Eratosthenes Circumference of Earth:
252,000 stadia of 300 Egyptian cubits, so 700 stadia per degree, and one ten millionth of radius is 630.5 millimetres for a cubit of 524 millimetres.
Newton knew Egyptian cubit was 1.719 Egyptian feet from King's Chamber of Great Pyramid, which converts to 524 millimetres.
Conjectural model of globe, potentially considered by Newton
Let perimeter of King's Chamber be a Pi/40 million model of the quadrants of the globe so that a quadrant is Pi/10 million. This yields a ten millionth of radius as 637.1 millimetres, but Newton did not know that the Earth's average radius is 6371 kilometres.
John Taylor spotted that Newton's hypothetical cubit of 24.8 inches was one ten millionth of his estimate of Earth's polar radius, so 629.9 millimetres
Newton multiplied the Egyptian cubit of 1.719 feet by the ratio 6/5 to create a giant-sized cubit of 24.76 inches which appears bizarre unless he calculated models of Earth's radii on a 1 to 10 million scale.
Earth's circumference from the conjectural model is 2 x pI x radius of Earth:
Radius = 40 stadia or 12,000 Egyptian cubits x square of 100/Pi which is 12,000 x 0.524 metres x 100/Pi x 100/Pi
3000 Egyptian cubits of 1.719 English feet is 1719 English yards, nearly a mile or 1572 metres, so possible to walk at 12,000 Egyptian cubits per hour.
The time to walk around the circumference of the globe would then be 'a' hours, and Earth's radius divided by 'a' corresponds to a quadrant of 10,000 divisions before the invention of the metre if this was Newton's conjectural model.
This also means Earth's centripetal acceleration is 3000 Egyptian cubits (1572 metres) divided by the square of the time for the time to rotate a hundredth of a quadrant.
At the current rate of rotation it takes 215.41 seconds to rotate a hundredth of a quadrant, and 1572 metres divided by (215.41 x 215.41) is 0.0338782 metres per second squared.
The centripetal acceleration can be determined as 6378/6357 x 0.0338782 metres per second squared now we know the ratio of equatorial radius to the polar radius, so 0.0339901 metres
This is very close to the classical calculation as Ra x 4 x Pi x Pi divided by T x T, so 6378.14 x 4 x Pi x Pi divided by (86,164 x 86,164) = 0.0339158 metres per second squared
Newton needed to know the ratio of the equatorial gravity to the equatorial centripetal acceleration which reduces gravity to calculate the equatorial expansion of 1 part in 230 which is now known to be 1/f where f is (6378.14 - 6356.75)/ 6378.14 = 298.2 probably due to the higher density core, so Earth is closer to a sphere than the theoretical model.
Newton was the first to provide geophysical evidence that Earth rotates by calculating the reduction in the period of a pendulum which is affected by the globe's centrifugal force..
John Taylor's book on the Great Pyramid was republished in 2014.
Newton's dissertation on cubits was reviewed in the BBC book Pyramid Beyond Imagination in 2002.
It does seem as if Newton may have used a one to ten million scale model of the globe to pick up on ancient conjecture on the size of the globe in conjunction with a modern assessment of the size of the globe, and in so doing invented the modern metric division of the globe.
Mark
PS
Firsov's empirical determination of the stadium of of Eratosthenes yielded a length of 157.7 metres, and 300 Egyptian cubits 0.524 metres is 157.2 metres, so Eratosthenes may also have found it strange that the Egyptian cubit corresponded so well to the circumference of the globe, which I think was unbeknown in the Pyramid Age.
Edited 1 time(s). Last edit at 09/28/2023 06:27PM by Mark Heaton.
