The Mayall & Mayall Reclining-Declining formulas given in the notes for the wikipedia sundial article give the right answer for a horizontal dial. ...if R is taken as the inclination from the horizontal, and (as the author of that wikipedia article section defined it) D is the azimuth that the up-tipped dial is facing. Then, if R = 0, and D = 0 (a horizontal dial), the Mayall & Mayall Reclining-Declining formulas in the notes give the right answers. I like the word "inclining" better than "reclining", because "reclining" implies distance from the vertical. But departure from the horizontal is how the dial departs from a horizontal dial, the ordinary dial. For example, as I mentioned, a horizontal has R = 0 and D = 0, when R is defined as departure from the horizontal.
As I mentioned before, differences in how variables are defined can result in different but equivalent formulas. ...which might mistakenly be judged as incorrect for that reason. Michael Ossipoff
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