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A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Lunars: Thomson's Tables
From: Frank Reed CT
Date: 2006 Apr 2, 03:23 EDT
From: Frank Reed CT
Date: 2006 Apr 2, 03:23 EDT
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