The standard in the Great Pyramid, according to Messrs. Taylor and
Smyth, for _linear_ measurements, is the length of the base line or
lines of the pyramid. This, Professor Smyth states, is "_the function
proper of the pyramids base_." It is professed also that in this base
line there has been found a new mythical inch--one-thousandth of an
inch longer than the British standard inch; and in the last sections of
his late work Professor Smyth has earnestly attempted to show that the
status of the kingdoms of Europe in the general and moral world may be
measured in accordance with their present deviation from or conformity
to this suppositious pyramidal standard in their modes of national
measurement.[253] "For the linear measure" (says Professor Smyth) "of
the base line of this colossal monument, viewed in the light of the
philosophical connection between time and space, has yielded a standard
measure of length which is more admirably and learnedly
earth-commensurable than anything which has ever yet entered into the
mind of man to conceive, even up to the last discovery in modern
metrological science, whether in England, France, or Germany."
The engineers and mathematicians of different countries have repeatedly
measured arcs of meridians to find the form and dimensions of the earth,
and the French made the metre (their standard of length), 1/10,000,000
of the quadrant of the meridian. Professor Smyth holds that the basis
line of the pyramid has been laid down by Divine authority as such a
guiding standard measure.
* * * * *
_What, then, is the exact length of one of its basis lines?_ The sides
of the pyramid have been measured by many different measurers. Linear
standards have, says Professor Smyth, "been already looked for by many
and many an author on the sides of the base of the Great Pyramid, even
before they knew that the terminal points of those magnificent base
lines had been carefully marked in the solid rock of the hill by the
socket-holes of the builders." But--as in the case of the cubic
capacity of the coffer--these measurers sadly disagree with each other
in their measurements, which, in fact, vary from some 7500 or 8000
inches to 9000 and upwards. Thus, for example, Strabo makes it under 600
Grecian feet, or under 7500 English inches; Dr. Shawe makes it 8040
inches; Shelton makes it 8184 inches; Greaves, 8316; Davison, 8952:
Caviglia, 9072; the French academicians, 9163; Dr. Perry, 9360, etc.,
etc.
At the time at which Professor Smyth was living at the Pyramids, Mr.
Inglis of Glasgow visited it, and, for correct measurement, laid bare
for the first time the four corner sockets. Mr. Inglis's measurements
not only differed from all the other measurements of "one side" base
lines made before him, but he makes the four sides differ from each
other; one of them--namely, the north side--being longer than the other
three. Strangely, Professor Smyth, though in Egypt for the purpose of
measuring the different parts of the pyramid--and holding that its base
line ought to be our grand standard of measure, and further holding that
the base line could only be accurately ascertained by measuring from
socket to socket--never attempted that linear measurement himself after
the sockets were cleared. These four corner sockets were never exposed
before in historic times; and it may be very long before an opportunity
of seeing and using them again shall ever be afforded to any other
measurers.
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 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]