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    Re: Formula to determine GHA of Sun?
    From: Bill B
    Date: 2014 Sep 13, 00:04 -0400

    On 9/12/2014 10:11 PM, Samuel L wrote:
    > Thank you for the method. I read Henry's comments on the Time Sight
    > method but I know nothing about it other than that. Can you direct me to
    > a clear exposition of it?
    
    Seem to caught in a time warp. The time site clarification was sent
    AFTER the longer message. BTW typo: a time sight uses Ho, not Hc.
    
    For a complete answer, I would search the archives--I don't have a pointer.
    
    Brief answer:
    
    Prior to the current intercept method (St Hilaire method) longitude
    could be calculated from a time sight. Lore has it a good sailor ALWAYS
    knew his latitude. (Not too difficult with dead reckoning and a recent
    LAN observation. Not so much in rough seas and bad weather if they did
    not have a fix for several days.)
    
    Input was:
    --Ho derived from an observation at a given time with the usual
    corrections for index error, dip and refraction.
    --AP latitude
    --Declination at the time of the observation.
    The result was the Local Hour Angle (LHA).
    
    If LHA (west lon) = GHA - AP longitude
    Then GHA (at time of observation) - LHA = Longitude
    
    (Memory is foggy on the following in this paragraph). Back in the day
    they used the equation of time, perhaps converted from time to arc
    coupled with a mean GHA and adjusted for time after the hour to arrive
    at the GHA for the time of observation?
    
    Unless you are a purist, with the current NA that's a waste of time. The
    GHA in the almanac reflects the equation of time. So simply calculate
    the GHA for the time of the observation and subtract the LHA from it for
    longitude.
    
    My sequence on the TI for azimuth is sin mem3 - sin mem1 x sin mem2
    /(cos mem1 x cos mem2) = cos azimuth.
    sin dec - sin lat x sin Hc / (cos lat x cos Hc) = cos azimuth
    
    If you swap out Hc/Ho fand or dec in the above formula, it becomes a
    time sight.
    sin Ho - sin lat x sin dec / (cos lat x cos dec) = cos azimuth
    
    For me 4 keystrokes swaps out Hc/Ho and dec, and I can proceed with my
    usual Az mem... sequence with no further thought required.
    
    For extra credit (Reader's Digest version), Sumner discovered the line
    of position via time sights a bit by accident. He had not had a fix in
    days and did not have enough sea room to go boldly forward. So he sat
    there awaiting better conditions and figured his possible longitudes
    based on an observation and using different latitudes. Connected the
    dots and what he saw was a line that he was on somewhere along depending
    on his latitude.
    
    He subsequently wrote a book (a made for TV dramatization IMHO), became
    a bit famous, and went quite mad.
    
    And that is my Friday eve bedtime story :-)
    
    
    

       
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