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    Dip, dip short, distance off with buildings, etc.
    From: Frank Reed CT
    Date: 2006 Jan 5, 20:44 EST

    In Bowditch and elsewhere, there are formulas  for dip, dip short, Table XV
    for distance based on measured height, maximum  visibility distance, etc., and
    they all have various mysterious corrections for  "mean refraction". I've got
    this stuff all figured out pretty well now, and it  turns out that there is a
    really easy, though somewhat bizarre (!), way of  thinking about the effect of
    refraction in terrestrial, or coastal navigation,  situations.
    You can calculate dip or the altitude of a tall building  peeking up from
    beyond the horizon using straight Euclidean geometry and  trigonometry ignoring
    refraction completely. Then to include refraction, you  simply change the
    radius of the Earth from R to R/(1-x) where x depends on the  temperature gradient
    of the atmosphere. On average it's about 0.15 but it can  easily be anywhere
    in the range 0.13 to 0.17 and sometimes it's as low as 0 or  as high as 1.0
    (temperature inversions yield higher values of x).
    This  works perfectly to derive the equations in Bowditch for dip, dip short,
    Table  XV, and apparently everything else where terrestrial refraction is
    involved.  Details upon request...
    42.0N 87.7W, or 41.4N  72.1W.

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