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    Lunars & Don Jose de Mendoza y Rios
    From: Frank Reed CT
    Date: 2004 Aug 5, 21:12 EDT
    A few days ago, George H wrote:
    "To me, Mendoza's appears to be a remarkably complex and long-winded method,
    even though it avoided the necessity for using long 5-figure or 6-figure
    logarithm tables."

    My first impression was similar, but I've since tried it and it's really not much more work than, say, Witchell's method (which would have been its chief competitor). It has one ENORMOUS advantage over some other methods. It does not suffer from "an embarassment of cases", as they used to say. And this is important in a practical method. If you accidentally mis-apply one of the "if - then" rules which are common in so many lunar methods, you have to re-do a large part of the calculation. A calculational method with a linear unbranching path through its steps has advantages

    And the Mendoza Rios method was popular for a very long time --most of the period when lunars flourished. It was one of only two methods in Moore c.1800 (the other being Witchell's) and it was included in most of the standard navigation manuals (Bowditch, Norie) up through 1850 at least when lunars were in rapid decline.

    Also the rather famous First Method of Bowditch is really a very slight variation on the method of Mendoza Rios (MR's method was published in 1796). Bowditch combined a few repetitive calculations from MR's method into special tables. For example, adding that "constant logarithm" 9.6990 is a waste of time in the standard MR method, and (if I am remembering correctly) Bowditch prepared a special table with that constant log folded into the main table. In my opinion, Bowditch's importance to nautical astronomy and nautical mathematics is more legend than fact. Mendoza Rios deserves to be better known. I think I'll work on that...

    Frank R
    [ ] Mystic, Connecticut
    [X] Chicago, Illinois

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