NavList:

David Pike, you wrote:
" Is there ... a list of the angular difference on the celestial sphere between the 57 navigational stars, or would you have to start off with up-to-date SHA and declination and do the spherical trig? Not my favourite cup of tea."

You need to start thinking like a 21st century calculator. :) There are billions of devices that perform that great circle calculation in hardware (the GPS chips in smartphones and other devices compute great circle distance all day long...). Of course long before those came along, there were a great many web sites that would calculate great circle distance between points on the Earth, and they work just fine for star-star angles. Find any one of these, especially one that takes input in degrees and minutes of arc, and enter the declinations of the stars as latitudes and the SHAs (or GHAs) as longitudes. Get the result in nautical miles. Divide by 60 to see that as degrees and minutes.

Note that you need to use coordinates of the stars for the week of observation, primarily to account for aberration (identical to that compression of the constellations in the direction of travel that those 'passengers' would have seen aboard that starship in the goofy movie we were discussing). This aberration changes during the year and for stars separated by 90° it amounts to +/-0.34' in the annual cycle. Precession does not affect the star-to-star angles so most of the coordinate change from one year to the next is irrevelant. You could use an almanac from ten years ago with no issues. Over longer terms you have to worry about proper motion of the stars which does change star-to-star distances but there are very few stars for which this is a major concern (except Alpha Centauri and Arcturus, the latter for the extraordinary reason that it is not part of the main disk of the Milky Way).

You also wrote:
"I am aware that you would have to choose your stars to minimise differences in refraction."

There is some navigator's lore on this topic that can get you into trouble. It used to be believed, in the latter half of the 20th century, that refraction between stars was insignificant when they are at the same altitude. This was simply wrong. You should always correct for refraction, and the process is quite analogous to clearing a lunar distance, but since the corrections are always small and have the same functional form for both bodies, the correction can sometimes be significantly simplified.

One useful case (this is one of my discoveries, by the way): when both stars have altitudes above 45°, the effect of refraction on the star-to-star distance is a simple compression by one part in 3000, regardless of how the stars are located or oriented relative to each other on the celestial sphere. That compression by 1/3000 is equivalent to 0.1' for every 5° distance. Thus when you measure your star-to-star distance with your sextant, add 0.1' for every 5° of measured angle. Then compare  that corrected angle with the geocentric angle derived from almanac data.

For lower altitudes, I'll point you to a two-part essay I wrote thirteen years ago: star-star sights.

Note that using lunars will generally yield better results, but for basic tests of arc error, for example for the homemade sextants we've been discussing, these star-to-star angles are more than enough.

You wrote:
"Another possible solution would be to compare horizontal angles of ground features with those measured with a real sextant of known good quality, but the features would need to be quite a way away for repeatability."

I have tried this in various ways over the years, and unless you have access to a salt flat or maybe a frozen lake, it's relatively impractical. The targets need to be at extreme range. An angle of one minute of arc is a ratio of 1/3438, so moving a target ground feature (or moving the sextant itself) by one foot at a range of 6400 feet, e.g., changes the observed angle by 0.5'. By the way, this was certainly a popular and reasonable method for testing sextants in the late 18th century. Mendoza Rios (if my memory is right) mentioned observing church steeples, which, in the era before tall buildings created a nice array of reliable distance markers around a city like London. He also pointed out that you don't have to measure the angles directly with some "standard sextant" since there is a consistency check: you measure angles all the way around the horizon and they better add up to 360°! This is easiest to see if you picture four steeples all near the cardinal compass points as seen from your observing location. Let's call them N, E, S, W. They don't have to be precisely separated by 90°. Suppose you measure from N to E and get 93° 15'. From E to S you get 85° 45'. From S to W you find 90°30', and from W back to N you get 90° 35'. When you total up those angles, if the steeples are arranged around your horizon without much deviation due to hills, then the angle should add up to 360°. In the example I've given here (assuming my arithmetic is correct), the total adds up to 360° 05'. This immediately tells us that the sextant is reading long by about 5' for angles near 90°. The process can be repeated, with vairations of procedure, for other smaller angles.

There'as another approach you can try if you have a good-quality sextant available as a standard. Place the test sextant and the standard sextant on a table both looking at some distance object with their index mirrors nearly touching. Set both to some angle, like 30° exactly. The "good" sextant now "feeds" light that has been deflected by that exact angle to the test sextant. When you look through the test sextant, you should see the distant object direct and reflected in the index mirror, too. It's very much like an index correction test. Line up the two images, and (with a few details left out for brevity) any difference in angle is the error of the test sextant at that angle. This should provide a very quick way of creating an approximate calibration table for a homemade sextant which more or less eliminates the (otherwise quite critical) problem of centering error.

Frank Reed
ReedNavigation.com
Conanicut Island USA