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    Re: Bowditch Table 15
    From: Bill B
    Date: 2005 Jan 25, 15:59 -0500

    > 2. Controversy remains about whether the first term or first two terms
    > should be under the square root sign.
    In my copy it is table 15, and it only shows the first term (radicand) under
    the square root sign (radical symbol).  As I pointed out in an earlier post,
    this must be wrong.
    1.  The square root of the first term squared is the term (positive).  Call
    it x.  Then the formula is reduced to x + (H-h) - x.  X's cancel out,
    leaving D = H-h for any angle.
    2. By trial and error with Excel, I tried placing 1, 2, and 3 terms under
    the radical symbol.  The only combination that produced the same values as
    the table were the first 2 terms under the radicand, and the third outside.
    Will be happy to send you the spreadsheet if you request it off list.
    > 3. How should the Dip correction be applied?  Add?  Subtract?  See my new
    > Figure 1 and tentative explanation of the Dip correction for Table 15 at
    > http://jimthompson.net/boating/CelestialNav/CelestNotes/Bowditch15.htm
    > and ignore the rest of that page for now.  I am not at all confident that I
    > have any of it right.
    Dip, always subtract.
    > 4. How is H-h calculated?  I had assumed that one subtracted the observer's
    > height of eye from the know height of the object above its sea level.
    That is my take, and using an observed angle (prior to corrections) of zero,
    the Table 15 formula distance match up with distance figured by the
    geographical-range quick formula.

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