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    Re: Lunar distance accuracy
    From: George Huxtable
    Date: 2007 Oct 24, 12:10 +0100

    Frank Reed refers to the paper from E J White, in the Proceedings of the
    Royal Society of Victoria, Vol 1 June 1889, that we've seen a year ago.
    
    It can be found at-
    http://www.clockwk.com/lunars/ejwhite
    
    And indeed, it's a well-informed article, describing some years of
    painstaking observation, and raising several interesting questions.
    
    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?
    
    He records Sun lunars, well spaced in time, by days, weeks, or months, taken
    from the same spot on land, to the highest precision he can achieve, looking
    for consistency and conformance with his longitude from Greenwich, known
    from telegraphic determinations.
    
    White uses a Troughton "pillar-sextant" from the early 1800s. That term has
    been used elsewhere in two different contexts.
    
    Occasionally, it's been used for a handheld sextant in which, to save
    weight, the frame was made from two thin brass sheets, spaced apart by short
    brass pillars, which should more properly have been called a double-frame
    sextant, and usually was.
    
    Otherwise (and this is the meaning that seems to be relevant here) it's a
    sextant firmly mounted on a pillar stand, for use on land, not at sea. It is
    usually arranged so that the whole sextant can be easily rotated about a
    polar axis, parallel with that of the Earth, just as a telescope can. In
    this way the two views from the sextant can be aimed appropriately at the
    two objects (such as Sun and Moon) and then the instrument can be slowly
    rotated about the polar axis to keep them in view, for as long as desired.
    That allows the observer to perfect the alignment of the two bodies taking
    as much time as he wishes, and then time the result, without being
    constrained by the lasting-power of his arm muscles. It aso allows the
    sextant itself to be larger and therefore heavier that a handheld instrument
    could be. It would have been intended for measuring precise longitudes from
    on land (just as Evans was doing) in exploration, and perhaps also for
    measuring star-to-star distances in sky surveys. One would expect the
    ultimate in precision when using it. It would, of course, have been a
    Vernier instrument, not micrometer, but will have been machine-divided, to
    the highest standards, for which Troughton were renowned at that time. Arc
    division of sextants did not get much better over the following century and
    a half.
    
    It's also interesting to note that he was taking lunar distances that
    frequently exceeded 120 degrees, the greatest being just over 130. That has
    some interesting implications. First, that his sextant could cope with that
    excess angle, in its length of scale and in depth of view in its index
    mirror (though that wasn't uncommon). Second, that as an observer he fould
    it possible to get Sun and Moon aligned in the plane of his sextant when so
    far apart. That's a matter that many observers find really difficult with
    large angular distances, and perhaps his pillar-mounting would help,
    allowing him to take his time over the job. And thirdly, that although the
    early Nautical Almanac had restricted its Sun lunar distance predictions to
    120 degrees, by White's date that limit had increased to over 130.
    
    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.
    
    White compares his longitudes as being only 4.8s out from those determined
    by the electric telegraph. I wonder how recently the telegraph had arrived
    in Melbourne, and how precisely time from Greenwich could then be determined
    in that way? The responses of early telegraph receivers were slow, and no
    doubt there were several relay stages along the way, with perhaps human
    hands required to pass the signals on. No doubt a lot could be done by
    timing round-trip loops to decide a figure for the delay. But if Greenwich
    Time could be transferred to Melbourne to within decimal parts of a second,
    that was pretty good going, in 1889. Not that I am questioning it, just
    remarking on the achievement.
    
    Another point that White refers to is the errors in Moon predictions in the
    Nautical Almanac, which "forty years ago" he says (i.e. 1849) could amount
    to 22 miles in longitude. That was a disgraceful state of affairs, little
    better than Mayer's predictions of a century before. Improvements came first
    in the American ephemeris, followed later by Greenwich.
    
    ===========================
    
    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.
    
    ====================
    
    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. 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.
    
    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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