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    Re: Lunar distance accuracy
    From: Alexandre Eremenko
    Date: 2007 Nov 4, 22:50 -0500

    > How many lunars do you
    > shoot per week, on average?
    This is a good example where unqualified "average"
    is meaningless:-)
    Average over WHAT PERIOD?
    Over my life so far? Zero.
    Over last week? Let me see... 7 series 5 shots each.
    Because the weather was nice and Moon was well-positioned
    with respect to my balcony every morning. So I took 5
    shots every morning while drinking my morning coffee.
    I never do just a single shot. If I go into the
    trouble of take my sextant from the box, and a notebook
    and go out to shot, I would certainly do at least 3-5 shots.
    That's one of the reasons that taking one shot single
    per week seems strange to me.
    > He did not set out to investigate the
    > accuracy of lunars,
    You think so? Then what is his paper about?
    > Sorry, Alex, but I can't understand
    > how you could begin to say this. What
    > makes you say his results are "highly suspicious"?
    That he neglected a systematic correction that
    than the typical error of his published "observation".
    (The word "observation" is in quotation mark because I
    am still not sure whether his single observation is
    a single shot or an average).
    > The formula in Simms was one of the
    > first attempts to deal with the issue of
    > arc error.
    Paper of White makes me think that the arc error of his own
    sextant was determined by the Simms recipe.
    > Yes. That was the case at hand, wasn't it?
    I read White's paper twice. My impression was that he
    is had in mind using lunar observations at sea,
    rather than determination of the
    longitude of fixed observatory by long-term observations.
    > Surely you agree with what I
    > wrote previously, that we can
    > average sets of four in White's list and get
    > reduced error?
    We can do whatever we want, this is a free country:-)
    But when we are discussing the accuracy
    of lunar observations with a sextant, having in mind
    their application in sea or land travel, it is a different
    problem from the accuracy of determination of longitude
    of a fixed observatory. Do let us distinguish these
    two problems, and call them Problem A and Problem B,
    for simplicity.
    I say that in Problem A, averaging observations taken
    over long time period is meaningless.
    In Problem B it is meaningful, as well as the use
    of tripods and other mountings.
    It is clear that given long enough time, the accuracy
    achievable in Problem B will be much higher than that
    in Problem A.
    > But people always have agendas.
    Not always. Politicians have agendas. Unfortunately,
    many people who say that they do "scientific research"
    also do. I don't want to discuss this much.
    But real scientists (on my opinion) have QUESTIONS,
    not agendas. They ask themselves a question.
    And then try to find the true answer to it.
    This is somewhat different from havin an agenda and
    trying to push it.
    > Incidentally, my German is too poor to read the details
    > in the paper by Bolte. Why was he conducting such a study
    My German is also poor, but I tried to do my best,
    and have some general impression
    of what is going on in the paper. (Jan Kalivoda also
    added some explanation, but I think I was able to understand
    most of the paper myself, except perhaps some very small
    He does not say
    whether he is a professional sailor, a navy oficer,
    a scientist or just an amator. I have his other paper,
    (a large one, almost a little book)
    of more theoretical nature where he discusses at length
    the known methods of chronometer correction at sea,
    with long and comprehensive explanation of Lunars,
    with tables etc. Chauvenet style. I can post this too.
    He calls himself
    "Doctor F. Bolte of Hamburg", so probably he is not a
    Navy oficer. I would guess he was a professor in some
    Naval academy. The observations
    were taken during his
    voyages "to Australia (1886-7) and Western South America
    (1887-8). That's all he says.
    He wanted to investigate the "Accuracy of CelNav
    observations at sea", this is how his paper is titled.
    Lunars is only a small chapter (last chapter) in the paper.
    He used dead reconing and chronometer observations.
    As I understand, chronometer(s) were carefully tested before
    and after the voyage, and the correction interpolated.
    He investigates:
    a) Latitude from Polar star
    b) Latitude from Meridian observation of two stars, one
    in the South and one in the North of the meridian.
    c) Latitude from two altitudes and difference in hour angle.
    d) Longitude from heights of two stars near East and West
    e) Chronometer correction from Lunar distances.
    > Evidence of actual practice --that's the key to it all:
    > if you want to
    > understand the history of navigation,
    In this particular discussion my goal is more modest.
    To understand the accuracy of the method of Lunar distances.
    I don't see how the primary cource documents you
    mention can help me in this.
    > And maybe evidence of accuracy,
    > too, if you can puzzle it out.
    That's the question: how to puzzle it out.
    Besides I have no access to these documents, and no time
    to get involved really seriously.
    (Besides, the topic looks too exotic to me for a serious
    even in this list at most 2-3 people seem to be interested
    in the accuracy of sextant measurements of distances).
    That's why I am mostly looking
    at secondary sources: research already done on this
    question and my own experiments:-)
    Unfortunately very little previous research seems to be
    available: I have only White and Bolte.
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