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    Re: Lunars: Thomson's Tables
    From: Frank Reed CT
    Date: 2006 Apr 19, 23:12 EDT

    Hello, Jan, you wrote:
    "But I saw his early  edition in Paris two years ago, where his first method
    of lunars stood only in  the appendix and therefore Thomson's method (later
    the second) held the first  position in the main text, if I remember it well.
    Not very important, of  course."
    
    No, not important, of course. For what it's worth, here are some  details:
    
    1795: Bowditch develops a modification of the standard series  method for
    clearing lunars. I call this "Bowditch's Original Method". Word  spreads rapidly
    in New England that there is a mathematical "genius" in Salem.  Someone arr
    anges an honorary Harvard degree for him to give the self-educated  expert a
    little paper respectability.
    1799/1800: Bowditch and Blunt insert  Bowditch's new method in their
    Americanized edition of Moore's Practical  Navigator, replacing a variant of Lyons's
    method. The second method included is  the same one Moore included: Witchell's.
    1802: After a more extensive  revision, Blunt and Bowditch retitle the book:
    the New American Practical  Navigator. The two lunars methods are Bowditch's
    Original Method and Witchell's  Method. There is a small note in the preface,
    in this edition only, noting that  his 1795 lunars method is "somewhat similar"
    to one published by Mendozo Rios  [sic] in 1797. In fact it is identical to a
    method previously published by  Mendoza Rios. Bowditch has been beaten to
    press. Since the claim of a new and  unique method of clearing lunars seems to
    have been important for sales of the  Navigator, I suspect Bowditch was strongly
    encouraged to enhance his  method.
    1804: Bowditch publishes an unbound supplement to the Navigator. It  was
    known as an "appendix" but we wouldn't call it that today. This contains  tables
    and directions for his enhanced version of his original clearing method.  I
    call it "Bowditch's Principal Method". It incorporates a number of simple
    tabular tricks for shortening the length of the calculation and avoiding
    subtraction (which is always more error-prone than addition), but it is  fundamentally a
    refinement of the same method published previously.
    1807: The  second edition of the New American Practical Navigator is
    published. It  incorporates the tables from the 1804 supplement. Bowditch's Principal
    Method is  now described first --it is "method 1". The original method is
    pushed back to  method 2, and Witchell's method is now method 3.
    1811: In the third edition  of the Navigator, Bowditch notes with some pride
    that his Principal Method has  been described (reviewed?) in the Connaissance
    des Temps for the year  1808.
    1826: Several editions have gone by with no significant change to the  lunars
    methods or tables. In this edition, there is a "new form" to Table XX.  This
    is the double-entry quadratic correction table required in most of the  series
    methods in this era. Bowditch has realized by this point that he can add  in
    the quadratic cross-term and gain a little extra range of reliability (at
    lower altitudes and somewhat shorter distances) without adding any work at all
    for the practicing navigator. The trick here is the same as in Thomson's tables
     but the resolution is coarser in Bowditch's Table XX so interpolation would
    be  required for high accuracy. It's better than Thomson's though under
    non-standard  atmospheric conditions.
    1837: Several more editions pass without significant  change to the lunars
    material, but in this edition there is a big change. The  major table from
    Thomson's method has been added to the book. This is accurate  and easy to use but
    it suffers from its dependence on a mean value for the  Moon's HP and mean
    values for the state of the atmosphere. Bowditch's modified  version of Thomson's
    method is given position 2 in the list of methods. Since  this is a direct
    descendant of Lyons's method, which Bowditch deleted from the  Navigator 38
    years earlier, it is impressive that this method is bumped up to  second place.
    Several editorial errors creep in at this edition. The phrase  "regulation of
    the watch", which refers to setting the deck watch to local time  is erroneously
    replaced with "regulation of the chronometer". The intent of the  passage is
    not really lost, and I doubt it caused any trouble in the era, but  it's
    clumsy. Also, there is a "typo" in the directions for Bowditch's Original  Method
    (third method now) which might have caused some real problems for  navigators
    trying to use it.
    
    The methods for clearing lunars in the  Navigator from 1837 until 1880 are:
    1) Bowditch's Principal Method 2) Thomson's  method (modified slightly) 3)
    Bowditch's Original Method, otherwise known as the  method of Mendoza Rios, and 4)
    Witchell's method.
    
    Nathaniel Bowditch died  in 1838. His son Ingersoll took over the publication
    and though he was a major  patron of astronomy, he did little to improve the
    Navigator. I don't think it  interested him, and it seems to have sold
    reasonably well regardless. The plates  and rights to the Navigator were sold to the
    US Navy in 1868. They continued to  publish the book without any real changes
    until 1880 while working on a major  overhaul. Right up until 1880 the
    examples in the chapter on lunars are based on  observations and almanac data from
    the year 1836.
    
    The overhaul of the  Navigator was completed in January of 1881. It's an
    entirely new book after this  date in most respects. All of the methods for
    clearing lunars are dropped and  replaced by Chauvenet's rather eccentric method. It
    is interesting to note that  Chauvenet scoffed at the method of "one Mendoza
    Rios", which he had seen  recently in Raper, when he first described his new
    method. Ironic considering  that this was almost exactly the same as Bowditch's
    Original Method.
    
    Chauvenet's method shifts to an appendix in 1903 and finally disappears
    after 1912 (the year the pre-computed lunar distance tables were dropped from  the
    American Nautical Almanac). It is remarkable that a few paragraphs from the
    explanatory material and advice on shooting lunars have been copied unchanged
    from edition to edition of Bowditch all the way from 1802 to  1912.
    
    -FER
    42.0N 87.7W, or 41.4N  72.1W.
    www.HistoricalAtlas.com/lunars
    
    
    

       
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