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    Re: No Lunars Era
    From: Ken Muldrew
    Date: 2004 Dec 6, 13:03 -0700

    On 6 Dec 2004 at 13:27, Alexandre Eremenko wrote:
    > On Mon, 6 Dec 2004, Ken Muldrew wrote:
    > > Professional astronomers and surveyors had no difficulties with reducing
    > > their own sights. The problems with the L&C data were not due to any
    > > inherent problem with lunars per se.
    > As I understand the story, L&C were specially taught by
    > the best available teachers how to do lunars.
    > Still they:
    > a) did not understand that it is desirable to take altitudes
    > (even for the simple reason that taking altitudes reduces
    > the amount of calculations). I do not accept the argument that
    > "they had other more important things to do". Look how many
    > sights they took!
    I think that they were instructed not to take altitudes. Problem 4th in
    Paterson's notebook shows how to calculate altitudes and this probably
    wouldn't have been included if altitudes were to be taken. Also, altitudes
    were never taken by the land-based navigators who mapped out the North
    West in Canada (contemporary with L&C), demonstrating that L&C were
    following current practice.
    > b) tried and were unable to reduce their own sights.
    > Then, they brought the results of their observations to the
    > same highly qualified teachers to reduce... and we know
    > what was the result.
    Actually, they were instructed *not* to reduce their own sights. This was
    a critical mistake (in my opinion) since celestial navigation is an art
    that requires both ded reckoning and celestial observations to provide
    necessary feedback to each other.
    > >From my point of view this story demontrates that the method was
    > too complicated for an average XIX century mariner.
    I disagree with this inference. First I think L&C would have become expert
    navigators if they had reduced their lunars as they went. Second, I don't
    think the average XIX century mariner was a navigator.
    > > tables were in common use and arithmetic calculation was heavily drilled
    > > at school,
    > Norie's 1828 book begins with a special chapter on "decimal
    > arithmetic".
    > I doubt this would be necessary if "arithmetic calculation was heavily
    > drilled at school at that time":-)
    Of course it depends on the school. Those attending mathematical school,
    who might be chosen as navigators, would be drilled in arithmetic.
    > > Confidence in the result would come from comparing the lunar
    > > longitude with the ded reckoning.
    > I suppose you could check your lunars against GPS or some other
    > modern tool. I am very curious to know what was the average error?
    > (I mean, the error in the measurement of the distance).
    If you like, I can provide you with some land based lunars taken by
    explorers in the Canadian West ca. 1800. The easy ones are where they take
    repeated lunars at the same place (often separated by years) as you can
    get a good idea of their accuracy from this data. I can't do this today,
    but let me know and I'll try to dig some up later in the week if you're
    Or did you mean the accuracy of my own lunars? If this latter, then I can
    tell you that I am usually within 10 miles (longitude). When I make errors
    in the calculation, then I'm not even in the same time zone. The errors
    are easy to catch, but sometimes hard to track down (my copy of Raper's
    tables is old and rather fragile, so I have to page through it somewhat
    > P.S. 1828 Norie is especially interesting to me, not only because of
    > navigation, but also from the point of view of my main profession:
    > mathematical education. It tells me a lot about the general state
    > of mathematical education in England in the beginning of XIX century... The
    > XX century books in navigation do not explain decimal arithmetic, and they
    > use formulas instead of "word recipes". Just try to forget all you know,
    > and follow one of the Norie recipes for reducing lunars:-)
    I first learned lunars from Moore (1796) using the written recipes. I
    wasn't able to forget all that I knew, but it wasn't much to begin with
    Ken Muldrew.

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