Having made a number of disclaimers in various places the last several days about how metrology systems turned out for John Michell and John Neal, I am pleased to be able to say for trying to give them both as much benefit of a doubt as possible, I may have indeed found that the several suggested ratios between units, 441/400 and 176/175, do indeed resemble ratios in decimal that may have been helpful for trying to organize a more coherent and sensible system of metrological unit relationships.
Below is what I’ve come up with so far to try to reorganize things to better cover the bases and fill in the gaps so that there are geodetic values for all three circumference values – polar, mean, and equatorial.
I’m not completely sure what to make of it. Half of it is new to me for not having looked at things quite this way before. There are a number of surprises. I’m still in a state of disbelief over what’s a happened to the mile but the lower values for it are “good numbers”. It’s probably not a bad scheme.
Note that a mile of 5256.289167 ft would be 432 Remens of 1.216733603. Perhaps some of the Standard Units given below have their own geodetic properties?
Keep in mind that this is merely units for geodetic modelling at a foot:(mile x 10^n) ratio. Geodetic measurement may be another issue, as may be geodetic modelling or measuring of the Earth in feet, whereas the present study only looks at the circumference values in miles.
Most of these units made it onto here at this stage because of how well the arrangements accommodate known or proposed unit values for them. I’m pleased to see things like 3.282806350, 3.289868132, 1.096622711 and others. The arrangement for the meter has Indus Foot values at the right, which boosts my confidence in the idea put forth by several researchers that the Indus Foot is a form of the meter, or vice-versa.
3.289868132 has been discussed so much from time to time that if memory serves I think it’s gone through three names now – the “Guachimontones Meter”, the “Cholula Meter”, and “The Third Meter”.
I’m not sure what I’ve gotten myself into with the Remen (probably the Hashimi Cubit / Pied du Roi either) but the puzzle pieces may actually be fitted into the right places here. The first three Remen values I ever proposed all fit neatly into the boxes for short, medium and long in this scheme. The long value is also known as the “Thoth Remen”, which is something of a long story involving Carl Munck and 1.111111111^2 = 1.234567901, but the gist of it is the Thoth Remen in feet is equal to (1.234567901 x (Pi^2)) / 10 = 1.2184696979 ft.
It might tend to sound a bit like a cheap parlor trick (even to me), but of course 1.234567901 is a natural mathematical curiosity just like “the Golden ratio” Phi 1.618033989, and more importantly the “Thoth Remen” has the “pedigree” of being able to be formed from 360 and the squared Royal Cubit: 360 / (1.718873385^2) = 1.218469680 x 100.
What I think is interesting that I actually did find ratios similar to 176/175 and 441/440 to be serviceable in the organization and conversion of units, and even more interesting that even for adding missing ratios (in decimal) I seem to have been able to reduce the number of necessary units as if several of Neal’s proposed unit transactions might possibly lead to unnecessary or purely abstract units.
If it did nothing else, the very useful and common 1.000723277 ratio between short and medium units helps reconcile the links between units through squares, rectangles, triangles, or cubes, with the links between units through circles https://pijedi.home.blog/2020/04/15/relating-units-of-measure-through-circular-geometry/
These ratios, .32 Pi = 1.005309649 and 1.006036766 (about 176/175 = 1.005714286), and 1.002151140 (about 441/440) are ratios I’ve known and worked with for quite some time. I’ve written much about 1.006036766 and 1.002151140. I’ve found them in the fine ratios of data for Egyptian architecture, such as the data from Miroslav Verner, The Pyramids for Giza subsidiary pyramids, and numerous other sites. http://grahamhancock.com/phorum/read.php?1,1198957,1203974#msg-1203974
Small correction, the diagram should read .32 Pi rather than 3.2 Pi, sorry.
I’m sure this must be only part of the story of ancient metrology and geodesy, but I’d be pleased if I can think of it as a good start.
Here is an example of what Neal’s metrological scheme looks like
There might still be too much of a good thing in a couple of places there.
If the works of Michell and Neal are missing some fractions then, what might they look like? Good question. Here are some possibilities I haven’t yet started to explore.
Hopefully, this is starting to point a little more in the right direction now.
–Luke Piwalker
Luke Piwalker 