Papers on the Great Pyramid (1870)
Download: PDF — Papers on the Great Pyramid (1870)
This is a digital copy of a book that was preserved for generations on library shelves before it was carefully scanned by Google as part of a project to make the world's books discoverable online.
It has survived long enough for the copyright to expire and the book to enter the public domain. A public domain book is one that was never subject to copyright or whose legal copyright term has expired. Whether a book is in the public domain may vary country to country. Public domain books are our gateways to the past, representing a wealth of history, culture and knowledge that's often difficult to discover.
Marks, notations and other marginalia present in the original volume will appear in this file - a reminder of this book's long journey from the publisher to a library and finally to you.
Usage guidelines
Google is proud to partner with libraries to digitize public domain materials and make them widely accessible. Public domain books belong to the public and we are merely their custodians. Nevertheless, this work is expensive, so in order to keep providing this resource, we have taken steps to prevent abuse by commercial parties, including placing technical restrictions on automated querying.
We also ask that you:
Make non-commercial use of the files We designed Google Book Search for use by individuals, and we request that you use these files for personal, non-commercial purposes.
Refrain from automated querying Do not send automated queries of any sort to Google's system: If you are conducting research on machine translation, optical character recognition or other areas where access to a large amount of text is helpful, please contact us. We encourage the use of public domain materials for these purposes and may be able to help.
Maintain attribution The Google "watermark" you see on each file is essential for informing people about this project and helping them find additional materials through Google Book Search. Please do not remove it.
Keep it legal Whatever your use, remember that you are responsible for ensuring that what you are doing is legal. Do not assume that just because we believe a book is in the public domain for users in the United States, that the work is also in the public domain for users in other countries. Whether a book is still in copyright varies from country to country, and we can't offer guidance on whether any specific use of any specific book is allowed. Please do not assume that a book's appearance in Google Book Search means it can be used in any manner anywhere in the world. Copyright infringement liability can be quite severe.
Google's mission is to organize the world's information and to make it universally accessible and useful. Google Book Search helps readers discover the world's books while helping authors and publishers reach new audiences. You can search through the full text of this book on the web at http://books.google.com/ PAPERS
ON
THE GREAT PYRAMID.
ST. JOHN V. DAY.
302049875
302049875
Mr. Griffith .
PAPERS
D. π 6
ON
THE GREAT PYRAMID;
INCLUDING
A CRITICAL EXAMINATION
OF
SIR HENRY JAMES'
BY
"NOTES ON THE GREAT PYRAMID OF EGYPT."
ST. JOHN VINCENT DAY, C.E., F.R.S.E.,
FELLOW OF THE ROYAL SCOTTISH SOCIETY OF ARTS, MEMBER OF THE INSTITUTION OF MECHANICAL ENGINEERS, MEMBER OF THE INSTITUTION OF ENGINEERS IN SCOTLAND,
HON. LIBRARIAN PHILOSOPHICAL SOCIETY OF GLASGOW.
ETC.
EDINBURGH: EDMONSTON AND DOUGLAS. 1870.
GLASGOW: PRINTED BY J. AND D. RENFREW,
EDMONSTON AND DOUGLAS.
LONDON, . . . . . . . . HAMILTON, ADAMS, AND CO.
CAMBRIDGE, . . . . . MACMILLAN AND CO.
GLASGOW, . . . . . . JAMES MACLEHOSE.
ASHMOLEAN MUSEUM
EX LIBRIS
F. LL. GRIFFITH
ET
N.C.C. GRIFFITH
OXFORD TO
C. PIAZZI SMYTH, F.R.S.S.L. & E.,
Astronomer Royal for Scotland, Professor of Practical Astronomy in the University of Edinburgh,
THAN WHOM THERE IS NO MORE SINCERE INQUIRER AFTER PRIMEVAL TRUTH IN ITS MOST COMPREHENSIVE AND ENLIGHTENED SENSE,
These Papers are Inscribed,
NOT ONLY AS AN INDEX OF PERSONAL FRIENDSHIP, BUT ALSO AS AN ACKNOWLEDGMENT OF
THE EMINENT SERVICES HE HAS RENDERED IN PROSECUTING INVESTIGATIONS OF SUCH VAST IMPORTANCE
TO MANKIND.
PREFACE.
The following pages have been written during some of those short intervals of leisure which I have been able, though actively employed in professional pursuits, to dedicate to the investigation of a subject that in richness as a field for research and for elevated character is not surpassed; a subject by the greater portion of the literary and scientific world looked upon with disfavour, yea, even with suspicion—such being an almost necessary result in many cases by reason of the labour of investigation requisite to its right and complete understanding; nevertheless, one needing but to be more carefully dealt with by those who turn attention to it, in order to be rightly appreciated.
A former published Work on the subject, besides one or two Papers in the Transactions of a Scientific Society, have of necessity brought me into contact with every shade of opinion, as to the various theories respecting the Pyramid and the facts belonging to it, which from time to time, from age to age rather, have been propounded and brought to light. I have thus been enabled, both by verbal and written discussions and arguments, to ascertain the weight of evidence on which theories, assertions, contradictions, and alleged facts, have been supported; and I can only state that in those cases where the Pyramid subject has been examined into with a diligent spirit of inquiry, that is with the aim of not merely strengthening preconceived notions or prejudices, but to evolve absolute realites, I have not yet met anyone but who is more or less convinced by the modern theory originated by John Taylor, and based by him upon the admeasurements of Howard Vyse and Perring.
On the other hand I have met many, such as are always to be found, no matter what the subject is, who declare against it; but who on being questioned, do by the very peculiarity of their opposition, show to what extent they have given themselves the pains to comprehend it to the full.
To myself, the chief matter of regret which I entertain is, that some one more able had not taken charge of the duty, which, however poorly, it has been my endeavour to fulfil, in exposing the gross misrepresentations pointed out in the following pages as existing in a recently published official document.
The style of writing—that of exact criticism became imperative for reasons which will shed their own light on the reader as the investigation is passed through; this I can but regret, yet the circumstances were none of my own controlling.
of the greater part of it were submitted to Sir Henry James before the edition was thrown off; as I considered it only fair to afford him the opportunity of correcting any of his errors either in arithmetic, fact, or history, beforehand.
The two other Papers were written about two years ago, but they have not been previously published.
The first Paper would not have been written, but for Sir Henry James himself having opened and continued a correspondence on the Pyramid with me up to the time when the Mount Sinai and Great Pyramid Survey Expedition was organized and started from this country, a correspondence wherein he laid the foundation of what was afterwards to appear in his published "Notes;" so that I felt, and was advised by others, that the onus of exposing his misconceptions and perversions rested in my hands. If any other reason for what I have written is asked of me I have none to give, other than the promptings of duty to expose fallacies so authoritatively flung into the midst of mankind. The truth is as I have told it.
If the Papers have numerous and great short-comings I could not avoid them, but still venture to hope they contain a few things worthy of notice; and in conclusion can only say, as others have already said, with the unassuming writer of the Book of Maccabees, "If I have done well and fitting the story, it is that which I desired; but if slenderly and meanly, it is that which I could attain unto."
GLASGOW, September, 1870.
ON SIR HENRY JAMES' CONTRIBUTIONS TO THE LITERATURE OF
THE GREAT PYRAMID.
I. —On November 9th, 1867, Colonel Sir Henry James, R.E., in writing to the Athenæum, under a heading, "The Great Pyramid of Egypt,"* asserted that "the length of one of the sides of the base of the Great Pyramid is precisely 360 derahs or cubits of Egypt. This can scarcely be regarded as a mere accidental numerical agreement. The derah is a land measure still in use, and is stated by Woolhouse, in his 'Weights and Measures of all Nations,' to be 25·488 inches in length; but 25·488 inches × 360 = 764 feet, which is the exact length of one side of the base of the Pyramid, 'with the casing stones,' as measured by Colonel Howard Vyse."
The degree of exactitude professed by the investigator is marked by the two sets of words which the writer has italicised in the preceding quotation. Surely, then, it will generally be admitted that the least feature to look for in any endeavour at expounding the proportions and dimensions of such a structure, over the nature and objects of which men through all ages have so severely contended, is, that the arithmetic involved had been keenly eyed, and its results faithfully stated; for, after all, precision of language, that is to say, of mere words, in no case, more especially in such an instance, is of any importance, where accuracy of numerical statement as to the results is either wilfully or unconsciously set aside.
It is barely necessary to mention here, that above every feature in the whole structure, our closeness of approach to a perfect knowledge of the true proportions of the Great Pyramid depends on a precision of linear measures, which (in so important and universally recognised a ratio* as that which it is believed was with exactitude expressed in the dimensions of the original perfect building) is seriously affected with every few inches by which these measures may be given in error; yet all the while, the Director-General of the Ordnance Survey has not scrupled to treat as unimportant not merely an inch, or even two or three whole inches, but really 0.64 of a foot = 7.68 British inches, for he puts it thus—
$
2 5 ^ {\mathrm {I n c h e s}} \times 3 6 0 = 7 6 4
$
whereas this result is by 0.64 of a foot too small, that is to say—
$
2 5 ^ {\mathrm {I n c h e s}} \times 3 6 0 = 7 6 4 ^ {\mathrm {F e e t}}
$ Lest it should be thought by any who perchance may read this page, and who have not studied the geometry of the structure on which it touches, that the writer is bent on hypercritical error-finding, and that, too, over quantities which may seem to them, in comparison with the huge dimensions of the building, as utterly trivial, he would only here add, in self-defence, that the arithmetical error alluded to at this place (the very outset, indeed) well nigh vanishes when it is brought face to face with misstatements of whole facts, make-believe results, which the factors employed cannot produce.
The writer has above remarked that, by every few inches with which the true length of the dimension under consideration is given to us in error, the resulting ratio of height to base is seriously affected; and as he is desirous here to propose nothing but what can be completely proved, he accordingly, to set this assertion at rest, deems it the better course to resort at once to a trial; and that, too, with the same figures which Sir Henry James has chosen, viz., those of Colonel Howard Vyse, but which are well ascertained as being circumscribed with serious departures from precision. Nevertheless, taken as they are, they are sufficient to bear out the truth of what is above stated.
Colonel Vyse gives the Pyramid height as \equiv 4 8 6 British feet, and the base = 7 6 4 British feet. Now, using these figures on the π theory (which Sir Henry James admits, and thus, although from an opposing standpoint, has happily done his part in testifying to one great fact enshrined in the primeval Pyramid), we find
$
\frac {7 6 4 \times 2}{4 8 6} = 3 ^ {\cdot} 1 4 4 0;
$
or, as compared with the usual arithmetical approximation of π —
$
3 ^ {\cdot} 1 4 4 0 - 3 ^ {\cdot} 1 4 1 5 9 = + 0 ^ {\cdot} 0 0 2 4 0 \mathrm {i n e r r o r}.
$
Yet, if we add half a British foot only to this 764 (and which is much less than the error by which the base length is misrepresented in the Athenæum), we get a resulting ratio in which the error is very nearly doubled, or as the figures themselves show—
$
\frac {7 6 4 + 0 . 5 \times 2}{4 8 6} = 3. 1 4 6 0
$
and
$
3 ^ {\cdot} 1 4 6 0 - 3 ^ {\cdot} 1 4 1 5 9 = + 0 ^ {\cdot} 0 0 4 4 1.
$
How much more serious, then, is the indifferent treatment of 7.68 whole inches? which considerably more than doubles the error from the true or closest practically used approach to the value of π . Inevitably, then, the writer cannot avoid the counter-assertion that the figures which Sir Henry James has used prove that the length of one side of the base of the Great Pyramid is not precisely 360 derahs, or units of 25.488 inches.
The derah is stated by the Ordnance Survey Director-General to be "a land measure still in use."
Accordingly, if this same measure is that by which the Pyramid's base length was set out, it must have been devised 4000 years ago; and if it be the case that in Egypt the standard unit of linear measure has been preserved through such ages in a land which has encountered such vicissitudes, and yet has not varied by even the smallest fraction, even so that it will fit into the Pyramid's base to-day with the same exactitude as it is now professed to have fitted in the day of its founder, how greatly must we not marvel at the comparatively enormous errors which have crept into our own and all modern metrical units; so much so, that, from various causes, their true length cannot be exactly stated, and we are compelled to show our shortcomings of the appreciation of a true standard by an inevitable + or - quantity, in face of the existence of this immutable derah, which, if what is now asserted for it by the officer at present in charge of the Ordnance Survey in Great Britain be fact, must have been the forerunner of the imperious principle which has been recognised as embodied only in the imaginations of the Median and Persian legislators.
Such an unalterable, and so primeval a possession of mankind—older even than Abraham himself—does Sir Henry James declare this derah to be, that surely it must possess an unparalleled interest to the living nations of to-day. Hence, then, the writer has felt it his duty to consider the weight of evidence upon which the assertion rests.
Colonel Sir Henry James quotes the length of the derah from Mr. Woolhouse, the writer of a small volume on the "Weights and Measures of all Nations" in Weale's Rudimentary Series: a series, by the way, to which in our school-days many of us have been indebted, but it will scarcely be believed that any high professional man versed in the methods of science and seeking for standard information would consign himself thereto, and thereon rest his researches.
Immediately after the appearance of the letter in the Athenæum—a journal wherein it was certain to engage the attention of some observant minds—the weight of probability upon which the asserted length of the derah rested was ably investigated by Mr. Petrie,* and that alongside of a standard unit which the modern investigators of the Great Pyramid have developed as being recorded in the length of its base side, namely 25.025 British inches; but with this latter we will not deal at present further than by stating that Mr. Petrie's research points out the weight which should be assigned to either of the numbers.
As chief among other reasons for assigning a foremost place to the derah, and for so directly connecting it to the Pyramid, is the assertion because it exactly divides that building's base-side line into 360 equal parts; hence, then, either 360 of these derahs happened to be fixed upon accidentally by the builder, or, to take the alternative proposition, it was so specially recognised a number, and being of so much importance, was therefore pre-eminently chosen before any other number.
If we, then, enquire as to the special references or uses of 360, we find one only, namely, the division of the circle; and this division is on trustworthy ground believed to have been the work of Babylonian astronomers (if, peradventure, we may distinguish them by so exalted an appellation), as in the very choice their ignorance of fact is emblazoned, for they are believed to have so divided the circle because they thought there were 360 days in the year: and although it has also been proposed by some that whilst these Babylonians really knew the exact uneven number of days in the year, 360 was chosen because of its being a whole and divisible number, and therefore more convenient than the larger and fractional quantity; yet the writer ventures to throw discredit on this latter aspect, for it seems to him that if the Babylonians were really accurate in their knowledge of the true quantity representing the earth's revolutions in traversing her complete orbit, or of methods by which the real quantity is obtained, it is scarcely conceivable but that they should also foresee the tendency to introduce further errors and perpetuate blunders; in fact, create interminable difficulties by the institution of a concrete quantity purporting to have such sublime significance.
Assuming even, that this same number was represented by the division of derahs into the Pyramid's base, it is clear that such a division could have nothing to do with the Babylonian quantity, for the Pyramid preceded the independence and activity of Babylon by about 1500 years.
Hence, then, we are forced to the conviction that, if the alleged derah value is the 360th part of the original Pyramid's base-side, it is merely accidental, and not resulting from any prime importance being at the time of the building attached to that quantity. The derah is said by Sir H. James to be a "land measure," and, therefore, some one may urge that it was consequently of immense importance, and so was, of course, with set purpose embodied. Whilst the writer admits the force of this suggestion, yet he is also bound to point out that, if the perpetuation of the derah was the object, still the choice of 360 of these must have been an affair of secondary or rather dependent importance, and a mere result from some other influence primarily governed by altitude or angle. Almost needless, from the writer's point of view, is it to have been at the pains he has used to point out the flimsy basis of the proposed base-length and derah connexion without looking into the more important question as to whether either of these have been truly stated, at least as closely as a value can be assigned to them from the data possessed of both;* therefore, it has now to be inquired, 1st, What was the original length of the finished Pyramid's base side? and, 2nd, Is the derah an even division of it?
The only admissible approximations we possess of the Pyramid's true and ancient base-side length, as defined by the all-important sockets, are those given by Howard Vyse, the measures of the French savans (repeated apparently by Mahmoud Bey), those of Mr. Inglis (taken for his employer, Mr. Aiton, and in conjunction with Professor Piazzi Smyth, by whom, with the consent of Mr. Aiton, they were first published to the world in "Life and Work at the Great Pyramid"), and, lastly, that of the Royal Engineering party, in their recent return from the Sinai Survey; the quantities assigned by each of whom stand thus, including a deduction from the first three by Piazzi Smyth:—
British Inches.
British Feet.
Vyse, for One side, viz., the Northern,...
=764.0
French Savans, for the same side,...
9163.44
=763.6
Aiton and Inglis's mean of Four sides,...
=759.2
Piazzi Smyth's concluded mean,...
=761.8
Royal Engineers' mean of Four sides,...
=760.8
The same, corrected by Sir Henry James,...
=760.0
How, then, with any of these six quantities, or the mean of the six-or, with what is most probably the closest approximation to the truth, namely, the mean of the two first—does the derah value of 25.488 inches stand? Precisely thus does it stand, viz., that it is not an even 360th division of any of them; for 360 times the derah = 9175· 68 inches, or more than any one of the whole side's contents! What more, then, need be said of the suggested derah and base relationship, but that it is untrue in fact.* The writer cannot do better, in concluding this section of his commentary, than quote Mr. Petrie's words :—
"The best that can be said of the connexion of such existing Egyptian measures with the base of the Great Pyramid is, that if the existing Egyptian gasab (for this will suit the case better than its fourth part, the derah) be descended from far beyond historic antiquity, or even probably so, and its ancient length were (101· 839)=· 113 of an inch, or about 1-1000th part shorter than our present (Sir Henry James') information assigns as its existing length, it would then become probable that this measure was derived from the Pyramid's base."
But is there any such measure, i.e., in assigned length? for the name of derah is merely Egyptian Arabic for cubit, and is equally used for cubits of various lengths, and of known foreign introduction, within recent times.
II. After Mr. Woolhouse's derah value of 25.488 inches had been questioned, as before alluded to (vide page 8), Sir Henry James himself suddenly lost faith—or acted as though he had—in his own positive assertions and claims for that derah which has now been discussed; it behoves us, therefore, to look into his further dealings with the questions at issue.
Sir Henry James has not endeavoured to confirm his original assertions by seeking out further proof of the derah value which he had previously employed, nor has he sought to eliminate his own errors in stating the base measure; but, finding the hollowness of his assertions woefully exposed, he quietly throws them overboard, abolishes the 25.488 inch derah entirely, and in a letter to the Athenæum, dated August 1, 1868, says:—
"The accuracy of Woolhouse's length of the Egyptian cubit has since been questioned, and this has led me to a further investigation of the dimensions of this (the Great) Pyramid—or, I should rather say, of the units of measure employed in its design or execution;* for we may consider 763.6 feet as the true length, from corner to corner, of the sockets which were cut into the rock at the four corners of the Pyramid, to receive the corner stones. These sockets are 8 inches deep, and the Pyramid was surrounded with a pavement 1 foot 8 inches in depth, by which the length of the sides would be diminished 2 feet 11 inches at each end, and the side of the visible finished Pyramid would be reduced from 763.6 to 757.5 feet; and as no one ever designed or spoke of the dimensions of any building but with reference to the work which was visible and finished, we may consider 757.5 as the true length of the side of the base.
"Now, Herodotus tells us, Euterpe, 168, that the arura or Egyptian acre 'contains a square of 100 Egyptian cubits,' and I infer that the side of the base was made 500 of these cubits, and that the area of the base was therefore exactly 25 aruræ. This would make the Egyptian cubit equal to 1.515 English feet, 5 0 0 ×1. 5 1 5=7 5 7. 5 feet,the length as measured. But 1.515 feet, equal 18.18 inches, is the length of the Egyptian cubit given in the great work of the French savans, 'Description de l'Egypte,' and described by them as the 'coudée des Grecs d'Hérodote, juste, mediocre, commune des Arabes = 0.4618 metre.'
The Egyptian cubit, according to Herodotus, being equal to that of Samos.
"The height of the Pyramid above the plane of the pavement was 481 feet. The chambers and passages of the interior were set out with the cubit of 20.699 inches, i.e., of the same length as that of Karnak, which is preserved in the British Museum. The arrangement of the passages was obviously made to facilitate the transport of weights, including the King's body in its case, from the entrance to the centre. The inclination of the ascending passages being made equal to that of the descending, a weight on a truck at the bottom would counterbalance, by means of a rope and a pulley, a load descending from the entrance to the point where the passages meet, and be itself drawn up towards the same point, and it would counterbalance the same load when it is being drawn up the ascending passage to the centre, whilst in the same time it descended to its original position. A very slight amount of mechanical skill would be required to re-establish such a mechanical arrangement for visitors to the interior of the Pyramid."
(Signed) HENRY JAMES, Col. R.E.
A reprint of the letter from which the preceding quotation is made was enclosed to the writer in a letter from the author himself, who thereby spontaneously opened up a correspondence on the subject, the first letter being dated August 17, 1868. In this letter the author, in a circuitous way, asked the writer's judgment of the part he had taken in Pyramid investigations. Knowing, as Sir Henry James must, from having read a paper on the subject in the Proceedings of the Glasgow Philosophical Society, that the writer held views directly opposed to his own, he must surely have been sensible that the writer could not homologate such wholesale confusion, such an attempt to promulgate fiction for truth, such stratagem to subvert realities, as that which he had employed.
Accordingly, the writer could not do otherwise than reply to the letter, by exhibiting his extraordinary errors, a task most unsought for, and most distasteful to his own feelings; yet, before proceeding to commit to writing a statement of the extraordinary errors, in deference to his own feeling of dislike to wage a scientific warfare with anyone, more especially one who had volunteered to address him from so elevated an office in the scientific departments of Her Majesty's service, he deemed it proper, first, to reply to the letter by asking if Sir Henry James really wished him to express in writing his views as to the part he (Sir Henry James) had played in reference to the Pyramid, stating that, if he did not hear to the contrary within a certain time, he would write down and transmit the conclusions drawn. To this letter no reply was received within the time named; accordingly, Sir Henry James was written to as desired. In order, then, to make it clear that the errors were straightforwardly pointed out to the Director-General of the Ordnance Survey shortly after he laid his assertions before the writer, he deems it right now to print a portion of the letter which was written on the occasion, for, by so doing, the present purpose in exposing the style of the investigation will be partly met:—
Extract of Letter to the Director-General of the Ordnance Survey, dated 25th August, 1868.
"In your letter to me, dated the 17th inst., you state that 'In the geometrical figure of the Great Pyramid we should be sure to have preserved a record of the units of measure employed in its design, and you, as an engineer, will be able to judge whether I have been able to correctly determine them,' thus tacitly referring me to the papers published over your name in the Athenaeum for November 16, 1867, and August 8, 1868, respectively.
In my reply to your letter under reference, I stated that 'it appeared from the mode in which you expressed yourself, that you desire to have my opinion on the part which you have taken in the recent discussions concerning the testimony of the Pyramid, and that if I did not hear from you to the contrary within a few days, I would do myself the favour of writing down and transmitting to you the views which I had formed thereon;' and as I have since then received no further communication from you, I proceed to consider the matter. At the same time, I beg to remark that, if the necessity of the case should cause me to be a little severe in what I have to say, I sincerely beg your indulgence.
"In your letter to the Athenaeum of August 8th, you allude to your previous letter to that journal, in which you had propounded a theory as to the proportions under which you believed the Pyramid had been erected, also mentioning what you believed to have been the unit of measure employed by the builders; but as the accuracy of the unit of measure then proposed has since been questioned, it has naturally enough seemed to you desirable to re-investigate your previous grounds for concluding as you did, and you now find it necessary to abandon in toto what you had previously arrived at, for the sake of adhering to what you are pleased to consider a more recent and convincing discovery, and which, from having published the ideas leading up to it in a Metropolitan weekly journal, we are bound to conclude that you consider as unequivocal and ultimate.
"Pray allow me to follow you throughout this last investigation. You formerly took 764 feet for the base length, and now assert this as erroneous, by declaring the base length to be absolutely 757.5 feet, whilst the fact is, that on the only first-rate occasion of the base side being well measured—namely, in 1799, by the French savans—they determined the length of the base at the north side of the structure to be 763.6 feet; and you explain that we must nevertheless take your now alleged 757.5 to be the true length, because you affirm that the base was surrounded with a pavement 1 foot 8 inches thick, and that, therefore, the French measured length must be diminished to the distance between two points at the corners of the original stone casing, at a height of 1 foot 8 inches above what has always by every authority been considered as the bottom of the original finished Pyramid.
This deduction of 1 foot 8 inches from the Pyramid's height will have the effect, you say, of diminishing the base length by 2 feet 11 inches at each end—but do you really mean to assert this seriously, or suppose that anyone will accept it without testing the accuracy of your arithmetic? And on testing it, what do we find—nothing short of an error, so large and so obvious, that it is beyond conception how you could have overlooked it; but here it is, and I trust my pointing it out now will enable you to correct it ere it be too late to attempt to do so. Taking θ (angle at base of the Pyramid) = 51°51' as the best ascertained value, and P=1 foot 8 inches (thickness of your alleged pavement), then B (the horizontal distance from a point on the side of the Pyramid 1 foot 8 inches above the present base to a perpendicular raised from the line where the base and pavement really meet) is not 2 feet 11 inches, but 1 foot 3.7 inches, which, being doubled and subtracted from the length given by the French Savans, would make your alleged base line not 757.5 feet but 761 feet.
"Your assertion that the Pyramid was surrounded with a pavement of such a height above the absolute base, is a piece of information of which no one had previously heard, for Col. Howard Vyse explains that the pavement was certainly under the sloping sides,* except at the four corners, where sockets were cut to receive the four lowermost corner stones—and to Col. Vyse we certainly may trust completely, whilst he is the only modern authority who had the opportunity of seeing the two casing stones remaining in his day and the pavement, so it is perfectly clear that the base length, as measured by the French, needs no correction for any upraised pavement which never existed.
"You then assume that the base length contained 500 of a certain alleged cubit, equal to 1.515 English feet, or 18.18 inches long. Now, it is confirmed by all reliable authorities, including Sir Gardner Wilkiuson and Wm. Osburn, that the cubit in ordinary use never varied in the early ages from 20.7 English inches very nearly; and, in reply to a recent enquiry, Professor Smyth informs me 'that the assumption of 18.18 inches as the length of the Egyptian cubit in the days of the Pyramid depends on no more than this, that the Greek cubit was of that length nearly, and when the Greeks overran Egypt, 1500 years after the Pyramid had been built, they brought that cubit with them,' so that you have now to show how the builders of the Great Pyramid came to know of the Greek cubit 1500 years before it was imported into their country.
"You then go on to say that the height of the Pyramid above the pavement was 481 feet. Now the best deduced height from all the measurements show it to have been (when the Pyramid was entire) 486.2 feet, so that, if we even substitute this 1 foot 8 inches of pavement which you declare for, we do not get 481 feet, but 484.45 feet.
"Hence the whole conclusion that one can arrive at, I regret deeply to say so, is, that your deductions are of no value whatever and entirely erroneous, because they begin upon false assumptions, and from first to last are full of the gravest errors in simple arithmetic.
"The latter remarks in your letter, published August 8th, are as amusing as they are impossible. I allude to the employment of ropes and pulleys in the passages. It would have been prudent to reconsider all the facts of the structure before propounding such an assumption; besides, I may most reasonably ask for your authorities as to the knowledge of the rope and pulley in the day of the Pyramid's building."
Hence then, under the single plea of Mr. Woolhouse's linear value of the derah being questioned, Sir Henry James reforms one and every part of his previously very confidently asserted dimensions, and insists, 1st, the base to be no longer 764 feet, but 757.5 feet; 2nd, that the important number to determine the size of the greatest builted monument is not 360, as he formerly declared for, but 500; and 3rdly, that the ancient Egyptian cubit was not 25.488, but so small a thing as 18.18 inches, and he finally exults that 1 8 · 1 8 × 5 0 0 = 7 5 7 · 5 feet, "the length as measured."
All this is asserted so strongly, and by the Director General superintending the Ordnance Survey, that the public may be ready to accept it at once; but inasmuch as the assertions in all their particulars for totally different quantities, were just as strong on the former occasion above noticed, it certainly lay across the writer's path of duty to point them out, and the more especially, that on this second occasion they are based on nothing short of a triple error.*
The letter above given, long as it was, was not even long enough to point out all the errors in the several assertions, for in view of this the writer need but allude to what is said regarding the corner sockets, which are asserted to be 8 inches deep, yet compare this with the various measures of every one of them, given by the only men who have ever seen them, namely, Messrs. Aiton and Inglis of Glasgow, Civil Engineers, and the Astronomer Royal for Scotland, from which we learn that they are all on different levels and all of different depths, so that, on the socket question, there is not the shadow of a reason for concluding that 757.5 feet was the length of the base of the original finished Pyramid.
Hence, then, a weaker theory at all points was never put forth than Sir Henry James' second attempt to settle why the Great Pyramid was made of the size we find it to be; whereas, in dealing with the question of the angle of the passages, he omits altogether to notice the remarkable astronomical azimuth and the delicate adjustment of their angles of altitude, which have given other men, as Sir John Herschel, such especially interesting and important problems in astronomical chronology to investigate; nay, but puts forward his wheel, pulley, and weight transport notions, which are too ridiculous to waste words upon.
Not receiving any acknowledgment of the lengthy communication made to the Director General of the Ordnance Survey, the writer had begun to suppose that he had abandoned the subject, but whilst travelling in the South of England in the following September, this letter reached him :—
MY DEAR SIR,
MOSSGAIT LODGE, ISLE OF LEWIS, 12th September, 1868.
I am sorry to have put you to the trouble of writing so long a letter respecting the Great Pyramid, and to find that you do not agree with me in thinking that it was built according to the simple directions I have supposed to have been given for its construction, viz., to make the rise at the corners 9 in 10, and to make the side of the square base 500 cubits, and its area 25 aruræ.
Any other view of the subject seems to me to be mere moonshine, but I may be wrong for all that.
I am, my Dear Sir,
Your obedient Servant,
(Signed)
ST. JOHN VINCENT DAY, Esq., C.E., &c.
HENRY JAMES.
The tone of this letter made clear to the writer's mind that something had happened which perhaps the Director-General little suspected, viz., that some one would test the accuracy of his arithmetic; for it is not unusual, when a proclamation is issued from so elevated an official source, for men to accept the dicta as infallible, therefore they do not frequently deem it worth while to investigate the truth for themselves; but, under the circumstances, it would at least have looked better in the eyes of men of science, if Sir Henry James had, without resorting to slang words, had the candour to confess the discrepancies in mere multiplication, addition, and subtraction into which he had so positively fallen, yet not a word of acknowledgment over blunders that a mere schoolboy at his class would be well chastised for. The writer could not, then, do otherwise than express himself in reply as in the following abstract:—
GLASGOW, October 28, 1868.
MY DEAR SIR,
Your letter of September 12 was forwarded to me in Devonshire, and I regret in having been prevented from replying to it earlier. Not that in reality there is any necessity for reply after the statement of your views in so positive a manner, at once indicative of your fear to submit those views of the great Pyramid which you have propounded to the crucial test of examination, based upon ascertained facts, and the unerring laws of simple arithmetic and geometry. It is too palpable a sign of weakness, when errors are pointed out, to shuffle away from argument in the manner you now try to avoid calm and fair discussion.* Such positivism characterizes all which you have written, whether to the public press or to me privately, on these Pyramid questions, that I am disposed to doubt whether you have ever really given due consideration to that side of the question which is opposed to what you take.
It is, however, to be hoped from the words with which your letter concludes, that you have not concluded with the subject but intend to pursue it further, as opportunity may offer; and may I venture to hope that closer investigation will—under the guidance of equal avidity which has marked your previous enquiries concerning the wondrous work of the first engineer—lead you to understand how accurate his work is, and free from those blemishes with which so many of our friends deplore to find you have endeavoured to stigmatise the designer. May it lead you to be reconciled to views as different from those published in the Athenaeum of August 8th last, as they differ from your first arrived at conclusions published in the same journal, and dated November 9, 1867.
If after you acknowledge your extraordinary arithmetical errors, so palpable, indeed, as to form ground of complaint to the most inaccurate mind, you shall then conclude in the true sense of the term, that the view of the Pyramid which I have adopted is "mere moonshine"—I shall then, as I do now, feel most happy in your having confessed that the exalted ideas of "moonshine," as well as "the Pyramid," appear to owe their origin, most probably, to one and the same source.
I am,
Your obedient Servant,
(Signed) ST. JOHN VINCENT DAY COL. SIR HENRY JAMES, R.E., &c.
During the time that the foregoing correspondence was being carried on, the expedition for surveying Mount Sinai was being organized, chiefly under the auspices of the Palestine Exploration Association, and the public was appealed to by lecturers and advertisements for subscriptions; but not until now did it appear that the Royal Engineers were to survey the Great Pyramid on their return home.
In a shortly succeeding number of the Athenæum, appeared the following communication :--
ORDNANCE SURVEY OFFICE, SOUTHAMPTON, November 23, 1868.
The expedition under Captains Wilson and Palmer, R.E., arrived at Suez on the 8th inst., and was to camp at Ain Musa on the 11th, on their way to Jebel Musa. The work of the survey has therefore been commenced, and it only remains with the public to say whether, by their contributions to the cost of the survey, it shall be completed. If the party should have time for the purpose, I have instructed the officers to measure and bring home an accurate plan of the Great Pyramid; strange to say, no accurate plan of this Pyramid yet exists. The French savans made the length of the side of the Pyramid about 746 feet, and the distance between the sockets at the four corners about 764 feet, agreeing very closely with the measures of Vyse and Perring. These numbers give 9 feet as the breadth of the casing stones, and therefore, the distance from the corners of the Pyramid to the furthest corners of the sockets 12.7 feet, that is, the diagonal of the square of 9 feet. But in the French plan this distance is made about 29.2 feet or 350 inches, and the Astronomer Royal for Scotland, from his "own measures," made it also about 350 inches at each of the four corners. These numbers are utterly irreconcilable; in one case, the finished Pyramid with its casing stones would entirely cover the sockets cut in the rock, which are about 12 feet square;* and in the other, it would not reach to the nearest part of them.
Whilst such discrepancies exist, it is impossible to say what was the real length of the side of the Pyramid, or the relation of the Pyramid to the sockets. These points I hope will be cleared up by our surveyors, and we shall then have, I believe for the first time, trustworthy data for discussing the units of measures employed in the design of the Pyramids.
HENRY JAMES, Col. R.E.
On the day following the date of this communication, its author addressed the writer to a similar effect:—
MY DEAR SIR,
SOUTHAMPTON, 24th November, 1868.
As regards the Great Pyramid—having no theory to maintain* I seek information and assistance from every quarter, to learn what was the unit of measure used in setting out the base of the Pyramid. I have lately had an opportunity of reading Perring's and Le Pere's works, and if you can assist me in explaining what has perplexed me not a little, I shall feel much obliged as an engineer yourself no one ought to be better able to do so.
According to Le Pere's and Perring's measures, the length of the side as it now exists is 746 feet (we omit decimals here), and 764 feet the length of the finished Pyramid, and the distance between the angles of the sockets 9 feet, being according to Perring the breadth of the casing stones. This is quite plain and intelligible. But on the French plan of the Pyramid, the
distance between the furthest corners of the sockets to the corners of the Pyramid as it exists is 29 feet instead of 12.7 feet, and Professor Smyth, from his "own measures" at all four corners, made the distance also 29 feet.
I do not understand this, and shall be glad if any one can explain it, for before it is explained it is clear we cannot understand the relative positions of the corners of the Pyramid to the sockets, or the construction of the works.
Yours truly,
(Signed) HENRY JAMES.
ST. JOHN V. DAY, Esq., C.E., &c.
Certainly these letters, at first sight, tend to make it appear that there are such numerous discrepancies between the measures referred to, that any attempt to reconcile them would be useless; but, on taking into consideration the state of the Pyramid corners, the discrepancies at once vanish. Accordingly the writer replied to Sir Henry James thus:—
GLASGOW, December 9, 1868.
MY DEAR SIR,
I beg that you will pardon my delay in replying to your letter of the 24th ult. After reading that letter it became to me very clear as to what circumstances had misled you to the apparent discrepancies to which you draw my attention, and as you ask me to explain the difficulty I can only add with what readiness I do so.
Le Père and Perring give the distance from the side of the Pyramid, that is to say, from the bottom of the present flank to the lowermost outer edge of the casing stones or where they join the pavement, or half the difference of their dimensions of the present and original base length at 9 feet (here I avoid decimal exactitude, because Mr. Perring states his measures to the nearest inch only). Now these flanks, everywhere else except at the corners, have, ever since the time El Mamoun stripped off the casing stones, been protected from deterioration—either by the mischievous breaking away of man or scaling off through the effects of climate (which in Egypt are comparatively little) by the very thick overlying mass of rubbish; this accidental covering being comparatively small at the corners, and attaining its maximum at the centre of each flank.
Not only then have the actual corners long been exposed, but by being so exposed, and from the mere fact of their being corners, I am sure I need scarcely explain to you as an engineer, that the stones at these corners were more easily removed than at any other part of the building; and the truth is, they are and have been removed more or less to the extent of 29 feet or thereabouts, as measured diagonally from the outer angle of the corner sockets. Any good photograph of the corners, of which there are several, shows them now to be abruptly or bluntly terminated, in place of continuing down to the platform at the original corner slope. Thus,
Elevation
On this point I refer you to page 133, Vol. II., also Plate 3, Vol. III., of "Life and Work." We see then, that in the measures of Le Pere and Perring they supplied the defect of length due to the breaking away of the corners, whereas, the French plan gives 29 feet as the diagonal distance from the outer corners of the two sockets, which they saw, to the corners of the Pyramid, as it was in the days of the French Institute. The same or nearly the same length from the outer corners of the sockets to the present broken corners is deducible from Professor Smyth's measures; so that, on the whole, where the
conditions of each system of measures are truly taken into consideration, their comparative close agreement as rough measures of very rough and destroyed features is truly convincing.
If I have failed to make this quite clear to you, I beg you will acquaint me wherein you find still a difficulty, and I shall be glad to do my best to remove it.
You say in the first paragraph of your letter that you have no theory to maintain; my impression, from your letters to the Athenaeum, was, that you had proposed three different theories: am I now to understand that these are abandoned in toto?
Yours very truly,
(Signed)
ST. JOHN VINCENT DAY.
COL. SIR HENRY JAMES, R.E., &c.
To this letter Sir Henry James replied :—
ORDNANCE HOUSE,
SOUTHAMPTON, December 26, 1868.
MY DEAR SIR,
I have no theories respecting the Great Pyramid to abandon. I find the length of the side of the base to be 3 6 0 ×2 5 ·4 8 8 inches, the length given for the derah by several writers. I also find that this length, as given by Inglis, is 500 Greek or Egyptian cubits; but Inglis differs in his measures from Perring and the French savans, and until we really know what the true length of the side is, it is hardly worth while to further discuss the subject.
I have given directions for the party of surveyors I have sent to Mount Sinai to measure the Pyramid on their way home, if they have time for it.
Very truly yours,
(Signed) HENRY JAMES.
ST. JOHN VINCENT DAY, Esq., C.E., &c.
P.S. Your explanation of the measures on the diagonals is probably correct.
This was the last letter received from the Ordnance Survey Director-General. The writer did not reply to it for reasons which must be obvious to any one who has taken the trouble to examine into the assertions and contradictions which Sir Henry James had made, determining rather to await the result of the Sinai surveyors' measure, since Sir Henry James evidently considered that to be the stronghold for data on which to carry out future investigations as to measures and geometry. The postscript shows that that gentleman was convinced by the explanation given him, in the writer's letter dated December 6th, of the apparent discrepancies which he had stated to exist between Le Père and Perring, the French and Piazzi Smyth's measures.
A certain alleged result of the Sinai surveyors' measures is now published, and we shall presently look into the inferences which have been drawn from them; but, before doing that, we cannot pass over certain incidents which occurred during the intervals between the date of this last letter and the publication of the said result.
Sir Henry James having to the writer privately admitted the correctness of the explanation given to him, and therefore the fallacy of his own inferences, it was natural to expect that he would lose no time in declaring the discrepancy to be cleared up, in the same public manner as he had all along proclaimed his other assertions in the pages of a weekly journal.
The writer had communicated the points of the correspondence to the Astronomer Royal for Scotland, who also looked out for a similar open and candid public confession; but weeks and months rolled on, the Athenæum pages not figuring with any further communication. At last, to ascertain the intent of this long silence, with the public calumny against the work of certain scientific gentlemen allowed to remain uninvestigated, my friend Professor Smyth wrote Sir Henry James:—
1 HILLSIDE CRESCENT EDINBURGH, 12th March, 1869.
DEAR SIR HENRY JAMES,
In the Atheneum of November 28, 1868, you have charged upon the French savans, Col. Howard Vyse, Mr. Perring, and myself, an error, or "utterly irreconcilable discrepancy," of 16.5 feet in the length of the side of the base of the Great Pyramid.
My friend, Mr. St. John Vincent Day, C.E., pointed out to you soon after, that the error existed only in your own misapprehension of the real state of the case, a case fully and abundantly described in the volumes of my "Life and Work at the Great Pyramid."
May I ask if you have taken any steps, and what, to remove the aspersion which you so needlessly cast in the most public manner? and I remain,
Yours very truly,
(Signed) C. PIAZZI SMYTH.
To this the following reply was written :— ORDNANCE SURVEY, SOUTHAMPTON, 15th March, 1869.
MY DEAR SIR,
I have sent a letter to the Athenaeum, stating that I had no desire to misrepresent you in my letter of the 28th November last, and that I regretted having fallen into the mistake I made in not seeing that the 16.5 feet of the masonry of the Pyramid had been removed at the corners, as well as the casing stones.
I hope this will prove satisfactory to you,
I remain, Yours truly,
(Signed) HENRY JAMES.
PROFESSOR PLAZZI SMYTH, Astronomer Royal, Scotland.
The letter referred to in that from Sir Henry James to the Astronomer Royal for Scotland is as follows:—
ORDNANCE SURVEY OFFICE, SOUTHAMPTON, March 15, 1869.
I am anxious to be allowed to correct a statement which is contained in my letter which appeared in the Athenaeum of the 28th November last, respecting the measures taken by Professor Smyth at the corners of the Great Pyramid.
From the frequent mention of the length of the side of this Pyramid, as it stands, to be 746 feet or thereabouts, and that with the casing stones the length must have been about 764 feet, it followed that 12.7 feet only had been removed at the corners, and I stated that the measure of about 16.5 feet more, making a total length removed from the corners of 29.2 feet, was irreconcilable with the above measures. I had no desire to misrepresent Professor Smyth, and I regret that I had inadvertently fallen into this error, as it appears that this 16.5 feet of masonry of the Pyramid has also been removed at the corners.
The chief point of interest connected with the dimensions of this Pyramid lies in the fact that, having the corners of the sockets for all four corners of the Pyramid perfectly preserved in the rock in which they are cut, we have the data for ascertaining the length of the common Egyptian cubit at the time the Pyramid was built; in the same manner that we have obtained the length of the Greek foot and cubit from the measures of the Parthenon.
Mr. Inglis, a practical engineer, measured the distance from corner to corner of the sockets, and found the lengths of the sides to be 9120, 9114, 9102, 9102 inches, the mean being 9110 inches. Stuart obtained 12.138 inches as the length of the Greek foot from the measures of the Parthenon, and Penrose 12.16 from them, the mean length of the two being 12.149, and the mean cubit, therefore, 18.224 inches, which, multiplied by 500, gives 9112 inches, differing only 2 inches from Inglis' mean measure. If we take Stuart's length of the Greek cubit 500 times, its length only differs 11⁄2 inches from Inglis' length of two of the sides, being 9102 inches; and if we take Penrose's length of the Greek cubit, it gives us exactly 9120 inches—Inglis' largest measure.
These results appear to me to demonstrate that, as Herodotus has stated, the Egyptian cubit was equal to that of Samos, that is, to the Greek cubit; and that the sides of the Great Pyramid were made exactly 500 Egyptian or Greek cubits, and that the Pyramid covered exactly 25 arurae or Egyptian acres; the arura, according to Herodotus, being a square of 100 cubits.
The height of the Pyramid was determined, as I have said before, by giving the structure a rise of 9 in 10 at the corners.
(Signed)
HENRY JAMES, Col. R.E.
As the assertions in this letter are repeated in a subsequent publication, they are for the present passed over until reached in the order in which they occur to be examined in the next part of this criticism.
III. In the preface to "Notes on the Great Pyramid of Egypt," * the author states, "My chief object in writing these short 'Notes' has been to obtain a knowledge of the true lengths of the units of measure employed in setting out the external and internal dimensions of this Pyramid; or, in other words, to recover, if possible, the true lengths of the cubits in use upwards of 4000 years ago."
The investigations instituted for the purpose above stated are detailed in eight notes and addenda, which the writer now proposes to review, in order to estimate the degree of reliability attaching to the results stated as being thenceforth educated.
(a.)—"On the length of the common cubit of Egypt which was employed in setting out the external dimensions of the Great Pyramid."
The reader will not fail to observe the assertion (in the title of the first note immediately preceding), to make which prominent the writer has in part italicised. In order that an assertion may be accepted as infallible it must be proved, and the author of the "Notes" appends what he professes to be a proof, in which he states that Herodotus tells us "the Egyptian cubit is equal to that of Samos," that is, to the "Greek cubit." Reasoning for the present apart from further enquiry as to what the true interpretation of the Herodotean passage is, it does not appear absolutely impossible that a nation (the Greek) rising into prominence and overrunning Egypt 1700 years after the completion of the Pyramid, may have found a measure in use there equal or nearly equal to some linear unit of their own, but it is highly improbable; and, when we consider the difference in length of the two cubits (even allowing for the moment Sir Henry James' length of the Greek cubit, viz., 18.2415 British inches, and placing against it the cubit of Memphis of 20.70 inches), we see so large a difference, impossible to account for, especially when we know the cubit was so religiously guarded a thing, even in Pantheistic Old Egypt; and it is, indeed, far more likely that they (the Greeks) at that period brought away the cubit then in use in their own country and endeavoured to introduce it into Egypt.
Yet the mere granting or refusal to admit either of the foregoing suppositions is immaterial, for it may be asked, although it really was the fact that the lengths of the said alleged cubits agreed at the time Herodotus wrote, does that alleged coincidence at that particular period prove that the Pyramid was built according to the selfsame cubit? or even that a cubit approximately of the same length as the Greek cubit was ever known in Egypt at the time of building the Pyramid? or does it show that the length of a cubit had remained unaltered through the said 1700 years? Further, supposing that a cubit really had been found in Egypt by the Greeks of a length equal to their own cubit, is the mere literary statement of Herodotus to be held as an index of the precision with which the Greeks when in Egypt compared the two alleged cubits? Have we any precedent for warranting us in giving the Greeks credit for possessing instrumental means for making such a comparison for the identity of two units of length? a comparison, indeed, to conduct which with positive accuracy would baffle the skill and refinement of the most renowned instrument makers and users of this nineteenth century.
It is too well known a fact by everyone versed in refined measurements, that they cannot be made with that positive accuracy attending the statements of dimensions in the assertive character of the "Notes," throughout which there is no allowance for even an almost vanishing value of ± x . Whilst, again, if we are to infer anything from Greek architecture—that is to say, of its mere structural quality-alas, how altogether second-rate is it when placed in the face of that transcending masonry of the oldest built monument of Egypt!!
It is barely necessary to remind the reader that the writer is speaking here quite regardless of architectural styles, having only to do with the excellence of mechanical construction as touching metrological conditions and data. The author of the "Notes" evidently feels satisfied with answering the above questions in the affirmative, for he says, "In the Hecatompedon of the Parthenon, at Athens (so called because the platform on which the columns stand was made a double square of exactly 100 feet), we have preserved the length of 100 Greek feet at the time this Templet was built, viz., about 440 B.C.;" and in support of this he cites the measures thereof made by Mr. Penrose, thus—"From the measures of Penrose, taken with the greatest care, see his letter from Athens of the 8th Nov., 1846, addressed to the Society of Dilettanti."
Yet after all the foregoing, it still has to be asked, What did Herodotus mean when he wrote, Euterpe, 168, "the Egyptian cubit is equal to that of Samos?" Sir Henry James asserts he meant to convey to posterity that the Egyptian and Grecian cubits were equal. Yet, during the time that the present criticism has been written, the true signification of the Halicarnassian's words have been closely investigated by the Astronomer-Royal for Scotland, and published, with the after-mentioned result, in a report to the Edinburgh Royal Observatory Board, dated June 29, 1870. The passage wherein the quotation from which Sir Henry James has inferred so unwarrantable a conclusion, runs thus in Professor Rawlinson's translation:—
And regarding which the said Astronomer-Royal remarks:— to Asia Minor, and so far from Greece) as 'foreigners;' and in Thalia, 56, he himself characteristically speaks of a siege of Samos by the Lacædemonian Dorians as 'their first expedition into Asia.'
…