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    Re: Graphs of Lunar Distances.
    From: George Huxtable
    Date: 2010 Oct 2, 00:09 +0100

    Time for another look at recent mailings about lunar distances.
    Frank wrote-
    "With those objects as the "other body" in lunars, I routinely get results
    with a standard deviation of about a quarter of a minute of arc in
    individual observations and about twice as good when sets of four are
    and in his next mail-
    "As I have noted, I can routinely get lunar distances accurate to nearly a
    tenth of a minute of arc (standard deviation) when sets of four are
    averaged. A tenth of a minute of arc error in the angle is generally
    equivalent to twelve seconds error in the resulting Greenwich Time."
    That's not the first time we have seen such a claim from Frank. I have no
    wish to dispute his prowess, but it does raise a few questions, to which
    I've tried to get answers before.
    It's true that when observations are affected by statistical random
    scatter, then averaging a set of four will halve that scatter. But that
    averaging won't affect any non-random, "systematic" error. The analysis
    that Frank has provided can apply, only if the inherent systematic error is
    precisely zero. So I ask him to estimate an upper-limit value on what such
    non-random components of error might possibly be. That estimate could
    include the following- Imprecision in index-error checking; scale
    calibration error of sextant, collimation error, shade prismatic error;
    personal error in estimating position of Moon limb. There may be other
    possible sources, that Frank may think of that I've missed. Let's have an
    informed estimate of what each of these might possibly be contributing. If
    zero, state zero. When this question was asked before, an answer was
    evaded. If Frank considers it to be an unfair question, he can say so (and
    Frank added, in a claim which we've also seen before-
    "I have conducted a number of workshops in lunars since 2004, and when
    observers without previous experience in lunars shoot them with a properly
    adjusted sextant fitted with a decent telescope, I find that they, too, can
    get observations with a standard deviation of about a quarter of a minute
    of arc. There's no law to this, and there are plenty of ways to screw it
    up, but I can assure you that it's not just me."
    And yet, when I've appealed, on Navlist, for anyone who claims to get
    comparable precision, repeatably, not a single hand has gone up. I ask
    again; can anyone else reproduce the results that Frank claims anyone can
    Now we come to the matter of the Elephant in the Room, that nobody has yet
    mentioned. Conclusions are being drawn about lunars taken at sea, on the
    basis of observations made under completely different conditions, on land.
    We know that Douglas has taken his lunar distances from a firm footing,
    on-land. We might presume that all the observations that Frank has
    described were also made on land, though he hasn't said so. Perhaps he will
    correct that presumption, if it's wrong. Yet on the basis of that
    experience, he presumes to tell us what precision a navigator in the era of
    lunars could expect to achieve. And how real navigators should go about
    making such observations, as in the following-.
    "... you mentioned putting the sextant on a tripod. For some purposes that
    may be a good idea. Another trick you can use is to sit down on the ground
    with a knee up and your elbow resting on that knee. This adds stability,
    reduces fatigue, and we know that navigators actually did things like this
    in the 19th century. It's a trick that would work nearly as well on the
    deck of a ship at sea back then as in our backyards today."
    It may be a trick that might work in today's vessels of many tens of
    thousands of tons, such as Jeremy reports his lunars from. But in the
    "lunar era", typical vessels were around 100 to 300 tons, small vessels
    which, in ocean conditions would be expected to jump around; motion which a
    sextant user had to counteract, and which would call for complete freedom
    of movement of the instrument to do so. Flinders and Bass used lunars at
    sea in exploring van Diemen's land, in a 25-tonner. Cook's seven Atlantic
    crossings (made just before he learned about lunars) were made in a 70-ton
    brig. Backyard techniques were not appropriate on such ships, except in
    millpond weather. In the past Frank has claimed, unconvincingly, that
    there's little difference in precision between measurements made at sea and
    on land. I don't believe it. In recent years, we've had no reports, that I
    can recall, of Navlist members taking lunars from on board small craft at
    sea; not since Steven Wepster's Atlantic observations of ten years or so
    ago. Why not? It isn't an easy task; that's why not.
    We now learn, for the first time, that when Frank made his claims for
    extraordinary precision, a x9 telescope was in use. That is not a tool for
    use at sea. Even a 3x telescope can present real problems, in keeping the
    two bodies in view, when the vessel is bucking around. Every sextant is
    always provided with a 3x (or thereabouts) telescope for regular use at
    sea, and sometimes with an additional 6x (or so) for special conditions
    when it was possible to use it.  Cook frequently observed lunars without a
    telescope, writing that it was impossible for him to say "whether those
    made with the telescope are the nearest the truth, circumstances seem to be
    in favour of both- we certainly can observe with greater accuracy with the
    telescope when the ship is sufficiently steady which seldom happens so that
    most observations at sea are made without". This was on Resolution, 336
    tons. So it's clear how completely inappropriate Frank's 9x telescope would
    be, in such conditions.
    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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