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    Lunars by Huxtable & Bowditch
    From: Bill Noyce
    Date: 2002 Jan 30, 8:45 AM

    I'll echo the thanks to George Huxtable for his treatise on lunars.
    And I would like to take him up on his offer to spell out Borda's
    method for clearing the distance longhand.  Young's formula seems
    to require converting out of logs to do additions.
    I'd also like to thank Dan Allen for posting the pages on lunars
    from Bowditch.  I haven't gotten as far as trying to understand why
    the A,B,C,D calculations work, because I'm hung up on an earlier
    point: I don't see where the Horizontal Parallax is adjusted by
    (approximately) cos(Altitude) to give (what we now call) Parallax
    in Altitude (PinA).  The step that looks as if it ought to be
    doing that is the first paragraph labeled "Moon's Reduced Parallax
    and Refraction," which gives "Moon's Reduced Parallax."  But it
    supposedly uses the latitude, not the altitude, and it looks as
    if the result is a small correction, not one that could reduce the
    parallax to zero for high altitudes.
    I guess it's possible that the rest of the formulas account for
    using HP instead of PinA -- that would be pretty clever.  But then
    we need to account for simply adding "Reduced Refraction" to the HP.
    Oh! That table, "Reduced refraction for Lunars" has a suspicious
    title, and the values in it are a bit funny -- isntead of decreasing
    to zero at an altitude of 90 degrees, they're still about a minute.
    Perhaps they represent Refraction/cos(Altitude), so that they can
    be added to HP (= PinA/cos(Altitude), approximately) and enter into
    the same calculation.
    I was struck by the level of precision in the Bowditch tables --
    tenths of seconds of arc!  Do the other tables go this far?
    And he includes the "other corrections" George Huxtable alluded to.
    It seems nice that Bowditch's A,B,C,D calculation starts from the
    relatively small values of (Parallax+Refraction), rather than
    the way Young's formula depends on cos(m+s)*something - cos(M+S)
    to nearly cancel out.  Perhaps this is why Bowditch can get away
    with only 4-digit logs for his tables?
    It was interesting that the second paragraph of Art. 305 seems to
    use "time" unqualified to mean "local time" -- that which you can
    deduce from measuring the altitude of the Sun in the east or west.

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