A YouTube video by Brady Haran, Mapping the Meridians - Objectivity 97, ended in a cliff hanger (the answer not found by Brady, and Keith Moore of The Royal Society). It's with regard to the Anglo-French Survey of the late 18th century. From Wikipedia, which does not explain the problem:

In 1783 Cassini de Thury addressed a memoir[1] to the Royal Society in which he expressed grave reservations of the measurements of latitude and longitude which had been undertaken at Greenwich Observatory.

From the citation, Concerning the Latitude and Longitude of the Royal Observatory at Greenwich; With Remarks on a Memorial of the Late M. Cassini de Thury. By the Rev. Nevil Maskelyne, D. D. F. R. S. and Astronomer Royal, I concluded—disclaimer: I'm not knowledgeable enough of the then-problems associated with such surveys, and their astronomical (no pun) implications—of concerns raised regarding the accounting or lack thereof of the refractive effects of the atmosphere on the observations undertaken at Greenwich, and thus its coordinates based on polar stars. Continuing on Wikipedia:

The final report of 1790 presents figures for the distance between Paris and Greenwich as well as the precise latitude, longitude and height of the British triangulation stations.

Given my aforementioned position, I'm at a complete loss in the latter bigger document. Given the above summary on Wikipedia, and how the video ended, I'm guessing the direct answer to my question was not explicitly stated.

Based on comments by @PieterGeerkens: the subsequent movement of the meridian when a new instrument at a new location was used, does not address the earlier error being asked about.

Kindly note: I'm asking about what was found in 1790, not what was found in the 20th century using "a new triangulation".

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    By way of setting scale. a nautical mile is defined as one "the meridian arc length corresponding to one minute (1/60 of a degree) of latitude" Thus errors as discussed in your reference of 2" or 4" are respectively 1/30 or 1/15 of a nautical mile: which at a total of 1076 feet corresponds to errors respectively of 202 or 405 feet. More can be found at Greenwich Meridian: "*Four separate meridians have passed through the buildings, defined by successive instruments ... *" – Pieter Geerkens Jun 20 at 10:51
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    Cont.: "Since the first triangulation of Great Britain in the period 1783–1853, Ordnance Survey maps have been based on an earlier version of the Greenwich meridian, defined by the transit instrument of James Bradley. When the Airy circle (5.79 m to the east) became the reference for the meridian, the difference resulting from the change was considered small enough to be neglected. When a new triangulation was done between 1936 and 1962, scientists determined that in the Ordnance Survey system the longitude of the international Greenwich meridian was not 0° but 0°00'00.417" (about 8 m) East" – Pieter Geerkens Jun 20 at 10:52
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    @PieterGeerkens: please see added note in the question to clarify what I mean. – ymb1 Jun 20 at 11:09
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    Just to point out a typo in @PieterGeerkens comment: the nautical mile is 6076 feet, not 1076 (and the rest of the numbers in comment would make no sense if 1076 was correct). – alephzero Jun 21 at 2:23
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    I thought it was impossible to have an error in the determination of the longitude of Greenwich!? ;-) – Peter - Reinstate Monica Jun 21 at 23:41

I found the answer. In 1790, no error was found.

Roy [who headed the survery] probably did not know that in 1785 Maskelyne [who was confident of the coordinates of Greenwich] had equipped his assistant Joseph Lindley with a number of watches and sent him on a secret "chronometer run" to Paris, to determine the time difference between the capitals. Lindley's result (9 minutes 20 seconds) verified Maskelyne's astronomically deduced value, published in 1787, which was later found to agree with the result of Roy's triangulation.[31] Roy avoided admitting this embarrassing consistency [...] [emphasis mine]

Source: Widmalm, Sven. "6. Accuracy, Rhetoric, and Technology: The Paris-Greenwich Triangulation, 1784-88." The quantifying spirit in the eighteenth century. University of California Press, 2020. 179-206. p. 188

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