Chapter V: Is the Great Pyramid of Gizeh a Metrological (9)

Lately, Sir Henry James, the distinguished head of the Ordnance Survey Department, has shown that the length of one of the sides of the pyramid base, with the casing stones added, as measured by Colonel H. Vyse--viz. 9168 inches--is precisely 360 derahs, or land cubits of Egypt; the derah being an ancient land measure still in use, of the length of nearly 25-1/2 British inches, or, more correctly, of 25.488 inches; and he has pointed out that in the construction of the body of the Great Pyramid, the architect built 10 feet or 10 cubits of horizontal length for every 9 feet or 9 cubits of vertical height; while in the construction of the inclined passages the proportion was adhered to of 9 on the incline to 4 in vertical height, rules which would altogether simplify the building of such a structure.[254] The Egyptian derah of 25.48 inches is practically one-fourth more in length than the old cubit of the city of Memphis. Long ago Sir Isaac Newton showed, from Professor Greaves' measurements of the chambers, galleries, etc., that the Memphis cubit (or cubit of "ancient Egypt generally") of 1.719 English feet,[255] or 20.628 English inches, was apparently the _working_ cubit of the masons in constructing the Great Pyramid[256]--an opinion so far admitted more lately by both Messrs Taylor and Smyth; "the length" (says Professor Smyth) "of the cubit employed by the masons engaged in the Great Pyramid building, or that of the ancient city of Memphis," being, he thinks, on an average taken from various parts in the interior of the building, 20.73 British inches.[257] According to Mr. Inglis' late measurement of the four bases of the pyramid, after its four corner sockets were exposed, the length of each base line was possibly 442 Memphis cubits, or 9117 English inches; or, if the greater length of the French Academicians, Colonel Vyse, and Mahmoud Bey, be held nearer the truth, 444 Memphis cubits, or 9158 British inches.

But Professor Smyth tries to show that (1.) if 9142 only be granted to him as the possible base line of the pyramid; and (2.) if 25 pyramidal inches be allowed to be the length of the "Sacred Cubit," as revealed to the Israelites (and as revealed in the pyramid), then the base line might be found very near a multiple of this cubit by the days of the year,[258] or by 365.25; for these two numbers multiplied together amount to 9131 "pyramidal" inches, or 9140 British inches--the British inch being held, as already stated, to be 1000th less than the pyramidal inch. Was, however, the "Sacred Cubit"--upon whose alleged length of 25 "pyramidal" inches this idea is entirely built--really a measure of this length? In this matter--the most important and vital of all for his whole linear hypothesis--Professor Smyth seems to have fallen into errors which entirely upset all the calculations and inferences founded by him upon it.

* * * * *

_Length of the Sacred Cubit._--Sir Isaac Newton, in his remarkable _Dissertation upon the Sacred Cubit of the Jews_ (republished in full by Professor Smyth in the second volume of his _Life and Work at the Great Pyramid_), long ago came to the conclusion that it measured 25 unciae of the Roman foot, and 6/10 of an uncia, or 24.753 British inches; and in this way it was one-fifth longer than the cubit of Memphis--viz. 20.628 inches, as previously deduced by him from Greaves' measurements of the King's Chamber and other parts of the interior of the Great Pyramid. Before drawing his final inference as to the Sacred Cubit being 24.75 inches, and as so many steps conducting to that inference, Sir Isaac shows that the Sacred Cubit was some measurement intermediate between a long and moderate human step or pace, between the third of the length of the body of a tall and short man, etc. etc. Professor Smyth has collected several of the estimations thus adduced by Newton as "methods of approach" to circumscribe the length of the Sacred Cubit, and omitted others. Adding to eight of these alleged data, what he mistakingly avers to be Sir Isaac's deduction of the actual length of the Sacred Cubit in British inches--(namely, 24.82 instead of 24.753)--as a ninth quantity, he enters the whole nine in a table as follows:--

_Professor Smyth's Table of Newton's data of Inquiry regarding the Sacred Cubit._[259]

"First between 23.28 and 27.94 British inches.
Second " 23.3 27.9 "
Third " 24.80 25.02 "
Fourth " 24.91 25.68[260] "
And Fifth, somewhere near 24.82."

"The mean of all which numbers" (Professor Smyth remarks) "amounts to 25.07 British inches. The Sacred Cubit, then, of the Hebrews" (he adds) "in the time of Moses--_according to Sir Isaac Newton_--was equal to 25.07 British inches, with a probable error of +-.1."

But--"_according_ to Sir Isaac Newton"--the Sacred Cubit of the Jews was _not_ 25.07, as Professor Smyth makes him state in this table, but 24.75 British inches, as Sir Isaac himself more than once deliberately infers in his Dissertation.[261] Besides, in such inquiries, is it not altogether illogical to attempt to draw mathematical deductions by these calculations of "means," and especially by using the ninth quantity in the table--viz. Sir Isaac's own avowed and deliberate deduction regarding the actual length of the Sacred Cubit--as one of the nine quantities from which that length was to be again deduced by the very equivocal process of "means?" Errors, however, of a far more serious kind exist. The "mean" of the nine quantities in Professor Smyth's table is, he infers, 25.07 inches; and hence he avows that this, or near this figure, is the length of the Sacred Cubit. But the real mean of the nine quantities which Professor Smyth has collected is not 25.07 but 25.29--a number in such a testing question as this of a very different value. For the days of the year (365.25) when multiplied by this, the true mean of these nine quantities, would make the base line of the pyramid 9237 inches instead of Professor Smyth's theoretical number of 9142 inches; a difference altogether overturning all his inferences and calculations thereanent. And again, if we take Sir Isaac Newton's own conclusion of 24.75, and multiply it by the days of the year, the pretended length of the pyramid base comes out as low as 9039.

_Alleged "really glorious Consummation" in Geodesy._

The incidentally but totally erroneous summation which Professor Smyth thus makes of the nine equivocal quantities in his table, as amounting to 25.07, he declares (to use his own strong words) as a "_really glorious consummation_ for the geodesical science of the present day to have brought to light;" for he avers this length of 25.07--(which he forthwith elects to alter and change, without any given reason whatever, to 25.025 British inches)--being, he observes, "practically the sacred Hebrew cubit, is _exactly_ one ten-millionth (1-10,000,000th) of the earth's semi-axis of rotation; and _that is_ the very best mode of reference to the earth-ball as a whole, for a linear standard through all time, that the highest science of the existing age of the world has yet struck out or can imagine. In a word, the Sacred Cubit, _thus_ realised, forms an instance of the most advanced and perfected human science supporting the truest, purest, and most ancient religion; while a linear standard which the chosen people in the earlier ages of the world were merely told by maxim to look on as _sacred_, compared with other cubits of other lengths, is proved by the progress of human learning in the latter ages of time, to have had, and still to have, a philosophical merit about it which no men or nations at the time it was first produced, or within several thousand years thereof, could have possibly thought of for themselves." Besides, adds he elsewhere, "an _extraordinarily_[262] convenient length too, for man to handle and use in the common affairs of life is the one ten-millionth of the earth's semi-axis of rotation when it comes to be realised, for it is extremely close to the ordinary human arm, or to the ordinary human pace in walking, with a purpose to measure."

Of course all these inferences and averments regarding the Sacred Cubit being an exact segment of the polar axis disappear, when we find Sir Isaac Newton's length of the Sacred Cubit is not, as Professor Smyth elects it to be, 25.025 British inches; nor 25.07, as he incorrectly calculated it to be from the mean of the nine quantities selected and arranged in his table; nor 25.29, as is the actual mean of these nine quantities in his table; but, "_according_ to Sir Isaac Newton's" own reiterated statement and conclusion, 24.753. (See footnote, p. 245.) A Sacred Cubit, according to Sir Isaac Newton's admeasurements of it, of 24.75 inches, would not, by thousands of cubits, be one ten-millionth of the measure of the semi-polar axis of the earth; provided the polar axis be, as Professor Smyth elects it to be, 500,500,000 British inches.[263]

AXIS OF THE EARTH AS A STANDARD OF MEASURE.

The standards of measure in France and some other countries are, as is well known, referred to divisions of arcs of the meridian, measured off upon different points of the surface of the earth. These measures of arcs of the meridian, as measurements of a known and selected portion of the surface of the spheroidal globe of the earth, have, more or less, fixed mathematical relations with the axis of the earth; as the circumference of a sphere has an exact mathematical ratio to its diameter. The difference in length of arcs of the meridian at different parts of the earth's surface, in consequence of the spheroidal form of the globe of the earth, has led to the idea that the polar diameter or axis of the earth would form a more perfect and more universal standard than measurements of the surface of the earth. In the last century, Cassini[264] and Callet[265] proposed, on these grounds, that the polar axis of the earth should be taken as the standard of measure. Without having noticed these propositions of Cassini and Callet,[266] Professor Smyth adopts the same idea, and avers that 4000 years ago it had been adopted and used also by the builders of the Great Pyramid, who laid out and measured off the basis of the pyramid as a multiple by the days of the year of the Sacred Cubit, and hence of the Pyramidal Cubit while the Sacred or Pyramidal Cubit were both the results of superhuman or divine knowledge, and were both, or each, one ten-millionth of the semi-polar axis of the earth. We have already seen, however, that the Sacred Cubit, "_according_ to Sir Isaac Newton," is not a multiple by the days of the year of the base line of the Great Pyramid; and is not one twenty-millionth of the polar axis of the earth, when that polar axis is laid down as measuring, according to the numbers elected by Professor Smyth, 500,500,000 British inches.

* * * * *

But is there any valid reason whatever for fixing and determining, as an ascertained mathematical fact, the polar axis of the earth to be this very precise and exact measure, with its formidable tail of cyphers? None, except the supposed requirements or necessities of Professor Smyth's pyramid metrological theory. The latest and most exact measurements are acknowledged to be those of Captain Clarke, who, on the doctrine of the earth being a spheroid of revolution computes the polar axis to be 500,522,904 British inches, calculating it from the results of all the known arcs of meridian measures. If we grant that the Sacred Cubit could be allowed to be exactly 25.025 inches, which Sir Isaac Newton found it not to be; and if we grant that the polar axis is exactly 500,500,000 British inches, which Captain Clarke did not find it to be; then, certainly, as shown by Professor Smyth, there would be 20,000,000 of these supposititious pyramidal cubits, or 500,000,000 of the supposititious pyramidal inches in this supposititious polar axis of the earth. "In so far, then" (writes Professor Smyth), "we have in the 5, with the many 0's that follow, a pyramidally commensurable and symbolically appropriate unit for the earth's axis of rotation." But such adjustments have been made with as great apparent exactitude when entirely different earth-axes and quantities were taken. Thus Mr. John Taylor shows the inches, cubits, and axes to answer precisely, although he took as his standard a totally different diameter of the earth from Professor Smyth. The diameter of the earth at 30 deg. of latitude--the geographical position of the Great Pyramid--is, he avers, some seventeen miles, or more exactly 17.652 miles longer than at the poles.[267] But Mr. Taylor fixed upon this diameter of the earth at latitude 30 deg.--and not, like Professor Smyth, upon its polar diameter--as the standard for the metrological linear measures of the Great Pyramid; and yet, though the standard was so different, he found, like Mr. Smyth, 500,000,000 of inches also in his axis, and 20,000,000 of cubits also.[268] The resulting figures appear to fit equally as well for the one as for the other. Perhaps they answer best on Mr. Taylor's scheme. For Mr. Taylor maintained that the diameter of the earth before the Flood, at this selected point of 30 deg., was less by nearly 37 miles than what it was subsequently to the flood,[269] and is now; a point by which he accounts for otherwise unaccountable circumstances in the metrological doctrines which have been attempted to be connected with the Great Pyramid. For while Mr. Taylor believes the Sacred Cubit to be 24.88, or possibly 24.90 British inches, he holds the new Pyramidal cubit to be 25 inches in full; and the Sacred and Pyramidal cubits to be different therefore from each other, though both inspired. In explanation of this startling difference in two measures supposed to be equally of sacred[270] origin, Mr. Taylor observes--"The smaller 24.88 is the Sacred Cubit which measured the diameter of the Earth _before_ the Flood; the one by which Noah measured the Ark, as tradition says; and the one in accordance with which all the interior works of the Great Pyramid were constructed.[271] The larger (25) is the Sacred Cubit of the _present_ Earth, according to the standard of the Great Pyramid when it was completed."

Surely such marked diversities and contradictions, and such strange hypothetical adjustments and re-adjustments of the data and calculations, entirely upset the groundless and extraordinary theory of the base of the pyramid being a standard of linear measurement; or a segment of any particular axis of the earth; or a standard for emitting a system of new inches and new cubits;--seeing, on the one hand, more particularly, that the basis line of the pyramid is still itself an unknown and undetermined linear quantity, as is also the polar axis of the earth of which it is declared and averred to be an ascertained, determined, and measured segment.

M. Paucton, in 1780, wrote a work in which he laid down the base side of the pyramid as 8754 inches; maintained, like Mr. Taylor and Mr. Smyth, that this length was a standard of linear measures; found it to be the measure of a portion of a degree of the meridian, such degree being itself the 360th part of a circle;--and apparently the calculations and figures answered as well as when the measurement was declared to be 9142 inches, and the line not a segment of an arc of the circumference of the earth, but a segment of the polar axis of the earth; for De l'Isle lauds Paucton's meridian degree theory as one of the wondrous efforts of human genius, or (to use his own words) "as one of the chief works of the human mind!" Yet the errors into which Paucton was seduced in miscalculating the base line of the Pyramid as 8754 inches, and the other ways he was misled, are enough--suggests Professor Smyth--"to make poor Paucton turn in his grave."

SIGNIFICANCE OF CYPHERS AND FIVES.

M. Paucton, Mr. Taylor, and those who have adopted and followed their pyramid metrological ideas, seem to imagine that if, by multiplying one of their measures or objects, they can run the calculation out into a long tail of terminal 0's, then something very exact and marvellous is proved. "When" (upholds Mr. Taylor), "we find in so complicated a series of figures as that which the measures of the Great Pyramid and of the Earth require for their expression, _round numbers_ present themselves, or such as leave no remainder, we may be sure we have arrived at _primitive_ measures." But many small and unimportant objects, when thus multiplied sufficiently, give equally startling strings of 0's. Thus, if the polar axis of the earth be held as 500,000,000 inches, and Sir Isaac Newton's "Sacred Cubit" be held, as Professor Smyth calculated it to be, viz. 24.82 British inches--then the long diameter of the brim of the lecturer's hat, measuring 12.4 inches, is 1-40,000,000th of the earth's polar axis; a page of the print of the Society's Transactions is 1-60,000,000th of the same; a print page of Professor Smyth's book, 6.2 inches in length, is 1-80,000,000th of this "great standard;" etc. etc. etc.

Professor Smyth seems further to think that the figure or number "five" plays also a most important symbolical and inner part in the configuration, structure, and enumeration of the Great Pyramid. "The pyramid" (says he) "embodies in a variety of ways the importance of five." It is itself "five-angled, and with its plane a five-sided solid, in which everything went by fives, or numbers of fives and powers of five." "With five, then, as a number, times of five, and powers of five, the Great Pyramid contains a mighty system of consistently subdividing large quantities to suit human happiness." To express this, Mr. Smyth suggests the new noun "fiveness." But it applies to many other matters as strongly, or more strongly than to the Great Pyramid. For instance, the range of rooms belonging to the Royal Society is "five" in number; the hall in which it meets has five windows; the roof of that hall is divided into five transverse ornamental sections; and each of these five transverse sections is subdivided into five longitudinal ones; the books at each end of the hall are arranged in ten rows and six sections--making sixty, a multiple of five; the official chairs in the hall are ten in number, or twice five; the number of benches on one side for ordinary fellows is generally five; the office-bearers of the Society are twenty-five in number, or five times five; and so on. These arrangements were doubtless, in the first instance, made by the Royal Society without any special relation to "fiveness," or the "symbolisation" of five; and there is not the slightest ground for any belief that the apparent "fiveness" of anything in the Great Pyramid had a different origin.

GREAT MINUTENESS OF MODERN PRACTICAL STANDARDS OF GAUGES.

In all these "standards" of capacity and length alleged to exist about the Great Pyramid, not only are the theoretical and actual sizes of the supposed "standards" made to vary in different books--which it is impossible for an actual "standard" to do--but the evidences adduced in proof of the conformity of old or modern measures with them is notoriously defective in complete aptness and accuracy. Measures, to be true counterparts, must, in mathematics, be not simply "near," or "very near," which is all that is generally and vaguely claimed for the supposed pyramidal proofs, but they must be entirely and _exactly_ alike, which the pyramidal proofs and so-called standards fail totally and altogether in being. Mathematical measurements of lines, sizes, angles, etc., imply exactitude, and not mere approximation; and without that exactitude they are not mathematical, and--far more--are they not "superhuman" and "inspired."

Besides, it must not be forgotten that our real _practical_ standard measures are infinitely more refined and many thousand-fold more delicate than any indefinite and equivocal measures alleged to be found in the pyramid by even those who are most enthusiastic in the pyramidal metrological theory. At the London Exhibition in 1851, that celebrated mechanician and engineer, Mr. Whitworth, of Manchester, was the first to show the possibility of ascertaining by the sense of touch alone the one-millionth of an inch in a properly-adjusted standard of linear measure; and in his great establishment at Manchester they work and construct machinery and tools of all kinds with differences in linear measurements amounting to one ten-thousandth of an inch. The standards of the English inch, etc., made by him for the Government--and now used by all the engine and tool makers, etc., of the United Kingdom--lead to the construction of machinery, etc., to such minute divisions; and the adoption of these standards has already effected enormous saving to the country by bringing all measured metal machinery, instruments, and tools, wherever constructed and wherever afterwards applied and used, to the same identical series of mathematical and precise gauges.

THE SABBATH, ETC. TYPIFIED IN THE PYRAMID.

The communication next discussed some others amongst the many and diversified matters which Professor Smyth fancifully averred to be typified and symbolised in the Great Pyramid.

One, for example, of the chambers in the Great Pyramid--the so-called Queen's Chamber--has a roof composed of two large blocks of stone leaning against each other, making a kind of slanting or double roof. This double roof, and the four walls of the chamber count six, and typify, according to Professor Smyth, the six days of the week, whilst the floor counts, as it were, a seventh side to the room, "nobler and more glorious than the rest," and typifying something, he conceives, of a "nobler and more glorious order"--namely, the Sabbath; it is surely difficult to fancy anything more strange than this strange idea.[272] In forming this theory liberties are also confessedly taken with the floor in order to make it duly larger than the other six sides of the room, and to do so he theoretically lifts up the floor till it is placed higher than the very entrance to the chamber; for originally the floor and sides are otherwise too nearly alike in size to make a symbolic _seven_-sided room with one of the sides proportionally and properly larger than the other six sides. Yet Professor Smyth holds that, in the above typical way, he has "shown," or indeed "proved entirely," that the Sabbath had been heard of before Moses, and that thus he finds unexpected and confirmatory light of a fact which, he avers, is of "extraordinary importance, and possesses a ramifying influence through many departments of religious life and progress."

He believes, also, that the corner-stone--so frequently alluded to by the Psalmist and the Apostles as a symbol of the Messiah--is the head or corner-stone of the Great Pyramid, which, though long ago removed, may yet possibly, he thinks, be discovered in the Cave of Machpelah; though how, why, or wherefore it should have found its way to that distant and special locality is not in any way solved or suggested.

GREAT PYRAMID ALLEGED TO BE A SUPERHUMAN, AND MORE OR LESS AN INSPIRED METROLOGICAL ERECTION.

Professor Smyth holds the Great Pyramid to be in its emblems, and intentions and work "superhuman;" as "not altogether of human origination; and in that case whereto" (he asks) "should we look for any human assistance to men but from Divine inspiration?" "Its metrology is," he conceives, "directed by a higher Power" than man; its erection "directed by the _fiat_ of Infinite Wisdom;" and the whole "built under the direction of chosen men divinely inspired from on high for this purpose."

If of this Divine origin, the work should be absolutely perfect; but, as owned by Professor Smyth, the structure is not entirely correct in its orientation, in its squareness, etc. etc.--all of them matters proving that it is human, and not superhuman. It was, Professor Smyth further alleges, intended to convey standards of measures to all times down to, and perhaps beyond, these latter days, "to herald in some of those accompaniments of the promised millennial peace and goodwill to all men." Hence, if thus miraculous in its forseen uses, it ought to have remained relatively perfect till now. But "what feature of the pyramid is there" (asks Professor Smyth) "which renders at once in its measurements in the present day its ancient proportions? None." If the pyramid were a miracle of this kind, then the Arabian Caliph Al Mamoon so far upset the supposititious miracle a thousand years ago--(of course he could not have done so provided the miracle had been truly Divine)--when he broke into the King's Chamber and unveiled its contents; inasmuch as the builders, according to Professor Smyth, intended to conceal its secrets for the benefit of these latter times, and for this purpose had left a mathematical sign of two somewhat diagonal lines or joints in the floor of the descending passage, by which secret sign or clue[273] some men or man in the far distant future, visiting the interior, should detect the entrance to the chambers; and which secret sign Professor Smyth himself was, as he believes, the first "man" to discover two years ago. The secret, however, thus averred to be placed there for the detection of the entrance to the interior chambers in these latter times, has been discovered some 1000 years at least too late for the evolution of the alleged miraculous arrangement. And in relation to the Great Pyramid, as to other matters, we may be sure that God does not teach by the medium of miracle anything that the unaided intellect of man can find out; and we must beware of erroneously and disparagingly attributing to Divine inspiration and aid, things that are imperfect and human.

* * * * *

The communication concluded by a series of remarks, in which it was pointed out that at the time at which the Great Pyramid was built, probably about 4000 years ago, mining, architecture, astronomy, etc., were so advanced in various parts of the East as to present no obstacle in the way of the erection of such magnificent mausoleums, as the colossal Great Pyramid and its other congener pyramids undoubtedly are.

FOOTNOTES:

[Footnote 233: See on other proposed significations and origins of the word pyramid, APPENDIX, No. I.]

[Footnote 234: In the plain of Troy, and on the higher grounds around it, various barrows still remain, and have been described from Pliny, Strabo, and Lucia down to Lechevalier, Forchhammer, and Maclaren. In later times, Choiseul and Calvert have opened some of them. Homer gives a minute account of the obsequies of Patroclus and the raising of his burial-mound, which forms, as is generally believed, one of those twin barrows still existing on the sides of the Sigean promontory, that pass under the name of the tumuli of Achilles and Patroclus. Pope, in translating the passage describing the commencement of the funeral pyre, uses the word pyramid. For

... "those deputed to inter the slain,
Heap with a rising _pyramid_ the plain."

Professor Daniel Wilson, in alluding, in his _Prehistoric Annals_, vol. i. p. 74, to this account by Homer of the ancient funeral-rites, and raising of the funeral-mound, speaks of the erection of Patroclus' barrow as "the methodic construction of the Pyramid of earth which covered the sacred deposit and preserved the memory of the honoured dead."]

[Footnote 235: Colonel Pownall, while describing in 1770 the barrow of New Grange, in Ireland, to the London Society of Antiquaries, speaks of it as "a pyramid of stone." "This pyramid," he observes, "was encircled at its base with a number of enormous unhewn stones," etc. "The pyramid, in its present state, is but a ruin of what it was," etc. etc. See _Archaeologia_, vol. vi. p. 254; and Higgins' _Celtic Druids_, p. 40, etc.]

[Footnote 236: In his _Prehistoric Annals of Scotland_, Dr. Daniel Wilson states (vol. i. p. 87), that "the Chambered Cairn properly possesses as its peculiar characteristic the enclosed catacombs and galleries of megalithic masonry, branching off into various chambers symmetrically arranged, and frequently exhibiting traces of constructive skill, such as realise in some degree the idea of the regular pyramid." He speaks again of the stone barrows or cairns of Scotland as "monumental pyramids" (vol. i. p. 67); of the earth barrow being an "earth pyramid or tumulus" (p. 70); of Silbury Hill as an "earth pyramid" (p. 62): and in the same page, in alluding to the large barrow-tomb of the ancient British chief or warrior, he states, "in its later circular forms we see the rude type of the great pyramids of Egypt." The same learned author, in his work on _Prehistoric Man_, refers to the great monuments of the American mound-builders as "earth pyramids" (p. 202), "huge earth pyramids" (p. 205), "pyramidal earth-works" (p. 203); etc.]

[Footnote 237: In his _History of Scotland_, Mr. Burton speaks of the barrows of New Grange and Maeshowe (Orkney), as erections which "may justly be called minor pyramids" (vol. i. p. 114).]

[Footnote 238: In mentioning the great numbers of sepulchral barrows spread over the world, Sir John Lubbock observes--"In our own island they may be seen on almost every down; in the Orkneys alone it is estimated that two thousand still remain; and in Denmark they are even more abundant; they are found all over Europe from the shores of the Atlantic to the Oural Mountains; in Asia they are scattered over the great steppes from the borders of Russia to the Pacific Ocean, and from the plains of Siberia to those of Hindostan; in America we are told that they are numbered by thousands and tens of thousands; nor are they wanting in Africa, where the pyramids themselves exhibit the most magnificent development of the same idea; so that the whole world is studded with these burial-places of the dead."--_Prehistoric Times_, p. 85. See similar remarks in Dr. Clarke's _Travels_, 4th edition, vol. i. p. 276, vol. ii. p. 75, etc.]

[Footnote 239: Sir J. Gardner Wilkinson thinks that the pyramids of Sakkara are probably older than the other groups of these structures, as those of Gizeh or the Great Pyramid erected during the fourth dynasty of kings.--See Rawlinson's _Herodotus_, vol. ii. chap. viii. Manetho assigns to Uenophes, one of the monarchs in the first dynasty, the erection of the Pyramids of Cochome. See Kenrick's _Ancient Egypt_, ii. p. 112, 122, 123; Bunsen's _Egypt_, ii. 99, etc.]

[Footnote 240: On these Archaic forms of sculpture, see APPENDIX, No. II. In many barrows the gallery in its course--and in some as it enters the crypt--is contracted, and more or less occluded by obstructions of stone, etc., which Mr. Kenrick likens to the granite portcullises in the Great Pyramid. See his _Ancient Egypt_, vol. i. p. 121.]

[Footnote 241: Mr. Birch, however--and it is impossible to cite a higher authority in such a question--holds the cartouches of Shufu and Nu Shufu to refer only to one personage--namely, the Cheops of Herodotus; and, believing with Mr. Wilde and Professor Lepsius, that the pyramids were as royal sepulchres built and methodically extended and enlarged as the reigns of their intended occupants lengthened out, he ascribes the unusual size of the Great Pyramid to the unusual length--as testified by Manetho, etc.--of the reign of Cheops; the erection of a sepulchral chamber in its built portion above being, perhaps, a step adopted in consequence of some ascertained deficiency in the rock chamber or gallery below. Indeed, the subterranean chamber under the Great Pyramid has, to use Professor Smyth's words, only been "begun to be cut out of the rock from the ceiling downwards, and left in that _unfinished_ state." (Vol. i. 156.) Mr. Perring, who--as engineer--measured, worked, and excavated so very much at the Pyramids of Gizeh, under Colonel Howard Vyse, held, at the end of his researches, that "the principal chamber" in the Second Pyramid is still undetected. See Vyse's _Pyramid of Gizeh_, vol. i. 99.]

[Footnote 242: The Mexican Pyramid of Cholula has a base of more than 1420 feet, and is hence about twice the length of the basis of the Great Pyramid of Gizeh. See Prescott's _Conquest of Mexico_, book iii. chap. i., and book v. chap. iv.]

[Footnote 243: Herodotus states that the Egyptians detested the memories of the kings who built the two larger Pyramids, viz., Cheops and Cephren; and hence, he adds, "they commonly call the Pyramids after Philition, a shepherd, who at that time fed his flocks about the place." They thus called the Second, as well as the Great Pyramid, after him (iii. Sec. 128); but, according to Professor Smyth, the Second Pyramid, though architecturally similar to the first, and almost equal in size, has nothing about it of the "superhuman" character of the Great Pyramid.]

[Footnote 244: The extracts within inverted commas, here, and in other parts, are from--(1.) Mr. John Taylor's work, entitled _The Great Pyramid--Why was it Built, and Who Built it?_ London, 1859; and (2.) Professor Smyth's work, _Our Inheritance in the Great Pyramid_, Edinburgh, 1864; (3.) his later three-volume work, _Life and Work at the Great Pyramid_, Edinburgh, 1867; and (4.) _Recent Measures at the Great Pyramid_, in the Transactions of the Royal Society of Edinburgh for 1865-66.]

[Footnote 245: Professor Smyth has omitted to state--what, after all, it was perhaps unnecessary to state--that one set of these measurements, which he has tabulated and published, viz., that given by Dr. Whitman, was taken for him "by a British officer of engineers;" as, when Dr. Whitman visited Gizeh, he did not himself examine the interior of the Great Pyramid.--See Colonel Vyse's work, vol. ii. p. 286.]

[Footnote 246: "Its contents," says Mr. Taylor (p. 299), "are equal in cubic inches to the cube of 41,472 inches--the cubit of Karnak--viz., to 71,328 cubic inches." Elsewhere (p. 304) he states--"The Pyramid coffer contains 256 gallons of wheat;"--"It also contains 256 gallons of water, etc."]

[Footnote 247: At a later meeting of the Royal Society, on 20th April, Professor Smyth explained that, among the numerous instruments he carried out, he was not provided with calipers fit for this measurement.]

[Footnote 248: See plate iii. Fig. 1, in his great folio work on the _Pyramids of Gizeh from Actual Survey and Admeasurement_, Lond. 1839. "The sarcophagus is," he remarks, "of granite, not particularly well polished; at present it is chipped and broken at the edges. There are not any remains of the lid, _which was however_, fitted on in the same manner as those of the other pyramids."]

[Footnote 249: "The western side," observes Professor Smyth, "of the coffer is, through almost its entire length, rather lower than the other three, and these have _grooves_ inside, or the remains of grooves once cut into them, about an inch or two below their summits, and on a level with the western edge; _in fact_, to _admit a sliding sarcophagus cover or lid_; and there were the remains of three fixing pin-holes on the western side, for fastening such cover into its place." (Vol. i. p. 85.)]

[Footnote 250: For age, etc., of Al Hakm, see Dr. Rieu in APPENDIX No. III.; and Jomard on length of the Sarcophagus, No. IV.]

[Footnote 251: In the original Arabic, the expression is "birdlike (or hieroglyphic) characters writ with a reed."]

[Footnote 252: See Greaves' _Works_, vol. i. p. 61 and p. 115. In Colonel Vyse's works are adduced other Arabian authors who allude to this discovery of a body with golden armour, etc., etc., in the sarcophagus of the King's Chamber; as Alkaisi, who testifies that "he himself saw the case (the cartonage or mummy-case) from which the body had been taken, and that it stood at the door of the King's Palace at Cairo, in the year 511" A.H. (See _The Pyramids of Gizeh_, vol. ii. p. 334). See also to the same effect _Abon Szalt_, p. 357; and Ben Abd Al Rahman, as cited in the _Description de l'Egypte_, vol. ii. p. 191. "It may be remarked," observes Dr. Sprenger in Colonel Vyse's work, "that the Arabian authors have given the same accounts of the pyramids, with little or no variation, for above a thousand years." (Vol. ii. p. 328.) See further APPENDIX, p. 270.]

[Footnote 253: See APPENDIX, No. VII.]

[Footnote 254: Our great Scottish architect, Mr. Bryce, believes that, with these data given, any well-informed master-mason or clerk of works could have drawn or planned and superintended the building.]

[Footnote 255: See Newton's _Essay_, in Professor Smyth's work, vol. ii. 360; and Sir Henry James' masterly _Memorandum on the Length of the cubit of Memphis_, in APPENDIX, No. V.]

[Footnote 256: Sir Isaac Newton says--"In the precise determination of the cubit of Memphis, I should choose to pitch upon the length of the chamber in the middle of the pyramid." Greaves gives this length 34.38 = 20 cubits of 20.628 inches.]

[Footnote 257: Yet this, the Memphian cubit, "need not" (somewhat mysteriously adds Professor Smyth), "and actually is not, by any means the same as the cubit _typified_ in the more concealed and _symbolised_ metrological system of the Great Pyramid."]

[Footnote 258: Godfrey Higgins, in his work on _The Celtic Druids_, shows how, among the ancients, superstitions connected with numbers, as the days of the year or the figures 365, have played a prominent part. "Amongst the ancients" (says he) "there was no end of the superstitious and trifling play upon the nature and value of numbers. The first men of antiquity indulged themselves in these fooleries" (p. 244). Mr. Higgins points out that the old Welsh or British word for Stonehenge, namely Emrys, signifies, according to Davies, 365; as do the words Mithra, Neilos, etc.; that certain collections of the old Druidic stones at Abury may be made to count 365; that "the famous Abraxas only meant the solar period of 365 days, or the sun," etc. "It was all judicial astrology.... It comes" (adds Mr. Higgins) "from the Druids."]

[Footnote 259: See this table in Professor Smyth's _Life and Work at the Great Pyramid_, vol. ii. p. 458. The table professes to give some of Sir Isaac Newton's data regarding the Sacred Cubit by changing the measurements which Sir Isaac uses of the Roman foot and inch into English inches. But all the figures and measurements are transferred into English inches by a different rule from that which Sir Isaac himself lays down--viz., that the English foot is 0.967 of the Roman foot; and, consequently, _in every one of the instances given_ in Mr. Smyth's table, the lengths in English inches of these data of Sir Isaac Newton are assuredly _not_ their lengths in English inches as understood and laid down by Newton himself.]

[Footnote 260: The fourth line in the table presents a most fatal and unfortunate error in a special calculation to which the very highest importance is professed to be attached. This fourth line gives the measurement of the Sacred Cubit as quoted by Newton from Mersennus, who laid down its length as 25.68 inches of Roman measurement. Professor Smyth changes this Roman measurement into 24.91 English inches, and then erroneously enters these same identical Roman and English measurements of Mersennus--viz., 24.91 and 25.68--not as _one_ identical quantity, which they are--but as _two_ different and contrasting quantities; and further, he tabulates this strange mistake as one of the "methods of approach" for gaining a correct idea of the Sacred Cubit. Never, perhaps, has so unhappy an error been made in a work of an arithmetical and mathematical character.]

[Footnote 261: Thus, after deducing the length of the cubit of Memphis from the length of the King's Chamber, Sir Isaac Newton observes:--"From hence I would infer that the Sacred Cubit of Moses was equal to 25 unciae of the Roman foot and 6/10 of an _uncia_." (See his _Dissertation on the Sacred Cubit_, as republished in Professor Smyth's _Life and Work at the Great Pyramid_, vol. ii. p. 362.) Again, at p. 363, Sir Isaac speaks of "the cubit which we have concluded to have been in the time of Moses 25-60/100 inches" of the Roman foot; and at p. 365, in closing his Dissertation, he remarks--"The Roman cubit therefore consists of 18 unciae, and the Sacred Cubit of 25-3/5 unciae, of the Roman foot." In other words, according to Sir Isaac Newton, the Sacred Cubit of 25.60 inches of the Roman foot is equal to 24.75 British inches; for, as he calculated, the Roman foot "was equal to 967/1000 the English foot." (See p. 342.) This is the measurement of the Roman foot laid down by Sir Isaac Newton in his Dissertation, and the only standard of it mentioned in Professor Smyth's _Life and Work at the Great Pyramid_; yet in that work Professor Smyth calculates Sir Isaac's Sacred Cubit to be 24.82 instead of 24.75 British inches. In doing so, he has calculated the English foot as equal to .970 of the Roman foot; but was he entitled to do so when using Sir Isaac's own data, and when employing Sir Isaac's own calculated conclusion as to the length of the Sacred Cubit? In the published _Proceedings_ of the Royal Society, in consequence of following the calculation by Professor Smyth of Sir Isaac Newton's conclusion from Sir Isaac's own data as to the length of the Sacred Cubit, it was erroneously spoken of as 24.82, instead of 24.75 British inches.]

[Footnote 262: This word "extraordinarily," was, by a clerical or printer's error, spelled "extraordinary" in the _Proceedings_ of the Royal Society; and a friend who looked over the printed proof, and suggested two or three corrections, placed the word (sic) on the margin after it, from whence it slipped into the text:--accidents to be much regretted, as, from Professor Smyth's remarks to the Society on the 20th April, they had evidently given him much, but most unintentional offence.]

[Footnote 263: At the close of a subsequent meeting of the Royal Society, on the 20th April 1868, Professor Smyth gave away a printed Appendix to his three-volume work, in which he has acknowledged the erroneous character--as pointed out in this communication--of his all-important table, p. 22, on the length of the Sacred Cubit, by withdrawing it, and offering one of a new construction and character, but without being able to make the length of the cubit come nearer to his theory. See further, APPENDIX, No. VI]

[Footnote 264: _Traite de la Grandeur et de la Figure de la Terre._ Amsterdam edition (1723), p. 195.]

[Footnote 265: _Tables Portatives de Logarithmes._ Paris, 1795, p. 100.]

[Footnote 266: The same idea of using the earth's axis as a standard of length has been suggested also by Professor Hennessy of Dublin, and by Sir John Herschel. See _Athenaeum_ for April 1860, pp. 581 and 617.]

[Footnote 267: The diameter of the earth in latitude 30 deg. is really about 20 miles longer than the polar axis. But Mr. Taylor obviously did not know the nature of the spheroidal arcs of the meridian, and so falls into the most inconsistent assertions respecting the length of this particular diameter. Thus, in pp. 75 and 87, he asserts the diameter in latitude 30 deg. to be 500,000,000 inches [that is = 7891.414 miles], which is 7.756 miles _less_ than the polar axis--_the least_ diameter of all; whereas, in p. 95, he states this diameter in lat. 30 deg. to be 17.652 miles _greater_ than the polar axis.]

[Footnote 268: "The diameter of the earth, according to the measures taken at the Pyramids, is 41,666,667 English feet, or 500,000,000 inches." (See _The Great Pyramid_, p. 75.) "Dividing this number by 20,000,000 we obtain the measure of 25 (English) inches for the Sacred Cubit" (p. 67).]

[Footnote 269: "When" (says Mr. Taylor, p. 91) "the _new_ Earth was measured in Egypt after the Deluge, it was found that it exceeded the diameter of the _old_ Earth by the difference between 497,664,000 inches and 500,000,000 inches; that is, by 2,336,000 inches, equal to 36.868 miles."]

[Footnote 270: _Alleged Sacred Character of the Scottish Yard or Ell Measure._--Professor Smyth tries to show (iii. 597), that if Britain stands too low in his metrological testing of the European kingdoms and races, its "low entry is due to accepting the yard for the country's popular measure of length." But long ago the "divine" origin of the Scottish ell--as in recent times the divine origin of the so-called pyramidal cubit and inch--was pleaded rather strenuously. For when, in the 13th century, Edward I. of England laid before Pope Boniface his reasons for attaching the kingdom of Scotland to the Crown of England, he maintained, among other arguments, the justice and legality of this appropriation on the ground that his predecessor King Athelstane, after subduing a rebellion in Scotland under the auspices of St. John of Beverley, prayed that through the intervention of that saint, it "might be granted to him to receive a visible and tangible token by which all future ages might be assured that the Scots were rightfully subject to the King of England. His prayer was granted in this way: Standing in front of one of the rocks at Dunbar, he made a cut at it with his sword, and left a score which proved to be the _precise_ length of an ell, and was adopted as the regulation test of that measure of length." This legend of the "miraculously created ellwand standard" was afterwards duly attested by a weekly service in the Church of St. John of Beverley. (See Burton's _History of Scotland_, ii. 319.) In the official account of the miracle, as cited by Rymer, it is declared that during its performance the rock cut like butter or soft mud under the stroke of Athelstane's sword. "Extrahens gladium de vagina percussit in cilicem, quae adeo penetrabilis, Dei virtute agente, fuit gladio, quasi eadem hora lapis butirum esset, vel mollis glarea; ... et usque ad presentem diem, evidens signum patet, quod Scoti, ab Anglis devicti ac subjugata; monumento tali evidenter cunctis adeuntibus demonstrante." (Foedera, tom. i. pars ii. 771.)]

[Footnote 271: Elsewhere (p. 45) Mr. Taylor corroborates Sir Isaac Newton's opinion that the _working_ cubit by which the Pyramid was built was the cubit of Memphis.]

[Footnote 272: The interior of any Scottish cottage, where the inside of the thatched or slated roof is left exposed by uncovered joists within, contains, on the same principle, six sides, and a seventh or the floor.]

[Footnote 273: "The _clue_ was not prepared for any immediate successors of the builders, but was intended, on the contrary, to endure to a most remote period. And it has so endured and served such a purpose even down to those our own days." (Professor Smyth's _Life and Work at the Great Pyramid_, vol. i. p. 157.) "The builders, or planners rather, of the Great Pyramid, did not leave their building without sure testimony to its chief secret; for there, before the eyes of all men for ages, had existed these _two diagonal joints_ in the passage floor, pointing directly and constantly to what was concealed in the roof just opposite them, and no one ever thought of it. Practically, then, we may say with full certainty that these two floor marks were left there to guide _men_ who, it was expected, would come subsequently, earnestly desiring, on rightly-informed principles, to look for the entrance to the upper parts of the Pyramid." (Vol. i. p. 156-7.) At p. 270 Professor Smyth again alludes to this supposed mark, made up by two diagonal joints in the passage floor, as evading the notice of all visitors, except "those very few, or perhaps even that _one only man_, who had been previously instructed to look for a certain almost microscopic mark on the floor."]