Before the corner sockets were exposed, Professor Smyth attempted to measure the bases, and made each side of the present masonry courses "between 8900 and 9000 inches in length," or (to use his own word) "about" 8950 inches for the mean length of one of the four sides of the base; exclusive of the ancient casing and backing stones—which last Colonel Howard Vyse found and measured to be precisely 108 inches on each side, or 216 on both sides. These 216 inches, added to Professor Smyth's measure of "about" 8950 inches, make one side 9166 inches. But Professor Smyth has "elected" (to use his own expression) not to take the mathematically exact measure of the casing stones as given by Colonel Vyse and Mr. Perring, who alone ever saw them and measured them (for they were destroyed shortly after their discovery in 1837), but to take them, without any adequate reason, and contrary to their mathematical measurement, as equal only to 202 inches, and hence "accept 9152 inches as the original length of one side of the base of the finished pyramid." He deems, however, this "determination" not to be so much depended upon as the measurements made from socket to socket.
The mean of the only four series of such socket or casing stone measures as have been recorded hitherto by the French Academicians (9163), Vyse (9168), Mahmoud Bey (9162), and Inglis (9110), amounts to nearly 9150. The first three of these observers were only able to measure the north side of the pyramid. Mr. Inglis measured all the four sides, and found them respectively 9120, 9114, 9102, and 9102, making a difference of 18 inches between the shortest and longest. Professor Smyth thinks the measures of Mr. Inglis as on the whole probably too small, and he takes two of them, 9114 and 9102—(but, strangely, not the largest, 9120)—as data, and strikes a new number out of these two, and out of the three previous measures of the French Academicians, Vyse, and Mahmoud Bey; from these five quantities making a calculation of "means," and electing 9142 as the proper measure of the basis line of the pyramid—(which exact measure certainly none of its many measurers ever yet found it to be); and upon this foundation, "derived" (to use his own words) "from the best modern measures yet made," he proceeds to reason, "as the happy, useful, and perfect representation of 9142," and the great standard for linear measure revealed to man in the Great Pyramid. Surely it is a remarkably strange standard of linear measure that can only be thus elicited and developed—not by direct measurement but by indirect logic; and regarding the exact and precise length of which there is as yet no kind of reliable and accurate certainty.
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 unciæ 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.