The Egyptian system of measures had its starting point in a unit that I call geographic cubit = 461.693504 mm. This unit was related to the length of Egypt, assumed to be 7 degrees 30 minutes, from the latitude 31 degrees 30 minutes North to Latitude 24 degrees 00 minutes North. This interval was defined as 1,800,000 geographic cubits.

This calculation implied that a degree is 240,000 geographic cubits = 360,000 geographic feet. Hence, a minute of degree is 4000 geographic cubits = 6000 geographic feet, and a second of degree 100 geographic feet. According to this system the standard unit of itinerary distance is the stadion of 400 geographic cubits = 600 geographic feet = 184.667 meters, equal to 1/10 of minute of degree.

According to the value assigned by the Egyptians to the degree of meridian a great circle passing through the poles is:
86,400,000 geographic cubits = 39,890,318.9 meters

According to the new system a great circle is:
86,400,000 Greek cubits = 39,952,637.9 meters

Calculating by the exact value of p, the two radii of the Earth compare as:

6,348,741.4 meters
6,358,658.8 meters
__________________
Difference: 9,918.4 meters

The last figure would be how much the water was raised because of the Deluge. That one would describe the shift in geodetic system as a Deluge is understandable when one considers that according to the new system the level of the sea rose by 9,918.4 meters in relation to the center of the Earth.

A problem that is implied in the biblical account of the Deluge is that of calculating the difference between geographic cubits and Greek cubits; as I have stated the two cubits are in a relation quite close to 640:641.

Reckoning in Roman cubits, as the Hebrews did, it was assumed that whereas according to the new system a degree is 250,000 cubits, according to the Egyptian system it was 390 cubits less, i.e., 249,610 cubits = 110,806.421 meters

The calculation for the great circle was:
90,000,000 - 140,400 = 89,859,600 cubits = 39,890,311.8 meters.

This calculation implied that the Egyptian system gave dimensions that are 1/641.02564 less. This calculation involved the trivial error of 7 meters in a great circle.

There was also another calculation that was simpler but less accurate:
90,000,000 - 140,000 = 89,860,000 cubits = 39,890,489.5 meters.

This calculation differed from the exact one by only 177.6 meters in a great circle.

Hence the increase in the radius of the Earth could be reckoned, assuming p = 3 1/8, in two ways:

     14,400,000                    14,400,000
    -14,377,536                   -14,377,600
     __________                    __________
         22,464 cubits                 22,400 cubits
       =  9,972 meters               =  9,943 meters

We shall see that the biblical account of the Deluge, which is a composite of several versions of the same story, employs both figures and further employs a rounded version of the first one as 22,500 cubits = 9988 meters.

I am convinced that the explanation has to do with the introduction of a new system of measures by which the basic value of the degree is taken to be 110,979.444 meters or 222,222 trimmed barley (Mesopotamian) cubits. The Old Testament for the early period reckons by Roman cubits, so that the same length is taken to be 250,000 cubits. The use of this figure is supported by Ezekiel's plan for a new Israel.

The Romans calculated the same amount by saying that a degree is 75 miles of 5000 feet. The Hebrew reckoning by cubits may have reckoned the degree as 50 miles of 5000 cubits. If we add 15 cubits to each mile, that is, 1/333, that is, reasoning as cuneiform mathematical texts do, add what is obtained by multiplying by the inverse of 300 we have a degree of 250,750 cubits; this would mean a degree of 111,318.6 meters, which obviously is a degree of Equator. The figure may have been a good practical approximation to the length of an equatorial degree. In my Appendix I have reported that according to my finding the Egyptian figures for the Equatorial degree vary in this range: 212,380 royal cubits = 111,318.6 meters
212,392 royal cubits = 111,328.4 meters

What the Book of Genesis may mean is that the waters rose in such a way that the Earth became a perfect sphere.

In the new system of units the degree is assumed to be 250,000 Roman cubits, which means that the circumference of the Earth is 90,000,000 cubits and its radius 14,323,944 cubits.

If the equatorial degree is 250,750 cubits, the equatorial circle is 90,270,000 cubits and the equatorial radius 14,366,916 cubits. Difference 42,972 = 19,076 meters.

The difference between the two radii, which is the height of the water in the Deluge, is 19,600 cubits = 140 x 140 cubits. Counting by the natural barley cubit, which was the scientific standard of Mesopotamia, 19,600 cubits are 9922.5 meters. I have calculated that, counting by the exact value of p, the height of the water of the Deluge should have been 9918.4 meters. Hence, there was a rounding of the figure by only 4 meters. I have explained that the difference between Egyptian lineal units and the new lineal units could be taken as 640:641.

It can be concluded that the Mesopotamians computed the new circumference as 78,918,800 cubits and the Egyptian circumference as 1/640 less (78,918,800 - 123,100 = 78,795,700). The difference between the two radii then is:

     12,555,263.64
     12,535,679.556
     ______________
         19,584.084

78,795,691.6 natural barley cubits
78,918,790.9 natural barley cubits

Calculating by p = 3 10/11, the corresponding radii are:

12,563,305.2
12,543,708.7

Difference:

19,596.5 cubits = 9920.7 meters

Considering that the old and the new geographical units were assumed to be related as 640:641, the radii may have been expressed as:

140 x 140 x 641 = 12,563,600 cubits
140 x 140 x 640 = 12,544,000 cubits

The difference is:

140 x 140 = 19,600 cubits

78,795,691.6 cubits
78,918,790.9 cubits

Counting by p, = 3 1/7 the correponding radii are

     12,555,262.20
     12,535,678.22
     _____________
         19,583.98

     12,563,305.2
     12,543,708.7
     ____________
         19,596.5

p, the corresponding radii are:
          12,540,723.6 cubits
          12,560,315.4 cubits
          ___________________
difference:   19,591.8 cubits

Hence, by using the starkly and elegantly simple formula 140 x 140, the Mesopotamians indicate a value for the height of the water of the Deluge that differs by less than 9 cubits, i.e., by less than 5 meters, from the one that could be obtained by the greatest possible precision.

The basic calculation of the dimension of the Earth in Mesopotamia is based on the assumption that the equatorial radius is
6,300,000 double cubits
12,600,000 barley cubits
8,400,000 great cubits
6,378,750 meters

assuming polar flattening 1/300
polar radius 2/3 p, = 2.1
p = 3.15

Ark of Gilgamesh based on equatorial radius of

          12,600,000 natural barley cubits
          140 x 90,000
           6,375,750 meters
                            about 1/2 km too long
                            polar flattening 1/280
                            139.5 x 90,000
          12,555,000 natural barley cubits
           6,355,696 meters
                            about 1 km too short

Standard calculation, Euboic standard
110,974.56
222,222 trimmed barley cubits to degree
111,111 double cubits
10,000,000 to quadrant of meridian
quadrant of meridian 10,000,000 double cubits

Roman cubit ("of Moses") = 443.9182 mm.

Babylonian-Egyptian cubit = 532.7018 mm.

natural barley cubit = 506.25 mm.

"great cubit" = 759.375 mm.

5 Roman cubits/6 Babylonian-Egyptian cubits = 1

2 "great cubits"/3 natural barley cubits = 1

polar radius = 6356.8 km

equatorial radius = 6378.2 km