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    Re: The rapid-fire fix
    From: John Karl
    Date: 2009 Apr 27, 14:39 -0700

    Frank,
    I don't understand the sight reduction of your "quick fix".   You
    start with one (averaged) altitude at 0930 and get the longitude by a
    time sight.  But longitude by a time sight requires some other info,
    normally the latitude, which is not known.  So what am I missing here
    in your discussion??
    
    Then you get the latitude form the two sights at 0910 and 0950.  I do
    understand how this is possible because we now have two pieces of
    information, two H's and the time interval.  For example, using the Sin
    (H) altitude equation, the two unknowns are one latitude and one LHA
    (the second LHA is not another unknown because it is the original LHA
    + earth-rate * time).  However, these two trig equations in two
    unknowns would be tricky to solve explicitly, maybe impossible, but
    certainly numerically.  I don't understand your explanation of "using
    the rather complicated methods found in most 19th century navigation
    manuals, we would get latitude from the two altitudes and the time
    interval between them."  Are you referring to something like I just
    discussed?
    
    On the other hand, there is explicit method in my book on pp 78-79,
    eqs 7.5.  These are a simple, understandable, application of the
    familiar H and Zn equations.  The method uses only one more trig
    equation than two St. Hilaire LOPs.  And it gives both Lat and Lon
    explicitly, without requiring tables or the 0930 calculation.
    --JK
    
    
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