Here is the link to an article I recently finished and posted:

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Here are a few excerpts and comments:

The title of the article is: The Measure of the Remen and the Royal Cubit and the Meridian of Egypt and the Earth

‘The area of one square royal cubit is double the area of one square remen. The linear measure of one royal cubit is equal to the linear measure of the remen times the square root of two. Evidence suggests that the remen was the original measure, from which the royal cubit was derived. Given .5238 meters, or 20.62 inches, for the length of the royal cubit, the length of the remen is .3704 meters or 14.58 inches. The meridian circumference of the earth is 40,008,000 meters or 111,133 meters per average degree of latitude. 300,000 remen times .3704 equals 111,120 meters. 5000 remen equals one minute of latitude and 500 remen equals one tenth of one minute of latitude. Given 20.62 inches for the length of the royal cubit, the remen expresses the length of an average degree of latitude with greater accuracy than the modern meter, that was fixed before the exact length of the meridian circumference was known to its creators, and unlike the meter, the remen is in unity with minutes and degrees of latitude. Archaeological and textual evidence from throughout ancient Egyptian history, as well as textual evidence from ancient Greek and Roman sources, support a conclusion that the correspondence between the length of the remen and the royal cubit, and the meridian length of Egypt and the earth, was known to its creators.’

Several pages of the article are about the inscribed cubit rods that were discovered at Karnak in 1906. I believe the cubit rods are good evidence of the meridian measure of Egypt and I discuss comments and proposals about the location of Pi-Hapi and the length of an itr from before and after the discovery of the cubit rods. Following the discovery of the cubit rods, an itr measure of 20,000 cubits was proposed, and is now regarded as more or less the accepted measure, although, for reasons explained in the article, I agree with a few commenters who believe the length of the itr is 15,000 cubits.

The article also gives an explanation for the purpose and location of the small pyramids as station points for an early period meridian survey of Egypt.

‘100,000 digits, or 5,000 remen, equals one nautical mile, or one minute of latitude. 300,000 remen equals one degree of latitude. Given 15,000 remen, equal to the number of royal cubits in an itr, 20 remen itr equals one degree of latitude. The definition of a maritime league is three nautical miles, or three minutes of latitude, or one remen itr. 10,000 digits is 500 remen or 1/10th of one minute of latitude. 300,000 remen is 20 leagues or one degree of latitude. 300 leagues is 15 degrees, or one hour of rotation.'

'7200 leagues is the 360 degree meridian circumference of the earth. 1618 itr, or 1000 itr × phi, is the polar diameter. 1618 itr × sq. rt. 2 = 2288 leagues. 7200/2288 = 3.1468, the proportion between the meridian circumference and the polar diameter produced by earth’s ellipsoidal meridian. 3.1468/pi = 1.0016 and 7200 × 1.0016 = 7212 leagues for the equatorial circumference. 7212/7200 = 601/600 and 40,008 km × 601/600 = 40,075 km.’

‘The length of the meridian circumference includes the flattening of the poles and the bulge of the equator. The polar diameter only includes the flattening of the poles, making the difference between the polar and equatorial diameters twice the 600/601 difference between the meridian and equatorial circumferences. 7212/pi = 2296 leagues for the equatorial diameter. 2296 × 300/301 = 2288 leagues, or 1618 itr, for the polar diameter.’

Because Kepler gave some credit to ancient Egypt for his third law of planetary motion, I read a translation of Harmonices Mundi, and after reading it I did a couple of calculations and noticed that based on Kepler’s second and third laws: For any given period of time, the areas swept by any two planets are proportional to the square root of their mean distances from the sun. I am not sufficiently conversant in astronomy to know if this is common knowledge, but I think it is interesting, and mention it in the article.

I enjoyed working on this article and I hope you will take a look at it.

The article has a couple of fairly high resolution pictures and a few diagrams. File size about 2.5mb