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° 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°—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°, 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.