NavList:

Lars, I have read through your analysis three times. You may be onto something (or several somethings!), but I'm not convinced yet that you have an explanation for those odd constants. Could you possibly work up a couple of examples, maybe one where the correction is "additive" and another where the correction is "subtractive"? How would the work look in modern terms --without the use of the scale of chords? Does that eliminate the constants 53 and 62? I think you're on the right track that a factor 57.3 is required to use the scale of chords. That makes sense. But why bump it up and down by 8%?

You wrote:
"To summarize: D = D’ ± γ · HP + 0.08 · γ · HP. 
The last term, 0.08 · γ · HP, is always positive and is an approximation of the “third” or “Q-“ correction given in Bowditch (1851) table XLVIII. "

This is where I'm skeptical. The "third correction" listed in Bowditch T48 ("borrowed" from Thomson's tables) is, first of all, not the "Q" or "quadratic correction" alone. It's equivalent to two terms of the quadratic correction plus the refractions of both bodies, as projected onto the lunar arc. This is negligibly different from saying "everything else" --except the Moon's primary parallax correction. In general this third correction is not going to be proportional to the Moon's parallax correction even as a crude approximation. It's possible the original author of this graphical method had that in mind, but it does not appear to improve the clearing process.

I would still contend that this proposed graphical method of clearing lunars was just a bad idea --an intriguing novelty in the long tail end of the history of lunars that was junked as soon as the letters to the editor started pouring in...

Frank Reed