(ENDNOTE 4 Continues)
It would be left to David Davidson in the 1920s, long after Petrie and others had decimated Smyth’s reputation, to demonstrate the “authentic example” which Petrie claimed didn’t exist.
Now, as seen in the last line of explanation in the above illustration, Davidson made three measurements of a Pyramid’s side. (It is important to remember that the points A,B,C,D are not exactly the same for Petrie and Davidson.) Two of these measurements Davidson physically measured; a third measurement was extrapolated based on where legs BG and CH would meet (at d) if they continued. Davidson then showed that these three ways of
measuring the perimeter led to an amount of cubits per side which represented the three types of years. The solar year is a little less than 365¼ days, the sidereal year a little more than 365¼ days, and the anomalistic year just a little longer than the sidereal year.
But how close do Davidson’s three measurements actually come to representing the three types of years?
Davidson, like Taylor and Smyth before him, believed that the basic unit of measurement along a base’s side was barely over 25.” The exact figure Davidson gave was 25.0275” (i.e. British inches), 1/10,000,000th of the polar radius of the earth as calculated at that time. (Today’s figure is not much different, at 25.0265 B.”) Davidson believed that the British inch, as well as certain other nations’ inch, had their origin in the type of inch used in the Great Pyramid, or 1/25th of 25.0275 B.,” derived from 1/25th of a sacred (or biblical) cubit. Thus Davidson’s Pyramid inch = 1.0011 of a British inch. Incidentally, since Davidson believed 25 such Pyramid inches were equal to 1/10,000,000th of the polar radius of the earth, he notes that 500,000,000 Pyramid inches was the diameter of the earth measured from its poles.
Davidson’s three measurements representing the three types of years are based on the following perimeters as measured in pyramid inches, with each perimeter then divided by 25 for the number of cubits in the perimeter and then divided by 4 for the amount of cubits per side (which represent the amount of days in the year). The same amount of cubits can result by taking the number of inches in the perimeter and dividing by 100. The three
measurements of the perimeter follow the points ABCD for the solar year, AEFBGHCJKDPR for the sidereal year, and AaBbCcDd for the anomalistic year.
Again, Davidson converted the
amount of British inches in these three types of geometric perimeters to Pyramid inches, and showed that they corresponded to the amount of days in the three types of years, based on 100 Pyramid inches
to the day.
Here are the three measurements Davidson used, based on Petrie’s distances surveyed from the outer corner sockets. ABCD is 36,524.2465 P.” (Pyramid inches). But we need to make an adjustment for the fact that the more-accurately measured polar radius of the earth today is 25.0265 B.” rather than the 25.0275 B.” used by Davidson. Davidson believed 1 P.” = 1.0011 B.”’ whereas the present value is 1 P.” = 1.00106 B.” And so we take Davidson’s number of Pyramid inches and multiply by 1.0011 to see what amount of B.” he began with, which was 36,564.42317 B.” Then we divide this number by today’s corrected value of 1.00106, which yields 36,525.70217 P.” We divide this number by 25 to get 1,461.0280868 sacred cubits for the perimeter, and divide this by 4 to get the number of cubits per side, which is 365.2570217. The cubits per side can thus also be calculated by taking 36,525.70217 P.” and diving by 100 (pyramid inches to the day) to get 365.2570217 cubits, representing the number of days in the solar year. But 365.2570217 days is slightly more than the present value of 365.2421891 days in a solar year. So we subtract the latter number from the former to get a difference of .0148326 of a day. We multiply this number by 86,400 seconds in a day to get 1,281.5 seconds. Since each pyramid inch represents 1/100th of 86,400 seconds, or 864 seconds, we divide 1281.5 seconds by 864seconds to get (what is represented by) 1.48 pyramid inches error for the entire perimeter. And so the error for one side of the Pyramid is 1.48 ÷ 4, or .3718 of a P.” per side. We multiply this by 1.00106 to get .3712 of 1 B.” more per side. This is a remarkably close measurement when one considers that a side of the Pyramid is 9,141.1 B.” The margin of error is only 1 part in 24,000.
The measurements for the sidereal and anomalistic years are figured accordingly. Davidson gives 36,525.6471536 P.” for the sidereal year (AEFBGHCJKDPR ). Subjecting this number to the same equations in the above paragraph in relation to the days in a sidereal year, result in .368 of a B.” more per side.
Finally, we have the anomalistic year. Davidson gives 36,525.997317 P.” After doing the same calculations as for the solar and sidereal years, the result is .374 of a B.” more per side.
The error of the three measurements for the Pyramid’s side is thus 3/8 of a B.”, i.e., 3/8” over the length of 2.5 American football fields. This incredible accuracy of three measurements in relation to the solar, sidereal, and anomalistic years, respectively, is why Davidson was able to justly claim that the New Construction was beyond coincidence, and therefore Divinely imparted to human agency. And thus Davidson redeemed the views of Taylor and Smyth, insofar that they believed a biblical cubit of just over 25” was the basic unit of measurement in constructing
the Great Pyramid. Moreover, the fact that all three measurements are 3/8” more than the years they represent, yet within 1/150th of an inch of each other, suggests that the original measurements were not in error at all, especially given that the Great Pyramid has experienced earthquakes that may have had a slight effect on the measurements. Or the measurements may actually represent the length of year at the time of the Pyramid’s construction, or else perhaps be a prophetic anticipation of the length of a year at a particular point in the future.
Finally, we return to an issue mentioned earlier, of the outer limestone casing of Menkaure’s pyramid. Here the limestone casing ‘‘erased’ the middle crease and pushed the limestone out to its four corners (A,D,C,D, so to speak), and thus did not mirror the hollowing-in of the base core masonry. Skeptics have used this example to try to discredit Davidson’s view that the outer limestone casing of the Great Pyramid would have been similar. But to do so is an apples to oranges comparison. First, only the Great Pyramid among all pyramids (including Menkaure’s) has a perimeter and a height which corresponds to the earth’s circumference and its polar radius, thus demonstrating π. Second, only the Great Pyramid has numerous chambers and passageways some of which reflect the basic unit of measurement—the sacred cubit—incorporated throughout the structure, and certainly used in all three base perimeter measurements. Third, Menkaure’s pyramid does not demonstrate the exact kind of hollowing-in effect of the Great Pyramid, which in the Great Pyramid comes down from the top in a single ‘crease’ but then broadens out in the lower courses such that a section in the middle of the sides are parallel to the AB, BC, CD, and DA sides (see illustration above which shows the Base Core Masonry), which in turn yields, at the Pyramid’s base, a length of cubits per side which correspond to the number of days in a sidereal year. Thus while Menkaure’s base core masonry supports the idea that its designers incorporated a similar (though not exact kind of) ‘crease’ found in the Great Pyramid, Menkaure’s pyramid demonstrates none of the Great Pyramid’s startling results, and so is really nothing more than a large tomb marker with little else than a single room to house a dead king.
One note of addendum here: Since in Chapter 3 I quote
Velikovsky’s extensive proofs of a 360-day year existing as late as the 8th century BC, I interpret the Great Pyramid’s measurements showing solar, sidereal, and anomalistic years as prophetic, since the Great Pyramid was constructed centuries or millennia earlier. As to who designed it we do not know. However, an educated guess might be Joseph, since God had shown that he gave Joseph information about the future in other dreams, and because Jospeh/Imhotep was known to the Egyptians in connection with building. If true, this does not necessarily mean the design was carried out in Joseph’s lifetime, nor for whom he may have intended it, if indeed it was intended for anyone. The design may have been a mere exercise in mathematics, with no intended use. Mainstream Egyptian chronologists believe it was built by Khufu in the 4th Dynasty. If this is the case, then the building came after Joseph, who lived during the 3rd Dynasty.
5 I share with readers an April, 2012 email to my brother regarding the “Darius cubit.” It is possible this cubit was also used by Darius’ predecessors, including Cyrus. The cubit is slightly longer than 13,” thus a little more than half the length of the sacred cubit of 25.0265.” Interestingly, bricks in Babylon measured 13 inches, and so perhaps the so-called Darius cubit was derived from this basic architectural element incorporated into that city.
As for what led me to research possible Persian cubits, I had for some time puzzled over a description in Ezra 6, where Darius quotes Cyrus’ permission that the Jewish Temple’s walls be rebuilt up to 60 cubits in height. This seemed odd to me, since Solomon’s walls are recorded as only 30 cubits in height. But when I found that there was a Persian cubit of just over 13 inches, the answer practically suggested itself:
Hi Dave,
Just found some possibly interesting info on the cubit. Darius the Great, who was king after Cyrus and Cambyses and ruled somewhere around 521 BC to 486 BC, is associated with a 33.60 cm royal cubit. This works out to 13.228+ inches. And so IF this were the same cubit used by Cyrus (can’t determine this for sure, though I have found no other cubit associated with Cyrus), then when Darius is stating that Cyrus gave permission for the Temple walls to be 60 cubits, it’s possible that Cyrus was rounding up to the nearest multiple of 10, and even of 5. In other words, Solomon’s 30-cubit high walls, assuming they are sacred cubits of 25.0265,” equal 750+ inches. 60 cubits at Darius’ cubit of 13.228 is about 794 inches. So Solomon’s temple walls would require 56.76 ‘royal’ cubits of Darius. So if Cyrus used the same royal cubit as Darius, then he simply gave a number that allowed for enough height to equal the former walls of Solomon.
I know this will excite you, though, of course it seems we can’t say for sure whether Cyrus’ cubits were the same as Darius’. But I think an argument could be made that Darius’ quotation of Cyrus without further explanation suggests that the cubit lengths were the same.
6 (See my brother’s calculations on the diagram of Solomon’s Sea, showing the golden ratio.)
Incidentally, in biblical measures 6 handbreadths = a profane cubit, and 7 handbreadths = a sacred (biblical) cubit. The measurements for Solomon’s Sea are 5 cubits deep and 10 cubits in diameter. This book presumes these are interior measurements referencing (1) total water capacity of 3000 baths if the Sea were completely filled; and (2) normal-use capacity of 2000 baths (I Ki. 7:26) for Temple use. The cast bronze [hemisphere] is stated to be one handbreadth thick.
7 During my blogging on websites about this book’s various points—theological, philosophical, and scientific—no other point received more derisive mocking than the sacred cubit’s use in Solomon’s Bronze Sea and the biblical bath’s volumetric connection to a “mole” in the metric system. Typical of the comments were “Oh, my! Apparently someone slept through the high school chemistry class that talked about….” Another fellow wanted to know if Solomon carried around a huge basin at sea level and waited for a certain degree centigrade, so that he would know the exact volumetric space of a biblical bath. This is because I had related my brother’s view that a biblical bath in Solomon’s Sea occupied the same volumetric space as a mole of ideal gas at standard temperature and pressure. And since a “mole” was interpreted by our critics as exclusively a metric system measurement, they wanted to know how Solomon anticipated the metric system by 3,000 years! It was necessary, therefore, for David to inform these critics that merely cubing the diameter of any hemisphere and multiplying by three would give the volume of a hemisphere in baths or ephahs (i.e., the basic unit of biblical measurement for liquid and dry measures), provided cubits equal to 1/10,000,000th of the earth’s polar radius were used in measuring the diameter. In essence, God would not have needed to go into all the scientific details, but merely to have given Moses the right length rod and the above straight-forward formula. (It should be remembered that “Moses was learned in all the wisdom of the Egyptians” (Acts 7:22), which would have included mathematics.) Additionally, my brother was compelled to explain the history of the metric system to these critics. Dave’s detailed explanation of the matter is below. In essence, Dave’s complaint is that metricists behave as if Avogadro’s number could not have been discovered unless the metric system was around to give it a name:
Re: Avogadro’s number: When scientists measured the atomic weights of all the chemical elements according to the original definition of a gram, no atomic weight of any element came out to an exact integer. Therefore when all the atomic weights of the elements were arbitrarily changed, it led to the misconception that Avogadro’s number was changed in order to make all the atomic weights different. This is not true. The changes in the atomic weights of all the elements can be likened to the turning of the adjustment screw on a weight scale. When this is done, everyone who gets on the scale weighs differently than before the adjustment screw was turned, but the number of atoms in their bodies has remained the same. No one has really changed in actual weight; only the scale reading of each one’s weight has been changed. In like manner, the adjustment screw was turned (so to speak) on all the atomic weights twice; once when oxygen was arbitrarily set as Avogadro’s number of oxygen atoms and declared to weigh exactly 16 grams (ca. the 1940s), and again later (ca. the 1970s), when Avogadro’s number of carbon atoms was arbitrarily set at weighing exactly 12 grams. (The reason for the change from oxygen to carbon was because it was thought spectroscopy promised a greater field of experimentation.) At the time of this writing, even Wikipedia—the most frequently consulted source of general information— doesn’t mention how these changes in the atomic weights
automatically changed the original definition of a cubic centimeter of water as a mass of one gram at 4°C, and so leaves readers to infer that Avogadro’s number is miraculously defined by an exact integer of grams of a specific element, giving an inflated status to the metric system. Further, when the oxygen standard was abandoned (ca. the 1940s) and Avogadro’s number of carbon atoms was arbitrarily set at exactly 12 grams, it again necessitated changing all the other atomic weights. I have an older chemistry text book from my student days which actually bothers to give the formula used to make the second change. (Old atomic weight) = (1.000043) x (new atomic weight)
So while it is now defined that 12 grams of carbon is a mole (i.e. Avogadro’s number of atoms), a statement technically true, this definition can be confusing because it incorrectly implies that Avogadro’s number is miraculously defined by an exact integer weight in grams of a specific element. Again, this gives an inflated status to the metric system, and masks the fact that it is Avogadro’s number which ultimately defines a “mole,” not the declared atomic weight of some arbitrarily chosen element.
So although the scale reading of the atomic weights of the elements was changed twice for various reasons, Avogadro’s number itself never changed (except slightly because of better precision in modern instrument measurements).
Now, it is shown by the ideal gas equation that Avogadro’s number of ideal gas molecules, unlike the real molecules in an actual gas, have no weight nor size, but only take up space by the movement imparted to them by temperature and pressure. Because Avogadro’s number of oxygen atoms is now declared to weigh 15.9994 grams, when it was formerly declared exactly 16 grams, we reiterate it is false to suppose there has been a change to Avogadro’s number, when in reality it is only the atomic weights of all the elements that were artificially changed.
A further analysis of the ideal gas equation shows that all this playing around with the atomic weights did not affect the value of Avogadro’s number nor the volume of one mole (i.e., what should be called one mole) of an ideal gas at STP for the following reasons. The first term of the ideal gas equation is “n” and stands for the number of moles of an ideal gas. The second term is 6.022045 x 1023 / mole. When the presently accepted value for one mole, namely “12 grams of carbon” is substituted into the first and second terms and are multiplied together, the numerator of the first term and the denominator of the second term cancel each other out. Thus the vaunted definition by metric enthusiasts of “12 grams of carbon” for a mole cancels out, leaving just Avogadro’s number as the product of the first two terms. Taking 16 grams of oxygen for a mole instead of 12 grams of carbon per mole would likewise cancel out. Indeed, any unit of weight that is declared to be a mole will cancel out when substituted into the ideal gas equation. In short, this shows that Avogadro’s number is not dependent upon the development of any particular system of weights and measures, including the metric system.
8 these skeptics assuming, as they must, that all such 360-day calendars used intercalation. In other words, they do not believe 360-day calendars ever represented a 360-day orbit of the earth. I actually came across the same problem with a ‘reveiwer’ at a prominent creationist website, who refused to address in any detail Velikovsky’s research, yet kept insisting the type of year since creation was the same as the present one of today. Not surprisingly, he claimed the details of calendar intercalation from the time of Genesis had been “lost.” Apparently the felt-need for uniformitarian assumptions afflicts certain young-earth creationists as much as old- earth evolutionists.
9 One young-earth creationist explanation is that massive electrical currents keep the ‘starfish’ arms in relative place.
10 such as alleged universe-producing ‘machines’ to discount the mathematical odds against evolution.
11 http://www.ancient-hebrew.org/
12 Incidentally, the biblical meaning of “Hekhal” seems restricted to the meaning of “Temple” (or “temple”), though in one instance (I Kings 6:16-17) it appears to mean the Holy Place only, in front of the Holy of Holies. In 70 of 80 occurrences of the word, the KJV translates it “temple,” otherwise it is rendered “palace.” However, wherever it has been rendered “palace” the context may just as easily mean “temple.”
13 Josephus agrees with this east to west description of a floor plan with an inverted “T” shape (though with 20-cubit ‘shoulders’ along the front, and as opposed to sloping or narrowing of the ‘stem’ part of the “T” toward its western end. The shoulders mentioned by Josephus are the broad and horizontal part of the “T” extending north and south along the front, behind which ran the stem of the “T” at a constant width. Says Josephus (V, 5, 4):
- 4. As to the holy house itself, which was placed in the midst [of the inmost court], that most sacred part of the temple, it was ascended to by twelve steps; and in front its height and its breadth were equal, and each a hundred cubits, though it was behind forty cubits narrower; for on its front it had what may be styled shoulders on each side, that passed twenty cubits further.
14 I feel the need to become personal with the reader for a moment. Having had to drive out-of-state to obtain a copy of Kaufmann’s article in the March/April ’83 issue of Biblical Archaeology Review (BAR) at a university library (an article I pursued because an atheist brought up Kaufman’s work on a discussion thread in an attempt to debunk the 25” sacred cubit), only to find Kaufman’s arguments rather Origen-like in their bizarreness, I have to confess that the whole matter put me into an ill-humor. And so any desire I once might have had to put forth a likewise effort to track down the writings of either Bahat/Ritmeyer or Sagiv, who, like Kaufman, locate the Temple on the Haram esh-Sharif, has left me. And so, frankly, I leave the fuller reproof of these others to someone cleverer than I, who will know either how to be remunerated for the time and expense it will take, or how to apply it to some practical end, such as a thesis or a degree. For despite my tendency to be a ‘complete-ist’ who wants to track down every main objection by every main antagonist so that it might be answered, I find that as I get older I don’t have the emotional stamina for such tasks. It is hard for me to express to the reader, if he has never engaged skeptics’ arguments, the process of coming across what at first are often plausible-sounding disputes by critics, which at length prove much shallower than when they first appeared, yet to expect of one’s self that the whole weary process of proving such arguments false ought to be to repeated ad infinitum ad nauseam. Much study is a weariness of the flesh, and fresher blood is needed. And so I won’t be baited (by myself, too) toward feeling much need to address these others besides Kaufman, whose ideas are likewise contrary to Martin’s. The lesson I am slowly learning is, even for the Christian apologist faith must “come by hearing, and hearing by the word of God,” and so not by ceaseless apologetic engagement. “Be still,” says the Lord, “and know that I am God.”
15 Some claim that what is attributed to Hecataeus was actually an edited version by Hellenized Jews of something written by the 3rd century BC Egyptian historian, Manetho. But even if this were the case, the point is irrelevant to our argument, except to point out that Manetho lived about a century later than Hecataeus.
16 In 1871 Clermont-Ganneau excavated one of the stones mentioned by Josephus which were posted to keep Gentiles out of forbidden zones. The seven-line inscription reads: “NO FOREIGNER/ IS TO GO BEYOND THE BALUSTRADE/ AND THE PLAZA OF THE TEMPLE ZONE/ WHOEVER IS CAUGHT DOING SO/ WILL HAVE HIMSELF TO BLAME/FOR HIS DEATH/ WHICH WILL FOLLOW.” Of course, unlike Hezekiah’s inscription affixed to the tunnel, Clermont-Ganneau’s excavated stone was separated from its original construction, or else had been a stand-alone sign.
Incidentally, some have rejected a southern Temple location at Gihon because of Ezekiel’s description (10—
11) of the glory of the Lord departing in what appears to have been a straight easterly direction, from the Holy of Holies to the Temple threshold, to the eastern gate, to the Mount of Olives. Some infer from Ezekiel’s description that the Lord departed over to the highest point on the Mount of Olives. However, Ezekiel does not say that the glory of the LORD departed over to the highest point of the mountain east of the city, but simply over the mountain east of the city. The ridge that runs along the top of the Mount of Olives becomes lower in
elevation as one goes south. But it is still the top of the Mount of Olives that lay east of the old City of David. The idea that the Temple was opposite the highest point of the Mount of Olives may sound more romantic and dramatic to us, because we like to imagine Christ looking down upon the City from the highest point on the Mount of Olives. But the idea has no explicit biblical support. Therefore the argument that the Temple must lay directly west of the highest point of the Mount of Olives is unsustainable.
Another statement for the Temple’s location is found in I Chronicles 22:1: “Then David said, “This [the threshing floor of Ornan the Jebusite] will be the house of the LORD God, and this will be the altar of burnt offering for Israel.” Now recall that the tent erected over the altar at Ornan’s threshing floor was at Gihon. And note, too, that immediately after I Chronicles 22:1 the Scripture states that David put stonemasons to work in preparing materials for the house of God. So the “house” was the future Temple, not David’s tent.
Another objection may be that Ornan’s threshing floor, which marks the Temple’s location, would not have been located at as high an elevation as the Dome of the Rock, to take advantage of hilltop winds to blow away the chaff. But since in Ornan’s time the Dome of the Rock area had not been leveled off into the Moriah Platform, the original land below the fill-in which now forms the Platform has (presumably) always been of rough rock, like the outcropping of rock located at the Dome of the Rock, and therefore an unlikely place for a threshing floor, though admittedly the craggy rock could have been cut to smoothness or built up to a level area to accommodate a threshing floor. Yet, again, all this ignores the evidence of Solomon’s Temple at or close by the Gihon Springs. But besides the Dome of the Rock area, there is another solution. For a windy area could also have existed in the concave depression that lay between the summits of the original city and the Ophel Mound (which lay above the Gihon Springs). David, and later, Solomon, began filling in this area (thus “millo” or “filling in”) after the Jebusite city became the Jerusalem of David. But before this filling-in was completed, the concave depression which (we contend here) served as the location of Ornan’s threshing floor would have funneled Jerusalem’s prevailing westerly winds (during wheat harvest) into the Kidron Valley/Brook. (Incidentally, Zion was at a higher elevation in David’s time, since the hill was later cut down in the 2nd century BC. This means the concave depression in David’s time was even more of a depression and funnel.)
Now, the Bible also tells us that Ornan was threshing wheat with oxen when the destroying angel from the Lord halted above Ornan’s threshing floor. Perhaps the site of beasts of burden and the crushing of kernels to obtain life-giving substance reminded God of his desire to send an obedient Servant who would be crushed for his people so that they might live, and so God relented. “…He was crushed for our iniquities…” says Isaiah (53:5). At any rate, in the Jerusalem area wheat is harvested in May and threshed afterward, mostly in. Examining average daily temperature ranges in Jerusalem for each month (which affects wind speed), as well as the de facto average monthly wind speed, reveals that June and July both average to the windiest of all Israel’s harvest months (April through November) at 11 mph (NW), and that May and June have the widest average daily temperature range at 19º. And so the declining sun on the mountain ridges above the Kidron would presumably have created winds that fell and funneled through the concave depression, moving NW to SE until they fell over into the steep Kidron Valley below. The point here is that a threshing floor in a concave depression between the summits of the original city and the Ophel Mound would have experienced sufficient winds to make possible a threshing floor, given the climate and contour of the original city at the time of the pestilence, thus reinforcing the view that this was where the temple was ultimately built. Incidentally, Chapter 6 will show how the sundial miracle in Hezekiah’s time means the equinoxes and solstices prior to the Hezekiah miracle, i.e., in David’s time, came earlier in the year by an average of 38 days, all things being equal. This does not affect the above information about months and their wind speeds per se; except that wheat threshing and all weather phenomena mentioned above fell earlier in the year (assuming the climatic cycle did not change for other reasons).
17 The Academy’s attitude toward the Bible has certainly changed over the centuries. As Piazzi Smyth points out, even so august a mathematician as Sir Isaac Newton bothered to ascertain the sacred cubit. Newton listed numerous ways of estimating its value, and believed this same cubit was used by the Hebrews in constructing the tabernacle of Moses and the temple of King Solomon. He believed it could be calculated
1. By notions from Talmudists and Josephus in terms of Greek cubits, which on calculation give as limits something between 24 and 24.30 British inches.
2. From Talmudists by proportion of the human body, giving as limits, from 94 and 23.28 British inches.
3. From Josephus’ description of the pillars of the Temple, between 16 and 23.28 British inches.
4. By Talmudists and all Jews’ idea of a sabbath day’s journey, between 16 and 23.28 British inches.
5. By Talmudists’ and Josephus’s accounts of the steps to the Inner Court, between 19 and 23.28 British inches.
6. By many Chaldaic and Hebrew proportions to the cubit of Memphis, giving 83 British inches.
7. From a statement by Mersennus, as to the length of a supposed copy of the sacred cubit of the Hebrews, secretly preserved amongst them, and concluded equals 24.9.
Newton’s final estimate of the sacred cubit was 24.88”, not far from the proper value of 25.0265”.