NavList:

Robert VanderPol II, you asked:
"Would adjusting the PM sight up or down by distance traveled (nm) N or S be an acceptable alternative methodology?"

Yes, absolutely. The tabular correction works well, and it's quicker. But simple addition of altitude offsets works well, too. One detail here: you said "the PM sight" as if you're considering only one. That's not terrible, but this process is significantly more effective if you have a half-dozen or a dozen sights centered on local apparent noon. That improves the accuracy considerably.

You mentioned Hewitt Schlereth's book devoted to this topic, and I do recommend it, but it's getting hard to find. The same process is discussed in the Admiralty Manual of Navigation from a theoretical point of view, and we can certainly re-derive it. Anyone interested in working through that? There's a relatively simple equation involving tan(Dec) and tan(Lat) that will tell us how many seconds we need to add or subtract to adjust for the large impact of observer motion on a longitude derived from a near-noon Sun curve.

Frank Reed