NavList:

Tim Ingham, you asked:
"Can anyone clarify what changes are required to be applied to the originally quoted latitude and longitude of a point which was based on when Greenwich Meridian was the zero Meridian and now, when Lat and Long are quoted in terms of WGS 84 and the zero meridian is about 5.3" east of the Greenwich Meridian."

You need to know the gravitational deflection of the vertical at the location you're interested in. Near the old Greenwich Observatory, that deflection is around 5 seconds of arc in longitude (and some small shift in latitude which I don't recall off the top of my head). At other points near the Prime Meridian, there are different deflection values. The Greenwich Meridian is still the zero of longitude. The astronomically-determined zero of longitude wobbles back and forth around the modern zero.

For the vicinity of St Paul's rocks in the mid-Atlantic, the deflection of the vertical is on the order of 12 to 20 seconds of arc at most. That's about 10% of the error of over two and a half nautical miles that you have detected.

David Pike mentioned geographic "datums". Fortunately that's not an issue here. Any coordinates relevant for celestial navigators should be astronomical latitudes and longitudes without reference to any grid or ellipsoid. Datums are now obsolete. Some bureaucratic organizations and some legal authorities still must map their corners of the world using local datums, but that's just inertia and the problem of "installed base". They should have switched everything to WGS84 decades ago. The calculations are trivial on paper, but paper is actually the problem. If there are extensive records that were committed to paper which have not been digitized, then they're stuck with old datums until digitization catches up. After that there is no ambiguity -- no benefit to any of those antique coordinate systems.

As I noted above, for celestial navigation we want astronomically-derived latitudes and longitudes. These coordinates are based on the local vertical. We observe the exact coordinates of any observer's zenith, and then apply that on the ground. Let's ignore longitude for the moment and consider latitude alone. When we shoot two independent stellar altitudes, the corresponding zenith distances determine the exact declination of the observer's zenith. There's the usual ambiguity (two circles of position cross in two points), but it's not a practical concern. That declination value is defined on a perfect sphere, the imaginary celestial sphere, and that's why pure spherical trigonometry solves the math problem for us. We pull that declination down to the ground along the local vertical. That becomes our latitude. The bumps and lumps and the overall ellipsoidal shape of the Earth's effective gravity field (which includes the centrifugal acceleration of rotation) are ignored. We don't correct for them. The declination is the latitude. End of story. But of course all of our datasets today are true coordinates, exact to the nearest few meters or better in three-dimensional space. Whether they come from the timing of satellite signals or measurements by surveying equipment on the ground, they determine true positions of points on the Earth and in nearby space. If we want to compare our astronomically-derived (celestial navigation) positions with true positions, then we have to apply a correction, And that's the DOV or "deflection of the vertical" (*). The DOV is especially large near "new" geology, like volcanoes, subduction zones (ocean trenches) and other tectonic plate boundaries, and young mountain ranges. 

You wrote:
"The query is prompted by a check on some data quoted in Lecky’s Wrinkles in navigation (1884)  which claimed 2 locations, St. Paul’s rocks and Cape Agulhas Lighthouse to be 'Both of these are very accurately observed positions'. The other locations are taken from his List of Time Signals."

I studied your spreadsheet. Interesting details. Thank you for providing that! I'm sure Lecky's confidence in those positions was based on what he had learned about the effort that went into acquiring those positions, but confidence is not a guarantee. It was an interesting problem in that era: how could you independently validate a geographic position?

You added:
"Also, I appreciate the need for caution when quoting “Mr Wikipedia”, but what information is there on the accuracy of Google Earth’s Lat and Long positions?"

Fortunately automated procedures were established years ago (if I remember correctly) to test the internal consistency of Wikipedia's databases of positional data. They're quite good. Or am I just applying the same misplaced confidence that Lecky had?? And Google's basic mapping data has been carefully aligned with proper (WGS84) coordinates for many years. There are still occasional errors on a scale of a dozen meters or so. By "basic mapping data" I'm excluding road network data which is primarily reported by national agencies in each country. Those data can be poor, and some may be intentionally adjusted for reasons of "national security". There are, of course, regular differences between mapped data and features driven by water levels, erosion, and deposition (for example, is Chappaquidick Island an island? --not since 2015 or so).

Frank Reed
Clockwork Mapping / ReedNavigation.com
Conanicut Island USA

* My apps handle that DOV correction.