This is my first post, and I've accidentally deleted almost all I've written!
a later edit with an answer
The RA of a culminating star gives you the local sidereal time and comparison with Greenwich Sidereal Time gives your local longitude by noting the difference between the two.
If local sidereal time is less than Greenwich, your position is west of the prime meridian at Greenwich; if it is more, then your position is east of Greenwich.
Four minutes of Right Ascension = One degree of longtitude.
One minute of RA = 15 arc minutes of longitude.
A worked example:
Greenwich Sidereal time 17:42
Local Sidereal time 16:36 hours
Greenwich is ahead (more) than local, therefore local is West.
The difference = 42 minutes plus 24 minutes
= 1 hour 6 minutes of RA to the west of Greenwich
Thus, 60 minutes = 15° longitude
Add 4 minutes = 1° longitude
Add 2 minutes = 0°30' longitude
= longitude 16°30'W
Which is accurate to 0°05' of the usually given figure for my location.
I use a Sidereal Clock app on my Android tablet, set to show both GST and local sidereal time at my location.
information for background
This is the historical background for the search for a reliable method of calculating longitude when at sea
The Quest for Longitude and the Rise of Greenwich – a Brief History
I've edited this several times because I'm finding my way around how this works and made several editing mistakes! I've also tried to add another link, and got an error message, but no explanation. Is there a limit to the number of hyperlinks permitted?