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