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    Re: Lunar distance accuracy
    From: Frank Reed
    Date: 2007 Oct 27, 20:38 -0400

    George H, you wrote:
    
    "White refers at one point to Dudley Observatory. Is that the local
    observatory in Melbourne, from where he made his observations? Does it still
    exist?"
    
    I don't know, but he says he kept his sextant at his quarters and mostly
    used it outside of work hours, so I assume that means he was actually making
    his sextant observations from his home near the observatory.
    
    And:
    "White uses a Troughton "pillar-sextant" from the early 1800s. That term has
    been used elsewhere in two different contexts."
    
    Just to reiterate, the term "pillar sextant" was ONLY used for the
    double-frame instrument. Of course a sextant can also be mounted on a stand
    and sometimes those stands were termed "pillar stands". But a sextant on a
    stand is NOT a "pillar sextant". Obviously, this is confusing terminology
    today, but it wasn't back then, and there is no evidence that White's
    sextant was mounted on a stand.
    
    And:
    "It's also interesting to note that he was taking lunar distances that
    frequently exceeded 120 degrees, the greatest being just over 130."
    
    You note that these are more difficult than shorter angles. That's true, but
    they're only a little more difficult. They're certainly less fun, in my
    personal opinion.
    
    And:
    "The telescope on his sextant was mounted on a "rising-piece", to alter its
    spacing from the frame, while keeping it parallel, and White explains how he
    used this to equalise the brightness of the images of the two bodies, so
    that he never needed to change shades."
    
    Yes, that struck me as excellent advice. Since most sextants today have the
    same ability to slide the scope in and out from the frame, this is
    definitely the way to go.
    
    And you wrote:
    "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." "
    And followed by:
    "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."
    
    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:
    "As evidence, those details support Alex's view of achievable precision."
    
    If Alex's view, which has been a moving target, matches what I have written
    in the previous paragraph, then I guess we're all in agreement.
    
    And, referring to E.J. White, you wrote:
    "Here is a professional astronomer"
    
    The fact that he is an astronomer is not particularly relevant except that
    it means he is a very good judge of the sources of error in his
    observations. The fact that he is a professional astronomer and enjoys
    shooting lunars after work for relaxation does, however, tell us something
    about his personality. :-)
    
    Of his sextant, you wrote:
    "the best of its kind that existed (from the early 19th century)"
    
    Right. And this is a CRITICAL point. Accuracy in lunars depends far more on
    the instrument than the observer. The sextant has to be high-quality and
    properly adjusted. But for the hobbyist lunarians on this list, that would
    seem to be the correct target. Also, in many ways, this is White's point. He
    writes at length about the poor quality of many late 19th century sextants
    (Lecky agrees with him). Of course, instruments only need to be sufficiently
    accurate for the intended observations. Since almost no one at sea was
    shooting lunars by this late date, the sextants only needed to be accurate
    enough for standard time sights, meridian sights, etc. A couple of minutes
    of arc error was no big deal for those observations.
    
    And you added:
    "correcting carefully for his index error, and even the temperature."
    
    It's always worth repeating that the index correction is the most important
    observational limitation on accuracy in fine sights like lunars. You have to
    get the I.C. correct first. As for temperature correction, well that's
    hardly impressive. It was known and emphasized in all the manuals from the
    earliest period that a navigator would get better results by correcting for
    temperature, and it takes only a few extra steps to do so.
    
    And you wrote:
    "And yet from one observation, to the next on another day, he records
    differences of a large fraction of an arc-minute."
    
    Large fraction? The standard deviation is 0.25 minutes of arc. Is that a
    large fraction? This is an almost perfect match for my accounts of expected
    lunar distance accuracy.
    
    And:
    "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."
    
    Are you suggesting that I have stretched the truth? I know you wouldn't
    question my intellectual integrity, so I would only say that I have indeed
    done this, with the single caveat that I don't drag in random people and
    force them to shoot lunars until I say they can leave. Naturally, only
    people with an interest choose to participate, and these people often turns
    out to be folks with interest and experience in other "geeky" optical
    fields, like photography and backyard astronomy. And also just a reminder:
    what I see is not "tenth of a minute" accuracy on individual sights, but
    that level on sets of four averaged.
    
    And:
    "Of course, these matters are relevant only to the question of the precision
    achievable in measuring a lunar distance from on land, in perfect conditions
    with precise instrumentation and a firm footing from an already-known
    position. That's a rather academic question, of interest to sextant
    enthusiasts who wish to test their prowess."
    
    Very true.
    
    And:
    "But it bears little relation to the difficulties that would have been faced
    by a real mariner, in a rolling, pitching, vessel, often doused with salt
    spray, with much of the sky obscured by square sails, and when his
    corrections depended on measured altitudes, not those deduced from a known
    position. We need to keep those differences in mind."
    
    Yes, but we also need to be careful not over-emphasize those difficulties.
    Historically, lunars were required perhaps once a week. That leaves plenty
    of opportunity to wait for better weather. As for the sails obscuring the
    sky, in fact, this is not a real issue. Spars and lines and other "features"
    in the sky over your head (think branches and power lines on land) make it
    easier to keep an eye on the Moon in daylight, which is when most lunars
    were done. Once you've found the Moon, which can remarkably difficult even
    when the Moon is bright, you note its position relative to the nearest spar
    (or branch) and then you can get back to it easily whenever you want.
    Finally, why do you think the observation of altitudes would consitute
    another "difficulty"? Those navigators back then measured the altitudes for
    lunar observations because it was EASY to do so and because measured
    altitudes were generally LESS suspect than calculated altitudes.
    
     -FER
    
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