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    Re: Lunars: Thomson's Tables
    From: Jan Kalivoda
    Date: 2006 Apr 19, 11:28 +0200

    Hello all and Frank Reed especially. As I see, I am returning in time.
    Several remarks to Frank's posting below:
    I had characterized the content of Thomson's main table as a secret for 
    ordinary seamen, not for navigational publicists or even several experts then 
    or now. In contrast to early approximative methods from Lyons, Maskelyne, 
    Witchell and so on, Elford's and Thomson's methods were not ever explained in 
    an "official" publication.
    Nevertheless, Thomson's table was unique by its small steps and in the 
    consequence, by many thousands of calculations that were needed for 
    constructing it. One secret remains - how Thomson could find time for 
    calculating it throughout his life of a mainline mate and later the captain 
    of the brig?
    Thomson's method was the FIRST Bowditch's method in his first editions. Only 
    later Bowditch moved his own (first) method from the appendix into the main 
    text and made it the chief lunar method in his compendium.
    I tried to download Zach's article on Thomson' table from the adress that 
    Frank hints at, but I got the paper from the year 1830, not 1829 I asked - 
    albeit from the page 144, where Zach's paper should begin. Alas!
    Jan Kalivoda
    >  ------------ P?vodn? zpr?va ------------
    >  Od: Frank Reed 
    >  P?edm?t: Lunars: Thomson's Tables
    >  Datum: 02.4.2006 09:26:42
    >  ----------------------------------------
    >  A few years back, Jan Kalivoda wrote a couple of posts to this list about
    >  Thomson's Tables for clearing lunar distances (which were adopted as Bowditch's
    >  Second Method in 1837). He noted that the calculation of the "third
    >  correction"  table was considered mysterious in the 19th century. For anyone who
    >  read
    >  this  account back then, I just wanted to note here that the table is not at
    >  all  mysterious, and it can be calculated directly. It's a lot of work because
    >  there  are thousands of entries, but the steps involved are simple, and the
    >  majority of  cases had already been tabulated before Thomson's time. Most
    >  similar
    >  works  tabulated the linear refraction plus the Moon's quadratic term.
    >  Thomson adds in  the quadratic cross-term. This additional calculation rarely
    >  changes the result  by even a tenth of a minute of arc (equivalent to three
    >  minutes
    >  of longitude in  the result) except when the lunar distance is less than 30
    >  degrees and even then  only when the Moon's altitude is rather low [Jan
    >  Kalivoda's earlier post noted a  difference of a full minute of arc however this
    >  was
    >  only correct for methods  which ignored the quadratic corrections entirely]. To
    >  a navigator, this was  simply a number to be extracted, never mind the
    >  details, and it was a very  popular method, involving about 30% less work than
    >  other
    >  similar  methods.
    >  By the way, I believe it was Baron von Zach who started the  urban legend
    >  that they're was something extraordinary in the calculation of  Thomson's
    >  table,
    >  although Thomson himself may have had a hand in it. There's a  paper about the
    >  tables by the Baron briefly described in the Monthly Notices of  the Royal
    >  Astronomical Society in 1829 which can be found on the web via  adsabs:
    >  http://adsabs.harvard.edu/
    >  (if you've never used this service,  when you do a search and it says 'zero
    >  records found', give it about thirty  seconds. It's working on it...)
    >  -FER
    >  42.0N 87.7W, or 41.4N  72.1W.
    >  www.HistoricalAtlas.com/lunars

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