The Battle of the Standards (1864)
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OF THE
STANDARDS.
THE
BATTLE OF THE STANDARDS.
PROJECTION OF THE GREAT PYRAMID WHEN ENTIRE AND COVERED WITH THE CASING STONES.
Length of each of the four sides at the base, 764 feet. Vertical height, 486 feet, to the apex.
a. Level of Surface of Ground.
b. Level of Chamber in Rock.
c. Level of Low Water in the Nile.
d. Descending Passage, in a straight line to Entrance of Chamber in Rock.
Polar Star, as seen from the bottom of the descending passage.
THE
BATTLE OF THE STANDARDS:
THE ANCIENT, OF FOUR THOUSAND YEARS, AGAINST THE MODERN, OF THE LAST FIFTY YEARS—THE LESS PERFECT OF THE TWO.
By JOHN TAYLOR,
AUTHOR OF "THE GREAT PYRAMID, WHY WAS IT BUILT?" ETC., ETC.
"THOU SHALT HAVE A PERFECT AND JUST WEIGHT, A PERFECT AND JUST MEASURE SHALT THOU HAVE: THAT THY DAYS MAY BE LENGTHENED IN THE LAND WHICH THE LORD THY GOD GIVETH THEE."—Deut. xxv. 15.
LONDON:
LONGMAN, GREEN, LONGMAN, ROBERTS, & GREEN. 1864.
100 90
LONDON:
PRINTED BY J. WERTHEIMER AND CO.
CIRCUS PLACE, FINSBURY.
CONTENTS.
Preface vii
The Great Pyramid, a Poem, by PATRICK SCOTT, Esq. 1
Sonnet, from Petrocchi, by the Rev. CHARLES STRONG 4
Origin of the Ancient Standard 5
Brief Memoir of the Great Pyramid 21
Supplementary Papers, Battle of the Standards.
(1). Two Letters, by Sir JOHN HERSCHEL, Bart., on the Modular Unit 39
(2). Leading Article, from the Times, on the Debate on Weights and Measures, July 2, 1863 45
(3). Letter from the Times, of July 9, on the Decimal and Metric Systems in Practice 48
(4). "The Metrical and Decimal Systems," from the Times of July 15 and 17, 1863 59
**As the Bill for legalizing the Metric System of Weights and Measures did not receive the Queen's assent, Mr. W. Ewart gave notice on July 28, 1863, that he should move for leave to bring in a new Bill for that purpose, at the next session; but "that, as the general opinion of the House seemed to be in favour of a permissive Bill, he should limit his motion to such a measure."—Times. Nos. 1, 2, 3, and 4, relate to this subject, which is most interesting to every Englishman.
OUR Motto, from Deuteronomy, points to a very important consideration: viz.—That the people who maintain a perfect and just weight, and a perfect and just measure, may expect lengthened days in the land which God giveth them. If any people were ever entitled to so great a favour, it might be the Inhabitants of this Country. They have had the same measures of Length, Capacity, and Weight, from the earliest times; and they have been blessed with a long and unbroken series of peaceful Governments. Greater freedom from external foes, and from internal dissensions, has not fallen to the lot of any other nation.
Another remarkable peculiarity of our Country is, that it has been the home of the oppressed, when they have been exiled from other nations. Here, they have met with personal safety and kind treatment. The fetters of the slave fall from him, as soon as he lands on our shores; yet we interfere not with the Laws of other countries. We set them a good example, and would help them to follow ours, as far as we may; but without interfering with their internal regulations, because we should object to their intermeddling with ours. If they wish to become one with us, we shall be glad to see them enjoy the same liberty, and that kind of Government which suits them best; but we presume not to dictate to any nation.
Four of the great Empires of the World have risen, flourished, and passed away, since the Great Pyramid was constructed. Our Government, which is that of a National Brotherhood, alone is left, as if to shew Mankind, that it is possible to belong to the same original Family of Man, without absorbing other states, or being absorbed by any of them. We are advancing towards the end of the Christian Dispensation; and it is most satisfactory to see that we still retain the same Standards of Length, Capacity and Weight, which were first established, by an Unwritten Revelation, about 700 years before the Jews were formed into a Nation by Moses under the Laws of a Written Revelation.
It is to be hoped, that Wars may cease, Conquests be disclaimed; and instead of one Country becoming greater at the expense of another, or by its downfall, all may make common cause, and try to lessen, by the interchange of kind offices, the sudden and unavoidable calamities which each may have to endure. We have had happy experience of this good feeling among the greater part of the Colonies and Countries with which we are associated, by the bounty which has been extended to our own land in aid of our distressed operatives; and we are generally willing to shew the same good feeling toward others.
"Oh! might we all our lineage prove,
Give, and forgive,—do good, and love;
By soft endearments, in kind strife,
Lightening the load of daily life!"
SEPTEMBER, 1863.
THE GREAT PYRAMID,
A POEM,
WRITTEN FOR THIS WORK BY PATRICK SCOTT, Esq. AUTHOR OF "A POET'S CHILDREN," "FOOTPATHS BETWEEN TWO WORLDs." ETC., ETC.
1.
DWELLING, like greatest things, alone,
Nearest to Heaven of earthly buildings, thou
Dost lift thine ancient brow
In all the grandeur of immortal stone,
And, like the Centuries' Beacon, stand—
Up-springing as a tongue of Fire,
light the Course of Time through Egypt's mystic land!
2.
'Tis not for Poet to inquire Why thou wast built? and when?
Whether, in monumental state,
So great thyself to tomb the great Beyond their fellow men?
Or whether thou dost still endure,
Work of dark times which thee did raise,
To carry on to future days
The notions of a natural Faith impure?—
Or dost thou, in thy bodily Magnitude,
Not uninform'd nor rude,
Declare the abstract ties which Science finds,
Seen by the light of geometric minds,
In fix'd proportions, each allied to each?
Or dost thou still, in inferential speech,
Reveal unto mankind the girth
Of the vastly rounded Earth;
And to the busy human race Bequeath a rule, to guide the range Of all the minor Measurements of Space Which Traffic gets, and gives, in endless interchange?
3.
Thou pointest, like an Index, to th' extremes Of Time and Life. For ever in thy sight Rolls that great River, the High Priest of Streams, As consecrated by old Night To minister to Memories of the past. He comes on like a Conqueror,—not for blood, But to subdue the waste. His waves have cast More riches round them, as the stream has roll'd Through many climes its solitary flood, Than if they surged in gold. O blesséd Spirit! of which no eyes behold The Source whence thou descendest in thy power To bid the Desert flower. Thus, from a Fountain veil'd to mortal eye, Heaven's bounty streams from high To fertilize two worlds, and cause to bloom The waste of Life, the desert of the Tomb.
4.
And near thee the Grand City spreads, where dwell Sprouts from all modern nations, making there A mixture of moralities and creeds, And customs and costumes, that needs Much time to comprehend, nor less to tell; And half-suggests a prayer, That the indignant Nile would rise, and hide Th' Augean sights that shock the purer-eyed, And through the chok'd streets flush its purifying tide.
5.
A thin line parts the living from the dead— A few steps forward, and we tread Where the long waste of ages wears the pall Of Desolation at our footsteps'-fall The Locust, rising from his rocky bed, Flits to some other spot, where he alone May share, without a peer, his Desert-bounded throne.
6.
Stupendous pile! the things which thou hast seen, In thy long life, pass by thee as a dream— This forms the Poet's theme. From thy old Kings, till now, the Great have been Subjected to thy gaze. That wondrous man, Miscall'd the MADMAN, in thy land began To work his schemes, when Commerce rose, By long-foreseeing Thought compell'd To choose her Habitation; and the East And Learning, in descending ages, held In Alexandria's bowers her intellectual feast.
7.
Different was he, that Brand of War, whose breath Chang'd, like the fell Simoom, the verdant sod Into a waste — Genius of Crime and Death, He the World's demon, and his Soldiers' god ! For still Reflection asks, for what great good The First NAPOLEON stain'd the peaceful Earth with blood.
8.
And in this land the Traveller yet may hear,
Attentive with historic ear -
As o'er the keel-plough'd deep
The battle-clamours sweep,
The Voice of NELSON cry aloud, to slip
The iron thunder-shower from each recoiling ship.
9.
Enduring pile! Thou art the link that binds The Memories of reflective minds Vast mass of monumental rock sublime, That to the present Age dost join the Youth of Time.
SONNET FROM PETROCCHL
Io chiesi al TEMPO; ed a chi sorse il grande Amplo edifizio che qui al suol traesti?
Ei non risponde, e più veloci e presti
Fuggitivo per l'aere i vanni spande.
Dico alla FAMA; O tu che all' ammirande
Cose d'ai vita e questi avanzi e questi!
China ella gli occhi conturbati e mesti,
Qual chi dogliosi alti sospiri tramande.
Io già volgea maravigliando il passo,
Quando sull' alta mole, altero in mostra,
Visto girsene OBBLIO di sasso in sasso;
Ah tu, gridai, forse apristi, ah! mostra —
Ma in tuono ei m'interrupe, orrido e basso,
Io di chi fu non curo; adesso è nostra.
TRANSLATED BY MY FRIEND, THE REV. CHARLES STRONG, M.A. F.R.A.S.; AND SINCE REPUBLISHED IN THE SECOND EDITION OF HIS "SONNETS," 1862.
I ask'd of TIME; "To whom arose this high Majestic pile, here mouldering in decay?" He answer'd not, but swifter sped his way, With ceaseless pinions winnowing the sky.
To FAME I turn'd: "Speak Thou, whose sons defy The waste of years, and deathless works essay!" She heaved a sigh, as one to grief a prey, And silent, downward cast her tearful eye.
Onward I pass'd, but sad and thoughtful grown, When, stern in aspect, o'er the ruin'd shrine I saw OBLIVION stalk from stone to stone.
"Dread Power!" I cried, "Tell me, whose vast design—" He check'd my further speech, in sullen tone; AN ESSAY ON THE STANDARDS, ETC.
THE appearance of the Great Pyramid was sufficiently striking to arrest the attention of all strangers visiting Egypt, even if the purport of its erection were unknown. On the left bank of the Nile, about seven miles from Cairo, is still to be seen a group of Pyramids of various sizes, called the Pyramids of Gizeh, the largest of which, when perfect, was about 764 feet in length, on each of the four sides at the base, and about 486 feet in vertical height at the apex. It was originally cased over with a dark-coloured marble, like the black marble of Ashford in Derbyshire, the same that is called Swine-stone by mineralogists; but this became white by the action of the sun in the course of years, and where it is now seen, it is of a bright straw-colour. The black marble of Ashford has changed to a whitish tint even in thirty years. There are two truncated columns of this marble, supporting two beautiful antique vases in the gardens at Chatsworth, which columns are now bleached throughout of a dead white—yet they have not been there, in that position, more than thirty years, as Sir Joseph Paxton informed me, when I saw them about three years ago.
The Swinestone of Egypt was brought from the Mokattam quarry, about fifteen miles higher up the River Nile, and was, like the black marble of Derbyshire, capable of receiving a very high polish.
It has often been asserted by some persons, that there never had been any prismatic casing-stones placed between the limestone blocks of which the kernel of the Pyramid is constructed; but, in 1837, Colonel Howard Vyse was so fortunate as to settle this question. He discovered, under the débris on the Northern side of the Great Pyramid, two of the casing-stones in their original position; and, before any change was made in them, Mr. Brettell, a civil engineer, ascertained the angle of their face with reference to its base, and found it to be exactly 5 1° 5 0′ 0 0′ ′ . The following remarks, on this discovery, are made by Sir John Herschel, in the last edition of his Outlines of Astronomy, 8vo, 1859, page 205:—
At the date of the erection of the Great Pyramid of Gizeh, which precedes by 3,970 years (say 4,000), the present epoch, the longitudes of all the Stars were less by 5 5° 4 5′ than at present. Calculating from this datum the place of the pole of the heavens among the stars, it will be found to fall near a Draconis: its distance from that star being 3° 4 4′ 2 5′ ′ . This being the most conspicuous star* in the immediate neighbourhood, was therefore the Pole Star at that epoch. And the latitude of Gizeh being just 3 0° North, and consequently the altitude of the North Pole there also 3 0° , it follows that the Star in question must have had, at its lower culmination at Gizeh, an altitude of 2 6° 1 5′ 3 5′ ′ . Now it is a remarkable fact, ascertained by the late researches of Colonel Vyse, " that of the nine Pyramids still existing at Gizeh, six
" (including all the largest), have the narrow passages
" by which alone they can be entered (all of which open
"out on the northern faces of their respective Pyra-
"mids), inclined to the horizon downwards, at angles as
“ First, or Pyramid of Cheops
26° 41′
“ Second, or Pyramid of Cephren
25° 55′
“ Third, or Pyramid of Mycerinus
26° 2′
“ Fourth,
”
”
27° 0′
“ Fifth
”
”
27° 12′
“ Ninth
”
”
28° 0′
“ Mean . . . . .
26° 47′
" Of the two Pyramids at Abousseir also, which alone
" exist in a state of sufficient preservation to admit
" of the inclinations of their entrance passages being
" determined, one has the angle 2 7° 5′ , the other 2 6°.
"At the bottom of every one of these passages, there-
"fore, the then Pole Star must have been visible at its
" lower culmination, a circumstance which can hardly
"be supposed to have been unintentional, and was
" doubtless connected (perhaps superstitiously), with
"the astronomical observation of that star, of whose
"proximity to the pole, at the erection of these wonderful
"record of the most imperishable nature."
It appears, from these observations, that 4,000 years ago, or about 2,160 years b.c., while Noah was still living, the Great Pyramid was constructed. It had been revealed to the Builders of that wonderful structure that the Earth was a sphere, the measurement of which they then made with great exactness; that it revolved daily on its axis, which was inclined 3 0° above the level of the horizon; that the axis was in a line with the Polar Star; and that the Earth's orbit was completed round the Sun in the course of a year.
Admitting all this for the present, it may be asked : " What proof have we that the same knowledge was not possessed by the Philosophers of Greece or Rome?" We answer : " There is not the least reason to believe " that they, for more than fifteen hundred years " later, had any conception of these things." But, to answer this question in the most satisfactory manner, we extract the following passages from " The Students' Manual of Ancient Geography," published under the superintendence of Dr. William Smith, in 1861, as the latest authority on the subject :—
"Homer had no idea of the spherical form of the Earth: he conceived it to be the upper surface of a body of great thickness, which was as round as the shield of Achilles, and so flat that it could be looked across. This circular surface was edged by a river named Oceanus, just as a shield is bordered by its rim." (p. 17).
"Hecataus of Miletus (who flourished about 500 B.c.) supposed the habitable world to be an exact circle, surrounded by the Ocean, with which the Nile was connected at its source." (p.26).
"The true view of the spherical form of the Earth originated with the Pythagoreans, and obtained general
" belief : its exact form (an oblate spheroid), was not
" known, although the revolution of the Earth on its axis, which leads to the compression of the surface at
" the poles, appears to have been surmised by Aris- " tarchus, b.c. 280." (p.60).
Herodotus, " as far as we can gather from his descrip tion, supposed the world to be oval, rather than
"circular, Greece holding a central position." (p.28).
" Eratosthenes (b.c. 276 to 196), a native of Cyrene, and educated at Athens, held the post of Librarian at
" Alexandria under Ptolemy Euergetes. He brought
" Mathematics and Astronomy to bear on the subject of
" Geography, and was thus enabled to construct a very much improved Chart of the World." (p. 46).
" Strabo, of Amasia in Pontus (b.c. 66 to A.D. 24), agrees generally with the views of Eratosthenes. He
" holds the Earth to be spherical, concentric with the "outer sphere of the Heavens, but immoveable." (p.49).
"Claudius Ptolemy completed the science of Geography in a work which served as a Text Book on the subject, not only in his own age, but down to the fifteenth century, when the progress of maritime discovery led to its disuse. . . . He flourished at Alexandria about A.D. 150." (p. 55).
This is what is taught in our schools; but it is now seen, from the evidence of the Great Pyramid, that a thousand years before the time assigned to Homer, and more than fifteen hundred before Pythagoras or Hecatæus or Herodotus flourished, the Great Pyramid had been constructed, so as to embody records of the Earth's form, size, and motion, far more accurate than any of those to which the Greeks or Romans ever attained.
Yet the Greeks of Alexandria, under Ptolemy Euergetes, in whose reign (276 to 196 b.c.), the Septuagint Translation of the Hebrew Scriptures was made, could hardly be ignorant of some of those discoveries which had been made by the sons, or grandsons, of Noah two thousand years before.
What shall we say then? Shall we admit, as evidence of this wonderful Revelation, a monumental Record of the most imperishable nature?
or shall we ignore its existence, and be content with what is taught, erroneously, as the Truth, in our Schools and Universities?
It is not possible to do justice here to the testimony of the Great Pyramid, but we may insert a Memoir on the subject which was drawn up in 1859, with the view of being read before the Royal Society. That Paper was not read, because it was thought more proper for the Royal Society of Antiquaries; but, as it contains the scientific grounds of the Author's belief, that the Revelation thus embodied in Stone was worthy of the notice of the Royal Society, he hopes he may be permitted to publish the Memoir here, and to appeal to the common sense of mankind for his justification.
It seems almost incredible, that a country, so recent as England appears to be from its history, should yet have had, from the earliest times, a Measure of Length (the Inch), which received its determination more than 4,000 years ago. Whether the Inch was brought to this country by any of those descendants of Noah, "by whom the isles of the Gentiles were divided in their lands; every one after his tongue, after their families, in their nations," (Gen. x. 5), we presume not to determine; but as it came from Egypt, where the custom of the country was to use a Cubit, and not a Foot, or a Yard, the Inch most probably formed a portion of that larger measure. In the estimation of Sir Isaac Newton, the Sacred Cubit was the length of 24·88 English inches. We have some reason to suppose that it a little exceeded this, being equal to 24·8832. But this measure forms so nearly 25 of our inches, that four Sacred Cubits (equal to 99·533 inches), are less by only half an inch than 100 inches.
Additional proof of the Antiquity of the English inch, is found in the measures of the Earth, as given in Herschel's Astronomy, (8vo, 6th Edit.
p.139).
There is a slight difference between the Estimates of Mr. Airy and M. Bessel; but it is too trifling to affect our present question.
English Feet. English Miles.
Greater or Equatorial Diameter 41,847,192(426)—7925·604(648)
Lesser or Polar Diameter . . 41,707,324(620)—7899·114(170)
Mean Diameter . . . . . 41,777,253(523)—7912·309(409)
The figures to which an Asterisk is prefixed, are those in which Mr. Airy's Estimate differs from M. Bessel's. We proceed now to place before our readers the true state of the case, by reducing these measures into English inches.
AIRY. English Inches.
BESSEL. English Inches.
Greater or Equatorial Diameter
. 502,169,112*
-502,166,304
Lesser or Polar Diameter
500,491,440*
Mean Diameter
. . . . . . ,
501,330,276*
We were induced to make this change, by the conviction at which we had arrived, from studying the Great Pyramid, that an even number of Inches was intended to be represented; and that this number was 500 Millions.
The difference between the English inches of the present day, and the original inches of 4000 years ago, may be seen by dividing the mean diameter of 501,330,000, by 500,000,000. The latter number requires the addition of 1 and 1⁄3 in 1000 parts of an inch, to be made equal to the earlier inch.
In the measure of the Diameter of the Earth before the Flood, which amounted very nearly to the same number of inches contained in the present Earth, were 20 millions of Sacred Cubits, of 24.8832 Englishinches; and, in the Diameter of the present Earth, are 20 millions of a Cubit Measure of 25 English inches.
It would have required 2,366,000 inches to bring up the Diameter before the Flood, to 500,000,000 of inches; but after the Flood, the mean measure of the Diameter is found to be 1,330,000, or 1,327,000, above 500 Millions. If the Ten Foot Rule taken out by Greaves, for the measure of the Pyramids, in 1636, were, as he says, perhaps two, in 1000 parts of an inch, less than it should have been, this difference would more than make up for the above number.
A similar increase is required for the same reason, in the estimate of the cubic inch, as contained in the Porphyry Coffer. We had previously shown, in the Great Pyramid, that the Coffer was intended to be 90 digits long,40 digits deep,and 30 digits wide, also that each digit was equal to .864 parts of the English inch. The total is 69,657 English cubic inches; but this number, in order to make up the cubic inches in the Karnak cubit, requires a little more than 2 in 1000 parts.
The Author had remarked ("Great Pyramid," p. 37) that one English foot bears the same ratio to the side of the Great Pyramid, which the circumference of the Earth bears to one hundred thousand millions of English feet. "This curious and novel relation," says Sir John Herschel, "may be most intelligibly expressed under the following form of announcement, viz:—That a belt encircling the globe, of the breadth of the base of the Great Pyramid, would contain one hundred thousand millions of square feet. . . If we suppose the belt meridional, and the area expressed in modular square feet, the approximation is within one part in 1,100. The fact is interesting, as offering the only tolerable approach, in round numbers, to an "arithmetical relation between any of the dimensions of the Pyramid and those of the Earth."
But in his next Letter to the Athenæum (May 1, 1860), Sir John qualifies this opinion by observing, "There is another and a remarkable one, which I do not find noticed by Mr. Taylor, or elsewhere; viz.: that the height of the Pyramid, including the casing, and measured from base to apex, supposed to terminate in a point, is the two hundred and seventy thousandth part of the Earth's circumference. Taking the equatorial circumference as unity, the error of this aliquot is one part in 736; but if the polar, is only one in 3,506, the former error being in defect, the latter in excess; so there exists somewhere or other on the globe, a diametral section whose circumference is exactly 270,000 times the original height of the building. Though not a meridian, it is not very remote from one." The proportion here stated, had been noticed by the Author, at pp. 26 and 27 of the "Great Pyramid," where he shows that there are 270,000 Roman miles (not 31,500, as Eratosthenes erroneously imagined) contained in the Earth's circumference of 130,909,000 English feet.
If the circumference of the Earth were divided by 763.9, it is equal to 130,907,200 English feet; if by 764, to 130,890,100 English feet. The Roman mile is equal to 4848.5 English feet: 270,000 miles are 130,909,500 feet.
The English inch does not appear to have been in existence before the Flood. At that time, we find the Sacred Cubit the only measure recorded. When the Great Pyramid was constructed, and the new Earth measured, the Cubit of 25 inches would take the place of the Sacred Cubit in the East; and, perhaps a 25-inch Rule may have been adopted in England. A two-foot Rule has long since superseded this Cubit, if it ever prevailed with us; but, it is worth restoring now, if it be only to shew mankind the size of the Sacred Cubit, and how correctly the 20-millionth part of the Earth's diameter may be represented by the 25-inch Rule, which is only the eighth of an inch longer than that Sacred Cubit, by which the Ark was measured, when it was built by Noah, under the direction of the Almighty.
According to the measure of the Sacred Cubit, the size of the Ark a little exceeded that of the "Great Eastern" Iron Ship (see p.308).
From what has been said in the preceding pages, it will be perceived, that a Divine Revelation was made to mankind, of which the Great Pyramid is the Record, about 700 years before the Revelation of which the Pentateuch is the Record. Although the Art of Writing was not communicated to mankind, until it was employed by Moses to reveal the word of God, in order that after-ages might have no reason to doubt the verity and authority of the communication; still the earlier Stone Revelation was quite as precise and indubitable. We cannot misunderstand its purport, nor hesitate to believe the Truths it was capable of imparting. No one has been so bold hitherto, as to deny the validity of the Evidences embodied in the Marble Monument, though some persons are to be found who appear to doubt the validity of the Written Memorial, and strive to discredit its Testimony.
There had been, of old time, Revelations made to certain persons chosen out for that purpose, before the communication which was made to the Founders of the Great Pyramid; and unless these Revelations had been made, that work could not have been completed. One related to the Art of Number, by means of the so-called Arabic Numerals. Without their aid, the various combinations of figures, increasing ten-fold in power as each preceded another, (reckoned in order from right to left), could not have been denoted.
The Art of Writing was then unknown, while Number had been long resorted to. 2. Geometry was understood, and practised, before the Flood as well as after. 3. The use of the Mechanical Powers, with the Art of Shipbuilding, must have been made known to NoAH by means of a Divine Revelation; since he could not otherwise have built the Ark.
We may go farther back, and say that the knowledge of the Arts of Common Life must have been communicated by Revelation to the First Man; and that, without a full command of Language, he could not have given "Names to all cattle, and to the birds of the air, "and to every beast of the field"; for "whatsoever Adam called every living creature, that was the name thereof." He was at once inspired with the Art of Language in perfection, and had not to learn it by slow degrees, as a child now learns it by the patient teaching and long continued care of its parents. The First Man could never have attained to the right use of words by this process, any more than an infant, without father or mother to take care of and instruct it, could ever learn to clothe, feed, and protect itself. In all these cases, Man's boasted Reason would prove but a sorry substitute for that Instinct with which the Almighty has endowed the inferior creatures. They never fall below what is required of them, but they never rise above it; they never fail, but they never improve. Man is able to surpass himself; but it is only by receiving Divine Instruction, when he feels the need of it, and asks it from his Heavenly Father.
The Knowledge revealed to Man, by the favour of God, is essentially different from that knowledge which men are able to acquire for themselves. "Lo, this "have I found, that God hath made man upright; but they "have sought out many inventions" (Eccles. vii. 29.) These are the words of "the Preacher, the Son of David," and they express a great Truth, which is too much lost sight of (it may be feared) in the present day. By the upright, Solomon means the righteous, (Jasher), a name applied to Noah. By "Inventions" he means such engines or machines as Uzziah employed, when it is said, "He made in Jerusalem engines invented by cunning men, to be in the towers, and upon the bulwarks, to shoot arrows and great stones withal" (2 Chron. xxvi. 15). Inventions here especially meant those engines by which men's lives may be destroyed; but the word is also applicable to those engines or machines by which men's lives may be preserved, or by which they themselves may be made more comfortable while they live.
In some important particulars the two kinds of Knowledge greatly differ. That peculiar knowledge, which is granted to the upright, is of a nature to which Man, by his own unaided reason, could never have attained: it is above his powers, and even beyond his imagination. Man's inventions, on the contrary, are beneath his powers, and under his own conception and control. Again, the knowledge revealed to man is perfect at the first; but that which is the effect of man's discovery is in a state of progressive improvement. These differences are well exemplified in the Great Pyramid. Although the divine knowledge indicated by that wonderful structure had been imparted so long, and though it exhibited such amazing evidence, as we now see, of those scientific truths which no one endeavours to gainsay or deny—yet all other men, except the few with whom the Pyramid originated, remained totally unmoved, uninfluenced, and uninstructed by its teaching.
It was not till about 2,000 years afterwards, that the knowledge it was capable of communicating was gradually made known, and this was probably done at Alexandria by means of the Hebrew Scriptures, and their translation into Greek. Even then the form of the Earth, and its revolution on its axis, as well as round the Sun, was not commonly known; nor were these facts generally believed in Europe till after the age of Galileo and Copernicus.
Moses was an upright or righteous man, and to him God said: "Come up to me in the Mount, and be there; and I will give thee Tables of Stone, and a Law and Commandments which I have written, that thou mayst teach them." They were written, in order that they might be taught. The necessity for this was the origin of all alphabetic writing. The Commandments were first written on two Tables of Stone by the finger of God." Moses, in consequence of the sins of which the Israelites had been guilty, during his absence in the Mount, brake the Tables by casting them from him on his return. The Lord then said to him: "Hew thee two Tables of Stone like unto the first, and come up unto me into the Mount, and make thee an ark of wood. And I will write on the Tables the words which were on the First Tables which thou brakedst, and thou shalt put them in the ark" (Deut. x. 1, 2). Here we see the commencement of all writing in alphabetic characters; and that it was revealed first to an upright or righteous man.
Some persons have supposed that because the art of writing, by means of Hieroglyphics, is evidently more imperfect than that of Alphabetic writing, it may be more ancient.
Upon this subject, the late Sir George Cornewall Lewis makes some valuable remarks in his " Historical Survey."
"The Egyptologists do not indeed pretend that any great amount of historical knowledge has been hitherto derived from hieroglyphic inscriptions. They profess to have read certain names of kings which they identify variously with names in Manetho's lists; but they do not assert that the inscriptions furnish either a coherent chronology, or events in the reigns of the kings. Brugsch, in his work on the Primeval History of Egypt, lays it down, that the ancient Egyptians had no Era, that they denoted events only by the year of the king's reign, and that this mode of reckoning affords no materials for a chronological system. The meagreness of the historical information which Bunsen and Brugsch profess to have extracted from the hieroglyphical inscriptions must be apparent to every reader. Bunsen, indeed, speaks of ancient Egypt as the 'monumental' nation; but its monuments are colossal buildings, not intelligible inscriptions containing historical records. If the hieroglyphical writings, which have been interpreted, have been interpreted correctly, and if they may be taken as a sample of the rest, we may be satisfied that there is nothing worth knowing. The work of Sir Gardner Wilkinson, upon Ancient Egypt, which speaks to the eye, is far more instructive than the efforts to address the mind through the restored language of the Egyptians. It may be feared that the future discoveries of the Egyptologists will be attended with results as worthless and as uncertain as those " which have hitherto attended their ill-requited and " barren labours."*
Greaves, in his "Discourse of the Romane foot and
"Denarius; from whence, as from two principles, the
" Measures and Weights, used by the Ancients, may be
" deduced," † makes the following important statement :—
"If any shall find some little difference from some originals, as five or six grains in the English pound, and it may be one or two parts of a thousand in the
"English foot, different from the standards in the Exchequer, or the Tower, or at Winchester, or some other place, it is not much to be wondered. For I have found as great differences in collating the English standards themselves."
Thus Greaves prepares us to expect that difference in his measure which Raper affirmed he had found, and which Dr. Hussey supposed to be as much as two in 1,000 parts of the English foot or inch.
The same difference is doubtless to be expected at the present day, but it is of less moment now than it formerly was, since we can restore the full measure whenever we please, as Sir John Herschel has shown us, in his Letter on the Modular Unit; and whether we add the thousandth part of an inch, or twice that quantity, it is practically of no real importance. The Man of Science can supply the defect at any time, when he is engaged in calculations which require the addition to be made; and, on all other occasions, it is not worth naming.
The Unwritten Revelation, made to mankind 4,000 years ago, gave rise to most of the measures which have since
Historical Survey of the Astronomy of the Ancients. 8vo 1862, p.395.
occupied the minds of men, however diversified they seem. By that Revelation it was made known, to a few persons at first, that Time was a Measure of Space, and that, while the Earth was revolving on its axis, it made a perfect measurement of itself every twenty-four hours. It would be easy to shew in what manner this was done; but the following results, with regard to the Pyramid foot of 1.0909 English, the Greek foot of 1.0101 English, and the English foot, may be sufficient for this place.
The EARTH, in twenty-four hours, reveals itself in a direct line under the Sun, to the extent of—
120,000,000 Pyramid feet of 1.0909; or, of
129,600,000 Greek feet of 1.0101; or,of
130,908,960 English feet of 1.000—
which are all the same measure. This is the Circumference of the Earth. But this measure may be as perfectly represented by 1,570,907,520 Inches, which will serve the better for comparison. To denote the Diameter, requires Twenty Millions of Cubits, each of Twenty-five English Inches—a New Measure with us, but probably the earliest of all Measures. The total is 500 Millions of Inches which, multiplied by 3 · 1416,* is equal to 1,570,800,000. The difference is 107,520 Inches, in the entire circumference, being very nearly the thousandth part of an Inch, required to be added to Greaves's measure, and possibly to the Inch of the present day, to compensate for what it may have lost in 4,000 years. If we wish to make the Inch theoretically perfect, we have only to add one-thousandth part to it, as Sir John Herschel proposes. It must be admitted, that within this limit, all measures are identical for any useful purpose.
See Great Pyramid, p. 81, Hindoo Ratio.
† See Supplementary Papers, p. 39.
BRIEF MEMOIR OF THE GREAT PYRAMID.
Why it was Built.
O
Offered as a Communication to be read before The Royal Society in 1859.
AN opinion has long been entertained, that the Pyramids of Gizeh were intended for the Tombs of Kings, and that the Stone Coffers, found in them, were their Sarcophagi. But, at the commencement of the present century, certain men of science, who accompanied the French expedition into Egypt, endeavoured to show that the Great Pyramid might have had a scientific object. M. Jomard thought that the present Egyptian cubit was intended to be contained 400 times in the side of the base of the Great Pyramid, and the common cubit, 500 times; as also that the side was the 480th part of a degree of the meridian proper to Egypt. The real Measures, however, fail to support any of these conclusions; and, after a lapse of more than fifty years, this theory is held to be as far from verification as it was at the commencement of the century; yet, it is in this direction, if in any, that we may hope to find a satisfactory answer to the question, "Why was the Great Pyramid built?" For if it were constructed on scientific principles, an accurate estimate of its measures would, perhaps, reveal its purpose. As a Sepulchre, of course, we could not expect it to be constructed on any well-defined system of proportion; and further scrutiny would be hopeless on that supposition.
The measures of the side of the base of the Great Pyramid, made by many different persons, at different times, seem so little to correspond with each other, that, at first sight, we can discover no chance of reconciling them. In English feet, they are represented, according to the best authorities, by the following figures; 693, 728, 746, and 764 feet, the smallest of these numbers being the earliest of all recent measurements making any claims to accuracy; and the largest being the latest of all. These several stages have one striking peculiarity running through them — they differ from each other apparently by a regular series of increasing numbers. From 693 to 728, there is an increment of 35 feet (or twice 171⁄2 ); from 728 to 746, of 18 feet; and from 746 to 764, of 18 feet. We might suppose, from this general result, that in some way or other the various measures are capable of adjustment; and, that if the right principle of increase were ascertained, the whole might be brought into some kind of harmonious relation. Unless this could be done, we should have no ground to proceed upon; but, if it could be satisfactorily established, that the various measures formed part of one uniform system, the difference between them, instead of obstructing, would assist us in our inquiries after that original measure, which must first be discovered before we can advance any farther.
The blocks of stones, which constitute the four lowest tiers of the Great Pyramid, as it now stands, are about 4 feet 10 inches in perpendicular height, and gradually diminish, as they approach the top of the structure, to 2 feet 2 inches.
In 1637, Mr. John Greaves, Savilian Professor of Astronomy in the University of Oxford, measured the Great Pyramid with extreme care, and made the side of the base 693 English feet.
Between 1646 and 1693, the French Mathematicians, from various measures made by de Monconys, Thévenot, de Chazelles, Fulgentius of Tours, de Nointel, etc., found the base to be 682 French feet, or 728 English.
Two Englishmen are named as confirming this measure, viz.: Melton and Graves.
In 1763, Davison, our Consul at Algiers, records the base as being equal to 746 feet. This measure was remarkably confirmed by M. Jomard in 1798, who found the base to be 227.32 mètres, or 745.8 English feet.
A year after this, Le Pere, the architect, and Colonel Coutelle, carefully surveying the platform on which the Great Pyramid was built, perceived two indentations in the rock, 8 inches deep, one at each extremity, in which a corner-stone might have been originally placed; and measuring carefully the base again with this addition, they affirmed it to be equal to 232.747 metres, or 763.6 English feet.
Finally, in 1837, about 200 years after Greaves had made his first attempt to determine the true measure of the base, Colonel Howard Vyse discovered two of the actual Casing-stones in their original position, under the débris which had been thrown down on the north side by forcing the present entrance. "The size and angle of the building could therefore be exactly determined and all doubts were removed respecting a revétement" (Vyse's Operations, vol.i.p.261). Each of the casingstones was equal to 8 feet 3 inches at the bottom,4 feet 3 inches at the top,4 feet 11 inches in perpendicular height, and 6 feet 3 inches in sloping height. Mr.Perring, the English surveyor employed by Colonel Howard Vyse, now measured the base to the extremity of the casingstones, and made it 764 feet; thus establishing, in the most conclusive manner, the truth of the conjecture of the French Savans in 1799, that the indentation at each end of the base had been occupied by a corner-stone, and confirming their measure of 763.6 English feet.
To Colonel Howard Vyse we are indebted for the discovery, that the casing-stones, being about 8 feet 3 inches wide at the bottom, and only 4 feet 3 inches at the top, must have sloped gradually upwards from the base of the Great Pyramid (where they were brought in contact with a pavement extending 33 feet 6 inches beyond the casing-stones), to the topmost-stone of the entire building.
The complete measure of the side of the base, including the casing-stones, is thus, by the French estimate, 763.6 English feet, and by the English, 764 feet. Exclusive of the casing-stones, the French made the base 745.8 English feet, and the English, 746 feet. The difference between the two measurements is only 5 inches in the entire measure, and 21⁄2 inches in the measure without the casing stones. The English and the French nations are both alike entitled to great credit in bringing about this result, after the Pyramid had existed for about forty centuries without any light being thrown on it.
If we deduct the measure allowed by the French mathematicians in 1798, for the casing-stones, viz.:—17.8 English feet from 745.8 English feet, we have 728 English feet left. This would be the measure of the base, if the lowest tier of stones were hidden by the sand; and this was the measure arrived at by the French authorities in 1693. Allowing for the next tier 17.5 English feet, of which there is no positive measure extant, and for the third tier of stones from the bottom, 17.5 English feet, we have to deduct 35 feet from 728; and this leaves 693 feet, which was the measure so carefully estimated by Greaves about 1637.
At this time, therefore, we may suppose, the three lowest tiers of stones, as they are now seen, were hidden by the sand. Thus all the various measurements are found to corroborate each other, though they were formerly thought to present irreconcilable differences; and the latest measurements, being those in which we are chiefly interested, are all but identical with each other, differing only about five inches in a line of 9,168 inches; though recorded in the measures of two different countries, France and England-measures which cannot easily be brought into exact agreement with each other.
The various estimates which have been made of the height of the Great Pyramid, are incapable of any nice adjustment. Greaves, in the first edition of his Pyramidographia, comes the nearest to the truth, when he affirms the perpendicular height to be 481 feet, and in his "Observations," published after his death, in which he states it to be 490 feet: it is about midway between the two numbers. But by the discovery of the casing-stones in situ, all doubt as to the original height is now removed. The angle which the face made with the base, was most exactly ascertained by Mr. Brettell, Civil Engineer, to be 51° 50′ . This angle, with a base line of 764 feet, gives for the vertical height, supposing the Pyramid ended in a point, 486 feet; or with a base line of 763.6 English feet (the French measure), 485.85 English feet.
What reason, it may be asked, can be assigned for the Founders of the Great Pyramid giving its face this angle with the base, and not making each face, as Greaves and others conjectured it to be, an equilateral triangle? The only reason we can assign is, that they imagined the Earth to be a perfect sphere, and as they knew that the radius of a circle must bear a certain proportion to its circumference, they then built a four-sided Pyramid of such a height in proportion to its base, that its perpendicular would be equal to the radius of a circle, whose circumference was equal to the perimeter of the base.
We can hardly imagine that the Founders of the Great Pyramid were able to determine the angle of the face of such a Pyramid with quite as much accuracy as it might be done at the present time; but if they had such an object in view as that which we are supposing, they would construct the Great Pyramid, so as to make the angle of each face with the base bear some near relation to the angle of 5 1° 5 1′ 1 4′ ′ , which is that ascribed to such a Pyramid by modern science. The actual angle of the face, according to the casing stones, was 5 1° 5 0′ . Can any proof be required more conclusive than this, that the reason which is here assigned for the building of the Great Pyramid, was the true reason? It was to make a Record of the measure of the Earth that it was built.
Herodotus says of the Great Pyramid, when he saw it (about 440 B. C.) "that, it is made of polished stone, jointed with the greatest exactness; and none of the stones are less than 30 feet." He saw the Pyramid when it was covered all over with the casing-stones, for his measure of the stones is evidently surfacemeasure. The lowest of the casing-stones, being 6 feet 3 inches in sloping height, would, with a width of 5 feet, yield 30 feet in superficial measure; and the highest of the casing-stones, with a sloping height of 2 feet 10 inches, would, on a length of 12 feet, yield the same surface. When the casing-stones were first seen by Colonel Howard Vyse, "they were quite perfect, had "been hewn into the required angle before they were built in, and had then been polished down to one uniform surface; the joints were scarcely perceptible, and not wider than the thickness of silver paper; and such is the tenacity of the cement with which they are held together, that a fragment of one that has been destroyed remained firmly fixed in its original alignment, notwithstanding the lapse of time, and the violence to which it had been exposed.
The pavement, beyond the line of the building, was well laid and beautifully finished, but, beneath the edifice, it was worked with even greater exactness, and to the most perfect level; in order probably to obtain a lasting foundation for the magnificent structure to be built upon it. I consider (says Colonel Vyse) that the workmanship displayed in the King's Chamber, in this pavement, and in the casing-stones, is perfectly unrivalled; and that there is no reason to doubt that the whole exterior of this vast structure was covered over with the same excellent masonry." *
The stones of which the body of the Great Pyramid consists, were quarried from the rock on which it stands. They are a free limestone, and abound with fossil remains. The casing-stones are a kind of marble, brought from a rock on the other side of the river, called the Mokattam Quarry. This rock is a compact limestone, which contains few fossils, and is termed, by Geologists, Swinestone or Stinkstein. It is at first of a dark colour; but the portions seen in the British Museum are now of a yellowish white, or cream colour, bleached throughout by the Sun in the course of so many centuries. It takes a very high polish; and if the purpose of the Founders had been to construct a building which should remain unimpaired for all future time, they would endeavour to cover it with casing-stones of remarkable hardness, whatever might be the colour.
They would join these stones together with the thinnest cement of extreme tenacity; they would so arrange the blocks, that all should expose a surface of equal extent in square feet; they would make the structure end in a point, to prevent the lodgment of anything on the top which might injure the permanency of the edifice; they would do, in short, all that has been done by the Founders of the Great Pyramid to preserve it from disintegration or decay, arising from the action of of the elements, or from the violence of man.
Let us now enquire for what probable reason they would take such extraordinary pains. Was it to raise an imperishable monument, to which all nations, before they became too widely dispersed, might appeal for a standard of measure? If so, we might expect to find embodied in the building some unequivocal proofs that this was their design: we might expect, that, as the proportion which the diameter of a circle bears to its circumference is now known to be that of 1 to 3.141592, something near this proportion would be that of twice the perpendicular height of the Great Pyramid to its perimeter. Let us try the question by this test.
The perpendicular height is 486 feet, and twice that number is 972 English feet. The perimeter is 3,056 feet. If we take the French measure, it gives us 485.85 English feet for the height; 971.7 for the double of that number; and 3,054 for the perimeter. In the diameter of a circle equal to 3,056 feet, there are 1,000 feet of 972 parts of the English foot; and in its circumference are 3,144 of such feet. Is there any ancient foot which comes near this measure?
This is (we find), the earlier Roman foot, sometimes called the Italian. Greaves says: "In the year 1639, I went into Italy, to view, as the other antiquities of the Romans, so especially those of weights and measures; and, to take them with as much exactness as it was possible, I carried instruments with me made by the best artizans.
"My first inquiry was after that monument of T. Statilius Vol. Aper, in the Vatican gardens, from whence Philander took the dimensions of the Roman foot, as others have since borrowed it from him. In the copying out of this upon an English foot in brass, divided into 2,000 parts, I spent at least two hours (which I mention to shew with what diligence I proceeded in this and the rest), so often comparing the several divisions and digits of it respectively one with another, that I think more circumspection could not have been used. It contains 1,944 such parts as the English foot contains 2,000."* This is precisely 972 parts of 1,000, equal to 11.664 English inches. Many other authorities might be quoted in corroboration of this measure.
"My next search," says Greaves, "was for the foot on the Monument of Cossutius, in hortis Colotianis, from whence it hath since received its denomination (though it be now removed), being termed by writers Pes Colotianus. This foot I took with great care, as it did well deserve, being very fair and perfect; afterwards, collating it with that Roman foot which Lucas Pætus caused to be engraven in the Capitol, on a white marble stone, I found them exactly to agree. Now this of Cossutius is 1934 such parts as the English "foot contains 2,000."* This foot, therefore, contains 967 parts in 1,000, equal to 11.604 English inches.
How may this difference between 972 and 967 be explained?
There is a passage in Pliny which throws light upon it. "Eratosthenes, who was skilful in all kinds of learning, but especially in this wherein he excels all other persons, and is by all esteemed a great authority, sets down the entire compass of the Earth at 252,000 stades, which measure, by the Roman computation, makes 31,500 miles. A startling conclusion! but yet so well supported by skilful reasoning, that we should be ashamed not to believe him." There is, however, a great mistake in this statement. If we regard the proportion which the perimeter of the Great Pyramid bears to twice its perpendicular height, and divide 3,056 English feet by 3,150 Roman feet, we obtain for the latter a foot of 970 of the English foot, or 11.640 inches. This was the measure of the Roman foot obtained by Raper, from a measurement of the most ancient buildings in Rome"; and it is also that of many other eminent authorities. This is sometimes called the later Roman foot, in contradistinction to the earlier, which is then called the Italian.
There is a mistake, as we have said, in Pliny's statement, which arose from a misconception as to the length of the Roman mile. In 5,000 Roman feet of 970 English feet are 4,850 English feet. This may be equal to a Roman mile; but 31,500 of these miles are equal to 152,775,000 English feet; and this number exceeds by one-seventh the actual measure of the Earth's circumference. There are only 27,000 Roman miles of 4,850 English feet in 130,950,000 English feet; which number is a little more than the measure of the Earth's circumference, when it is estimated in the latitude of the Great Pyramid.
If we deduct one-seventh from 152,775,000, it leaves for the measure 130,950,000 English feet.
Nouet, who accompanied the French expedition into Egypt in 1798, calculated the latitude of the Great Pyramid, and found it to be 2 9°5 9′4 9′′ ; only 11" short of 30°. Perring says, that the Pyramids extend from 2 9°1 6′5 6′′ to 3 0°2′3 0′′ , and that they occupy a space of fifty-three miles from North to South. Pinkerton calculates the degree, in latitude 30°, to contain 363,724 feet; and the circumference is, therefore, equal to 130,940,640 feet.
It is a remarkable property of the English foot, in its connexion with the base of the Great Pyramid, that if we divide unity by 764 (the number of feet contained in the side of the base), the quotient exhibits, very nearly, the number of feet contained in the circumference of the Earth, namely, 1⁄764=.00,130,890,052 English feet = 130·890·0.052⁄100·0·0·0·0·0 — that is to say, one English foot bears the same ratio to the side of the base of the Great Pyramid, that the circumference of the Earth bears to one hundred thousand millions of English feet.
The Greek foot, as well as the Roman, is found in the measures of the Great Pyramid. Eratosthenes erred in reckoning 252,000 Greek stades in the circumference of the Earth, as much as he erred in the Roman measure. Deducting one-seventh, as before, leaves 216,000 for the number of Greek stades, which, reckoning 606.06 feet for the stade, is equal to 130,908,960 English feet. This is the smaller Greek foot, equal to 1.0101 English feet. The larger Greek foot is that which Stuart derived from the measure of the Hecatompedon at Athens. He made that foot equal to 1.0115 English feet, or 12.138 inches; but Mr.F.Penrose estimates it at 1.01336 English feet, or 12.16 inches.
The smaller Greek foot is called the Ptolemaic foot.Eight stades of this foot are equal to one Roman mile,of 4,848.5 English feet.
A measure is recorded by Herodotus, as found in the Great Pyramid; but it is superficial or square measure, and not linear measure. He describes the Great Pyramid as being "four-sided, each face on every side "is eight plethra, and the height is equal" (Her.11.124.) As square measure, the plethron is often employed to represent the Latin jugerum, though this is said to have contained only 28,800 square feet. It is used by Herodotus for that quantity of land which in Egypt was called the Aroura; this was the square of 100 royal cubits. One of the smaller Pyramids, the middle one on the east side of the Great Pyramid, had a base originally equal to the square of 100 royal cubits, or 172 feet 6 inches, as it was measured by Mr. Perring. It would, in that case, contain 29,655 square feet.
The words of Herodotus, in the above extract, require some explanation. If each face of the Great Pyramid is eight plethra, and the height is equal, the height must be equal to eight plethra also. In this case, he must mean to say, that the number of square feet in the measure of each face, and the number of square feet in the measure of the height, are equal; but, if so, he must mean the square of the height, since he alludes only to superficial measure.
A sloping height of 618 feet, with a base of 764 feet, (at an angle of 5 1° 5 0′ ) allows for the content of each face,236,076 square feet; and a perpendicular height of 486 feet yields,for the square of that height,236,196 square feet. In the content of each face,are eight plethra of 29,510 square feet,and in the content of the square of the height are eight plethra, of 29,525 square feet.
The angle required to make the square of the height equal in content to the content of each face is 51°49′46′′ , a difference only 14" less than the angle of 51°50′ , as measured by Mr. Brettell.
Diodorus Siculus assigns 700 feet to the side of the Great Pyramid. He says, "It is in shape four-sided, and each side, at the base, contains 7 plethra," meaning linear measure. Each foot is equal therefore to 1.0909 of the English foot:-700 of these feet are 763.63, nearly 764 English feet.
Sir Isaac Newton says, that "the oldest feet of which any account has been transmitted to us, are the Roman, the Ptolemaic, and the Drusian foot, at Tongeren in Germany, the last of which is equal to 1 3 1⁄2 Unciæ of the English foot" (Newton's Dissertation on Cubits, in Greaves's Works by Dr. Birch, p.419). If we add to the Roman foot of 970 English feet, one inch and a half, it gives us exactly 1.0909 for this foot of Drusus.
The foot of Drusus, or of Diodorus Siculus, might properly be called the Pyramid foot. In the side of the base of the Great Pyramid are 700 feet of 1.0909 English feet, or 763.630 feet. In the circumference of the Earth are 120 millions of these Pyramid feet, of 1.0909, equal to 130,908,000 English feet. The English foot is most closely connected with this Pyramid foot: if we deduct one twelfth part from the Pyramid foot of 1.0909, it leaves the English foot without any remainder (1.0000).
The English Inch, finds its place most wonderfully at such a time among these measures of the greatest antiquity. If the circumference of the Earth be represented by 130,908,000 English feet, its diameter will be equal to 41,667,000 English feet, or 500 millions of English inches,—the only difference being that we must divide the circumference by 3.141792, instead of 3.141592,a difference of 2 in the fifth place.
Pliny says, "there are 883 feet in each side of the Great Pyramid." His words are, "Amplissima octo jugera obtinet soli, quatuor angulorum paribus intervallis, per octingentos octoginta tres pedes singulorum laterum." Greaves, mistaking the meaning of the word soli, which in this case means surface, says, "Certainly Pliny is much mistaken in assigning the measure of the side to be 883 feet, and the basis of the Pyramid to be but 8 jugera, or Roman acres." He thinks that "Pliny writ 28 jugera, instead of 8; or else in his proportion of the side to the area of the basis he hath greatly erred." As a means of correcting this supposed error in the number of feet in the side, M. Jomard would change the number 883, to 833, imagining that Pliny meant Roman feet, but this correction only brings up the measure to about five-sixths of the Roman foot. Pliny's measure, as it stands, is the right one. In the side of the Great Pyramid, when estimated at 763 feet, are 883 of·864 English feet; or 10·368 inches; but this is properly a Royal Span, one of the most ancient of all measures. The eight jugera of surface which are said by Pliny to exist in the equal intervals of the four angles, are the same as the eight plethra of Herodotus above mentioned, and both mean eight aroura, that same Egyptian measure which is equal to the square of 100 royal cubits.
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