NavList:

Thank you Lars. And there we have it. As confirmed by observation, your value of RA Altair is correct (19h51m41s) and mine is wrong (19h50m47s, epoch 2000). But I see mine quoted EVERYWHERE. (eg Wikipedia). I thought I had discarded the possibility of a web error, by going back to 1980 NASA docs and the like. It's not moving that fast so am I just being incredibly stupid and using the wrong epoch or something?

@Paul Hirose, I will post the worked example once we have debugged it. Lunars by Haversine are actually really easy: I am working off the description in "Astronomical and Nautical Tables" by James Andrew. 1805, referenced in Cotter and found in Google Books. The hardest part is parsing the sentence: I show the unparsed and parsed versions.

"Take the log-sines of half the sum and difference of the apparent distance and the difference of the apparent altitudes, the log-cosines of the true altitudes , and the log-secants of the apparent altitudes; and having added these six logarithms, rejecting the tens from the index, find the natural number corresponding to their sum, to which natural number add S.S.C. difference of true altitudes, and the sum will be the S.S.C. true distance required."

This is Young in S.S.C. (haversine) form, and pretty tractable really. I have forgotten why "S.S.C": square of the sine of the chord or some such. Parsed:

"Take the log-sines of half (the sum and difference) of ((the apparent distance) and (the difference of the apparent altitudes)), the log-cosines of the true altitudes , and the log-secants of the apparent altitudes; and having added these six logarithms, rejecting the tens from the index, find the natural number corresponding to their sum, to which natural number add S.S.C. difference of true altitudes, and the sum will be the S.S.C. true distance required."