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    Re: Lunar distance accuracy
    From: George Huxtable
    Date: 2007 Oct 28, 10:29 -0000

    Frank wrote-
    
    "in addition, the expression "pillar sextant" did NOT refer to
    | sextants mounted on stands back then. The terminology is bound to be in
    flux
    | in the year 2007 since sextants like this have not been manufactured in
    | almost a hundred years, but certainly when White was writing, there would
    | have been no question. "
    
    ans returned to this nomenclature question in several other postings,
    pointing to a Google search for the term "pillar sextant".
    
    Frank bandies words such as "certainly", and "no question", but there can be
    little certainty about whether an astronomer, taking measurements on land,
    did or didn't use the term "pillar sextant" to abbreviate the phrase
    "sextant on a pillar stand". That would have been the natural instrument for
    an astronomer to use for measuring lunar distances from on land, if it had
    been available. It remains an open question, in my view. Unlike Frank, I
    would claim no certainty, either way.
    
    However, I am impressed with the power of Google to provide evidence on such
    matters, and grateful to Frank for pointing out how to use it. It is, of
    course, selective, being useful only for those works which have been
    scanned, and in which the words have been transcribed by some form of OCR
    software, but there seem to have been many such works now, rapidly
    increasing. I now accept, from that evidence, that the general use of the
    term "pillar sextant " was, indeed, to describe a double-frame instrument
    rather than one mounted on a pillar. I'm quite happy to leave it at that.
    
    =======================
    
    I wrote the following, back in navlist 3547-
    
    "What I would like to question, however, is Frank Reed's treatment of
    White's
    scatter in longitudes, in writing- "If we take his lunars in sets of four
    and average them (which I consider the best approach with lunars), the
    results are generally within 0.1 minutes of arc. I would note that these
    results are very similar to my own experience."
    
    Just take as an example the quoted longitude errors (in seconds of time) for
    the first four of the 42 observations that White records, at four
    widely-spaced dates in 1887. I have added a third column in which those
    longitude errors are converted, roughly, to error in lunar distance.
    
    Aug 27,   -55 sec , -0.46'
    Sept 10,  +11 sec,  +0.09'
    Oct 8,     +30 sec,  +0.25'
    Nov 19,  -35 sec,  -0.29'
    
    It seems to me that these are numbers that Alex would recognise as being
    very similar in scatter to those that he reports from his own balcony. But
    in grouping that set of four into one, and averaging, Frank has reduced them
    to a mean error of 0.1', and in doing so he has discarded the baby with the
    bathwater, and the relevant information on the real scatter has been quite
    lost.
    
    As evidence, those details support Alex's view of achievable precision. Here
    is a professional astronomer, using gear with which he is thoroughly
    familiar, the best of its kind that existed (from the early 19th century),
    correcting carefully for his index error, and even the temperature. And yet
    from one observation, to the next on another day, he records differences of
    a large fraction of an arc-minute. In my view, it does not support Frank's
    contention, which I paraphrase, perhaps unfairly, that he can pull in anyone
    from the street, present them with a sextant to throw up, to achieve lunar
    distances to a tenth of a minute."
    
    To which Alex responded-
    
    "5. How Frank comes with the "mean error" of 0'.1,
    I don't know. But I cannot believe that Frank did what
    George's letter suggests: averaged the errors
    of observations taken in different weeks/months!"
    
    But that is exactly what he did.
    Frank has defended this practice, in 3653, in these terms-
    
    "George, how is this 'throwing out the baby with the bathwater'? For a
    rather
    long time, I have said that you can expect to get +/-0.25 minute of arc
    accuracy (in a standard deviation sense) in lunars with a good sextant for
    single observations, and that by averaging sets of four, you can expect
    double that accuracy. This article confirms that, so what's the problem??? "
    
    and Alex comments, in 3665,
    
    "Averaging observations taken a week or more apart
    has nothing to do with sea practice. Or even with
    land travel. It only makes sense when you determine
    longitude of a fixed observatory."
    
    ==================
    
    And that's exactly the point. It depends on your purpose. Averaging groups
    of observations, even those taken on different dates, makes good sense in
    determiming the longitude of Melbourne observatory. In fact, the more
    variety in the observations, in time-of-month, body-sighted, arc-region on
    sextant, whatever, the more trustworthy the overall averaged result is
    likely to be.
    
    But if you are trying to demonstrate the observational SCATTER, it's absurd
    to conflate readings taken on different dates, with different moon phases,
    wildly differing arc readings. If there are scale errors in the sextant, if
    there are prediction errors in the almanac, deficiencies in the clearing
    process, that procedure will average them out, whereas to demonstrate
    scatter, you need to show them up.
    
    Nothing wrong with averaging lunars taken in groups of four or whatever, as
    long as they have been taken together under similar conditions, and
    constitute as a whole a single observation. These do not.
    
    ==================
    
    In Frank's latest mailing, he defends his practice, saying-
    
    | Take them in sets of four and average. Yes, this is a legitimate procedure
    | when each sight is individually cleared to yield a longitude.
    
    It's legitimate for yielding a longitude. It's illegitimate for
    demonstrating scatter.
    
    George.
    
    contact George Huxtable at george---.u-net.com
    or at +44 1865 820222 (from UK, 01865 820222)
    or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
    
    
    
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