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    Re: Latitude by Noon Sun for Beginners
    From: John Karl
    Date: 2009 Apr 30, 09:14 -0700

    Boy, we've sure had a lot to say about the simple noon sun shot.  So I
    might as well  contribute more palavering by going back to the tables
    that were mentioned of Bowditch's (his tables 29 & 30, 1943-56 eds, or
    24 & 25, 2002 ed.).  These tables come from
    
    H = ho + (1.9635")*cos(L) * cos(d) t**2/( sin(L-d) )
    
    where H is the alt at LAN, ho is the alt observed at t minutes after
    (or before) LAN, d is the declination, and L is the latitude at LAN.
    [The sign in sin(L-d) is plus for L & d of opposite names.]  This
    expression comes from expanding the familiar sin(ho) alt equation in a
    power series about H in terms of t.  This expression, along with
    Bowditch's discussion of it (1943 ed), is rather useless in practicing
    CN in this GPS age.  However, it does give us some insight to the List
    discussions (I think).
    
    1st, it proves what several have mentioned, that ho (observed alt)
    versus time reckoned from LAN is indeed a parabola.
    2nd, that the parabola is not exact, but an approximation.
    
    3rd, that the idea of using this equation is rather murky (being
    polite here) because both the time, measured from LAN, and the
    latitude, are what we're trying to measure.  H, t, and L are all
    unknowns.  Generally, d is approximately quite well.
    
    4th, Bowditch (1943 ed) confuses his readers (me anyhow) in his
    discussion by giving the time of LAN in his examples of this
    "reduction to the meridian".
    
    5th, amusingly, the 2002 ed of Bowditch has an inconceivably complex
    discussion of finding Latitude from the LAN shot, given ho and time of
    LAN.  He manages long convoluted considerations using 31 lines of
    calculation, when we all know the answer is Latitude = Dec plus (or
    minus) coaltitude.   It's really just one calculation, given ho and
    the time of LAN, as in the example problem.
    
    Happy noon sun shots,
    --JK
    
    
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