Our Inheritance in the Great Pyramid (1874 Edition)

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PLATE I

FRONTISPIECE

FRONTISPIECE.

Ventilator

King's Chamber

Queens Chamber

Subterranean Chamber

High Nile Level in 1865 AD

VERTICAL SECTION | FROM SACAR TO NATHAN LEARNING WARE | OF THE GREAT PYRAMID OF JEZZEN

AT MINUTE TIME | IT CHEQUES IT OWN MASTER OUR INHERITANCE IN

THE GREAT PYRAMID

NEW AND ENLARGED EDITION

INCLUDING ALL THE MOST IMPORTANT DISCOVERIES UP TO THE PRESENT TIME

With Seventeen Explanatory Plates

BY

PIAZZI SMYTH, F.R.S.E., F.R.A.S. ASTRONOMER ROYAL FOR SCOTLAND

"BECAUSE THAT WHICH MAY BE KNOWN OF GOD IS MANIFEST IN THEM; FOR GOD HATH SHEWED IT UNTO THEM. FOR THE INVISIBLE THINGS OF HIM FROM THE CREATION OF THE WORLD ARE CLEARLY SEEN, BEING UNDERSTOOD BY THE THINGS THAT ARE MADE."

ROMANS i., 19, 20

W. ISBISTER & CO. 56, LUDGATE HILL, LONDON

1874 "David, in a choice of evils similar to these, said, 'Let me fall into the hands of the Lord, for very great are his mercies; but let me not fall into the hand of man' (1 Chron.

xxi. 13). The people of England know what it is to experience somewhat of the latter calamity; and though they are bound to acknowledge that their long-protracted griefs are to be preferred to the short but severe sufferings which the nations of the Continent had to endure, they must feel, after all, that it is a deep affliction which many have had to bear. But let them with Faith and Patience endure their troubles a little longer. Their redemption draweth nigh."

JOHN TAYLOR'S Wealth the Name and Number of the Beast, p. 149.

TO THE MEMORY OF THE LATE

JOHN TAYLOR, GOWER STREET, LONDON,

(DEPARTED JULY, 1864)

AUTHOR OF

"THE GREAT PYRAMID; WHY WAS IT BUILT, AND WHO BUILT IT?"

THIS FURTHER ATTEMPT TO APPLY ACTUAL

SCIENTIFIC EXAMINATION

TO TEST HIS MOST MOMENTOUS THEORY,

AND MOST PRECIOUS DISCOVERY OF THE AGE FOR ALL MANKIND.

IF TRUE,—

IS DEDICATED BY

THE FRIEND OF HIS FEW LAST YEARS,

BUT ADMIRER OF ALL HIS LONG AND EARNEST CHRISTIAN LIFE,

PLAZZI SMYTH.

EDINBURGH, 1874.

"THE GREAT, THE MIGHTY ,GOD, THE LORD OF HOSTS, IS HIS NAME, GREAT IN COUNSEL, AND MIGHTY IN WORK: . . . WHICH HAST SET SIGNS AND WONDERS IN THE LAND OF EGYPT, EVEN UNTO THIS DAY."

JEREMIAH xxxii. 18-20.

PREFACE.

WHEN the late worthy John Taylor, of Gower Street, London (originally of Bakewell, Derbyshire) published, first his larger work entitled "The Great Pyramid; why was it built, and who built it?" in 1859; and afterwards, in 1864, his smaller pamphlet which he called "The Battle of the Standards (of Linear Measure): the ancient of four thousand years, against the modern of the last fifty years—the less perfect of the two,"—he opened up for archæology a purer, nobler, more important pathway to light than that study had ever enjoyed before.

But Academic Archæology did not accept it; and meanwhile some portions of the new pathway were so little removed from much of my own scientific professional occupations, that I felt it something like a public duty to examine into the foundation of Mr. Taylor's theory as rigidly and extensively as I could, though by home work only, at first; and my publication of 1864 (i.e., the first edition of the present book) contained the findings so arrived at. Findings, in many confirmatory of the principal thread of Mr. Taylor's chief discovery; but exhibiting in the general literature of the subject a lamentable deficiency in the numerical data required for solid investigation; and which data of measure, nothing but practical examination at the place could hope to supply.

How, when no one else would volunteer, for the sake of Great Pyramid knowledge alone, and only one gentleman* in all the kingdom, throughout official and private circles alike, kindly tendered a subscription (£50) towards the expenses,—how, I say, my Wife and self determined to sail for Egypt; and did, very soon after Mr. Taylor's death, through four months of residence on the Pyramid hill itself, employ a large variety of scientific instruments, in obtaining many measures of the mighty monument, some of them to far more accuracy than had ever been attempted before, and others descending to numerous details unnoticed by former observers,—all this was described by me, first in abstract to the Royal Society, Edinburgh, in April, 1866; and afterwards (in 1867) at much more length to the world in general in my three-volume book, "Life and Work at the Great Pyramid in 1865."†

That last publication undoubtedly helped to spread a knowledge both of the importance of the question at issue, and the only means for solving it: especially as against the modern hieroglyphic scholars; who, whatever their learning may be concerning other Egyptian buildings, have never troubled themselves to examine the Great Pyramid in the manner now required, and remain singularly and perseveringly ignorant of its mathematical proportions and mechanical features.

Indeed, these literary Egyptologists are rather angered than otherwise to hear that such exact data of scientific measure, when collected by others than themselves, tend to establish that the Great Pyramid, though in Egypt is not of Egypt; and though built in the earliest ages of man upon earth, far before all history, was yet prophetically intended to subserve a high purpose for these days in which we live and the coming days. That it, the Great Pyramid, has never been even remotely understood yet by any race of men, though it has been a standing riddle guessed at by all of them in their successive ages; but that it is able nevertheless to tell its own story and explain its mission most unmistakably: not indeed by reference to, or use of, any written language, whether hieroglyphic or vulgar,—but by aid of the mathematical and physical science of modern times: a means fore-ordained both for preventing the parable being read too soon in the history of the world, and for insuring its being correctly read by all nations when the fulness of time shall have arrived.

This spread of purely-obtained Great Pyramid information, unalloyed by the Cainite profanities of Pharaonic Egypt, or the interested errors and perversions of the classic Greeks, brought by degrees several abl intellectualists into the field; and they have, during the last six years, applied so many of my own observations at the place to Mr. Taylor's theory, with a success beyond anything that he had ever hoped for,—that the matter has now completely outgrown its first book, and produced this publication as the best answer that I, with the assistance of the original publishers, can make to frequent demands from various quarters for more information.

And there are even some most interesting and hopeful circumstances in the evolution of the scientific contents of the Great Pyramid just now, causing the present time to be almost the beginning of a new era of increased certainty and more precise knowledge regarding all that that ancient building was originally intended for; and which certainly includes much of the sacred, as well as the secular.

And although some well-meaning persons may have too hastily concluded, merely because they do not find the very name of Pyramid written down in Scripture, that therefore there is nothing about the Great Pyramid in the Bible,—yet they may rest perfectly assured that there is a great deal about the Bible subject, in the Great Pyramid. Which building is moreover an earlier document in the history of the human race; while the putting together of its stones into the vocal and deeplymeaning shapes we see them in now, was absolutely contemporary with the first of the primeval events to which it was destined to bear indubitable witness in these latter days, and not sooner.

CONTENTS.

PART I.

GEOGRAPHY AND THE EXTERIOR.

CHAPTER PAGE

I. INTRODUCTORY STATEMENT TOUCHING THE GREAT PYRAMID 3

II. GEOMETRICAL PROPORTIONS 12

III. STANDARD OF LENGTH EMPLOYED IN THE GREAT PYRAMID 27

IV. FIGURE OF THE EARTH AND THE SUN-DISTANCE 40

V. GEOGRAPHICAL INDICATIONS IN THE GREAT PYRAMID 55

PART II.

HISTORY AND THE INTERIOR.

VI. STRUCTURAL ISOLATION OF THE GREAT PYRAMID AMONGST ALL PYRAMIDS . . . . . . . . . 73

VII. THE PYRAMID COFFER . . . . . . . . . 99

VIII. WHY OF THAT SIZE? . . . . . . . . . 118

IX. DENSITY AND TEMPERATURE . . . . . . 146

X. CONFIRMATIONS BY THE NEW SCHOOL . . . . 174

PART III.

NATIONAL WEIGHTS AND MEASURES.

XI. BRITISH METROLOGY, PAST AND PRESENT . . . . 199

XII. PYRAMID CAPACITY MEASURE . . . . . . . 225

XIII. PYRAMID WEIGHT MEASURE . . . . . . . 231

XIV. LINEAR AND SUPERFICIAL MEASURE . . . . . 244

XV. HEAT AND PRESSURE, ANGLE, MONEY, TIME . . . . 257 CONTENTS.

PART IV.

CHAPTER PAGE

XVI. THE SACRED CUBIT OF THE HEBREWS . . . . . . 281

XVII. “TIME MEASURES IN THE GREAT PYRAMID” . . . . 304

XVIII. MOSES AND THE WISDOM OF THE EGYPTIANS . . . 328

XIX. MECHANICAL DATA . . . . . . . . . . . 348

XX. SACRED, AND PROPHETIC, TIME . . . . . . 374

PART V.

INEVITABLE CONCLUSIONS.

XXI. HIEROLOGISTS AND CHRONOLOGISTS . . . . . 405

XXII. THE SHEPHERD KINGS . . . . . . . . . . 418

XXIII. SUPERIOR TESTIMONY . . . . . . . . . . 435

XXIV. PREPARATIONS FOR UNIVERSAL METROLOGY . . . . 444

XXV. GENERAL SUMMATION: SECULAR AND SACRED . . . . 460

APPENDICES.

APPENDIX I. Mr. Waynman Dixon's Casing-stone 489

", II. Dr. Grant's crucial Pyramid investigations 493

", III. Dr. Leider's supposed Pyramid 497

", IV. Mr. James Simpson's further Pyramid calculations. 499

", V. Rude stone monuments versus the Great Pyramid 505

", VI. Recent attempts to shorten both the Great Pyramid's base-side and the profane cubit of Egypt 511

INDEX . . . . . . . . . . . . . . . . 519 ILLUSTRATIONS.

(ENGRAVED BY ALEX. RITCHIE, EDINBURGH.)

PLATE

I. GENERAL SECTIONAL VIEW OF GREAT PYRAMID (Frontispiece).

Alluded to in Chapters I. and VI.; but of more or less serviceable reference throughout the book; and of especial use in showing the respective places of several particular parts of the monument which appear separately in subsequent plates.

II. CASING-STONE TESTIMONY TO GREAT PYRAMID'S π CONSTRUCTION.

Alluded to in Chapter II. The upper figure gives an illustration of John Taylor's π theory, requiring a particular side angle for the Pyramid; and the lower figures give the angle found by Colonel Vyse.

III. DIAMETER AND CIRCUMFERENCE RELATIONS.

Alluded to in Chapters II., IV., and X. Certain useful computation numbers, both in angular and linear measure, are entered in their appropriate places on the several Pyramidal figures, and will be found of frequent service.

IV. DIAMETER AND AREAL RELATIONS.

The upper figures alluded to in Chapters IV. and X., and the lower figure in Chapter XXV., where they are shown to confirm the numbers in Plate III. most remarkably.

V. GREAT PYRAMID'S PLACE IN EGYPT, AND EGYPT'S IN THE WORLD.

See Chapter V. This is a reduction and concentration of th several plates in my "Equal Surface Projection."

ILLUSTRATIONS.

PLATE

VI. ALL THE PYRAMIDS OF JEZZEH.

See Chapter VI. All these figures being on the same scale, show the Great Pyramid to be absolutely the largest of the Jeezeh group; and the only one with an ascending system of passages; and it enjoys the same superiority over all the Pyramids of Egypt.

VII. PLACING OF THE PASSAGES IN GREAT PYRAMID.

See Chapter X. These two figures illustrate a simple geometrical arrangement, which comes exceedingly close to the actual lengths and angles of the passages in the Great Pyramid.

VIII. THE CHAMBER AND PASSAGE SYSTEMS IN GREAT PYRAMID.

See Chapter VI. This is a generally useful plate to refer to, for the more interesting parts of the interior; when the frontis-piece fails from the smallness of its size.

IX. THE QUEEN'S CHAMBER.

See Chapters X., XIX., and XX. A chamber of important symbolisms, beginning with the excentricity of the niche by the amount, apparently, of the length of the sacred cubit.

X. THE ANTE-CHAMBER.

See Chapters IX. and X. A small chamber full of symbols, especially of the subdivision of the sacred cubit into inches; and the equal area equation of squares and circles.

XI. THE KING'S CHAMBER.

See Chapters VI., IX., X., XIX., and XXV. The final chamber of the ascending series of passages in the Great Pyramid, the most exquisitely constructed of all the chambers, and with the noblest symbolisms.

XII. THE GRAND GALLERY: ASCENDING AND DESCENDING.

See Chapters VI., XVII., and XX. The grandest interior feature of the Great Pyramid, unknown in any other Pyramid, and with supposed prophetic Christian symbolisms.

XIII. MOUTH OF THE WELL, IN LOWER CORNER OF GREAT PYRAMID.

See Chapters VI., XVII., and XX. Two views, one elevational, and the other in perspective, of the exit from the Grand Gallery to the symbolism of the bottomless pit.

ILLUSTRATIONS.

PLATE

XIV. STAR-MAP FOR SITE OF GREAT PYRAMID IN ANTEDILUVIAN TIMES.

See Chapter XVII. Exhibiting the constellations of hostile attributes to man, occupying the mid-heaven at the night beginning of the primeval autumnal year before the Flood.

XV. STAR-MAP FOR SITE OF GREAT PYRAMID AT EPOCH OF ITS FOUNDATION.

See Chapter XVII. Representing the constellations of friendly attributes to man, at the night beginning of the year of the Great Pyramid's foundation; after both the Flood and the Dispersion.

XVI. STAR-MAP FOR SITE OF GREAT PYRAMID AT THE PRESENT TIME.

See Chapter XVII. Representing the portion of time elapsed since the foundation of the Great Pyramid, as now indicated on the precessional dial of the Pyramid and the heavens.

XVII. THE NUMBERS MEASURED IN THE ENTRANCE PASSAGE OF THE GREAT PYRAMID.

See Chapter XX. The numbers entered here are Pyramid inches of distance from the north beginning of the Grand Gallery; and are supposed to represent years B.c.

THE KEY OF ENTRANCE INTO THE DESIGN OF THE GREAT PYRAMID,

AS INVOLUNTARILY PREPARED, YEARS AGO, BY MODERN MATHEMATICS; viz. :—

When a Circle's diameter d=c⁄π=4 a⁄c=2 √(a⁄π);

And its circumference c=π d=4 a⁄d=2 √(π) a;

And its area a=π⁄4 d2=\frac{c2}{4 π}=d⁄4 c;

Then

$

\begin{array}{l} \pi = \frac {c}{d} = \frac {4 a}{d ^ {2}} = \frac {c ^ {2}}{4 a}; \\ = 3 \cdot 1 4 1 5 9 | 2 6 5 3 5 | 8 9 7 9 3 | 2 3 8 4 6 | + \& c., \& c., \& c. \\ = \log . 0 \cdot 4 9 7 1 4 | 9 8 7 2 6 | 9 4 1 3 3 | 8 5 4 3 5 | + \& c., \& c., \& c. \\ \end{array}

$

And

$

\frac {\pi}{4} = 0 \cdot 7 8 5 3 9 8 1 6 + \& c. = \log . 9 \cdot 8 9 5 0 8 9 9 + \& c.

$

$

\frac {\pi}{6} = 0 \cdot 5 2 3 5 9 8 7 8 + \& c. = \log . 9 \cdot 7 1 8 9 9 8 6 + \& c.

$

$

\frac {1}{4 \pi} = 0. 0 7 9 5 7 7 4 7 + \& c. = \log . 8. 9 0 0 7 9 0 2 + \& c.

$

$

\frac {1}{6 \pi^ {2}} = 0. 0 1 6 8 8 6 8 7 + \& c. = \log . 8. 2 2 7 5 4 9 0 + \& c.

$

$

\sqrt {\pi} = 1 \cdot 7 7 2 4 5 3 8 5 + \& c. = \log . 0 \cdot 2 4 8 5 7 4 9 + \& c.

$

$

\frac {1 8 0 ^ {\circ}}{\pi} = 5 7 \cdot 2 9 5 7 7 9 5 1 + \& c. = \log . 1 \cdot 7 5 8 1 2 2 6 + \& c.

$

PLATE 11

Fig 1.

D C B

GROUND PLAN OF GREAT PYRAMID. ITS SQUARE BASE, AND A HYPOTHETICAL CIRCLE HAVING RADIUS EQUAL TO VERTICAL HEIGHT OF BUILDING: together with elevations of the direct and diagonal vertical sections of the same restored to ancient completeness of outline.

CROSS SECTION OF VYSE'S GREAT PYRAMID CASING STONE IN SITU.

when still attached to the Pavement, in middle of North side of BASE.

P A L Z I 8 0 7 9 E F L

A M I T C H L E D I N

THE KEY OF ENTRANCE INTO THE DESIGN OF THE GREAT PYRAMID,

AS INVOLUNTARILY PREPARED, YEARS AGO, BY MODERN MATHEMATICS; viz.:—

When a Circle's diameter d=c⁄π=4 a⁄c=2 √(a⁄π);

And its circumference c=π d=4 a⁄d=2 √(π) a;

And its area a=π⁄4 d2=\frac{c2}{4 π}=d⁄4 c;

Then

$

\begin{array}{l} \pi = \frac {c}{d} = \frac {4 a}{d ^ {2}} = \frac {c ^ {2}}{4 a}; \\ = 3 \cdot 1 4 1 5 9 | 2 6 5 3 5 | 8 9 7 9 3 | 2 3 8 4 6 | + \& c., \& c., \& c. \\ = \log . 0 \cdot 4 9 7 1 4 | 9 8 7 2 6 | 9 4 1 3 3 | 8 5 4 3 5 | + \& c., \& c., \& c. \\ \end{array}

$

And

$

\frac {\pi}{4} = 0 \cdot 7 8 5 3 9 8 1 6 + \& c. = \log . 9 \cdot 8 9 5 0 8 9 9 + \& c.

$

$

\frac {\pi}{6} = 0 \cdot 5 2 3 5 9 8 7 8 + \& c. = \log . 9 \cdot 7 1 8 9 9 8 6 + \& c.

$

$

\frac {1}{4 \pi} = 0. 0 7 9 5 7 7 4 7 + \& c. = \log . 8. 9 0 0 7 9 0 2 + \& c.

$

$

\frac {1}{6 \pi^ {2}} = 0. 0 1 6 8 8 6 8 7 + \& c. = \log . 8. 2 2 7 5 4 9 0 + \& c.

$

$

\sqrt {\pi} = 1 \cdot 7 7 2 4 5 3 8 5 + \& c. = \log . 0 \cdot 2 4 8 5 7 4 9 + \& c.

$

$

\frac {1 8 0 ^ {\circ}}{\pi} = 5 7 \cdot 2 9 5 7 7 9 5 1 + \& c. = \log . 1 \cdot 7 5 8 1 2 2 6 + \& c.

$

PLATE II

Fig. 1.

D B

GROUND PLAN OF GREAT PYRAMID. ITS SQUARE BASE, AND A HYPOTHETICAL CIRCLE HAVING RADIUS EQUAL TO VERTICAL HEIGHT OF BUILDING. together with elevations of the direct and diagonal vertical sections of the same restored to ancient completeness of outline.

CROSS SECTION OF VYSE'S GREAT PYRAMID CASING STONE IN SITU when still attached to the Pierment in middle of North side of BASE

PLEASE BE ONLY IN GREETING

EQUALITY OF AREAS N. 3.

Circle with Diameter Vert' Height of G Dyr.

Square with side computed by π.

$365 · 242 + &c = Base side length of G Dyr2 in Sacred Cubits$

$412 · 132 = King's Chord length in 1 Inches$

EQUATION OF BOUNDARIES AND AREAS.

Circles and Squares Inches Inside and Sacred Cubits

Outside Great Pyramid. See Ch. 25.

PLATE V.

Lat North32.0

Longitude East from Greenwich30 31 32

Lat North32.0

MEDITERRAN-EAN SEA

31.0

Rouetta Alexandria Racolis LONGITUDE MERIDIAN OF THE GREAT PYRAMID Dumietta Port Said Pelusium Ismailia DESERT ANCIENT MEMPHISO Great Pyramid Cairo Suez RED SEA ANCIENT MEMPHISO

31.0

30.0

THE GREAT PYRAMID IN THE CENTRE AND AT THE SAME TIME AT THE BORDER OF THE SECTOR-SHAPED LAND OF LOWER EGYPT.

30.0

Lat North90

Longitude From GreenwichW120 90 60 50 0 30 60 90 120 150 180

Lat North90

EQ.

EQ.

Lat South

LOWER EGYPT IN THE GEOGRAPHICAL CENTRE OF THE LAND SURFACE OF THE WHOLE WORLD(on the Equal Surface Projection)

Lat South

A R I T C H I F C I N P

See Ch a 5 & 25

PLATE VI

PLEASE SMITH DELI

A RITCHIE COIN*

PLATE VI

THE GREAT PYRAMID.

THE SECOND PYRAMID

GROUND PLAN OF THIS PYRAMID WHEN COMPLETE.

SOUTH. NORTH.

GROUND PLAN OF THIS PYRAMID WHEN COMPLETE

SOUTH NORTH

THE THIRD PYRAMID.

THE FOURTH PYRAMID.

THE FIFTH PYRAMID.

THE SIXTH PYRAMID.

THE SEVENTH PYRAMID.

THE EIGHTH PYRAMID.

THE NINTH PYRAMID

ALL THE PYRAMIDS OF JEEZEH IN VERTICAL AND MERIDIAN SECTION,

THEIR ANCIENT SIZE AND SHAPE BEING SHOWN BY THE DOTTED TRIANGLES OVER THEM.

Scale of Nature.

See Ch. 1 & 6.

P A B E Z G M N O P Q R

GENERAL PASSAGE ANGLE OF GR. PYR.

ADB = Direct or right. Vertical Section of Great Pyramid from North to south.

EFGH = Square and Circle of equal area to above.

Angle BCS = 26° 18' 10"

LENGTHS AND PLACES OF PASSAGES IN GREAT PYR.

Add to Fig 1, I C trisected & CK bisected by horizontal lines, then

ZY parallel to CS, marks entrance passage.

WT at an equal but opposite angle marks First Landing Passage and the Ground Gallery.

Angle BCP where C P side of equal area square = 30° - latitude appear.

See C1.3 6 17.9 & 20

CHAMBER AND PASSAGE SYSTEM OF GREAT PYRAMID. enlarged from the Frontispiece.

HORIZONTAL Masonry courses from the base upwards.

FIRST ASCENDING PASSAGE

1522 P. Incher

DESCENDING ENTRANCE PASSAGE

NATURAL ROCK

levelled on top previous to building

SUBTERRANEAN CHAMBER.

SCALE OF BRITISH INCHES.

PIAZZ BROWN CLI'

A R I T C H P I L E D I N G

Sne Ct. 10 19 & 20

PLATE IX.

NORTHERN CEILING

NORTH WALL.

EAST WALL.

W/Diagonal Channel

SOUTH WALL.

WEST WALL.

Widman Dusen Channel

THE SEVEN SIDES OF THE QUEEN'S CHAMBER.

LAID OPEN ON THE PLANE OF THE EAST WALL.

Scale of British Inches.

GIVAZI BMATH CHRIST

See C h3 0 & 10

A RITCHIE, EDINB

In Sectional parts, single line shading - Lime stone crossed lines - Granite.

SIDES OF ANTE-CHAMBER,

OPENED OUT ON PLANE OF EAST WALL.

Lime stone blocks marked L; others are Granite.

Scale of British Inches

PLATE XI

A R T C = 4 1 2 ^ { \circ }

VERTICAL SECTION (Looking West) OF KING'S CHAMBER; ALSO OF ANTE-CHAMBER, SOUTH END OF GRAND GALLERY, AND VYSE'S HOLLOWS OF CONSTRUCTION, ABOVE KING'S CHAMBER. CROSSED LINES INDICATE GRANITE.

Scale of British Inches

PLATE X

A

Sec Cn² 6 17 & 20

VERTICAL TRANSVERSE SECTION

WITH ARABS ASCENDING

THE GRAND GALLERY, DR. PYR.

VERTICAL TRANSVERSE SECTION

WITH ARABS DESCENDING

THE GRAND GALLERY, DR. PYR.

SCALE OF BRITISH INCHES FOR THE SECTIONAL PARTS ONLY

See Cn² 6 17 & 20

PLATE XIII.

SECTION

Critical and

longitudinal

LOOKING WEST

OF

LOWER OR

NORTHERN END

OF

GRAND GALLERY

IN

GR PYR P

Horizontal Passage

to Queen's Chamber

Top of First

Ascending

Passage

ENLARGED

PERSPECTIVE

VIEW

OF THE

BROKEN OUT

RAMP STONE

AND

THE ENTRANCE

TO THE

WELL.

See 0.56&70

See C.96 & 70

GROUND PLAN OF THE

CIRCLES OF THE HEAVENS ABOVE THE SITE OF THE THEN

UNBUILT GREAT PYRAMID:AT THE ANTEDILUVIAN DATE OF

3440 B.C.

a DRACONIS ON MERIDIAN BELOW POLE,AT ENTRANCE PASSAGE ANGLE:

PLEIADES AND VERNAL EQUINOX NOWHERE VISIBLE.

See Ch.17

GROUND PLAN OF THE

CIRCLES OF THE HEAVENS ABOVE THE GREAT PYRAMID, AT ITS EPOCH

OF FOUNDATION, AT MIDNIGHT OF AUTUMNAL EQUINOX

2170 B.C.

DRACONIS ON MERIDIAN,BELOW POLE.AT ENTRANCE PASSAGE ANGLE;

AND PLEIADES ON MERIDIAN ABOVE POLE IN G. * R. A.;

OR COINCIDENTLY WITH VERNAL EQUINOX.

GROUND PLAN OF THE CIRCLES OF THE HEAVENS ABOVE THE PRESENT GREAT PYRAMID IN THE AUTUMN OF 1881 A.D.

A DRACONIS ON MERIDIAN. BELOW POLE, BUT AT SEVEN TIMES EN. PASS. ANCLE; PLEIADES FAR FROM MERIDIAN. EASTWARD;

VERNAL EQUINOX FAR FROM MERIDIAN. WESTWARD;

BUT THE DISTANCE OF THEIR MERIDIANS APART, INDICATING ON THE PRECESSIONAL THE AGE OF THE GREAT PYRAMID.

PLATE XVII

VERTICAL SECTION Looking West. OF

UPPER OR NORTH END OF ENTRANCE - PASSAGE

OF GREAT PYRAMID.

as it is now, and also be dotted twice, as it is supposed to have been,

when originally finished and closed up.

SCALE OF BRITISH INCHES

PART I. GEOGRAPHY AND THE EXTERIOR.

"IN THAT DAY SHALL THERE BE AN ALTAR TO THE LORD IN THE MIDST OF THE LAND OF EGYPT, AND A PILLAR AT THE BORDER THEREOF TO THE LORD."

" AND IT SHALL BE FOR A SIGN AND FOR A WITNESS UNTO THE LORD OF HOSTS IN THE LAND OF EGYPT."—ISAIAH XIX. 19, 20.

CHAPTER I.

INTRODUCTORY STATEMENT TOUCHING THE GREAT PYRAMID.

THE ancient Pyramids of Egypt form somewhat of a long clustering group, extending chiefly over about a degree of latitude, and in nearly a central division of the country, as regards North and South, or Lower and Upper, Egypt.

One traveller claims to have noted forty-five, another says sixty-seven; and another still, mentions no less than one hundred and thirty as existing in the neighbourhood of Meroe, Noori, and Barkal in Ethiopia; though they ought, rightfully, to be classed under a very different head; for when we extend the name to such large numbers, very inconsiderable, various, and often comparatively modern, structures are then included, and too wide variations allowed in form and material from the more typical examples, or those really mathematically-shaped pyramids which, though few in number, are what have made the world-wide fame of their land's architecture from before the beginning of history.

Now it is precisely with those particular specimens, or the oldest examples of the country (probably not more than thirty-eight in number), and no others, that we have to do in this book; and selecting even further amongst them, we find, that of all the more important instances that have yet attracted the attention of mankind, there are none to equal the combined fame and antiquity, the purity of shape and excellence of construction, of the several stone pyramids near Jeezeh,* in view of the ancient Memphis, and not far from the present city of Cairo.

This group is situated on the western, or more thoroughly African, and desert, side of the river, but close to the southern point of origin, or sectorial centre of the delta-shaped land of Lower Egypt; planted there apparently on the very edge of the dry and rocky steppe, and overlooking on one side the sand-strewn wastes of the interior, and on the other the green and fertile plains of Nile, about 130 feet below them. But amongst these Jeezeh Pyramids, again, there is one that transcends in importance all the rest; one that has been named for ages past the "Great Pyramid;" and which stands out distinct and distinguished from all its fellows by its giant size, its wondrous internal structure, its superior age, exquisite finish, the ancient mysteries of its origination, and the hitherto inscrutable destiny of its purpose; the greatest of the seven wonders of the world in the days of the Greeks, and the only one which is still in existence on the surface of the earth.

With many of the smaller and later pyramids there is little doubt about their objects; for, built by the Egyptians as sepulchres for the great Egyptian dead, such dead were buried in them, and with all the written particulars, pictorial accompaniments, and strange sepulchral adornments of that too graphic religion, which the fictile nation on the Nile ever delighted in. But as we approach, ascending the stream of ancient time, in any careful chronological survey, to the "Great Pyramid," Egyptian emblems are gradually left behind; and in, and throughout, that mighty builted mass, which all history and all tradition, both ancient and modern, agree in representing as the first in point of date of the whole Jeezeh group, the earliest stone building also positively known to have been erected in any country,—we find in all its finished parts not a vestige of heathenism, nor the smallest indulgence in anything approaching to idolatry; not even the most distant allusion to Sabaism, or to the worship of sun or moon, or any of the starry host of heaven.

I have specified "finished parts," because in certain unfinished, internal portions of the constructive masonry discovered by Colonel Howard-Vyse in 1837, there are some rude markings for a temporary purpose to be presently explained; and I also except, as a matter of course, any inscriptions inflicted on the Pyramid by modern travellers, even though they have attempted to cut their names in the ancient hieroglyphics of the old Egyptians. But with these simple exceptions we can most positively say, that both exterior and interior are absolutely free from all engraved or sculptured work, as well as from everything relating to idolatry or erring man's theotechnic devices. From all those hieratic emblems, therefore, which from the first have utterly overlaid every Egyptian temple proper, as well as all their obelisks, sphinxes, statues, tombs, and whatever other monuments they, the Egyptians, did build up at any known historical epoch in connection with their peculiar, and, alas! degrading religion.

Was the Great Pyramid, then, erected before the invention of hieroglyphics, and previous to the birth of the Egyptian religion?

No! for there, both history, tradition, and recent exploratory discoveries, testified to by many travellers and antiquaries, are perfectly in accord; and assure us that the Egyptian nation was established, was powerful, and its spiritually vile hieratic system largely developed, though not arrived at its full proportions, at the time of the erection of the Great Pyramid ; that that structure was even raised by the labour of the Egyptian population ;* but under some remarkable compulsion and constraint, which prevented them from putting their unmistakeable and accustomed decorations on the finished building, and from identifying it in any manner, direct or indirect, with their impure and even bestial form of worship.

According to Manetho, Herodotus, and other ancient authorities, the Egyptians hated, and yet implicitly obeyed, the power that made them work on the Great Pyramid; and when that power was again relaxed or removed, though they still hated its name to such a degree as to forbear from even mentioning it,—yet with involuntary bending to the sway of a superior intelligence, they took to imitating as well as they could, though without any understanding, a few of the more ordinary mechanical features of that great work on which they had been so long employed; and even rejoiced for a time to adapt them, so far as they could be adapted, to their own more favourite ends and occupations.

Hence the numerous quasi-copies, for sepulchral purposes, of the Great Pyramid, which are now to be observed along the banks of the Nile; always betraying, though, on close examination, the most profound ignorance of that building's chiefest internal features, as well as of all its niceties of proportion and exactness of measurement; and they are never found even then at any very great number of miles away from the site, nor any great number of years behind the date, of the parent work.

The architectural idea, indeed, of the one grand primeval monument, though copied during a few centuries, yet never wholly or permanently took the fancy of the Egyptians; it had some suitabilities to their favourite employment of lasting sepulture, and its accompanying rites; so, with their inveterate taste for imitation, they tried what they knew of it, for that purpose; but it did not admit of their troops of priests, nor the seas of abject worshippers, with the facility of their own temples; and so, on the whole, they preferred them. Those more open and columned, as well as statued and inscribed structures, accordingly, of their own entire invention and elaboration, are the only ones which we now find to have held, from their first invention, an uninterrupted reign through all the course of ancient Egyptian history; and to reflect themselves continuously in the placid stream of Nile, from one end of the long-drawn lan Egypt to the other.

They, therefore, are Egypt. Thebes, too, with its hundred adorned Pylon templegates, is intensely Egypt. But the Great Pyramid is something perfectly different.

Under whose direction, then, and for what purpose, was the Great Pyramid built; and under what sort of special compulsion was it that the Egyptians laboured in a cause which they appreciated not, and gave their unrivalled mechanical skill for an end which they did not at the time understand; and which they never even came to understand, much less to like, in all subsequent ages?

This has been indeed a mystery of mysteries, but may yet prove fruitful in the present advancing stage of knowledge to inquire into further; for though theories without number have been tried by ancient Greeks and mediæval Arabians, by Italians, French, English, Germans, and Americans, their failures partly pave for us the road by which we must set out. Pave it poorly, perhaps; for their whole result has, up to the present time, been little more than this, that the authors of these attempts are either found to be repeating idle tales told them by those who knew no more about the subject than themselves; or skipping all the really crucial points of application for their theories which they should have attended to; or, finally, like some of the best and ablest men who have given themselves to the question, fairly admitting that they were entirely beaten.

Hence the exclusive notion of temples to the sun and moon, or for sacred fire, or holy water, or burialplaces, and nothing but burial places, of kings, or granaries for Joseph, or astronomical observatories, or defences to Egypt against being invaded by the sands of the African desert, or places of resort for mankind in a second deluge, or of safety when the heavens should fall, have been for a long time past proved untenable; and the Great Pyramid stands out now, far more clearly than it did in the time of Herodotus, as a pre-historic monument of an eminently grand and pure conception; and which, though in Egypt, is yet not of Egypt, and whose true and full explanation is still to come.

Under these circumstances it is, that a new idea, based not on hieroglyphics, profane learning, classic literature, or modern Egyptology, but on scientific measures of the actual facts of ancient masonic construction, was recently given to the world by the late Mr. John Taylor, of London, in a book published in 1859.* He had not visited the Pyramid himself, but had been for thirty years previously collecting and comparing all the published accounts, and specially all the best certified mensurations, of those who had been there; and while so engaged, gradually and quite spontaneously (as he described to me by letter), the new theory opened out before him. Though mainly a rigid induction from tangible facts of number, weight, and measure, Mr. Taylor's result was assisted perhaps by means of the mental and spiritual point of view from whence he commenced his researches, and which is simply this:—

That whereas other writers have generally esteemed that the mysterious persons who directed the building of the Great Pyramid (and to whom the Egyptians, in their traditions and for ages afterwards, gave an immoral and even abominable character) must, therefore, have been very bad indeed,—so that the world at large has always been fond of standing on, kicking and insulting that dead lion whom they really knew not,—he, Mr. John Taylor, seeing how religiously bad the Egyptians themselves were, was led to conclude, on the contrary, that those they hated (and could never sufficiently abuse) might perhaps have been pre-eminently good; or were, at all CHAPTER II.

GEOMETRICAL PROPORTIONS.

John Taylor's First Discovery.

MR. TAYLOR'S first proposition with regard to the Great Pyramid, when slightly but immaterially altered to suit convenience of calculation, is,—that its height in the original condition of the monument, when every one of its four sloping triangular sides was made into a perfect plane by means of the polished outer, sloping, surface of the bevelled casing-stones, and when those sides, being continued up to their mutual intersections, terminated at, and formed the summit in, a point,—that its height then was, to twice the breadth of its base, as the diameter to the circumference of a circle.

Or, as the case is graphically represented in the diagram (Plate II., Fig. 1), where the square E F G H represents the square base of the Pyramid, and the darkly-shaded triangle A B D exhibits a vertical section of the triangular mass of the building taken through the middle of opposite sides ;—

Then A C, the vertical height of the Pyramid, is to B D, the side or breadth of its base, when multiplied by 2, as the diameter to the circumference of a circle; or, A C:2 B D::I:3.14159+&c.; this last number, 3.14159, &c., being the quantity known amongst modern mathematicians under the convenient, to us now doubly convenient, designation π Or again, as shown more recently by Mr. St. John Day, the area of the Pyramid's right section, viz., A DB, is to the area of the base E F H G, as 1 to the same 3·14159, &c.

Or, as the same fact admits again of being differently expressed, the vertical height of the Great Pyramid, A C, is the radius of a theoretical circle, A I, the length of whose curved circumference is exactly equal to the sum of the lengths of the four straight sides of the actual and practical square base of the building, viz. E F, F G, G H, and H E.

Now this is neither more nor less than that celebrated practical problem of the mediæval and modern ages of Europe, "the squaring of the circle;" and the thing was thus done, truly and properly accomplished at the Great Pyramid, thousands of years before those mediæval days of our forefathers. For it was accomplished by the architect who designed that pyramid, when, over and above deciding that the building was to be a square-based pyramid,—with of course all the necessary mathematical innate relations which every square-based pyramid must have,—he also ordained that its height, which otherwise might have been anything, was to bear such a particular proportion to its breadth of base, as should bring out the nearest value of π as above mentioned: and which proportion not one out of millions, or of any number, of square-based pyramids would be necessarily endued with; and not one out of all the thirty-seven other measured pyramids in Egypt has been proved to be endowed with.

If, therefore, the quantity is really found built into fact with exactness at the Great Pyramid, it must have been the result either of some most marvellous accident, or of some deep wisdom not less than 3,000 years in advance of the world in its own time. And that wisdom apparently was building in confidence, not for its contemporaries, to whom it explained nothing and showed very little, but for distant posterity; knowing well that a fundamental mathematical truth like π would be understood both in and by itself alone, and without any written inscription, in that distant day when mathematics should come to be cultivated amongst mankind, even as they are now.

A most true conclusion too, for experience has shown that neither mathematics nor mechanics can progress in any country in modern times without knowing well the numerical value and calculational quantity of π . In testimony whereof I may mention that in Dr. Olinthus Gregory's "Mathematics for Practical Men," third edition thereof by H. Law, C.E., at page 64 of Appendix, there is a Table 5, of "useful factors in calculation," and consisting of that invaluable number or proportion π ,or 3.14159, &c., in no less than fifty-four different mathematical forms.

Enquiry into the Data.

Now of this scientific value of π there is, and can be, in the present day, no doubt anywhere; neither of the Great Pyramid's immense priority over all the existing architectural monuments raised, and much more over all known books ever written, anywhere by any of the sons of men; nor again that the numbers which Mr. Taylor gives for the vertical height and breadth of base of the Great Pyramid do realise the π proportion very closely. But, as we are to take nothing for granted that we can inquire into ourselves in this book, it becomes our duty to ask what foundation John Taylor may have had, for the numbers which he has employed being really those which the Great Pyramid was anciently constructed to represent, or does contain within itself, when duly measured and corrected for modern dilapidations.

In this research I soon found it necessary to read rather extensively in a particular branch of literature, the Egyptological; where the respective authors are not only numerous, but their accounts, as a rule, most strangely contradictory. Colonel Howard-Vyse, in the second volume of his important work,* published in 1840, gives either extracts from, or abstracts made with admirable fairness of, no less than seventy-one European and thirty-two Asiatic authors. Several more are now to be added to the list, and it is extremely instructive to read them all. Unless, indeed, a very great number be read, no sufficient idea can be formed as to how little faith is often to be placed in the narratives even of educated men on a very simple matter; and when measures are given, though they are measures which those learned authors report to having measured themselves, why then, and even because of all their book-lore and classical scholarship, ought we to feel most mistrust, according to the experience acquired in this looking up of pyramid literary modern authorities. Such at least cannot fail to be the unvarying case, unless there are other means of proving that some exceptional instance, among those often able men of letters and metaphysical philosophy, did also really understand what accurate measurement means, and is capable of.

It would be easy to string together a series of so-called measures, made by successive travellers, on the same parts of the Great Pyramid, which should show its blocks of solid stone expanding and contracting between different visits to it, like elastic india-rubber balls; but it will suffice for the present to indicate the necessity of weighing the evidence in every case most scrupulously; to have a large quantity of evidence, a great variety of observers, and to place in the first rank

"The Pyramids of Gizeh." (Fraser, Regent Street, London.) of authors to be studied in the original, closely in every word they have written, but not necessarily to be always followed therein:—

Professor John Greaves in 1638,

The French or Bonaparte Expedition in 1799,

Colonel Howard-Vyse in 1837; and

Sir Gardner Wilkinson from 1840 to 1858.

At present the Great Pyramid is, externally to the sight, a huge mass, rudely though regularly and masterly built of rough limestone blocks, in great horizontal sheets, or courses, of masonry; their outer, broken off edges necessarily forming a sort of rectangular steps up the sloping sides; and with a platform of sensible area, in place of a point, on the top. But this spurious or adventitious flattened top, as well as the spurious and adventitious steps on the sides, have all of them merely resulted from the mediæval dilapidations and removal of the pyramid's polished white-stone casing (with its outer surface bevelled smoothly to the general slope, see Plate II. Fig. 2), which had stood for more than 3,000 years, and had in its day given to the structure almost mathematical truth and perfection. This state of things was that described by Greek, Roman, and early Arabian writers, and it existed until the Caliphs of Egypt, about the year 1,000 A.D., profiting by the effects of a severe, and for Egypt very unusual, earthquake recorded to have happened in 908 A.D., began methodically to strip off the polished casing-stone, bevelled blocks; built two bridges to convey them more easily to the river, after chipping off the prismoidal angles and edges; and then employed them in building mosques and palaces; for the lining of the great "Joseph" well, and for other public structures which still adorn their favourite city El Kahireh, or the victorious—the Cairo of vulgar English.* It is evidently then the original, not the present, size which we require, and must have, for testing Mr. Taylor's proposition; and for approximating, by the degree of exactitude that may be found, to whether it was accident or intention which decided the shape of the building; and he has well pointed out, that no one had got the true base-side length until the French Academicians, in 1799, cleared away the hills of sand and débris at the north-east and north-west corners, and reached the levelled surface of the living rock itself on which the Pyramid was originally founded.

There, discovering two rectangular hollows carefully and truly cut into the rock, as if for "sockets" for the basal corner-stones, they measured the distance between them with much geodesic skill, and found it to be equal to 763.62 English feet. The same distance being measured thirty-seven years afterwards by Colonel Howard-Vyse, guided by another equally sure direction of the original building, as 764.0 English feet, we may take for the present problem where a proportion is all that is really required, the mean, or 763.81 feet, as close enough for a first approximation to base-breadth.

But the height of the Great Pyramid, which we also need to have for the solution of our problem, is not at all easy to measure directly with any sort of approach to exactness; and more difficult still, to reduce from its present to its ancient height safely, after so very much of the original top has actually been knocked away, as to leave a platform "large enough for eleven camels to lie down" in, or beneath, the very place where once the four triangular sloping sides were continued up to a point; a sharp point on which an angel, or, as the monkish writer argued, any number of angels, might stand, but not one man.

In fact, the key-stone of the whole theory of the Great Pyramid would have been entirely wanting, even up to the present day, but for Colonel Howard-Vyse's most providential finding of two of the "casing-stones" in situ, at the foot of the Pyramid; for they enable the problem to be attacked in a different manner; or by angular as contrasted to linear measure. And we might indeed accomplish the solution by reference to angle only; but having begun with linear measure, we may as well on the present occasion employ the angle merely in a subsidiary manner; or to supply, when used in connection with the one linear datum we have measured, the other linear datum, which we have not been able to measure directly; and both of them against John Taylor's linear numbers also.

Beginnings of Objections by Captious Individuals to the Data on which the Modern Scientific Theory of the Great Pyramid rests.

After reading my first paper on the subject to the Royal Society, Edinburgh, I was seriously warned that two very shrewd and experienced members there had objected to this part of the Pyramid research; one of them, an engineer, saying "that he had passed through Egypt, been to the Pyramids, saw no symptoms of casing-stones bevelled to any angle, and therefore did not believe in them." The other, an Indian naval officer, had also been to the Pyramids on a visit, and "found such heaps of rubbish about the great one, that he could not see how any man could measure even its base side length with any degree of correctness, much less casing-stones which he could not see."

The First Objector.

Both these speeches are only too faithful examples of the small extent of information on which many persons, of commanding social rank, will even yet persist in speaking authoritatively on both the present, and long past, state of the Great Pyramid. The first doubter about the casing-stones, should at least have read the accounts of Herodotus, Strabo, Pliny, and many early Arabian authors who described what they saw before their eyes when the casing was still complete, and eminently smooth and beautiful; and then should have taken up Colonel Howard-Vyse's own book, descriptive, in details vocal with simple, naïve truth, both of how he succeeded in digging down to, finding and measuring probably the two last of the bevelled blocks still in situ, adhering closely by their original cement to the pavement base of the building; and then how he failed, though he covered them up again with a mound of rubbish, to save them from the hammers of tourists and the axes of Mohammedan Arabs, doubly and deadly jealous of Christians obtaining anything really valuable from the country they rule over. Besides which, the large amount of casing-stones, bevelled externally to the slope, still existing upon other pyramids, as on the two large ones of Dashoor; the well-preserved ones of the second Jeezeh Pyramid, conspicuous near its summit, and on a bright day "shining resplendently afar," as says M. Jomard; and the granite ones of the third pyramid, so excessively hard that modern workmen have not cared to have much to do with them—all this, which has long been known, and more which I have presently to relate, should effect much in convincing unwilling minds as to what was the original state of the outside of the Great Pyramid. While a similar case of spoliation to what that building experienced in A.D.

840, was perpetrated only a few years ago, on the south stone pyramid of Dashoor by Defterdar Mohammed Bey, in order to procure blocks of ready-cut stones of extra whiteness wherewith to build himself a palace near Cairo.*

The Second Objector.

Then the doubter about the possibility of other men succeeding in measuring what would have puzzled him as he looked on idly, should have read the whole account of the French academicians in Egypt, of which the following extract, from p. 63 of "Antiquités, Description," Vol. II., \dagger is worthy of being more generally known than it is: viz., that after digging down through the rubbish, not merely looking on with their hands in their pockets, "They recognised perfectly the esplanade upon which the pyramid had been established; and discovered, happily, at the north-east angle, a large hollow socket (encastrement) worked in the rock, cut rectangularly and uninjured, where the corner-stone had been placed; it is an irregular square, which is 118 British inches broad in one direction, 137.8 British inches in another, and 7.9 British inches deep" (measures since then tested by myself, but only after several days spent in digging and clearing the locality by a civil engineer with a party of Arabs).

"They made the same research at the north-west angle, and there also discovered a hollow socket (encastrement) similar to the former: the two were on the same level. It was between the two exterior points of these hollows, and with much care and precaution, that they measured the base-side length. They found it 763.62 British feet."

The "encastrement," so discovered in the basal rock at the north-east angle, is duly figured in plan amongst the large French plates; and, as I have since verified at the place, has the inner corner curiously pared away, evidently indicating the well-shaped rectangular outer corner to be the true starting-point for measure; because, also, it was originally the terminal point of the Pyramid's substance at that lower angle or foot. From the outer corner of the north-east to the outer corner of the north-west "encastrements" of their happy discovery it therefore was, that the skilful French surveyors extended their measuring-bars, and with the result given above.

Mr. Taylor has assisted the explanation of, or presented some apology for, the errors of the better class of earlier observers, by imagining their having been really measuring along some of the elevated steps or ranges of stones, at a height up the sides of the Pyramid; when, from the sand not having been cleared away, they erroneously thought they were at the bottom of the pile. But the apology was hardly required; for none of them sufficiently realised the importance of accuracy in what they were engaged in; and if, indeed, any man really believed the Great Pyramid to be only a tomb, and never to have been intended for anything but a tomb, as too all our modern Egyptologists boastfully teach, why should he trouble himself to measure it as carefully as he would a scientific standard of measure?

For the length of the real, or ancient, base-side of the Great Pyramid, therefore, no measure previous to the French one (which is the first socket measure) should or need be used, or can be depended on to within a serious number of feet. And as the French measures cannot now be repeated or replaced by any decidedly better, without previously incurring a large cost in recovering the sites of those important "encastrements" or fittings-in of the outer corners of the Pyramid's base, and still more in clearing and levelling the much-encumbered ground between them, we must not let the said French measures drop out of sight.

Colonel Howard-Vyse, indeed, did go to much of this remarkable expense; and not only procured another measure of the very original pyramid base breadth of the builders on the north side from end to end, but, as already mentioned, found near the middle thereof two of the ancient exterior casing-stones still forming, on the rocky platform, both a firmly-cemented part of the old basal line, and a beginning of the northern upward-sloping side of the building.

Howard-Vyse's Casing-stones.

The extreme value residing in these angular relics, was not only because they were of the number of the original casing-stones actually in situ and undisturbed, and therefore showing what was once the veritable outside of the Great Pyramid, viz., smooth, polished, dense white limestone softer than marble in a sloping plane; but because they exhibited such matchless workmanship: as correct and true almost as modern work by optical instrument-makers, but exhibited in this instance on blocks of a height of nearly 5 feet, a breadth of 8 feet, and a length perhaps of 12 feet; with joints, including a film of interstitial cement, no thicker than "silver paper."

The angle of the inclined or bevelled outer surface, measured very carefully by Mr. Brettell, civil engineer, for the Colonel, came out 5 1° 5 0′ ; and being computed from linear measures of the sides, made for him by another engineer, came out 5 1° 5 2′ 1 5 · 5′′. Results extremely accordant with one another, as compared with the French determination (before there was anything on which to determine accurately, other than the present ruined and dilapidated sides of the edifice) of 5 1° 1 9′ 4′′ ; or of previous modern observers, who are found anywhere and most variously between 4 0° and 6 0°.

But the Colonel's engineers, though good men and true, were not accurate enough for the extraordinary accuracy and merits of the unique piece of ancient work they had to deal with; and in the linear measures which he gives in p. 261, Vol. I., of his great book (and the length measures of the sides of a triangle, as every practical surveyor knows, are capable of laying down its particulars on paper much more accurately than can be done by using the angles through means of an angle-showing protractor), there is one anomaly which seems to have escaped remark hitherto. The stone itself, in cross section, and its accompanying numbers, stand as in our Fig. 2 of Plate II.

The lengths, having been only attempted to be given to the nearest inch, are lamentably short of the refinement to which they might have been taken; and an accurate measure of such noble sides, would have given the angle by calculation far closer than it could have been observed to, by any clinometer then at the pyramids, or indeed in all Egypt, and perhaps Europe.

Sir John Herschel, Athenaum, April 23, 1860.

By subtracting the upper from the lower surface length the figure is reduced to a triangle for calculation; and we have what should be a right-angled triangle at B (Fig. 3), where a = 59, b = 75, and c = 48 inches all by measure. But the value of the angle A is then found to be so very different, accordingly as it is computed from b c, or a b, that we may soon perceive clearly that B is not a right angle; and on computing what it is from the three sides, it appears to be 88°22'52·6''. This, however, is such an egregious error for workmen like those of the Great Pyramid to have committed, and in their easiest angle, that I incline to think Mr. Perring must have made a mistake of an inch in his measure of the base breadth of the stone, his most difficult side to measure. Indeed it would need a little more than an inch to be taken off his number, to bring the angle B up to 90°; but as Mr. Perring does not deal in smaller quantities than an inch, and as none of the sides were likely to have fallen on an even inch exactly, I have not ventured to make so strong a correction upon one of them only, though too it would be to bring it up to the round pyramid number of 100 inches in length; and I leave the twin results of the Vyse casing-stones as given out to the world by their discoverer.

John Taylor's Proposition supported by Howard-Vyse's Casing-stone Angle.

On the whole, then, taking everything into practical consideration, the ancient angle of the Great Pyramid's slope may be considered to be certainly somewhere between the two measured quantities of 51°50′ and 51°52′15· 5′ , while there are many reasons for believing that it must have been 51°51′ and some seconds. How many seconds, the modern observations are not competent altogether to decide : but if we assume for the time 14.3", and employ the whole angle, viz.

5 1° 5 1′ 1 4 · 3” with the length of the base side as already given from linear measure = 7 6 3 · 8 1 British feet, to compute the height, we have for that element 486.2567; and from these values of height and base-breadth, computing the proportion of diameter to circumference, there appears 4 8 6 · 2 5 6 7 : 7 6 3 · 8 1 × 2:: 1 : 3 · 1 4 1 5 9 , &c.* And this result in so far shows that the Great Pyramid does represent the value of π ; a quantity which men in general, and all human science too, did not begin to trouble themselves about until long, long ages, languages, and nations had passed away after the building of the Great Pyramid; and after the sealing up, too, of that grand primeval and prehistoric monument of the patriarchal age of the earth, according to Scripture.

Further Confirmations of John Taylor's Proposition.

Hence the first stage of our trial terminates itself with as eminent a confirmation as the case can possibly admit of, touching the truth of John Taylor's proposition or statement; and I am even in a position now to add the absolute weight of personal examination, as well as of inquiries carried on at the place for a longer time and with better measuring instruments than any of my predecessors had at their command. I was not indeed so fortunate as Colonel Howard-Vyse in finding such large, entire, unmoved, and well-preserved casing-stones as he did; but was enabled to prove that the enormous rubbish mounds now formed on each of the four base sides of the Pyramid consist mainly of innumerable fragments of the old casing-stones, distinguishable both by the superior quality of their component stone and their prepared angle of slope always conformable, within very narrow limits, to Colonel Howard-Vyse's determination.

And a number of these almost "vocal" fragments are now deposited in the museum of the Royal Society, Edinburgh.

Also, by careful measures of the angle of the whole Pyramid along all four of its corner or "arris" lines from top to bottom, observed with a powerful astronomical circle and telescope, as more particularly described in my larger book, "Life and Work at the Great Pyramid," in 1865, the same result came out. For that corner angle so measured (see the outer triangle A db in Fig. 1, Plate II., and compare also Figs. 1 and 2 of Plate III.) was found to be 4 1° \, 5 9′ \, 4 5′′ nearly : and that gives by computation, according to the necessary innate relations of the parts of a square-based pyramid, for the side slope of this "Great" one, 5 1° \, 5 1′ and some seconds ; or without any doubt the representative of the angle Colonel Howard-Vyse did observe on the side; and the one which, if it is there, necessarily makes the Great Pyramid express the value of π , or the squaring of the circle, whatever the absolute linear size of the whole building may be.

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