# NavList:

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

**Re: lunar distance methods, Shadwell, 1881**

**From:**Frank Reed

**Date:**2013 Jan 28, 14:51 -0800

This book about lunar methods by Shadwell is an odd late 19th century curiosity. It reminds me somewhat of H. Wilberforce Clarke's "Longitude by Lunar Distances" also British and published just after, in 1885. Shadwell's text goes beyond Clarke's both in its quaint pomposity and its seemingly deliberate obfuscation. They both are trying to write like mathematicians. Shadwell in particular likes to use phrases like "rigorous solution" and "mathematical elegance" but he really doesn't know what he's talking about when he tosses these phrases about. Both Shadwell and Clarke were writing decades after lunars had disappeared from common use at sea. It's hard to see who this text was supposed to be targeting. It's not navigators. This is the sort of book that turns simple calculations into difficult math, and the practical suggestions tacked on at the end are a mix of the obvious and the incorrect. It's not targeted at mathematicians working in nautical astronomy, at least not in any useful way. They had long since moved on from the problem of lunars. It might be a sort of encyclopedic history, aimed at historians of the lunar method, but he's just repeating lore and myth when it comes to the history so on that score it would only qualify as amateurish history. I suppose his best target audience would have been "fellow experts in the field of lunarian mathematical calculations", or as we might call them today "fellow math geeks". Who was he trying to impress?

Shadwell includes the usual apologia at the end of his work offering up the usual complaints of "old men" expressing the "deep regret to all true lovers of Nautical Astronomy" over the "comparative disuse" of lunars in his era (which is a huge understatement!) and reminding us that if the chronometers fail there's nothing but lunars to save the day (cross out chronometers and write "GPS" and replace "lunars" with "celestial navigation" generally, and you can find the same argument today). He does, at least, speak honestly about why he really likes lunars. It's their indirect salutatory influence on the navigator that he emphasizes. He's a good late 19th century "schoolmaster" type, and he assure us that taking lunars will engender "acuteness of intelligence" and "encourage habits of accurate and skillful computation". These are the words of a teacher preaching from behind a desk, not someone who knew lunars in practice. Indeed, the mathematics of working a lunar using many common methods was scarcely different from the mathematics of working a time sight, which every navigator computed throughout the 19th century and well beyond. Navigators did not study the mathematics underlying their calculations unless they found such math entertaining. Navigators were human "computers" working spreadsheets on paper --spreadsheets that had been "programmed" by the authors of their navigation manuals. They required no great "intelligence" to take or clear lunars. The notion that this all required some amazing brain power is a mark of a subject that had fallen into deep decadence.

As an example of Shadwell's "textbook" knowledge of lunars, not founded in actual practice, he repeats a suggestion from Raper's manual of navigation published decades earlier. When the altitudes of the Moon and Sun are measured for clearing a lunar, he suggests that the one closer to the meridian should be of more concern. This just isn't true. While some practical navigators surely followed Raper's advice, it was mediocre advice. Shadwell simply repeats it as if he knows what he is talking about.

There are a couple of historical details in this book that may be worth mentioning since Shadwell has them wrong. He apparently had read an article by Baron von Zach published c.1835 in which the Baron speculated that one large table in Thomson's tables for clearing lunars must have been calculated in a uniquely herculean labor-intensive fashion. Thus began the legend that Thomson's tables were some sort of "mystery table" like the Martelli tables we've discussed recently. It was good for sales, and Thomson apparently didn't deny it (Thomson died soon after). But that big table is, in fact, relatively easy to calculate. For the mathematically inclined, it includes the effect of refraction on the distance as well as the principal quadratic correction (same as any series solution to the lunars problem as known since the 1770s) and ALSO it includes the small effect of the quadratic "cross-term" making its net value essentially the same as many other tables in navigation manuals, such as the "improved" Table XX found in Bowditch from 1826. Thomson's tables were the subject of some discussion ten years ago in NavList messages, and unfortunately the legend was expanded by suggesting that these tables are "more accurate" than anything similar. They are not. They're quite accurate, just like those for various other navigation manuals. Their advantage was ease-of-use and speed. Shadwell gets rather upset at Thomson and Janet Taylor, too, for not explaining the mathematics underlying their work. But this makes them no different from other creators of navigation manuals. Shadwell does not seem to understand that these authors were publishing to turn a profit while aiding practical navigators --not servicing his needs as a lunarian math enthusiast.

For anyone new to lunars, if you read Shadwell, I would warn you that you MIGHT be grossly misled. Lunars were not a branch of mathematics! And there weren't endless different methods for clearing them. Shadwell's book is not as bad as Cotter's chapter on lunars in his "History of Nautical Astronomy" (published 86 years later), but it's close. Both provide encyclopedic accounts of minor methods of clearing lunars with a more or less superficial relationship to actual practice. They're like butterfly collectors, chasing down rare specimens to complete their lists ... but blind to the spectacle of a field filled with swallowtails.

-FER

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