TITLE: Is the definition of a nautical mile ultimately incorrect?
QUESTION [0 upvotes]: From many sources the nautical mile is defined as exactly 1852 meters (with minor variances). Based on history it was calculated around one minute of latitude, which is one sixtieth of a degree of latitude.
Now if we calculate a nautical mile based the equitorial radius $ R_e $ of earth, 6378136.6 meters (was the most accurate value I could find)
$$
M = (R_e2\pi)/360/60
$$
which comes to 1855.32473
Is there something im missing ultimately from how the exact definition has become defined because 1852 Meters would in theory not sensibly match up (run short or run over) if an imaginary line was layed around the equator.
Reversing this calculation to calculate the equatorial radius based on the nautical mile being 1852 meters exact we end up with an equatorial radius of 6366707.0194937075
which is a somewhat large difference.
Granted as earth is such a large body and is not a uniform sphere (more of an Ellipsoid with a flatening factor of $ 1 / 298.257223563 $), the amount of error is unpredicatable, but one would hope there is a reasonably accurate value of 1 nautical mile calculated.
Am I over complicating this?

REPLY [1 votes]: You are holding 18th century measurements to a 20 century standard.
These are supposed to be based on the circumference around a longitude and not around the equator.
In theory, 1 nautical mile corresponds to one arcminute of latitude.  There are $5,400$ arcminutes from the equator to the north pole.
Also, in theory it is $10,000,000$ meters from the equator to the north pole (along the Paris meridian).
Since they are based on the same definition it should be exactly $1 \text {M} = \frac {10,000}{5400} \text{m}$
As the earth is oblate, 1 arcminute of latitude is not the same at the poles as it is at the equator.  The nautical mile is based on the arcminute at the 45 degree parallel.
Aslo, since in the late 18th century, there was no way to precisely measure the length of the meridian that defined the meter, the French made their best guess based on the technology of the time and created a meter stick that would become the standard meter.  It was never exactly $10,000,000 $ meters from the equator to the north pole.
In the 20th century the mile was established as exactly 1852 meters.
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