# NavList:

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

**Re: Easy Lunars in 1790**

**From:**Frank Reed CT

**Date:**2006 Apr 27, 22:31 EDT

Ken Muldrew, you wrote: "One of the real gems among the gold mine of 18th century navigation documents that everyone has been downloading is Margetts' Longitude Tables by George Margetts, published in 1790. "Tables" was probably a poor choice for a title as the collection is really a series of graphs allowing one to clear a lunar distance by interpolating the necessary corrections." Yes, they're wonderful, aren't they? Speaking of peculiar terminology, you've probably noticed that Margetts (also a few years later, Norie) uses "formulae" to refer to fill-in worksheets or work forms (formulae --> forms, I suppose). You noted that you could clear a lunar in 5 minutes with Margetts tables while Witchell's method required an hour. I gotta say, I don't think this would be a fair comparison for most people. Yes, you can get some speed with those look-up graphs in Margetts's book, but you can also become efficient at using Witchell's method. The total process of clearing a lunar and working the time sight via Witchell, in my opinion, takes about 25 minutes. The same total time with Margetts might require five minutes less. It's a savings, yes, but surely not an order of magnitude improvement. And: " In short, the "problem" of clearing lunar distances was just as fast and easy to solve in 1790 (if you had Margetts' book) as it is in 2006 using a pocket calculator." Over the past 240 odd years, time and again commentators on navigation have assumed that lunars would be more popular if only there was a different way of clearing them. I think this is fundamentally mistaken. Lunars are not difficult mathematically. There are numerous methods. Some are a bit more tedious than others, but they all have a lot in common and none of them is really difficult from a calculational standpoint. It's true that deriving lunars calculations and analyzing them involves some mathematical difficulty, but that's another matter entirely. And you wrote: "Each of these lines is for a horizontal parallax of 53'. There are also dotted lines on the graphs (maybe 10-20 per graph) that give the parallactic correction for a horizontal parallax of 62' over 53'." This is the really clever part of the diagrams. At the most complete level, clearing any lunar distance is a function of the following variables: d, the observed lunar distance h_s, the Sun's or other object's altitude h_m, the Moon's altitude P, the Moon's parallax p, the Sun's or other object's parallax T_P, the temperature/pressure factor and L, observer's latitude (for oblateness). If we ignore L, p, and T_P, as Margetts does, we've only got four variables. It's not too difficult to use graphic plots to read off a quantity that depends on three variables, but it's tricky when you get to four. Margetts's procedure handles it beautifully. You also wrote: "One only needs to calculate the corner cosines to find out the relative contributions of correction for each value of the moon's altitude (see Frank Reed's posts in the archives on "Easy Lunars" for a full explanation of this operation). Basically, one needs to solve the following two equations: dM=[sin(s_alt)-cos(d)sin(m_alt)]/cos(m_alt)sin(d) dS=[sin(m_alt)-cos(d)sin(s_alt)]/cos(s_alt)sin(d) where dM and dS are the corrections for the moon and star(sun) respectively, s_alt is the altitude of the star(sun), m_alt is the altitude of the moon, and d is the distance between them." I know you're just giving this as an example of how it might be calculated, but, for what it's worth, I think Margetts probably used Shepherd's Tables, instead of a series approach. And you asked: "So the question is, why is the history of navigation utterly silent on this brilliant method to clear lunar distances? In 1790, clearing the lunar distance could have been made the most trivial part of finding one's longitude, yet navigators persisted in flipping through log tables and following arcane recipes, torturing themselves to clear the distance (well, not exactly torture, but certainly an unpleasant half hour even at the best of times)." I don't think it was all that painful, as I've said above, but it's still an excellent question: why isn't this book better known? I've got a few thoughts on this... Fos starters, we're talking about a commercial product, in competition with many other products. Margetts made these tables to sell. If they performed poorly in the marketplace, there could be a number of explanations. Maybe he priced them too high. Maybe they were perceived as a poor value considering that they were useful for only one topic in navigation. But they certainly weren't a total flop commercially. I note that Edmund Blunt was selling them in 1817. In an advertisement for his very successful store in Manhattan, he lists navigation books for sale in this order, "Rio's Tables for Navigation and Nautical Astronomy [Mendoza Rios]; Bowditch's Practical Navigator; Lyon's Tables for working the longitude at sea, being the shortest method used; Margett's Tables; Mackay's Longitude, 2 vols." along with other non-navigational publications. So they were available in New York decades after their first publication, though that doesn't prove they sold well. It's also worth noticing that graphs like his were almost impossible to copy. This was presumably good for Margetts's wallet since it made piracy more difficult but perhaps not so good for his fame in the long haul since they couldn't be re-published easily by compilers of other navigation books, like Nathaniel Bowditch. Also, there was a real bias against graphical methods in this era. Why? I don't know. As you note, this bias seems irrational to us. But maybe that just means we haven't gotten inside the heads of those folks back then yet. Finally, there is the purely technical matter of accuracy, which I consider least important in this case. Was anyone bothered by the fact that the refraction couldn't be corrected for temperature and pressure? The graphs also ignore the Sun's parallax. That's fine if you're using the stars, and it's a small correction anyway, but if most practicing navigators used the Sun considerably more often than the stars for lunars, this might have seemed like a point against Mr. Margetts and his "tables". -FER 42.0N 87.7W, or 41.4N 72.1W. www.HistoricalAtlas.com/lunars