Chapter 21

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.]