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    Re: Precision of sextant observations: taken from How many chronometers?
    From: Henry Halboth
    Date: 2009 May 9, 12:56 -0700
    To all,

    George is

    --- On Sat, 5/9/09, George Huxtable <george@hux.me.uk> wrote:

    From: George Huxtable <george@hux.me.uk>
    Subject: [NavList 8206] Precision of sextant observations: taken from [Navlist 8202] How many chronometers?
    To: NavList@fer3.com
    Date: Saturday, May 9, 2009, 7:06 AM

    Henry Halboth wrote in [8202], under threadname "How many chronometers?"
    this paragraph, which I have separated under a new threadname.

    "I do not question your often stated accuracy of LD observations to only
    within 1' of arc when using the instruments available at inception of the
    method, i.e. the late 1700's, however, by the 1850's much improved
    instruments were available and accuracies to within 10" of arc have been
    opined by writers of that era. In my opinion, for what it may be worth, an
    LD error of 1" of arc, by an experienced observer using a well-calibrated
    modern instrument would be enormous - no so, however, to quickly state, in
    an altitude measured on a questionable sea horizon. My last full, single
    observer, LD, worked up on July 27, 2007 (Greenwich date), in a known
    Longitude, cleared by Borda's Method, using 6-place Logarithms, with careful
    attention to the 2nd Correction, produced results to within 3-seconds of the
    true GMT; this result was posted on this List at the time."


    I suspect there's a typo in there, and that Henry intended to write-
    "... an LD error of 1' of arc, by an experienced observer using a
    well-calibrated modern instrument would be enormous", rather than "1" of
    arc". Perhaps he will confirm that (or otherwise).

    Compared with Henry's vast experience, from his many years on the bridge in
    all weathers, in the era when sextant observatios were still important, my
    own experience of astronavigation is puny. Mine has been done in a small
    craft, and usually with a plastic sextant, and only in Summer weather; fair
    weather if I could manage it. In the sort of sailing I've done, which hasn't
    included crossing an ocean, I've always known by other means reasonably well
    where I was, so the safety of my craft has never depended on my astro. I've
    never taken a lunar distance at sea, and know of only one small-craft
    navigator who has. So there's no way I would pit my experience against

    Have I stated that lunar distances with modern instruments can be made only
    to 1' of arc? I've often used phrases such as " each 1' of arc in a lunar
    distance gives rise to a corresponding error of 30' in deduced longitude",
    which is a rather different matter. I'm quite happy to concede that in the
    right conditions, a lunar distance can indeed be measured quite a lot more
    precisely than that.

    When we're discussing precision, and scatter of observations, it is, I
    suggest incumbent on us to be as clear as we can about what we are talking
    about. We have to use a bit of statistical language. When we discuss an
    accuracy of 1' (or whatever), is that in terms of one standard deviation (in
    which roughly one-third of the cases, it will be exceeded) or two standard
    deviations ( which will only be exceeded on one occasion in twenty)? There's
    an immense difference. And we need to be clear, too, about the conditions
    we're thinking of. Is a lunar distance being taken from on-land, as is done
    by many denizens of this list, or at-sea?  There's an immense difference.
    From a small-craft or a big-ship? An immense difference. In a mirror-sea
    calm or in rough conditions? An immense difference. By a grizzled old salt
    or a beginner?

    So it's hard to put an all-embracing simple number on the precision of a
    lunar distance. I doubt if I've ever tried to do so, or set a limit of 1',
    on this list, but could be proved wrong...

    We need to consider the instruments that were being used, throughout the
    lunar era, which would all be Vernier sextants, not micrometer types. I have
    such a sextant, which I haven't taken to sea. Using it on land, my old eyes
    have great difficulty, even with a good magnifier, perceiving which of three
    adjacent lines on the Vernier makes the best fit, even with really good
    illumination. Bill Morris, an expert on sextants if himself no navigator,
    has noted the same thing.

    I recall Henry's 2007 posting about those observations, but no longer have
    it on-board, and it could be useful if he provided another copy or a link. I
    remember that it showed a remarkably consistent series of observations,
    which proved his hand and eye remain as precise as ever. But as I recall,
    they were taken from on land, and though others may disagree (and have) I
    regard that as a  particularly benign environment for the taking of lunars.


    contact George Huxtable, at  george@hux.me.uk
    or at +44 1865 820222 (from UK, 01865 820222)
    or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.

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