Our Inheritance in the Great Pyramid (First Edition, 1864)

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OUR INHERITANCE

IN

THE GREAT PYRAMID.

ALEXANDER STRAHAN AND CO.

London, . . . . . . . . . 32, Ludgate Hill.

Edinburgh, . . . . . . . . 35, Hanover Street.

Glasgow, . . . . . . . . 1, Royal Bank Place.

Photographed by Francis Bedford, Esq on March 5th 1862. during the travels of

THE GREAT PYRAMID OF JIZEH.

THE GREAT PYRAMID OF JIZEH.

Photographed by Francis Bedford, Esq on March 5th, 1862, during the travels of His Royal Highness, The Prince of Wales.

OUR INHERITANCE

IN

THE GREAT PYRAMID.

BY PROFESSOR C. PIAZZI SMYTH, F.R.SS. L. & E. ASTRONOMER-ROYAL FOR SCOTLAND.

With Photograph, Map, and Plates.

LONDON:

ALEXANDER STRAHAN AND CO.

EDINPURGH : T. CONSTABLE.

PRINTER TO THE QUEEN, AND TO THE UNIVERSITY.

TO JOHN TAYLOR, ESQ., OF LONDON,

IN HIS EIGHTY-FOURTH YEAR,

AUTHOR OF " THE GREAT PYRAMID : WHY WAS IT BUILT !"

(In reference to which Lord Neaves, Vice-President in the Chair at the Royal Society, Edinburgh, on the evening of March 21, 1864, said:- "If these things are only coincidences, they are most extraordinary coincidences; but if they are facts, that is, if the metrical proportions indicated were designedly and purposely established, they form the most remarkable discovery of the age;"—

THIS ATTEMPT TO FOLLOW OUT SOME OF HIS ARGUMENTS, AND TO TEST THE TRUTH THAT IS IN THEM,

IS DEDICATED BY

THE FRIEND OF HIS LATTER YEARS, AND ADMIRER OF HIS TRUE AND EARNEST LIFE,

C. PIAZZI SMYTH.

EDINBURGH, June 1864.

In the short interval between the printing and publication of this book, the estimable John Taylor is dead.

During the late spring he had come to know, only too surely, that his mortal career was drawing rapidly to a close, while many years might still elapse before his Pyramid discoveries would be appreciated in the world; but he had already calmly resigned himself to believe, "that he must pass away, before the popular prejudice with which a new view is always received, can be forgotten."

"The Cause," he wrote recently in a private letter, "is the grand object; and if in any manner we are able, while on earth, to vindicate the ways of God to man,—we have not lived in vain." But again rather checking himself, he added: "Many must approve, before the thought will enter into the popular mind; and if that result ever takes place, I am only one among many who are entitled to any commendation; nay, there is no room for commendation to any one, for all do but impart what has been given;—'Paul plants, Apollos waters, but it is God gives the increase.' I suppose this is the meaning of the elders casting their crowns before the throne in Revelation iv."

Such was the spirit which fell asleep in the Lord, on the 5th of the present month.

July 1864.

PREFACE.

The following pages are the foundation of a paper which I had the honour of reading before the Royal Society of Edinburgh, on March 21, 1864, descriptive of researches specially undertaken to test the truth and importance of some of the very remarkable statements in Mr. John Taylor's altogether remarkable book, published in London in 1859, and entitled,—

The Great Pyramid; why was it built, and who built it?

They contain, therefore,—though without attempting to follow Mr. Taylor through the whole range of subject which his truly capacious mind and extensive reading had included,—the results of a not inconsiderable amount of investigation into original authorities on both the Pyramid and Egyptian monuments generally; as well, too, for the literature, as the mechanics, of those more scientific branches of the whole question which, from their nature, were not very far removed from much of my professional experience.

In the course of this proceeding I could hardly help both feeling and confessing, very much as Mr. Taylor had done before me, that the theory, meaning, and then even the very history of the Great Pyramid, open out almost spontaneously when viewed in connexion with right leading ideas. In many details I have arrived at the same results as Mr. Taylor, though by a different road; in others, by prosecuting them longer, I have been enabled to penetrate somewhat further; and in others again I may have a few slight differences from him, though the general and final result of the whole is eminently with him and his conclusions; both those of them bearing on the Great Pyramid, as being the most ancient of finished primeval monuments, and those also indicating the part which it has had already, and is intended still to perform, in organizing the metrology, or weights and measures, of many nations.

In this latter respect some of the conclusions are startling to a degree, especially as leading to a new and noble mission for science, and shadowing out something of the character, as well as place in the world's history, of the age in which we live.

Yet precisely some of the strangest and most soulthrilling of these conclusions, are those which are best supported by proof from various quarters. Indeed that very one which led to the choice for this book of the title, Our Inheritance in the Great Pyramid (our being used in a national sense), has been made the subject of a striking and apparently involuntary public acknowledgment in the press, within the last few weeks, by the highest authority in the whole country on general science.

For therein does it now stand asserted by that very great philosopher, that not the yard, as so often advocated by many men, but the inch, is really the unit of British linear measure; that it is, moreover, hereditary to the nation, and possesses some most admirable and even transcendent scientific recommendations; in illustration of one of which he proposes that a new standard shall be constructed, containing 25 such unit-inches very nearly; under the name of the " geometrical cubit;" whose remarkable adaptation to astronomical and many other purposes he points out with all the fervour of genius working in a new field.

These truly noteworthy qualities, however, of the British inch were first brought to light, if we mistake not, by Mr. Taylor, from his researches in connexion with the Great Pyramid; and with this most signal addition, viz., that that particular inheritance of our nation did not come to pass by accident or chance—but was, on the contrary, the result of settled intention and high purpose, arranged from the beginning of the world! In partial demonstration whereof it may be mentioned, that the remarkable length alluded to, of twenty-five such unit inches (increased by 1⁄1000 th on the present Parliamentary inch), formed in early ages the sacred cubit of the Jews; and was specially maintained by them for important purposes, in antagonism to the measures of profane nations, during all the period of Divine Inspiration to the chosen of their race.

A large part of the present book is therefore devoted to this branch of the question; and when it was prepared for the press, Mr. Strahan had just returned from a tour in the East, which he made during the late spring, in company with the Rev. Dr. Norman Macleod.

This was extremely fortunate, for what he had seen when in Egypt of the Great Pyramid, its magnitude, majesty, and the deep mystery surrounding it at the place, induced him to enter, with even more than his usual zeal, into the effective bringing out of what he, as well as myself, hoped might throw some little light on the earliest record of intellectual and civilized man contained in the whole earth.

Not only, therefore, did Mr. Strahan allow any number of plates which a due explication of the Pyramid might require; but, guided by his own experience at the locality, he selected for the frontispiece one of the series of high-class photographs taken by Mr. Bedford, during the recent tour of His Royal Highness the Prince of Wales; and has had it photographically copied, with special prohibition against all touching, "stopping of the sky," and anything else which should interfere in any manner or degree with the nature-painting of the whole scene.

This much, then, for the present aspect of the exterior of the Great Pyramid; while, touching its interior, Mr. Strahan reports that that deeply interesting vessel, the Porphyry Coffer, on which so many problems of human regard, as well as scientific value depend,—is still safe in the silent but ventilated darkness of the so-called King's Chamber; standing on the polished granite floor, close to the spot where it was deposited by the founders of the Great Pyramid, in a special astronomical direction, more than 4000 years ago; and, by its presence, enabling the mighty edifice still to carry out efficiently the purposes of its ancient name.

CONTENTS.

PART I.

GEOGRAPHY AND THE EXTERIOR.

CHAP. I.—Introductory Statement, . . . . . PAGE 1

II.—Geometrical proportions, . . . . . . 11

III.—Standard of Length of the Pyramid, . . 27

IV.—Figure of the Earth, . . . . . . 40

V.—Latitude indications, . . . . . . 47

Table of Dimensions of Great Pyramid, . 67

PART II.

HISTORY AND THE INTERIOR.

CHAP. I.—Structural isolation of the Great Pyramid amongst Pyramids, 75

II. —The Porphyry Coffer, 102

III. —Why of that Size? 119

IV. —Density and Temperature, 145 CONTENTS.

PART III.

NATIONAL WEIGHTS AND MEASURES.

CHAP. I. —British Metrology and the Government of Great Britain, 171

II. —Capacity Measure of the Pyramid, 198

III. —Weight Measure, 204

IV. —Linear, Square, and Cubic Measure, 211

V. —Heat, 224

PART IV.

MORE THAN SCIENCE.

CHAP. I. —The Sacred Cubit of the Jews, . . . 229

II. —Time Measures in the Pyramid, . . . 253

III. —Moses and the Wisdom of the Egyptians, . 275

IV. —Mechanical Data, . . . . . . 287

PART V.

INEVITABLE CONCLUSIONS.

CHAP. I. — Hierologists and Chronologists, 317

II. — Hyksos and Israelites, 328

III. — Superior Testimony, 351

IV. — Preparations for Universal Metrology, 368

V. — General Summation—Secular and Sacred, 379

INDEX, 391 ILLUSTRATIONS.

WOODCUTS.

FIG. 1.—Circumferential diagram of Great Pyramid, . PAGE 12

FIG. 2.—Section of one of the Casing-Stones, . . . . .

PLATES.

PLATE I.—Photograph of the Great Pyramid, taken by Mr. Bedford, . . . . . Frontispiece

II.—Map of the northern part of the “Pyramid-field,” in Egypt, . . . . . xvi

III.—Plan and vertical-section of the Great Pyramid, 52

IV.—Latitude angles, and Pyramid-passage diagrams, 56

V.—Large-sized Meridian section of the Great Pyramid, 60

VI.—Early history of the Great Pyramid, . . 76 xvi

ILLUSTRATIONS.

PLATE VIII. —Examples of Egyptian Pyramids, subsequent to Great Pyramid, . . . . . . 78

ix. —The same continued, . . . . . . 78

x. —A model Egyptian Pyramid, . . . . . 78

xi. —Large-sized sections of the Grand Gallery in the Great Pyramid, . . . . . 87

xii. —The Porphyry Coffer, . . . . . . 103

xiii. —Ante-chamber, in section and plan, . . . 138

xiv. —A Granite Portcullis, . . . . . . 143

xv. —Large-sized view of hypothesis of the time-passages in Great Pyramid, . . . . . 253

xvi. —Cross section of Grand Gallery, . . . . . 261

xvii. —Upper end of Grand Gallery, . . . . . 272

xviii. —Chambers of Construction over the King's Chamber in the Great Pyramid, . . . 291

xix. —A King's name in Hieroglyphics, . . . . . 330

A Purchase Lath. Edin

MAP OF THE NORTHERN PART OF THE ANCIENT PYRAMID FIELD IN EGYPT. SCALE = \frac { 1 } { 5 0 0 . 0 0 0 }

PART I.

GEOGRAPHY AND THE EXTERIOR.

CHAPTER I. INTRODUCTORY STATEMENT.

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 the Lower and Upper, or more properly Middle, Egypt.

One traveller has noted forty-five, another ninety-five; no less than one hundred and thirty are also mentioned as existing in the neighbourhood of Meroe, Noori, and Barkal in Ethiopia, though they ought, rightfully, to be classed under a very different head; and there may be, altogether, many more pyramids still, of various kinds, in one part or another of the long valley of the Nile. But when we extend the name to such large numbers, very inconsiderable, and often comparatively modern, structures are then included, and very wide variations allowed in form and material from the more typical examples.

Now it is precisely with these particular specimens, viz., the old examples of the country, 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 of the several stone pyramids near Jizeh, 1 in view of the ancient Memphis, and not far from the present city of Cairo. They are situated on the western, or more thoroughly African and desert, side of the river, and form a most remarkable and prominent group; planted apparently on the very edge of the dry and rocky steppe, and overlooking on one side the sandstrewn wastes of the interior, and on the other the green and fertile plains of Nile, about 130 feet below them. But amongst these Jizeh 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 and even exquisite finish, the deep mysteries of its origin, and the hitherto inscrutable destiny of its purpose.

With many of the smaller and later pyramids there is little doubt about their objects; for, built by the Egyptians as sepulchres for 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 time, in a chronological survey to "the Great Pyramid," Egyptian emblems are gradually left behind; and in and throughout that mighty builded mass, which all history and all tradition, both ancient and modern, agree in representing as the first and earliest in point of date of the whole Jizeh group,—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 the sun or moon, or any of the starry host of heaven.

We have specified "finished parts," because in certain unfinished portions of the masonry discovered by Colonel Howard-Vyse in 1837, there are some rude markings for a temporary purpose to be presently explained; and we also except, as a matter of course, any inscriptions inflicted on the Pyramid by modern travellers, even though they have attempted to write their names in the ancient hieroglyphics of the Egyptians.

But with these simple exceptions we can most positively say, that both exterior and interior are indeed absolutely free from everything relating to idolatry in art or man's device; and from all those hieratic emblems which have utterly overlaid all Egyptian temples proper, as well as all their obelisks, sphinxes, statues, tombs, and whatever other monuments they, the Egyptians, have erected at any historical epoch in connexion 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! there 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 great, and its hieratic system largely developed at the time of the erection of the Great Pyramid; that that structure was even raised by the labour of the Egyptian population; 1 but under some remarkable compulsion and constraint, which prevented them from putting their unmistakable and accustomed marks on the finished building, and identifying it in any manner direct or indirect with their impure and Pagan 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, for their own purposes, a few of the features of that great work on which they had been employed so long; and began to adapt them, so far as they could be adapted, to their own 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; though they seem always to betray more or less ignorance of its principal internal features, and are never found at any very great number of miles away from the site of the parent work. The architectural idea, indeed, though copied, yet never wholly took the fancy of the Egyptians; it had some grand suitabilities to their favourite employment of lasting sepulture, and the 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 structures, accordingly, of their own entire invention and elaboration, are the only ones which we now find to hold an uninterrupted reign, and to reflect themselves continuously in the placid stream of Nile, from one end of the long drawn land of Egypt to the other.

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 in all subsequent ages?

This is indeed a mystery of mysteries, but a noble one to inquire into. Theories without number have been tried, by ancient Greeks and mediaeval Arabians, by Italians, French, English, Germans, and Americans; but the result has, up to the present time, been little more than this, that their authors 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 notion of temples to the sun and moon, or for sacred fire, or holy water, or burial-places of kings, or granaries for Joseph, or astronomical observatories, 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 prehistoric monument of an eminently grand and pure conception; and which, though in Egypt, is yet not of Egypt, and whose true explanation is still to come.

Under these circumstances it is, that a new idea has been given to the world by Mr. John Taylor of London, in a book published four years ago. He has not himself visited the Pyramids, but has been for thirty years past collecting and comparing all the published accounts of those who have; and while so engaged, gradually and quite spontaneously, as he has described to me by letter, the new theory opened out before him. It was assisted perhaps by the point of view from whence he commenced his researches, and which is simply this : That whereas other writers have generally esteemed that those unknown and mysterious persons who directed the building of the Pyramid, and to whom the Egyptians gave abominable characters, must, therefore, have been very bad indeed; he, seeing how bad the Egyptians themselves were, thought, on the contrary, that those they hated (and could never sufficiently abuse) may perhaps have been very good, or, at all events, of a different religious faith from themselves; and then following up this idea by what the Bible itself records touching the most vital and distinguishing part of the Israelites' religion, and which is described some centuries after the building of the Pyramid as notoriously an "abomination to the Egyptians,"—Mr. Taylor deduces reasons for believing, that the directors of the building of the Great Pyramid were of the chosen race, and in the line of, though preceding Abraham; so early indeed as to be closer to Noah than to Abraham; and had been enabled by divine favour to appreciate the appointed idea, as to the necessity of a sacrifice for a sin-offering,—an idea co-eval with Abel and Cain, but which no man of Egyptian born would ever contemplate with a moment's patience.

On this groundwork it is that Mr. Taylor takes his stand, and announces that he has discovered in the arrangements and measures of the Great Pyramid, as it now exists, certain scientific results, which speak of much more than, or rather something quite different from, human intelligence; for not only do the results rise above, and far above, the extremely limited and almost infantine knowledge of science possessed by any of the Gentile nations of 4300 years ago,—the period usually agreed on by most men for the foundation of that Pyramid,—but they are also, in whatever they apply to, very essentially above the extremely advanced state of scientific knowledge in our own time as well.

This is indeed a bold assertion, but from its boldness capable of the completest refutation, if untrue; for the science of the present day compared with that of only a few hundred years ago, is capable of giving out no uncertain sound, both as to fact, and order, and time of discovery: much more then when applied to what little was known of it, in those more remote epochs, before physical science had begun to be seriously cultivated at all.

CHAPTER II.

GEOMETRICAL PROPORTIONS.

Mr. TAYLOR's first proposition is, when slightly but immaterially altered to suit convenience of calculation, that the height of the Great Pyramid,—in its original condition, when every side was made into a perfect plane by means of the polished surface of the bevelled casing-stones; and when those sides, being continued up to their mutual intersections, terminated in a point, that its height was, to twice its base, as the diameter to the circumference of a circle.

Or, as the case is represented in the following diagram (Fig.1), where the square EFGH represents the base of the pyramid, and the shaded triangle, ABD, exhibits a vertical section of the pyramid through the middle of opposite sides :

Then,

AC, the vertical height of the pyramid, is to BD, the side or breadth of its base, multiplied by 2, as the diameter to the circumference of a circle; or,

AC : DEFB::1 : circumference.

FIG. 1.

As Mr. Taylor further states the vertical height of the pyramid to be 486 feet, and the breadth of its base 764 feet, we have

$

4 8 6: 1 5 2 8:: 1: 3 \cdot 1 4 4.

$

Now, the true proportion of diameter to circumference being, as every one knows from pure mathematics in the present day, 3.14159, etc., we see that three numbers are correct, but the fourth is incorrect.

To have found, however, only three numbers built in correct into the primeval building, shows a striking achievement for that early time; seeing that one of the first of modern philosophers 1 has declared absolutely against the then Egyptians having had any approach to a calculus, by which they might have computed the proportion, even to a more moderate degree of exactitude.

Let us inquire, however, what foundation Mr. Taylor may have, for the numbers that he has employed, being really those which the Pyramid was constructed to represent, or does contain within itself.

In this research we have found it necessary to read rather extensively; the respective authors being 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, 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 to be placed in the narratives even of educated men on a very simple matter; and when measures are given, which they report to have measured themselves, then ought we to feel most mistrust; unless, indeed, there are other means of proving that those often able scholars and learned philosophers did really understand what accurate measurement consists in.

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 granite expanding and contracting between different visits 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 of authors to be studied in the original closely in every word they have written—

Professor John Greaves in 1638;

The French Expedition in 1799;

Colonel Howard-Vyse in 1837; and

Sir Gardner Wilkinson from 1840 to 1858.

At present the Great Pyramid is externally a huge mass, rudely built of rough limestone blocks in steps, and with a platform of considerable area on the top; but this has resulted from the removing of its polished marble casing, which had stood for more than 3000 years, and had given to the structure almost mathematical truth and perfection; as described by Greek, Roman, and early Arabian authors; until the Caliphs of Egypt, about the year 1000 A.D., began methodically to strip off the polished bevelled blocks, or portions of the Cyclopean glazing of the structure: built two bridges to convey them more easily to the river, 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 Káherah, or the Victorious—the Cairo of vulgar English.

Since then, too, according to M. Jomard of the French Expedition, there is such an inveterate hankering in the minds of European tourists who climb to the top of the Pyramid, to detach some of the uppermost layers of stones, and send them thundering, crashing, and destroying down the side,—that the height of the Pyramid is daily decreasing, and the breadth of the platform at the top increasing.

It is evidently then the original, not the present, size which we require, and must have, for testing Mr. Taylor's proposition; and he has well pointed out, that no one had got to the true base until the French, in 1799, cleared away the hills of sand and debris at the north-east and north-west corners, and reached the levelled surface of the rock itself on which the Pyramid was originally founded.

There, finding two hollows carefully, truly, and deeply cut into the rock, as if for " sockets" for the basal corner-stones, they measured the distance between them with all geodesic skill, and found it to be 232.747 metres, = 763· 62 English feet. The same distance being made thirty-seven years afterwards by Colonel Howard-Vyse, guided by another equally sure direction of the original building, = 764· 0 English feet, we may take, for the present problem, the mean, or 763.81 feet, as close enough for the base.

But the height of the Pyramid is not at all easy to measure directly, especially after so very much of the top has actually been knocked away, as to leave a platform "large enough for eleven camels to lie down," where once the four sides were continued up to a sharp point. In fact, the key-stone of the whole theory of the 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. Up to that time, all ideas of the angle which the original side formed with the plane of the base, even the very learned attempts of the French Academicians, were but guesses; and have turned out since to have been so far from the truth, as to be utterly incapable of maintaining the true geometrical analogy.

For ages it had been thought that the ruthless Caliphs had carried away every single casing-stone. But in their haste to make themselves rich by the supposed plunder of the interior of the pyramid, they had formed such a hill of debris at the place where they attempted to force their way in, that four of the valuable marble casing-stones were covered up. This they had apparently perceived some time after, and succeeded in extracting two of them by boring sideways through the hill of rubbish; but the other two remained either forgotten, or deemed impossible to reach, during 800 years, and until Colonel Howard-Vyse dug down to, and uncovered them, to the unspeakable intellectual benefit of the age in which we live.

Since reading a paper on this subject at the Royal Society, Edinburgh, we have been informed that two very shrewd and experienced men have objected to this part of the statement. One of them, an engineer, says, "that he has passed through Egypt, been to the Pyramids, saw no symptoms of casing-stones, and therefore does not believe in them." The other, an Indian naval officer, has also been to the Pyramids on a visit, and "found such huge heaps of rubbish about the Great one, that he cannot see how any man could measure the base correctly."

Both these speeches are only too faithful examples, of the small extent of information on which many persons will persist in speaking authoritatively on both the present, and long past, state of the Great Pyramid. The doubter about the casing-stones, should read first, the account of Herodotus, Strabo, Pliny, and many early Arabian authors when the casing was still complete, and eminently smooth and beautiful; and then Colonel Howard-Vyse's own book, descriptive both of how he succeeded in finding and measuring the two last of the blocks; 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 specimen-mongers. Besides which, the large amount of casing-stones still existing on other pyramids, as on the two large ones of Dashoor; the marble ones of the second Jizeh Pyramid, conspicuous near its summit, "with a polish 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—should effect much in convincing as to what was the original state of the Great Pyramid.

While a similar case of spoliation to that, was perpetrated only a few years ago, on the south stone Pyramid of Dashoor by Defterdar Mohammed Bey, in order to procure marble blocks wherewith to build himself a palace near Cairo.

Then the doubter about the possibility of other men succeeding in measuring what would have puzzled him,—should read the whole account of the French Academicians in Egypt, of which the following extract, from p. 63 of "Antiquités Description," vol. ii., is worthy of being more generally known, viz., that after digging down deep through the rubbish, "they recognised perfectly the esplanade upon which the pyramid had been established, and discovered happily at the northeast 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 3 metres broad in one direction, 3.52 metres in another, and 0.207 of a metre deep.

They made the same researches 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. They found it 232.747 metres."

The "encastrement," so discovered in the basal rock at the north-east angle, is duly figured in plan amongst the large French plates, and has the inner corner curiously pared away, evidently indicating the outer corner as the true starting-point for measure; and from outer corner to outer corner of the north-east and the north-west "encastrements" it therefore was, that the skilful French surveyors extended their measuring lines.

Mr. Taylor has assisted the discussion of errors of the better class of earlier observers, by imagining their having been really measuring along some of the 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; and he seems to prove his case perfectly.

For the length of the real base of the Pyramid, therefore, no measure previous to the French one, can be depended on to within a good many feet, though the measurers themselves might have noted what was before them pretty accurately; and the French measures cannot now be repeated, without first incurring a large cost in re-excavating the sites of those important "encastrements" or fittings-in of the lower corners of the Pyramid.

Colonel Vyse, however, did go to this remarkable expense; and not only procured another measure of the very original Pyramid base itself from end to end; but, as already mentioned, found two of the casing-stones still forming, on the rocky platform, a firmly-cemented part of the old basal line of the Pyramid, and nearly mid-way between the two terminations.

The extreme and further value residing in these 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 Pyramid, viz., smooth polished marble in a sloping plane; but because they exhibited such matchless workmanship,—as correct and true it was as modern work by optical instrument-makers, but exhibited in this instance on stones of a height of near 5, a breadth of 8, and a length of 12 feet, with joints 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′ ′ ; 1 results extremely accordant with one another, as compared with the French determination (before there was anything on which to determine, 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 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 work they had to deal with; and in the linear measures which he gives in p. 261, vol. i., of his great work, (and the 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 figure, a cross section, and its accompanying numbers, stand as in Fig. 2.

The lengths, being 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.

FIG. 2.

By subtracting the upper, from the lower, surface, the Calculation of sides. 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. But the value of the angle A is then found to be so very different, according 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 it from the three sides, it appears to be 8 8°2 2′5 2 ·6′′. This, however, is such an egregious error for workmen like those of the Pyramid to have committed, and in their easiest angle, that we incline to think Mr. Perring must have made a mistake of an inch in his measure of the base 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 9 0° ; 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, we have not ventured to make so strong a correction upon one only.

On the whole, taking everything into practical consideration, we have obtained three probable combinations of the computed angle at A, with Mr. Brettell's observed angle there; as thus,

5 1° 5 1′ 1 5 · 5′ ′, 5 1° 5 1′ 5 · 4′ ′, and 5 1° 5 1′ 2 2 · 0′ ′, of which three quantities the mean is 5 1° 5 1′ 1 4 · 3′ ′.

Next employing this angle with the length of base = 763.81 to compute the height, we have for that = 486.2567; and from these new values of height and base, computing the proportion of diameter to circumference, there appears

$

4 8 6 \cdot 2 5 6 7: 7 6 3 \cdot 8 1 \times 2:: 1: 3 \cdot 1 4 1 5 9, \& c.,

$

which is far closer to the truth than anything which was found out by men mathematically for ages after the building of the Pyramid; and from anything which we had a right to expect, from the wideness of errors among the best modern observations made upon the stones themselves, whether addressed to their angles or their sides.

Modern theoretical science no doubt both can compute, and actually has computed, the proportion to a far greater degree of closeness, to 300 places of decimals for instance; but modern science is unfortunately very unequal. Some theoretical points are pursued to an excessive extent past all visible use, while the application of others to nature and art is left in a sadly crude condition; and with regard to realizing the proportion now spoken of in a building, the moderns have never reached anything at all equal to the accuracy of the Great Pyramid.

Perhaps it may be answered that the moderns have never tried so to do; and we may allow them that they have not; but they have attempted at the Pyramid, over and over again, to measure the performances of those who have; and it is an acknowledged practical truth in every existing astronomical Observatory, that it is far easier to measure the state, and approximate to the error of any mechanical arrangement, than to make that state mechanically perfect.

In their measurements, therefore, of the Pyramid, the moderns have had an advantage over the primeval builders of it; and how have they come off in the trial? Why, it has been shown that the exactness of the Pyramid has improved under every advance of exactness in the measures applied to it; and whether the differences of modern measures, in their first stage of coarseness, differed from each other by several degrees, or subsequently by several minutes, and latterly by a few seconds only, the Pyramid itself was ever found in the mean position amongst them; like the bull's-eye in the centre of a target, though the bullet-holes of bad shooters might be found more frequently at all points of its circumference; and whose marks, therefore, seen by themselves, would give subsequent visitors exceeding trouble in concluding precisely what the marksmen had been firing at.

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 Mr. Taylor's proposition or statement; and adds intrinsic weight to the notable corollary which he deduces from it.

CHAPTER III.

STANDARD OF LENGTH EMPLOYED IN THE GREAT PYRAMID.

In the process of computing the exact circumferential analogy on p. 24, we arrived at improved statements of the absolute linear height, and length of side of base of the Great Pyramid, and these quantities were expressed in English feet; but it does not therefore follow that they, or indeed any foot-measures, were employed by the ancient builders.

Certainly the length, complication, and inconvenience of the fractions obliged to be introduced, in order to represent the true proportions of the one Pyramid element to the other, in such terms, forbid the idea. No doubt, that a foot is something of a natural measure, and may have been extensively used in Egypt and through the East in many agricultural and other operations, which, if lowly, "are innocent and hurt not;" but still we think there is good reason for disputing, whether a "foot" was ever lifted up against that grandest building of antiquity, the Great Pyramid, by the authors thereof.

As a first step in such an inquiry, let us see whether an equally exact proportion between height and twicebase, to what our long fractions of feet gave, cannot be obtained from some simpler numbers. After many trials we have selected,

If then a foot-measure was not likely, what sort of measure was likely, to have been employed there?

5：366.0.

These are not exact, as no simple numbers can be, when the proportion itself belongs really to the incommensurables; but it is an astonishingly close approach for such plain and small numbers to make; and the exceedingly small fraction 1 by which the one should be increased, or the other decreased, does not, in the existing state of our knowledge, make any practical difference upon any of the questions which we shall have presently to take up.

Are there, however, any other reasons why we should adopt those particular numbers?

1 116.5014 : 366.0000, or 116.5000 : 365.9956, would be closer.

There are so.

In the first place, 366, which represents here the circumferential analogy of a circle (and what circle so notable to man as the circle of a year), is also the nearest even number of days in a year. We now know that the exact quantity is 36524221; but 366 is vastly closer than the 300, or 360, with which divers ancient priests were afterwards trying to make their theories suit the recurrence of the seasons.

It is also the number of days in one of our practical years—of leap-year; and further, it is the very number that we ourselves would adopt in any mechanical case, where the measure of the year was one, but not the first, and only, problem to be accomplished.

We are all the bolder in making this assertion, because the fact actually occurred, and in a perfectly independent manner, only last year in the University of Edinburgh. 1

In the second place it may be stated, that that portion of the Pyramid employed in the problem under discussion, when it comes to be divided into 366 parts, gives each of them a length equal to 1⁄10 millionth of the earth's axis of rotation!

This is a feature, in all sober truth, of the most extraordinary importance. It is only since Newton's time that men have attributed anything peculiar in its size to the earth's axis of rotation; and every modern civilized nation has, during the present century, been obliged to perform gigantic trigonometrical operations, and "degree measurings," in order to arrive at any exact knowledge of the true length. Their various results oscillate about 500,500,000 English inches, or, as Sir John Herschel 1 thinks, 500,495,000; but some of them, even the best modern ones, profiting by our long Indian arc for low, and the immense Russian arc for high, latitudes, are as great as 500,560,000, and others as small as 500,378,000. Such are the limits of uncertainty in which England, France, Germany, and Russia are placed at the present moment; and yet they are immensely closer in accord, and nearer to the truth, than they were only fifty years ago, and have performed their difficult parts right well for men.

We wish that as much skill and accuracy had been expended on the measures of the Great Pyramid.

There, our two best observations, already quoted—the French one and Colonel Howard-Vyse's—differ by 0.4 of a foot on a length of 764 feet only. 1

The French measure looks the more accurately attempted of the two, and gives for the 366th part in inches of the circumferential representative of the Great Pyramid (i.e., twice its base) multiplied into 10 millions, = 500,734,000; or if we defer to the 366th division having a remainder of incommensurability about it, and take 365.9956 instead, the quantity becomes = 500,740,500.

But the English measure by Howard-Vyse and Perring, similarly tested, yields 500,990,000. There are reasons, however, for considering their measure not only rude, as it evidently is from the small refinement that they go to in subdivisions, but erroneous also, in having too short a standard scale, and therefore putting too many inches into every measure they made.

In fact, if we compare their measures of the interior of the "Porphyry Coffer" (see further on, Part II.), which ought to have been their most accurate possible, with those of Professor John Greaves, we find as follows :—

<tr><th colspan="4">HOWARD-VYSE AND PERRING.

GREAVES.

Inches.

Inches.

Length,

78·0

77·856

Breadth,

26·5

26·616

Depth,

34·5

34·320

139·000

138·792

But inasmuch as Greaves' observations are said to labour under a similar fault (though by an early writer in the Philosophical Transactions, who may be just as much in error), and to require 0.002 in. to be subtracted from every inch, it would result from this that Howard-Vyse and Perring's measures should be multiplied by 0.99651, to make them give true British inches. This correction, duly applied, causes their Pyramid measure to give for the earth, only 499,242,000. This, however, appears in our eyes to be depending too much on the assertions of Greaves' correctors; 1 and we shall be safer if we take a mean between the entirely uncorrected, and the probably over-corrected, measure of Howard-Vyse and Perring, which gives 500,116,000.

We then have a quantity, which, when combined with the deduction from the French measure, gives so nearly the same result as the mean of all the modern measures of the earth's axis of rotation, that we can hardly but allow the two to have been equally intended for the same thing, viz., the Polar axis of the earth. Set side by side, in a manner to show the errors of observation in either case, we have,—

From Earth&#x27;s Measure.

From Pyramid&#x27;s Measure.

500,560,000

500,990,000

500,560,000

2500,740,500

500,495,000

500,740,500

500,495,000

500,740,500

1500,378,000

499,242,000

500,497,600

500,490,700;

the equatorial axis of the earth being at the same time somewhere between 502,000,000,and 503,000,000 English inches.

1 Only half the weight of the others is given to this last observation, agreeably with the opinion expressed of its merits by General de Schubert, Sir J. Herschel, and others.

2 The French measure is repeated three times, so as to have a share, in the proportion of three to two in the mean, with the English; having been previously pronounced the more carefully executed measure of the two.

Taking then the earth's polar axis to be really equal to 500,495,000 English inches, i.e., continuing to show more respect to Sir J. Herschel's conclusion than our own, and our Pyramid proportion to come practically to the same thing—then, each of the lengths, of which 366 were used in a remarkable manner in laying out the base of the Pyramid, are equal to 50·0495 English inches. That was in fact the standard measure of the Pyramid 4300 years ago, and was without doubt then divided into 50 inches evenly; for we learn from other sources that inches were used, that fractions were eliminated as much as possible, and that much importance was attached to the number 5; the Pyramid itself being a five-angled, and, with its basal plane, a five-sided solid, in which everything went by fives or numbers of five, and powers of five.

Let it be clearly understood, however, that there is a radical difference between a "standard measure," and a "unit of measure;" for a "standard" may be any number of the units, strung in a manner temporarily together to make a convenient whole-length, suitable for some particular subject of human employment or research. That whole-length of course is, or should be, exactly the same length, as if we took the prescribed number of the units separately, at the time; but then it is arrived at, in practice, by using the standard already constructed, much more quickly; and much more correctly too, for there is always a source of error in applying hastily one material separate measure to another.

Hence, when the Royal Astronomical Society of London, under the leadership of Mr. Baily, were preparing the new British standards for Government after the burning of the ancient ones in the fire of the Houses of Parliament, they adopted a greater length than before, viz. 5 feet in place of 3, for the standard; though the unit of length they intended to remain precisely what it was before, even to the 1⁄10,000 th of an inch.

Standards therefore may vary much, and they have varied in our country from 1 foot to 3 feet, 5 feet, 6 feet, and 10 feet, according to what was required of them at the time; but at the Pyramid, it would appear, not that the standards were varied from time to time, but that there were several in use for different purposes, all of them however bearing a fixed relation to the unit of linear measure, and being some convenient multiple thereof.

Thus the unit, an indefeasible and unalterable quantity, was, 1 inch = 1⁄500,000,000 th of earth's axis of rotation.

Fifty of these units strung together, made the "Grand standard" for all the most difficult and scientific questions, and was therefore = 1⁄10,000,000 th of the earth's axis of rotation.

But as that was an inconveniently large quantity or length of staff to be dealing with indoors, and on all ordinary occasions,the half of it,or 25 inches,seems to have been held as a "Small standard,"and then amounted to 1⁄20,000,000 th of the earth's axis of rotation.

Again, to suit the plodding purposes of mechanic men employed in tilling the soil, something smaller still, and suitable to what they trod on, was required; and then, twelve of the units were strung together, to make a standard foot. The unit inch was still preserved accurately; but the standard's scientific connexion in an even fraction with the earth's axis of rotation, or its numerical alliance with the arithmetical relations of the Pyramid, was gone.

Now, all these standards we have it in our power to restore at once; for the ancient Pyramid unit, the inch, being, as before stated = 1⁄500,000,000 th of the earth's axis of rotation, and that length being, within the limits of errors of the best modern observation, = 500,495,000 English inches,—plainly We have thus arrived by an independent inquiry of our own, at a result which Mr. Taylor obtains by a different and somewhat less direct process; and what a result it is, in whatever point of view we look upon it, or by whatever road we have attained to it!

The nations of the world 3000 years ago, of their own selves and by their own knowledge, cared little about their national measures, and knew nothing, but what was childish with regard to the size of the earth; so that all our present exact acquaintance with it, is confined within the history of the last hundred years. The great attempt of the French people to abolish alike the Christian religion, and the hereditary weights and measures of all nations; and to replace the former by a worship of philosophy, and the latter by a scheme depending on one feature in the magnitude of the earth, as well as to substitute the week of seven days, by an artificial period of ten days,—is only seventy years old. And how did they, the French philosophers, endeavour to carry out the metrological part of their scheme? By assuming as their unit of length, the 1⁄10,000,000 th of a "quadrant of the earth's surface!"

Well may we ask if that was all that science, trusting in itself, was able to do for them. For the grasp and understanding of the subject, that took a portion of the earth's surface, in place of the axis of rotation, was truly inferior in the extreme.

As Sir John Herschel has well said, but only after Mr. Taylor's statement about the Pyramid had lighted up his mind with the exquisite thought, of how near after all the British hereditary inch is to an integral earth-measure, and the best earth-measure that he had ever heard of,—so long as the human mind continues to be human, and retain a power of geometry, so long will the diameter, be thought of more primary importance than the circumference, of a circle; and when we come to a sphere, and in motion, the axis of its dynamical labour should hold a vastly superior importance still.

Again, the French philosophers of seventy years ago, in fixing on a quadrant of surface, had no idea that within the last three years the progress of geodesy would have shown that the earth's equator is not a circle, but a rather irregular curvilinear triangle, so that it has many different equatorial axes, and therefore also different lengths of quadrants in different longitudes. They, the savants of Paris, could not indeed foresee these things of the present day, or a state of geodesic science beyond them; and yet these things were all taken into account by the Mind that directed the building of the Great Pyramid 4300 years ago; and the reference for the unit then adopted, is now shown to be the only really scientific one which the earth possesses.

Through those long mediæval periods, too, of darkness and confusion and war, when our nation thought of no such things, the same Master-mind likewise prevented our hereditary unit of measure, the inch, from losing more than the thousandth-part of itself by the friction of ages; for this is the result, if it turns out, as Mr. Taylor believes—and as he was the first of men in these latter days both to believe and to publish his belief—that the Great Pyramid is the one necessarily-material centre from which those material things, weights and measures, in a primeval age, somewhere between the time of Noah and Abraham, take whatever chronology you will, were Divinely distributed to every leading people and tongue.

CHAPTER IV.

FIGURE OF THE EARTH.

The results just arrived at, from our connexion of the double base of the Pyramid with the earth's axis of rotation, are, as already intimated, very similar to those which Mr. Taylor obtained by pursuing his own mode of inquiry.

But it will be worth while to bestow some special attention on two of the analogies which he discovered; and which, on being examined soon after by Sir John Herschel, were declared by him to be, so far as he knew, the only relations between the size of the earth and the size of the Pyramid which had up to then been made out; though at the same time he expressed his belief that they were only approximate.

Let us, however, test them over again, and by the analogy which we ourselves have obtained; for inasmuch as that allows us to speak of the Pyramid in the primal measures employed by its builders, we may thereby be enabled to put their work to a stricter test.

We will accept, then, as before, the old or primal unit of measure, viz. an inch, each one being the 1⁄500,000,000 th of the earth's axis of rotation; and the "grand standard," a primal metron of fifty such inches; of which metrons, 116.5 measure the height, and 183 the side of the base, of the Pyramid; and as this, the base, is at the foot of the Pyramid, we will give it in feet also, of twelve such primal inches to the foot.

FIG. 4.

$

\mathrm {A C} = 1 1 6 \cdot 5 \mathrm {p r i m a l m e t r o n s}, =

$

$

5 8 2 5 \cdot 0 \mathrm {p r i m a l o r P y r a m i d i n c h e s}.

$

$

\begin{array}{l} \mathrm {A n d B D} = 1 8 3 \cdot 0 \mathrm {p r i m a l m e t r o n s}, = \\ 9 1 5 0 \cdot 0 \mathrm {p r i m a l o r P y r a m i d i n c h e s}, = \\ \end{array}

$

$

7 6 2 \cdot 5 \mathrm {p r i m a l o r P y r a m i d f e e t}.

$ The first of Mr. Taylor's two size-analogies is, when put into the form subsequently chosen by Sir John Herschel, "a band encircling the earth, of the breadth of the base of the Great Pyramid, contains one hundred thousand million square feet."

Adapting this statement to our primal feet, and to a form suitable to bring out the diameter rather than the circumference, and in inches, we have for such a diameter :—

1 0 0, 0 0 0, 0 0 0, 0 0 0⁄\frac{7 6 2 · 5{1 2} ×3 · 1 4 1 5 9 , etc. primal or Pyramid inches.

Noting only that this is a very different quantity from the rotation axis in primal inches, we proceed to Mr. Taylor's second analogy; or, that "the height of the Pyramid is, 1⁄2 7 0, 0 0 0 th of the earth's circumference."

Before submitting this statement to computation, we felt inclined to inquire, why 270,000 : for it is not a very round number, and has no apparent connexion, by fives or in any other way, with the Pyramid ?

Finding, however, that the area of the base of the Pyramid in hundredths of feet has, when thrown into a circular shape, a circumference equal to 270,299, we presumed that that might be accepted as a reason; and then, trying the case in a form to bring out the axis in inches, obtained—

$

\text {H e i g h t o f p y r a m i d i n i n c h e s}, \times \frac {2 7 0 , 2 9 9}{3 \cdot 1 4 1 5 9} = x, \text {o r}

$

$

5 8 2 5 \cdot 0 \times 8 6 0 3 8 \cdot 9 0 1 = 5 0 1, 1 7 6, 4 0 0 \mathrm {p r i m a l i n c h e s}.

$

Here is a quantity, then, very different again from the last and from the Polar. But if any special result be given by the height of the Pyramid itself, what is so likely to have been intended as the terrestrial diameter in its (the Pyramid's) own latitude, or 29°59′6′ ′ N.; and, in the former case, when a band enveloping the earth is given, what so likely to be typified there, as the latitude of 45°? To test this idea, we have computed according to the usual formula, with a compression of 1⁄300, the favourite quantity in the present day, the diameter of the earth in different parallels assuming its Polar diameter = 500,000,000; and placed the three Pyramid analogies by the side of them, thus—

Computed Earth Diameters. Pyramid Analogies.

Polar = 500,000,000 Polar = 500,000,000

Lat. 6 0°=5 0 0,4 2 0,0 0 0 Lat. 6 0°=

Lat. 4 5°=5 0 0,8 4 0,0 0 0 Lat. 4 5°=5 0 0,9 4 6,7 0 0

Lat. 3 0°=5 0 1,2 5 7,0 0 0 Lat. 3 0°=5 0 1,1 7 6,4 0 0

Equator = 501,672,000 Equator =

From the close approach to agreement here manifested, there can hardly be any doubt but that the differences between the several parts of the Pyramid were intended: and we then have a spectacle never seen in the world before, or since, of a standard measure which indicates the shape, as well as the size, of the earth; or which, if it has had chosen for it one particular axis to form the unit upon, and the best axis or diameter for that purpose, though the least of all, does not leave us under any false ideas as to the true size of the entire world on which we live.

While, however, the great majority of what seemed at first to be most anomalous excesses at the supposed 45° and 30° of Mr. Taylor's two size-analogies, is undoubtedly capable of being cleared away by reference to a compression of 1⁄300, there is a small residual quantity on each which cannot be so removed, for it is in excess at one, and defect at the other. We have got then herein to the full extent, as far as the mere mathematical idea of a regular ellipsoidal figure of a certain amount of compression for the earth will help us; 9⁄10 ths of the whole anomaly are explained, but 1⁄10 th remains; and that is too small a quantity for the geodesists themselves to be certain of in their measures.

…