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    Re: Easy Lunars in 1790
    From: Ken Muldrew
    Date: 2006 May 1, 10:26 -0600

    On 27 Apr 2006 at 22:31, Frank Reed wrote:
    > 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.
    I did a little experiment and the results were what they were. It was
    clearly a bad result using Witchell's method but the reason it was bad
    (aside from a lack of practice with tables) was that the method is so
    prone to error. A mistake near the beginning of the algorithm negates
    pretty much everything afterwards. Margetts' graphs seem to give much
    better insulation from making careless errors (so much so, that it would
    seem an advantage to first clear a lunar with those graphs before using a
    tabular method just to spot any mistakes made with the latter (if one was
    hell-bent on using the tables no matter what)).
    > The total  process of clearing a
    > lunar and working the time sight via Witchell, in my  opinion, takes about
    > 25 minutes.
    That's very fast; perhaps the very best I've ever managed was about 25
    minutes without the time sight. I can see one becoming familiar enough
    with the tables to do the whole thing in 25 minutes, but only with a risk
    of error.
    > The same total time with Margetts might require  five minutes
    > less. It's a savings, yes, but surely not an order of magnitude
    > improvement.
    Five minutes less if the time sight takes 15 minutes on its own. As a
    complete beginner to those graphs, I was able to clear a lunar in 5
    minutes (no time sight). If one applied the same enthusiasm to using the
    graphs as would be required to get through Witchell's method in record
    time, the clearing could probably be done in under 3 minutes. My opinion
    is that Margetts' graphs improve the speed of clearing by a factor of
    about 3-5 and the propensity to make errors is reduced by an order of
    magnitude (though this last could reasonably be due to my lack of training
    using tables during my formative years (we had one week using log tables
    in grade 11 math when I was in high school)).
    > 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
    The tedium, of course, and the time (as implied by the tedium) are at the
    root of this claim. Did Nathaniel Bowditch become famous because he had
    made a simpler method for clearing lunars? If so, then it was because the
    people actually doing the clearing were looking for simpler methods. If we
    compare a pocket calculator to Margetts' "tables" to Witchell's method,
    understanding doesn't enter into the picture at all. The only concern is
    how simple it is to get an accurate and error-free result.
    > 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.
    I hadn't actually looked at those tables before (except for brief glances
    at pages 1, 51, 101, etc.), but yes, I think you are quite right that he
    just used those tables.
    > 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.
    All possible explanations, but the lack of success is still curious.
    > 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.
    Could be; it sure would be nice to find an example of someone actually
    giving a reason for not recommending these graphs.
    > 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".
    These factors might also have played a role, although for most shipboard
    navigation they seem pretty unimportant. You would also think that for
    teaching lunars to students that these graphs would be a remarkable
    pedagogical aid. The fact that they weren't seems to speak to your point
    about not yet getting inside their heads yet.
    Ken Muldrew.

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