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    Re: Troughton and Simms
    From: Frank Reed
    Date: 2013 Jan 12, 13:02 -0800

    Norm,

    You wrote:
    " I know that Bowditch said he found numerous errors in existing tables. Again, it would be nice to find some documentation about even ONE of these errors, even if it didn't cause a documented disaster."

    Bowditch admitted that the vast majority of the errors that he found were in the last place, the least significant digit, in tables of logarithms. He was very clear in noting that these were of no practical significance for navigation but he proposed that the published tables might be used for some other purpose, e.g. astronomy, so we might as well get them right even in that least significant digit. If you want to find some of those earlier errors, I would suggest looking in the "Tables Requisite" from 1781 (I posted a link in an earlier message today). That was the "gold standard" of navigational tables in the late 18th century, and other authors of navigation manuals generally just copied from that official work. Bowditch was probably a bit obsessive in his youth. Re-calculating all of the tables from scratch was probably not necessary. In later years, he liberally borrowed from other tables, and his own later tables contain some errors. For example, the "Improved" version of Table XX (20) in Bowditch's Navigator after the 1820s, which was a small correction for working lunars, includes one rather significant error (significant in the context of the smallness of the correction itself). If you're curious, you can probably find this error even without knowing how the table has been calculated. It's a small table so you could enter the values by hand into a spreadsheet. Then if you plot first and second differences, the bad number should be obvious.

    You also wrote:
    "I even once used an OCR program to tabulate in Excel the entries from a page of a Victorian era log table to see if, perchance, there was an error."

    That "Victorian era" covers a helluva lot of time! :) Her reign included 63% of the 19th century (starting a year before Nathaniel Bowditch died) and extended into the first three weeks of the 20th. I do think you can find more errors in navigational tables in the 1830s. The error in Bowditch Table XX that I mentioned above was never corrected and continued in print until 1880 (lunars were only rarely practiced at sea after about 1850). But after 1875, normally, I think you can bet on nearly perfect tables in nearly all of the major navigation manuals, at least if we include the "errata" as part of the tables themselves.

    -FER


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