# NavList:

## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

**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