides the
lines of sawing may be plainly seen: horizontal on the N., a small patch
horizontal
on the E., vertical on the S., and nearly horizontal on the W.;
showing that
the masons did not hesitate at cutting a slice of granite 9o inches
long, and
that the jewelled bronze saw must have been probably about 9 feet
long. On the
N. end is a place, near the W. side, where the saw was run too
deep into
the granite, and was backed out again by the masons; but this fresh
start they
made was still too deep, and two inches lower they backed out a
second time,
having altogether cut out more than (1/10)-inch
deeper than they
intended. On
the E. inside is a portion of a tube drill hole remaining, where
they tilted
the drill over into the side by not working it vertically. They tried
hard to
polish away all that part, and took off about 1/10-inch
thickness all round
it; but
still they had to leave the side of the hole o deep, 3 long, and 1.3 wide;
the bottom
of it is 8 or 9 below the original top of the coffer. They made a
similar
error on the N. inside, but of a much less extent. There are traces of
horizontal
grinding lines on the W. inside. Reference should be made to
section 129
for the subject of stone-working in general.
58. The coffer was
very thoroughly measured, offsets being taken to 388
points on
the outside, to 281 points inside, or 669 in all; besides taking 281
caliper
measures.
Before raising it from the floor to
measure the bottom, its place as it stood
on the
chamber floor, tilted up at the S. end by a large pebble under it, was
observed
thus:—
Sect. 59-]
COFFER, OFFSETS TO SURFACES. 85
N.E. to N. Wall. N.W. to N.
N.W. to W. S.W. to W. S.W. to
S. S.E. to S.
Top 47.70 48.90 53.34 56.50 67.92 [68.60]
Base 48.35 50.06 53.32 56.54 67.62 68.06
S.E. to S.
wall in brackets, was taken at 10 below top, owing to breakage
above that.
On raising the coffer no trace of
lines was to be found to mark its place on
the floor,
nor any lines on the floor or bottom of the coffer.
The flint pebble that had been put
under the coffer is important. If any
person
wished at present to prop the coffer up, there are multitudes of stone
chips in the
Pyramid ready to hand. Therefore fetching a pebble from the
outside seems
to show that the coffer was first lifted at a time when no breakages
had been
made in the Pyramid, and there were no chips lying about. This
suggests
that there was some means of access to the upper chambers, which was
always
available by removing loose blocks without any forcing. If the stones at
the top of
the shaft leading from the subterranean part to the gallery had been
cemented in place, they must have been smashed to break
through them, or if
there were granite
portcullises in the Antechamber, they must also have been
destroyed;
and it is not likely that any person would take the trouble to fetch
a large
flint pebble into the innermost part of the Pyramid, if there were stone
chips lying
in his path.
59. The
measurements of the coffer surfaces by means of offsets from
arbitrary
lines, have all been reduced in both tilt and skew, and are stated as
offsets or
variations + and – (i.e., in excess or deficiency of stone) from a set
of
mean planes.
These mean planes, then, are supposed to lie half in and half out
of the
stone, being in the mean position and direction of the face. The mean
planes
adopted for the E. and W. sides, both in and out, are all parallel; hence
variations
from these planes represent errors of flatness of the surfaces, and also
errors of
parallelism of the quasi-parallel surfaces. The mean planes adopted
for the N.
and S. ends, both in and out, are similarly all parallel. The mean
planes adopted
for the bottom, both in and out, and the top, are also parallel
These mean
planes of the E. and W. sides, and of the N. and S. ends, are all
square with
the planes adopted for the bottom and top. There is no exception
from
parallelism in the system of comparison planes; and but one exception
from
squareness, in that the N. and S. planes are not adopted square with the
E. and W.
planes. There was such difference from squareness in the work, that
to make the
planes square with each other, would have altered the offsets so
much as to
disguise the small curvatures of the faces; and adopting the planes
slightly out
of square, makes no difference in taking out quantities of length,
surface, or
bulk, from the tables of offsets.
The mean planes to which the coffer
surfaces are referred here, and from
86 THE
INSIDE OF THE GREAT PYRAMID. [Chap. vii.
which the
actual surfaces differ by an equal amount +and –,
yield the following
dimensions:—
N. end thick
5.67 E. side thick 5.87 Inner
depth 34.42
Inside
length 78.06 Inside width 26.81 Base
thick 6.89
S.end thick 5.89 W. side thick 5.82 ———
——— ——— Outer height 41.31
Outside
length 89.62 Outside width 38.50
Ledge
depth 1.70
The vertical
planes all square with the horizontal; but N. and S. planes cut
E. and W.
planes at 89° 47' at N.E. and S.W. corners, and at 90° 13' at N.W. and
S.E.
corners.
For convenience of reference the
whole coffer was divided by imaginary lines
or planes, 6
inches apart in each direction, and represented by rows of chalk
spots during
the actual measurements. Thus at the S. end the first vertical
plane across
the coffer from E. to W. is A, through the midst of that end; the
second plane
is B, which passes 3 inches clear of the end ; then C; and so on to
O, which is
3 inches clear of the N. end; and P the last line, through the midst
of the N.
end. Then at the
W. side the first plane is α, the second β, an inch
clear of the
side, then γ, δ,
ε, ζ , an inch clear
of the E. side, and η
through the E.
side. Then
vertically the plane b is 4 inches above the inside bottom, and
c, d, e, f,
are at six-inch intervals; occasionally, in the most perfect parts,
another
line, g, could be measured on the outside, just at the top. The inside
plane, a,
was taken at only 3 inches below b, or 1 inch over the bottom; but the
outside
plane, a, was taken the full six inches below b, i.e., 4 or 5 inches above
the outside
bottom. In taking means in the inside the offsets to a are only
allowed half
weight, as they belong to a much shorter space than the others;
they ought,
theoretically, to have even less weight, but as the inner planes
gather in
rapidly, just at the bottom below a, this half weight probably gives
the truest
results.
Having, then, adopted the above
mean planes for the sides, and divided
them for
reference at every six inches, we can state all the variations of the
actual
surfaces as being either + (ie., an excess of stone beyond the plane)
or – (i.e.,
a deficiency of stone), either inside or outside the coffer.
These variations are as follow,
stated in hundredths of an inch:—
Leftside text: West outside.
South
end. North end.
Top. A
B C D E F
G H J K L
M N O P
¦ g +2 - 1 - 3
West ¦ f +10 + 8 + 8 + 4 +3 –4 + 1 + 1
0 - 1 - 3 - 1 0 + 1 - 1
out ¦ e +12 + 7 +14 + 5 +1 -1 - 5 - 6 - 8
-10 -12 - 8 - 5 + 3 + 5
si ¦ d +14 + 8 +12 + 9 +1 -7 -13 -14 -16
-14 -15 -12 - 8 + 1 + 1
de. ¦ c +17 +10 +10 + 9 +6 -2 - 8 -11 -13
-13 -13 -10 - 6 0 + 3
¦ b +20 +10 + 9 + 9 +2 -4 - 9 -10 -14
-12 -11 - 7 0 + 8 +12
Base. ¦ a +21 +10 + 9 + 0 -6 -8 - 9 - 8 - 6
- 2 + 2 +10 +17 +26 +31
[Directly from the Petrie table
(»rythmic series») — Font: Courier New]
Sect. 59-]
COFFER, OFFSETS TO SURFACES. 87
Leftside text: East outside. ¦ MBA,
much broken away
South
end. North end.
Top. A B
C D E F G
H J K L M
N O P
¦ g M + 5 + 8 + 8 + 9
East ¦ f B –
7 -5
–4 + 3 0 + 1 + 2 + 4 + 7 + 7 +
7 + 9
out ¦ e A – 8 –
6 -5
-3 - 2 0 0 + 2 + 2 + 5 + 5 + 4 + 7
si ¦ d –13 –11 – 7 – 5 -4 -3 - 0 + 1 + 1
+ 3 + 2 + 5 + 5 + 5 + 8
de. ¦ c –12 –11 – 8 – 7 -5 -3 - 2 + 1 + 1
+ 2 + 2 + 6 + 6 + 5 + 8
¦ b –12 –10 – 8 – 7 -4 -4 - 1 + 1 + 1
+ 2 + 3 + 7 + 7 + 7 + 8
Base. ¦ a – 9 – 9 – 7 + 4 -0 +1 + 1 + 2 + 3
+ 4 + 5 + 8 + 8 + 5 + 6
Leftside text: North outside.
West
side. East side.
Top. α
β γ δ
ε ζ η
¦ g
+39 +35 +21
North ¦ f +35 +31 +29 +21 +21 +20 +18
out ¦ e +16 + 9 + 3 - 2 + 1 + 7 +13
si ¦ d +13 – 2 –14 –21 -15 - 6 + 2
de. ¦ c + 5 + 2 –10 –17 - 9 - 2 +23
¦ b – 3 – 3 – 3 – 9 - 9 - 4 + 2
Base. ¦ a – 6 –12 –20 -36 -27 - 4 +13
Leftside text: South outside.
West
side. East side.
Top. α
β γ δ
ε ζ η
¦ g
South ¦ f -12 - 7 + 1 + 2 +7 +24 +34
out ¦ e -12 -12 – 9 – 4 +3 +22 +34
si ¦ d -21 –24 –16 –11 -2 +22 +37
de. ¦ c -25 -27 –21 –15 +1 +22 +40
¦ b –27 –30 –20 –14 -4 +26 +47
Base. ¦ a –22 –32 –16 -13 -2 +29 +54
Leftside text: Bottom outside.
South
end. North end.
Top. A
B C D E F
G H J K L
M N O P
¦ α +15 +15 +17 +13
+12 +16 +11 + 5 + 1 - 7 + 9 + 4
Bot ¦ β +20 +15 +16 + 9
+14 + 4 + 6 - 1 -11 - 3 + 4 - 1
tom ¦ γ +22 +22 +19 + 8 +
8 - 2 + 1 - 4 - 9 -18 - 4 - 8
out ¦ δ
+10 +17 +21 +17 + 3 - 3 - 4 -
6 -11 -16 -15 - 9 -12
side. ¦ ε
+ 9 +17 +12 + 9 + 1 - 8 - 1
-11 -13 -25 -12 -10 -15
¦ ζ
+13 + 7 +12 + 4 - 2 - 6 - 7
-12 - 8 -17 -12 -20
Base. ¦ η
– 8 + 8 + 5 + 4 - 7 - 5 - 8
-13 -12 -10 -14 -15
α β
γ δ ε
ζ η
Leftside text: West inside.
South
end. North end.
Top. B
C D E F G
H J K L M
N O
¦
West ¦ f
+ 3 + 5 + 1 +5 +10 +11 +12 +14 +16 +15 +13 +12 +12
in ¦ e
- 1 + 1 – 3 +3 + 4 + 4 + 3 + 5 +10 +12 +10 + 9 + 9
si ¦ d
+ 1 – 1 – 0 +1 + 3
0 - 5 - 5 - 1 + 8 - 1 +10 +10
de. ¦ c
– 1 – 2 – 2 0 - 1 -11 -17 -16 -12 - 2 - 4 +10 +10
¦ b
+ 4 – 1 – 3 -2 -11 -22 -28 -27 -18 - 7 - 7 -10 +10
Base. ¦ a
+19 +14 + 8 -5 -19 +27 -33 -34 -24 - 7 - 8 + 7 + 7
88 THE
INSIDE OF THE GREAT PYRAMID. [Chap. vii.
Leftside text: East inside.
South
end. North end.
Top. B
C D E F G
H J K L M
N O
¦
East ¦ f
- 5 + 1 + 2 +7 + 7 + 7 + 4 + 2 + 2 + 3 -12 - 1 + 1
in ¦ e
- 5 + 1 + 2 +4 + 6 + 7 + 2 + 4 + 4 + 4 + 2 - 1 - 1
si ¦ d
- 4 + 2 + 4 +4 + 3 - 1 - 6 - 5 - 4 + 1 0 0
- 2
de. ¦ c
– 6 + 1 + 3 +3 + 5 + 1 - 7 -11 -11 - 3 - 3 - 1 0
¦ b
- 6 + 1 + 1 +2 + 6 +10 - 2 -12 -16 - 9 - 5 - 2 - 1
Base ¦ a
0 + 3 + 2 +1 + 5 +10 - 2 -10 - 8 + 3 + 6 + 5 + 4
Leftside text: North inside. Leftside text: South inside.
West
side. East side. West side. East side.
Top. β γ δ ε
ζ Top.
β γ δ
ε ζ
¦ ¦
North ¦ f
0 - 7 + 1 + 1 + 4 South ¦ f
+ 3 0 - 1 - 2 -10
in ¦ e
0 – 8 – 3 - 3 - 8 in ¦ e
- 5 – 5 – 4 - 5 - 9
si ¦ d
0 – 2 0 - 1 - 5 si ¦ d – 4 – 3 – 1 - 1 - 5
de. ¦ c
- 3 – 3 – 1 + 1 - 1 de. ¦ c
+ 1 0 + 2 + 2 - 4
¦ b
+ 1 + 1 – 1 - 1 + 2 ¦ b – 5 + 1 + 4 + 4 + 2
Base. ¦ a
+20 +16 +18 +10 0 Base ¦ a +11 +13 +24 +23 +17
Leftside text: Bottom inside.
South
end. North end.
West. B
C D E F G
H J K L M
N O
¦
Bot ¦ β
- 1 - 3 + 5 0 - 4 + 1 + 8 +
5 + 1 +10 + 9 +11 + 4
tom ¦ γ
- 8 - 5 - 3 -18 - 5 0 - 2 + 1
- 5 - 2 + 5 + 1 0
in ¦ δ
- 5 - 6 - 4 - 1 + 2 + 2 + 2 0 -
2 0 + 1 - 2 + 7
side. ¦ ε
+12 - 9 + 9 - 6 + 6 -13 - 2 -
1 - 2 + 1 0 -15 -12
¦ ζ
+ 2 + 5 + 3 + 2 + 5 +19?+ 2 +
1 +11?- 4 + 1 - 5 0
East. ¦
Rightside vertical text rows α - ε
: actual top.
— All brackets on numbers left out, except for the last line
South
end. North end.
A [B] [C] [D] [E] [F]
[G] [H] [J]
[K] [L] [M] [N]
[O] [P]
West. ¦ α
0 +
1 + 4 + 2 + 4 + 5 + 4 + 7 + 6 + 6 + 5 + 8 + 8
¦ β
- 2 - 1
¦ γ 0
Top. ¦ δ + 1
¦ ε 0
¦ ζ - 3 -1
East. ¦ η - 4 - 4 - 1 0 + 4
0 - 8
actual top - 4 - 4 0 +1 -3
Middle text, brackets left out:
(Offsets in
brackets are from points on the cut out ledge, raised 1.70
inches,
which is the mean level of the ledge below adjacent points
of the
remaining top; thus restoring the top as nearly as may be
from the
ledge. The actual top only remains at six points)
Petries
actual table:
[We have no idea why the Petrie man did lay down that much thorough
measuring work on that stone coffin — up to a thousand measuring points .. as if
it would have great importance .. but not any further mentioning of (its
implied) important dignity .. the (mean) differences lie in the order of 0.01
inch .. .. Maybe the future will reveal the hidden secrets ..]
If, for
example, the length of the E. side of the coffer is wanted, from the
foregoing
tables, at the level of d, half way up; on referring to " North
outside"
and
"South outside" it will be seen that at d on East side the
coffer is in
excess of
the mean length by + .02 on N. and + .37 on S.; adding these to the
mean length
(89.62 + .02 + .37) = 90.01 is the
result for the E. outside of the
coffer half
way up. Similarly at 8 inches under the top on the same side, at
f it is (89.62
+ .18 + 34) = 90.14 in length; or at 4 inches above the bottom
(which is
about the lowest point uninjured) it is at a (89.62 + .13 + .54) = 90.29 in
length. Or
if the inside width is wanted, half way up the N. end, at d; referring
to
"West inside" and "East inside," at North end, d level, it is seen to be the
mean inner
width, 26.81,–.12 on W., +.02 on
E.=26.71; the signs being, of
course, reversed in adding internal offsets
together. Similarly at the middle of
the length
of the coffer (H, d) the internal width is 26.81 + .06 + .05= 26.92
Sect. 60.]
COFFER, CALIPERING. 89
If the
thickness of the middle of the bottom is wanted, referring to " Bottom
outside"
and "Bottom inside," at H, δ, it is seen that the mean
thickness, 6.89
is changed
by – .04 and + .02, and it is therefore 6.87
thick at that point. Or
if the
thickness of the middle of the N. end is wanted at d and δ,
referring to
"North
outside" and "North inside," it is seen to be (5.67 – .21 + 0) = 5.46;
or the
middle of the N. end at the top is (5.67
+ .21 + .01( =5.89. Thus
the dimensions
internal or external, or the thickness of any part, can be easily
extracted
from the tables by merely adding the corresponding offsets to the
mean
dimension.
60. The
thicknesses of the sides, however, are involved in the measurement
of the cubic
bulk of the coffer, and therefore need to be very accurately known,
in order to
test the theories on the subject. And by the above method the
thickness is
dependent on the combination of many separate measures, and
is,
therefore, subject to an accumulation of small errors. To avoid this
uncertainty,
the sides were independently calipered; observing at every six
inches, on
the same spots on which the offsets were read. And it is to these
caliperings
which follow that I would mainly trust for determining the solid
bulk of the
coffer. The
thickness is stated in hundredths of an inch.
Leftside text: Thickness of West side.
South end. North
end.
B C D
E F G H J K
L M N Ο
Top. f 598
599 587
593 597
604 593
597 599
597 600
599 598
e 592
597 583
579 586
584 580
579 582
585 590
590 597
d 595
591 594
590 578
568 561
561 570
577 581
589 597
c 596
589 592
588 576
561 555
553 559
571 579
591 596
b 600
590 592
582 561
548 541
542 553
571 587
594 593
Base. a 617
613 602
582 576
557 548
576 586
602 607
619 610
—— —— —— —— —— —— —— —— —— —— —— —— ——
Means 598 595 591 586
579 572
564 570
573 581
590 595
598
Leftside text: Thickness of East side.
South end. North
end.
B C D
E F G H J
K L M N O
Top. f 592
594 594
594 594
596 597
582 600
597
e 583 587 589
593 594
593 597
595 596
596 594
595
d 575
585 588
589 597
587 586
586 591
594 597
596 596
c 571
581 587
587 592
590 584
583 581
589 593
596 596
b 572 583
586 590
591 597
591 579
577 586
591 595
596
Base. a 591
587 592
591 598
603 597
601 601
597 602
599 613
—— —— —— —— —— —— —— —— —— —— —— —— ——
Means 575 585 588 590
594 593
590 589
589 593
592 596
597
Leftside text: Thickness of North end. Leftside text: Thickness of South end.
West side. East side. West side. East side.
β γ δ ε ζ β γ δ ε ζ
Top. f 596
583 589
589 595
Top. f 591 595
e 574
561 564
560 571
e 579 585 588 593
d 569
548 549
552 559
d 567 575 572 587 600
c 564
553 551
560 567
c 564 573 575 588 604
b 567
561 553
563 572
b 562 570 576 587 609
Base. a 580
578 563
561 570
Base. a 584 595 601 615 638
—— —— —— —— —— —— —— —— —— ——
Means 574 563 561 564
573 Means
574 581
584 594
609
N
90 THE
INSIDE OF THE GREAT PYRAMID. [Chap, vii.
From these caliperings the mean
thickness of each of the sides, as compared
with the
results of the offsets, are thus:—
Leftside
text: Thickness of
By Calipers. By Offsets. Difference.
¦ N. 5.67
5.67 0
¦ E. 5.90 5.87 –.03
¦ S. 5.88 5.89 +0.1
¦ W. 5.84 5.82 –.02
Hence there appears to be a
constant error of –.01 on an average,
making
the result
of the thickness by the offsets to be less than the truth. This may be
due to a
tendency to read the offsets too large, or else possibly to a slight
skewing of
the calipers, as 3º skew would make this difference on 6 inches.
To compare in detail the results by
calipers and offsets, over a small space,
let us take
the thickness of the N. end, along the lines c and d, which are near
the mid
height:—
β γ δ ε ζ
by
offsets 5.65 5.51 5.46 5.51 5.56
At d {
by calipers. 5.69
5.48
5.49
5.52
5.59
by
offsets 5.66 5.54
5.49
5.59
5.64
At c {
(by calipers. 5.64
5.53
5.51 5.60
5.67
Thus the mean difference between the
thicknesses as ascertained by the two
methods is .022, with a constant difference in one
direction of .012 on an
average. The
spots observed on in the two methods were not always exactly
identical;
and so some difference may be due to waves of short length in the
surface of
the stone.
In stating the offsets on the top,
the mean plane adopted is not the simple
mean of all
the offsets, but the mean of diagonally opposite pairs of offsets, so
far as they
can be taken. This is necessary in order to obtain a true result, as
otherwise
(the top being broken away all at one corner) any great tilt that it
may have
had, in relation to the base planes, would vitiate the result.
61. From the
foregoing data the cubic quantities may be calculated of a
simple
rectilineal box, omitting all notice of the attachments for the lid,
employing
the mean planes:—
Contents = 72,030; solid bulk = 70,500;
volume over all, 142,530 cubic inches.
Or by the
caliper results, instead of the mean planes, the bulk is 1/100 more, and
the contents
probably about 1/1000 less; hence the
quantities would be—
Contents = 71,960; solid bulk =
70,630; volume over all, 142,590.
These
quantities have a probable error of only about 60 cubic inches on
contents and
volume, and 10o inches on the bulk. The bulk of the bottom
is = 23,830;
and hence one side and end is on an average = 23,335. Bulk of
bottom x 3
is then=71,490; andx bulk of sides and ends = 70,000, subject to
about 100
cubic inches probable error.
Sect. 62.]
CHAMBERS OF CONSTRUCTION. 91
62. The spaces,
or "chambers of construction," as they have been called,
which lie
one over the other above the King's Chamber, are entered from a
small
passage which starts in the E. wall of the gallery, close under the roof.
This is apparently
an, original passage, and leads into the lower chamber; the
other four
spaces above that can only be entered by the forced ascent cut by
Col. Howard
Vyse. This latter passage is not so easy to go up as it might be,
as it is
nearly all in one continuous height, so that a slip at the top chamber
means a fall
of thirty feet; and as there are no foot-holes, and the shaft is wide,
and narrows
upwards, an Arab guide of Dr. Grant's refused to venture up it,
alleging
that he had a wife and family to think of. Ali Gabri, however, was
quite equal
to the business, and held a rope ladder to help me, which he and I
together
held for Dr. Grant.
The mouth of the passage out of the
top of the gallery is 26.3 wide
horizontally
at top, 26.2 at base, the S. side of it
being formed by the topmost
lap of the
S. end of the gallery. The top and base of the mouth follow the
slope of the
gallery, the top being the top of the gallery, and the base the
bottom of
the topmost overlapping; thus the mouth is 29.4
high, square with
the gallery.
The rough passage is 28½ wide, 32
inches high, and over 20 feet
long.
All these chambers over the King's
Chamber are floored with horizontal
beams of
granite, rough dressed on the under sides which form the ceilings, but
wholly unwrought
above. These successive floors are blocked apart along the
N. and S.
sides, by blocks of granite in the lower, and of limestone in the upper
chambers,
the blocks being two or three feet high, and forming the N. and S.
sides of the
chambers. On the E. and W. are two immense limestone walls
wholly
outside of, and independent of, all the granite floors and supporting
blocks.
Between these great walls all the chambers stand, unbonded, and
capable of
yielding freely to settlement. This is exactly the construction of the
Pyramid of
Pepi at Sakkara, where the end walls E. and W. of the sepulchral
chamber are
wholly clear of the sides, and also clear of the sloping roof-beams,
which are
laid three layers thick; thus these end walls extend with smooth
surfaces far
beyond the chamber, and even beyond all the walls and roofing of
it, into the
general masonry of the Pyramid.
The actual dimensions of these
chambers are as follow:—
N.
E. S. W.
Top 462 to 470 . . 468.4
247
4th 481 196
. 467
198
3rd 479 (?) . . . 472
198
2nd . . 204.65 4718
1st 460.8 . 205.8 . 464.6 205.9
(King's 412.8 . 206.4 . 412.5
206.1)
92 THE
INSIDE OF THE GREAT PYRAMID. [Chap vii.
But these dimensions are merely of
the rough masonry; and some lengths
could not be
measured owing to the encumbrance of blocks of stone and rubbish
left in the
chambers from Vyse's excavations.
63. In the first
chamber the S. wall has fallen outwards, dragging past
some of the
roof-beams, and breaking other beams at the S.E. corner. The
E. and W.
end walls have sunk, carrying down with them the plaster which had
been daubed
into the top angle, and which cracked freely off the granite roofing.
On the E.
end one block is dressed flat, but all the others are rough quarried.
In the second chamber are some
bosses on the N. and S. wall stones; and
several of
the stones of the N. wall are smoothed, and one polished like those in
the King's
Chamber, seeming as if some spare blocks had been used up here.
The S.E.
corner shows cracks in the roof .52
wide. The masons' lines, drawn in
red and
black, are very remarkable in this and the upper chambers, as they
show, to
some extent, the methods of working. Some of the lines in this
chamber, drawn
in red on the S. wall blocks of granite, are over some of the
plastering,
but under other parts of the plaster. These lines, therefore, were
drawn during
the building, and while the plaster was being laid on, and slopped
like
whitewash into the joints. The red lines are always ill-defined and broad,
about 1/4 to 1½
inch; but, to give better definition, finer black lines were often
used, either
over the red or alone, about 1/10 inch
wide. On the S. wall, starting
from a
drafted edge on the W. wall, 4 inches wide, there is a vertical mason's-
line at 22.3, a
very bad joint at 51.5, another line at
70.5, another at 435.8, and
the E. wall
at 471.8. Thus the two end lines are
413.5 apart, evidently
intended for
the length of the King's Chamber below them, and define the
required
limits of this upper space. On the E. wall is a vertical mid-line drawn,
with a cross
line and some signs; from this mid-line to a line at the S. end is
101.8, and to a line at the N. end of the wall
is 102.85; total, 204.65, intended
for King's
Chamber width. There is a large cartouche of Khnumu-Khufu,
nearly all
broken away by Vyse's forced entrance; but this and other
hieroglyphs
need not be noticed here, as they have been already published,
while the
details of the masons' marks and lines of measurement have been
neglected.
In the third chamber, the N. and S.
sides are of granite as before; but
they rest on
pieces of limestone, put in to fill up hollows, and bring them up to
level: this showing,
apparently, that the stock of granite supporting blocks had
begun to run
short at this stage of the building, and that any sort of pieces
were used
up, being eked out by limestone, which in the upper chambers
supplied
their places altogether. The flooring beams are very unequal in deptl.
and hence
the sides of many of them are exposed, and show us the masons
marks. On
the ist beam from the E. end is a mid-line on the W. face at 98
from the S.
On the 4th beam is a mid-line on the E. face, 102.8
to N., and 101
Sect. 63.]
CHAMBERS OF CONSTRUCTION, DETAILS. 93
to S. On the
6th beam is a mid-line on W. face, 100
to N. and 101.5 to S.;
these N. and
S. ends being merely the rough sides of the chamber. There are
two bosses on
the S. side of the chamber. The chamber sides are much slopped
over with
liquid plaster. On the N. side is a vertical line on the western
granite
block, over the edge of a limestone block beneath it, apparently to show
the builders
where to place it. From the W. end of the chamber this line is at
10 inches,
joints at 210 and 246, a red line at 260, chamber end at 479 (?), and
end of
granite blocks at 503.
In the fourth chamber the
supporting blocks along the N. and S. sides are
all of
limestone, and are much cracked and flaked up by top pressure. The great
end walls,
between which all these chambers stand, have here sunk as much as
3 inches in
relation to the floors and sides; as is shown by the ledges of plaster
sticking to
them, which have originally fitted into the edges of the ceiling. The
roof-beam by
the forced entrance has been plastered over, then coloured red, and
after that
accidentally splashed with some thin plastering. Along the N. wall,
from the E.
end of the floor as o, there is a line at 37.8, another at 58.5, another
at 450.6, and the W. end at 481 : thus the extreme
lines are 412.8 apart, with a
supplemental
line at 20.7 from one of them. This
last was probably put on in
case the end
line should be effaced in building, so that the workmen would not
need to
remeasure the whole length. One stone, 65 inches long, has a mark on
it of
"3 cubits." On the S. wall, from the E. end=0, there is a line at 32.6,
another at
384.7, another at 446.5, and the W. end at 467; here the extreme
lines are
413.9 apart, with a supplemental line 61.8
(or 3 x 20.6) from one end.
Along both
sides of the chamber is a red line all the way, varying from 20.6 to
20.2 below the ceiling; with the vertical lines
just described crossing it near
each end. Remembering
the Egyptian habit of building limestone courses in the
rough, and
marking a line to show to where they were to be trimmed down level,
this line
seems to have been put on to regulate the trimming down of these lime-
stone sides; either as a supplemental line, like those one
cubit from the true marks
on the
granite beams, or else placed a cubit lower than the trimming level, in
order that
it should not be effaced in the cutting. On the; E. floor-beam is a
line 98.6
from the S. end. On the third beam is a line 100 to N. and 96.2 to
S. end. On
the 4th beam a line 98.3 to N., and 100.6 to S. end. On
the sixth
beam a horizontal line running all along it, with a mid-line 98.0
to N. and
98.1 to S. end; and a supplemental line at 20.3
to 20.6
from S. end.
On the other side of the beam a line is at 98.1
to N. and
96 to S.
end. The rough tops of the floor-beams of this chamber show most
interestingly
the method of quarrying them; exactly as may be seen on the
rough tops of
the granite roofing inside the Third Pyramid. On the top of each
stone is a
hollow or sinking running along one edge; and branching from this,
at right
angles across the stone, are grooves 20 to 25 inches apart, about 4
94 THE
INSIDE OF THE GREAT PYRAMID. [Chap, vii.
wide, and 1½ deep. These seem to show that in cutting
out a block of granite,
a long
groove was cut in the quarry to determine the trend or strike of the
cleavage;
and then, from this, holes were roughly jumped about 4 inches
diameter and
2 feet apart, to determine the dip of the cleavage plane. This
method
avoids any danger of skew fractures, and it has the true solidity and
certainty of
old Egyptian work.
In the fifth or top chamber, the
width is quite undefined; and we can only
say that
between the points where the sloping roof-slabs appear is 247 inches.
The
roof-slabs have separated at the apex 1.55
at E. end, and 1.0 at W. end.
The end
walls are very rough, being merely the masonry of the core. On the
second
floor-beam are two horizontal lines 20.6
to 20.7 apart, with three vertical
lines across
them, 103.1 and 103.5 apart. They have triangles drawn in black
on
both the
vertical and horizontal lines, the triangle on the horizontal being 12:5 from
the end
vertical line, and therefore not apparently at any exact distance along
it. On the
fourth beam from the E. is a horizontal line on its W. side, with four
vertical
lines: these are a mid-line, others at 102.6
and 102.6 from it, and a
supplemental
line 20o from one of these. On the E. side of the same is a
horizontal
and three vertical lines; the two end ones 206:3 apart, and a
supplemental
line 21.0 from one end. Both of these
horizontal lines have a
small black
triangle, with one side on the line. The third beam from the E. has
four
verticals, with a triangle beyond the last. These are 103.3 and 103.25 from
a mid-line,
with a supplemental line 20.95 from one
end. The E. beam has five
verticals,
103.0 and 102.7 from the mid-line, with supplemental lines at 20.7 and
19.4 from the ends; it has also a horizontal
line, with a large red triangle on the
lower side
of it, and a smaller black triangle inside the red. On the S. side is a
line 29.3 from the W. end, apparently one terminal
of the 412-inch length. The
roofing-beams
are all numbered, beginning at the W. end of the N. side, going
along to the
E., turning to the S. side, and so back to the W. end. The numbers
visible on
the under-sides of the beams are 4, 18, 21, and 23; probably the
numbers of
the others are on the sides now covered.
From all these details of the
lines, it seems that the roofing-blocks had
usually a
mid-line and two end lines marked on their sides as a guide in placing
them; and,
in case of obliteration, extra lines were provided, generally a cubit
(20.6) from
each end, but sometimes at other points. The horizontal lines were
probably to
guide the workman in cutting the straight under-sides of the beams;
and it would
be desirable to measure through some cracks to find their distances
from the ceiling
side. The flooring of the top chamber has large holes worked
in it,
evidently to hold the butt ends of beams which supported the sloping
roof-blocks
during the building.
Sect. 64.]
SUMMARY OF INTERIOR POSITIONS. 95 [GoogleTextCopy
has a rare tendecy to misplace page info .. must be adjusted afterhand ..]
64. General
summary of the positions inside the Great Pyramid :
[A FIRST CHECK ON STRAIGHT COLUMNS shows that
• no web reader reproduces WORD
edited perfectly straight columns:
• web readers corrupt the
vertical tabs linearity in different manners, depending om web reader.
• The only way to present
straight tab columns would be to introduce regular TABLES — In this Petrie book
text copy there are some 80 of them — which would add (huge) extra memory.
Unless hopelessly inconvenient, we will continue without such changes
• possibly hoping for a more
precise global web reader standard (»non profitable cooperation on common
universal interests»)].
Horizontally. Vertically.
From
N. Base. From Centre. E. from Centre. Above Pavement.
Beginning of
entrance 524.1± .3 Ν.
4010.0 ± .3 mid.
287.0 ± .8 + 668.2 ± .1
S. end of
entrance passage 4228. ± 2.
N. 306. ± 2.
mid. 286.4 ± 1.
–
1181.
± 1.
S. end of N.
subterranean passage 4574. ±
2. S. 40. ± 2. mid. 286.3 ± 1. –
1178.
± 1.
Subterranean
Chamber, centre 4737. ±
2. S. 203. ± 2.
mid. 25.9
± 2. – 1056. ± 2. roof
N. end of S.
subterranean passage 4900. ±
2. S. 366. ± 2. mid. 284.9 ± 1. – 1219. ±1.5
S. end of S. subterranean passage 5546. ± 3.
S. 1012. ±
3. mid.
277.1 – 1213. ± 2.
Beginning
Ascending passage 1517.8 ± .3. N.
3016.3 ±.3
mid. 286.6 ± .8 + 179.9 ± .2
End of 2907.3 ± .8
N. 1626.8 ±.8 mid.
287.
± 1.5 + 852.6 ± .3
Queen's
Chamber, N.E. corner 4402.1
± .8 N. 102.0 +.8 side
308 ±3 + 834.4
± .4
mid. W.
roof 4533.8
± .8 N. .3
±.8 side 72° ±3° +1078.7 ± .6
roof
Gallery,
virtual S. end, floor 4534.5 ± .9
S. 61.7
±.9 mid.
284.4 ± .3. + 1689.0 ± .5
Gallery, top
of step face 4534.5 ± .9 S. .4 ±.9 mid. 284.4 ± .3. +
1694.1 ± .7
Antechamber,
N. end, floor 4647.8 ± .9 S. 113.7 ±.9 same? + 1692.8 ± .6
S. end, roof 4763.9 ± .9
S 229.8 ±
.9 same? + 1841.5 ± .6
roof
King's
Chamber, floor 4865.0
± .9 S. 330.9
±.9 mid. same? +
1692.8 ± .6
King's Chamber, N.E. wall base 4864.7 ± .9 S. 330.6 ±.9
side 305.0
± 3. + 1688.5 + .9
King's Chamber, roof +
1921.6 ± .6
to
1923.7 ± .6
[Petrie’s last summing table on the Cheops Pyramid Chapter 7, Section 64 (PDF page 119) for comparison]:
Note the marked last column’s Vertically 6:th
number: 
:;
Petrie himself reckons it on the resulting form
172.9 in PetrieCH7.39,
“.. of the E.
wall of the gallery (172.9+679.7)=852.6±.3
level above pavement ”
• This Petrie result is also confirmed through the Breakthrough
reckonings in UH (InSystem),
• rather than a Petrie error, it is most
likely a book typo setting error, however that we do not know here ..
• as well as noted by Ronald Birdsall
in his Petrie Web site remark
(Birdsall
March 21 2006, Last revisions August 27, 2014, also in Birdsall’s
Chapter 7, Section64,
.. birdsall.com/giseh/petrie/c7.html#64 — Birdsall’s URL:s
have been changed lately, the old [here in UH] Birdsall links does not work
properly anymore .. unless skipping the last previous URL ”index.htm” text — so
.. until we may test an accepting new URL status, we will not give further direct
links here).
96 THE
OUTSIDE OF THE SECOND PYRAMID. [Chap, viii.
CHAPTER
VIII.
THE OUTSIDE
OF THE SECOND PYRAMID.
..
Here we end the Petrie book
PDF copying. The rest of his work is in concern of the other pyramids, not
particularly in concern of the Cheops Pyramid.
Only if urge appears, also
these final parts of Petrie’s book will be continued in this document.
A final word on the GoogleTextCopy
As we can
see by comparison:
The
GoogleTEXTCopy becomes perfectly useless AsIs on Petrie's specified values —
and the typography it presents.
THE COPY
SHOULD BE CLEAR, SERIOUS AND DECENT TO THE ORIGINAL — it is called: mutual
Respect.
GOOGLE: Why do You have a CopyBookTEXTFunction, when You cannot handle
it?
— GOOGLE have,
of course, tested its CopyProgram many times .. recently .. very serious stuff
..
— Google Staff:
— ..You were
saying .. ?
People advertising such behavior on an industry floor are advised in
Routing on the sign that readis: EXIT.
— Irresponsible. Low educated.
Intellectually disabled: »accident generators». Perfect intelligence — no
interest in its content.
— Do correct if wrong. Faulty
statements are not allowed in this type of document.
RBPetrieCorrections: ¦ RBPC1 ¦ RBPC2 ¦ RBPC3 ¦ RBPC4 ¦ RBPC5 ¦ RBPC6 ¦ RBPC7 ¦
WE HAVE E GENERAL ISSUE WITH THE BIRDSALL URL:
the type (c7 CHAPTER 7)
https://ronaldbirdsall.com/gizeh/petrie/c7.html
works OK — but not the sectional reference added as advised by the
BIRDSALL SITE ITSELF:
• .. c7.html#55
— Attempting to add (in another htm-document) this last
sectional reference ”#55” is just ignored;
— Getting to the actual Section 55, though, is working OK
• IF, on the above URL,
• in the web reader’s
URL-box, a manually inserted ending ..
#55 is added,
or other appropriate section number.
— So in the following, we only address the Birdsall Petrie CHAPTER number
• and the reader must
click on the Birdsall’s tabled list of section links
(or manually add the # section in the URL-box).
(INTERNET IS NOT WORKING WELL .. ANYMORE .. Nov2025 ..)
RONALD
BIRDSALL MARKED PETRIE CORRECTIONS
https://ronaldbirdsall.com/gizeh/petrie/
Petrie text values marked by Ronald Birdsall
-------------------
https://ronaldbirdsall.com/gizeh/petrie/c7.html ¦ 55
PetrieCH7.55 p.83:
¦The
position of the King's Chamber in the Pyramid is defined thus: N.
wall
at base 330.6 ± .8 S. of centre of Pyramid ; S. wall 537.0 ± .8 from centre;
E.
wall (284.4 ± 20.7)
= 305.1 ± 3.0 E. of centre; W. wall 107.7 ± 3.0 W. of
centre.
Base of walls 1686.3 to 1688.5 ± .6 above pavement; actual floor 1691.4
to
1693.7 ± .6 above pavement; ceiling 1921.6 to 1923.7 ± .6 above
pavement.¦
Birdsall remark says:
¦Petrie’s sign error should read ”(284.4 + 20.7)”¦;
No further Birdsall info.
What
Petrie’s info reads by numbers (correct if
faulty):
Comment:
We
have no information what the Birdsall corrections means
other
than the correct math:
»284.4
+ 20.7 = 305.1» .. But ..
—
If we have some basic experience in Surveying
(»running in the woods with trigonometric tables and
optical instruments»,
sticks and hammers for polygon points),
and
its sometimes tight geometry with numbers
(how to add them up in significant manners),
• we would prefer the Petrie specifications
here,
• unless Birdsall and his friends can be more
specific.
—
We never speculate. We launch no theories. Just the plain numbers.
NOTE:
(rJ=7818.80” ¦ 7817.80136922046000”)/(Oh=27.48” ¦ 27.48238537445830”)
(the
rJ itself not included in the Resolution 217
table )
=
284.46589561640500..
PETRIE refers inches to the
number 284 on several places:
”
S. Door of Large Chamber .. 284.9”, p.59;
”..
of the Pyramid centre; and its middle is 284.4 ± 2.8
E. of the Pyramid centre.. ”, p.72;
”
E. wall (284.4 ± 20.7) = 305.1 ± 3.0
E. of centre ..”, as above, p.83
”
N. end of S. subterranean passage .. mid. 284.9 ± 1”, E. from
Centre., p.95
”
Gallery, virtual S. end, floor .. mid. 284.4
± .3.”, p.95.
(Learning
lesson: don’t mess with a Surveyor .. especially not an experienced one ..)
-------------------
-------------------
https://ronaldbirdsall.com/gizeh/petrie/c7.html ¦ 64
PetrieCH7.64 p95:
¦ Beginning
Ascending .. + 179.9 ± .2¦
Birdsall remark says:
¦Petrie’s value is in error. Click for correction¦;
Further Birdsall info:
¦”Coming
soon”, apparently not (yet) available (25Nov2025)¦
Correction
by Petrie himself (Birdsall’s correction confirmed):
Petrie
himself reckons it on the resulting form 172.9 in PetrieCH7.39 p.65,
“.. of
the E. wall of the gallery (172.9+679.7)=852.6±.3
level above pavement ”
• This Petrie result is also confirmed
through the Breakthrough reckonings in UH
(InSystem
¦ BpointDetermination),
• Rather than a Petrie error, it is most
likely a book typo setting error, however that we do not know here ..
(also
with some experience of types for print setting — »shit happens» ..
trigonometric tables during the 1900s had them .. a few only ..)
• as well as noted by Ronald Birdsall
in his Petrie Web site remark
Birdsall March 21 2006 Point5, Last revisions August 27, 2014,
https://ronaldbirdsall.com/gizeh/revisions.html
-------------------
-------------------
https://ronaldbirdsall.com/gizeh/petrie/c6.html ¦ 20
PetrieCH6.20 p38:
¦ Case Plane Sides. ¦
Birdsall remark says:
¦Petrie’s error should read ”Core Plane Sides.”¦;
No further Birdsall info.
Explain — »CORE masonry CASING PLANE SIDES»:
• The term CASE (the enveloping surface, »the Bag») and CASING (»the envelope’s property»)
might
render different meanings depending on application:
Consider:
The
optical PLANE that touches the outermost stone tips of the pyramid masonry
»The
Outer Stone Masonry CASE Plane Sides» (TheInnerStoneOuterOpticalCasing Plane,
illustrated):
• / Optical Casing Plane: Independent of observational position on
the pavement:
all views — side, up (almost)
along — share the same optical stone tip tangent.
• A to B, finding the actual core-casing lengths by (measuring on the markers for the)
opposing pyramid sides (N-S,
E-W), what we know:;
—
Petrie’s CoreCASE Plane Side Measuring METHOD
— as we could measure it the
same, according to Petrie’s instructions.
Petrie’s
(»opposite consecutive AB») values in
inches, PetrieCH6.20 p38
:
N(9002.3),
E(8999.4), S(9001.7), W(9002.5), Mean(9001.5).
HOW PETRIE RETRIEVED THE FINAL
PYRAMID BASE LENGTH 9068.80”:
ADDING
THE above quoted PETRIE CORE-CASE PLANE N.E.W.S VALUES with
the Petrie measured
socket-pavement lengths in his Plate.10
(Those additional numbers are not found in Petrie’s
book, what we know, only in his Plate.10)
NORTH (9002.3) +
West(27.7) + East(39.4),
EAST (8999.4) +
South(35.5) + North(32.8),
SOUTH (9001.7) +
West(32.3) + East(35.5), and
WEST (9002.5) +
South(31.0) + North(35.1)
gives the final paramount
resulting mean averaged 2bPetrie pyramid base 9068.80”, bPetrie 4534.40”:
Petrie
does not give the above type table summing overview, what we know, only the
final result in his PetrieCH6.21 p39
table.
See the Petrie PLATE.10 in
Birdsall’s reference
https://ronaldbirdsall.com/gizeh/petrie/photo/plate10.html
See a partly more ambitious
attempt to describe Petrie’s
found Cheops Pyramid base length 9068.80 inches, more in detail, in
-------------------
-------------------
https://ronaldbirdsall.com/gizeh/petrie/c6.html ¦ 20
PetrieCH6.28 p46:
¦ 2148.0 S. end. ¦ (“..
the dimensions of the rock bed of the basalt paving ..”)
Birdsall remark says:
¦This value is in question. Click for explanation.¦;
”
Caveat to Section 28: .. ”
https://ronaldbirdsall.com/gizeh/corrections/s28_caveat.html
Basalt
pavement details outside the Cheops Pyramid.
Birdsall
notes three, somehow (diffuse) different values ..
TWO
2148.0 (»with inner issues») one 2148.4 ..
..
connected to the four values below in RBPC5:
-------------------
-------------------
https://ronaldbirdsall.com/gizeh/petrie/c6.html ¦ 28
PetrieCH6.28 p46:
¦
S.E. corner
to S. trench axis . . .
. . 1022.6
S. trench
axis there, to Pyramid . . .
. 1125.8
S.E. corner
to N. trench axis, continued .
. . 1075.0
N. trench
axis there, to Pyramid . . .
. 1073.0
¦
(“.. the
dimensions of the rock bed of the basalt paving ..”)
Birdsall remark says:
¦This value is in question. Click for explanation.¦;
Further Birdsall info:
Same
as the above: FB4.
https://ronaldbirdsall.com/gizeh/corrections/s28_caveat.html
Basalt
pavement details outside the Cheops Pyramid.
-------------------
-------------------
https://ronaldbirdsall.com/gizeh/petrie/c6.html ¦ 29
PetrieCH6.29 p47:
¦
axial length
. . . . 2093.7 ¦
Birdsall remark says:
¦Petrie transposition error. Cortrect value is 2039.7¦;
No further Birdsall info:
-------------------
https://ronaldbirdsall.com/gizeh/petrie/c6.html ¦ 29
PetrieCH6.29 p48:
¦
Trial passages axis, E.
of central line, at the station marks ¦
Birdsall remark says:
¦Petrie confused his reference lines. Should read: ”E. of
base.”¦;
No further Birdsall info:
-------------------
No more found Birdsall
correction remarks up to CHAPTER7.
COMMENT:
—
IF a correction is correct, it is correct, unless incorrect
—
But unless RELATED, the statement of the incorrect (even if corrected correct)
is out of date.
No offense.
Meaning,
my personal interpretation:
—
Corrected errors without a detailed explanation, is like dropping the key in
the toilet,
flushing
it down with the rest of the wasted candy.
———————————————
Editor28Nov2025
RBPetrieCorrections ¦ RBPC1 ¦ RBPC2 ¦ RBPC3 ¦ RBPC4 ¦ RBPC6 ¦ RBPC7 ¦
Allmänna samband
END.
CAT2025CheopsPetrie — 14Nov2025
innehåll: SÖK äMNESORD på denna sida Ctrl+F · sök ämnesord överallt i SAKREGISTER
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ämnesrubriker
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CAT2025CheopsPetrie — 14Nov2025
Senast uppdaterade version: 2025-12-06
*END.
Stavningskontrollerat ¦ 19Nov2025 ¦ 28Nov2025 alla - korrigerade (tankestreck —, minus –, några missade decimalkomman).
*
referenser
[HOP]. HANDBOOK OF PHYSICS, E. U. Condon, McGraw-Hill
1967
Atomviktstabellen i HOP allmän referens i denna presentation, Table 2.1 MASS TABLE ¦ s9–65—9–86 ¦
concurrent — with such minor end decimal differences with Berkeley National 2003 and Nist/Codata 2005 — having no significance in this presentation
Comparing CODATA2005-HOP1967 ¦
mn =
1.0086652u
...................... neutronmassan i atomära massenheter (u)
[HOP Table 2.1 s9–65] — neutron mass
me =
0.000548598u .................. elektronmassan
i atomära massenheter (u) [HOP Table 10.3
s7–155 för me , Table 1.4 s7–27 för u]
m(1H1) = 1.007825200u .................... neutronmassan i atomära massenheter (u) [HOP Table 2.1 s9–65]
u = 1.66043 t27 KG .............. atomära massenheten [HOP Table 1.4 s7–27,
1967]
u = 1.66033
t27 KG .............. atomära massenheten [ENCARTA 99 Molecular
Weight]
u = 1.66041 t27 KG
............... atomära massenheten
[FOCUS MATERIEN 1975 s124sp1mn]
u = 1.66053886 t27 KG ........ atomära
massenheten [teknisk kalkylator, lista med konstanter SHARP EL-506W
(2005)]
u = 1.6605402 t27 KG .......... atomära massenheten [@INTERNET (2007) sv. Wikipedia]
u =
1.66053906660
t27 KG .... atomära massenheten [@INTERNET (2023) en. Wikipedia, Atomic mass]
u = 1.660538782 t27
KG ...... atomära massenheten [från www.sizes.com],
CODATA
rekommendation från 2006 med toleransen ±0,000 000 083 t27 KG (Committe
on Data for Science and Technology)]
c0 = 2.99792458 T8 M/S ......... ljushastigheten
i vakuum [ENCARTA 99 Light, Velocity, (uppmättes i början på
1970-talet)]
h = 6.62559 t34 JS ................. Plancks konstant [HOP s7–155]
e = 1.602 · t19 C ...................... FOCUS MATERIEN 1975s666
G = 6.670 · t11 JM/(KG)2
........ FOCUS MATERIEN 1975s666 (6,67 ·
10–11 Nm2kg–1)
—
Det internationella standardverket om universum sammanställt vid universitetet
i Cambridge, The Cambridge Encyclopaedia of Astronomy, London 1977.
[FM]. FOCUS MATERIEN 1975 — Fysikens, kemins och astronomins
historia. Allt från atomen till universum — fysik, kemi, jordvetenskap och
astronomi
[BKL]. BONNIERS KONVERSATIONS LEXIKON, 12
band A(1922)-Ö(1928) med SUPPLEMENT A-Ö(1929)
t för 10–, T för 10+, förenklade exponentbeteckningar
PREFIXEN FÖR bråkdelar och potenser av FYSIKALISKA STORHETER
Här används genomgående och konsekvent beteckningarna
förkortning för förenklad potensbeteckning
d deci t1
c centi t2
m milli t3
µ mikro t6
n nano t9
p pico t12
f femto t15
Alla Enheter anges här i MKSA-systemet (M meter, KG kilo[gram], S sekund, A ampere), alla med stor bokstav, liksom följande successiva tusenprefix:
K kilo T3
M mega T6
G giga T9
T tera T12
Exempel: Medan många skriver cm för centimeter skrivs här konsekvent cM (centiMeter).
MAC,
här ofta använd förkortning för Modern ACademy (»Modern Academic Corridors») —
etablerad vetenskap sedan början av 1800-talet
In UH often used abbreviation for modern academy — explicitly from the beginning of the 1800s
MAC — often used abbreviation in TNED for Modern ACademy
TNED —
Related PHYSICS And MATHEMATICS —
Se särskild djupbeskrivning av innebörden i begreppet relaterad framställning.
Toroid Nukleära
Elektro MEKANISKA Dynamiken —— Toroid Nuclear Electromechanical Dynamics
The Atomic Nucleus -- 1 - 4 ¦ TAN 1 ¦ TAN 2 ¦ TAN 3 ¦ TAN 4 ¦ AllKeplerMath ¦ AllKeplerMath+
FOR THE UNINITIATED READER (Sep2024):
On
the 10Jan2024 the below (217) specified
bPETRIE (1881-1883) finally proving resolution was discovered — after some
research on eventually matching integer numbers. The 217 match certifies, as we see (from The rJCIRCLE complex ¦ rJCIRCLEref) the bPETRIE 4534.40 inch
specified measure with a 99.9999832% precision. It is well enough to certify
the accurateness on Petrie’s Cheops Pyramid measurements. That also
consolidates the rJCIRCLE investigations on the subject;
—
Taking present (mJ) EarthMass on the Planck constant h=mcr deduced Neutron density Dmax gives a spherical radius of (all
natural constants, plus mJ) rJ = (h/c0)(3mJ/π·m4)1/3.
The
center of that sphere is precisely positioned in the sectional view of the
Flinders Petrie group (1881-83) measures so called Queens Chamber in the Cheops Pyramid.
The GOLDEN SECTION complex from the simple
form of Cheops
Rectangle bd=h² proves
(CALTEP
¦ CaseHistory)
the coherences in the Petrie measured Cheops Pyramid construct. The square
corners enveloping that type defined Pyramid, passes precisely on the edge of the calculated
rJ sphere’s surface. That was the initial discovery on the 1Nov2017.
Really.
SOON ENOUGH — after a cup of Tea, relaxing
on the new discovery, the 10Jan2024 — it was realized that the number 217 also connects to another Universal domain: UDHR10Dec1948. The Resolution 217(A) universal HumanRight
declaration. It is also the absolute foundation (special case history) for this
production in UniverseHistory (TNEDbegin1991).
We have two Resolution 217 in our known
history — detailed to the last universal atom;
IN ORDER OF DISCOVERY-RECOGNITION — Resolution
217Short:
• Resolution 217(A) UDHR10Dec1948
— Universal Declaration of Human Rights: 8 introducing paragraphs P1-8,
30
following articles A1-30 — study them and try to learn them from within
(test-question-analyze, 24/7).
—
Here in UH referred to as Humanright,
the only (reminded) known universal Humanright knowledge domain:
gravitation,
electricity: light, heat, magnetism — LIFE: The Periodic System of The Elements (KeplerResonances).
—
The Atoms’ Spontaneous assembly — no decision, no voting — to you and me (and
all the other fuckups).
P1: ” Whereas
recognition of the inherent dignity and ..”.
Guaranteed Eternal Protection. 24/7. No breaks.
• Resolution
217 (10Jan2024) — the
TNED deduced rJCIRCLE-CheopsPyramidEnvelopingSphereRadius
(rJ) number
defines
the actual Flinders Petrie 1883 measured Cheops Pyramid (half) base (b) — in to
a precision of
99.9999832%.
It verifies the (ContractedConstruct) TNED/Petrie investigated Cheops
Building Plan: All Petrie’s measured values verified (BpointDetermination). The Complex
(also, apparently: not much else left to chose
on) connects to The Origin of Script. See TheCLAIM — questioning the already long
ago 2000y questioned idea of a UNsanctioned
Geographic
Israel: (GUARD!)
the splitting of humanity — and the Quest of its reunion.
(Toroid Nuclear Electromechanical Dynamics), eller Toroidnukleära Elektromekaniska
Dynamiken är den dynamiskt ekvivalenta resultatbeskrivning som
följer av härledningarna i Planckringen h=mnc0rn,
analogt Atomkärnans
Härledning. Beskrivningen enligt TNED är relaterad, vilket innebär: alla,
samtliga, detaljer gör anspråk på att vara fullständigt logiskt förklarbara och
begripliga, eller så inte alls. Med TNED förstås (således) också
RELATERAD FYSIK OCH MATEMATIK. Se även uppkomsten av termen TNED
i Atomkärnans Härledning.
SHORT ENGLISH — TNED
in general is not found @INTERNET except under this domain
(Universe[s]History, introduced @INTERNET 2008VII3).
TNED or Toroid
Nuclear Electromechanical Dynamics is the dynamically equivalent resulting
description following the deductions in THE PLANCK RING, analogous AtomNucleus’
Deduction. The description according to TNED is related,
meaning: all, each, details claim to be fully logically explainable and
understandable, or not at all. With TNED is (hence) also understood RELATED
PHYSICS AND MATHEMATICS. See also the emergence of the term TNED in AtomNucleus’
Deduction.
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UTVECKLAT (Apr2010):
Samtliga kalkylkort med original från MsWors 4.0 finns nu i UNIVERSUMS HISTORIA. Se särskild beskrivning med förteckning i MANUAL.
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