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    Re: Haversine formula
    From: Frank Reed
    Date: 2008 Apr 08, 22:28 -0400

    There's also a much older application of a formula sometimes called the
    "haversine formula". In the 1790s, both Mendoza Rios (first) and Bowditch
    (probably independently) realized that the number of "cases" in a series
    solution of a lunar distance calculation could be reduced by replacing the
    standard cosine formula for the corner angle in a spherical triangle with a
    formula for the haversine. The latter was entirely multiplicative, so
    well-suited to logarithmic calculation, and there no problems with the signs
    of the arguments. The historical "cases" were what we understand today as
    the algebraic signs of the factors. The calculation is slightly longer when
    you use the haversine formula, but since there are no cases, it's apparently
    less prone to error.
    
    Those of you who attended the Navigation Weekend at Mystic Seaport in June,
    2006 heard me talk all about this (this was the chalkboard presentation on
    the second day). For the few people who are new to the list in the past few
    months, you're welcome to attend the next Navigation Weekend in Mystic in
    June of this year. It's shaping up very nicely, and I think it's going to be
    very successful. There's a web page describing it here:
    www.fer3.com/Mystic2008 .
    
     -FER
    www.HistoricalAtlas.com/lunars
    
    
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