NavList:

Hewitt, you wrote:
"I'm stumped too. Perhaps with a medium a planchette and a seance we could query Sig. Martelli directly? :-)"

Don't forget a translator. :)

I checked Cotter's various books, and he has a couple of descriptive paragraphs in his "History of Nautical Astronomy" (a book which is a train wreck when it comes to lunars, but excellent on many other topics). Quoting:

" An interesting navigational method was published in 1873 by the Italian G.F. Martelli. Martelli's original work, entitled 'Tables of Logarithms', contained no more than forty-nine small pages comprising five logarithmic tables. It appears that Martelli never divulged the principles upon which his tables are based, thus earning for them the appellation 'Martelli's Mysteries', by which the tables generally became known by British seamen.
Martelli's tables became very popular, and numerous editions have been published. Their popularity remains [writing in the 1960s], and many present-day navigators employ them for solving their Sun and star sights.
Martelli's method was designed for finding the angle P of the PZX triangle [in other words, LHA]. The formula was arranged to simplify tabulation and arithmetic. Although accuracy is not high, the tables are handy and nicely arranged [...]
Volume three of the 'Admiralty Manual of Navigation' described the quantities tabulated in each of Martelli's five tables. A mere glance at these descriptions is sufficient to indicate the complexity and apparent mystery of Martelli's methods."

This is a trick that may be familiar to some of you who remember Thomson's lunar tables, adopted whole into Bowditch in the 1830s with a claim (almost certainly false) that they had been re-calculated from first principles. Thomson, too, used somewhat arcane formulas to calculate the logarithms in his lunar tables and he offered no explanations, but the instructions were simple, and the tables became very popular. Part of the popularity was apparently their mysterious origins which made them marketable and also relatively difficult to duplicate except by direct theft (a la Bowditch). Legends developed around these tables making preposterous claims about how they were developed, which Thomson seems to have encouraged. Martelli seems to have followed the same path.

I would emphasize again that the popularity of these tables was mostly about sales and marketing, not science. Martelli's solution of the time sight problem is "no big deal". The standard approach found in any navigation manual, e.g. Bowditch, worked fine and was the by far most common approach. Martelli's tables are a curiosity more than anything else --not that there's anything wrong with that! Just don't mistake them for an improvement in the actual science of navigation.

By the way, with today's tools, it should not be too tough to puzzle out Martelli's tables even if you don't have access to vol. 3 of the Admiralty Manual of Navigation (I don't). Look for tricks like constant offset angles added to arguments.

-FER

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