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    Re: Time of meridian passage accuracy, Smart, and Cotter.
    From: George Huxtable
    Date: 2009 Sep 28, 09:54 +0100

    Good. Douglas Denny and I appear to have converged to the point where our
    differences are resolved.
    
    Two by-products of that discussion have emerged, which it may be profitable
    to explore further-
    
    ===============================
    
    The first relates to Smart's predictions for Equation of Time in chapter 6,
    on "Time", in his Text-book on spherical astronomy.
    
    Smart gives a general formula, in his equation 29, in my 1971 edition. That
    equation has also been reproduced in Meeus, as eq. 28.3. Meeus quotes
    Smart's 1956 edition, presumably the copy that was on his shelf. I expect
    it's also in the same form in Douglas Denny's 1977 edition of Smart, as it
    applies always. Meeus gives a way to calculate precisely the "constants" in
    that equation, as they are not actually constant, but vary slowly with time.
    
    In my 1971 edition, Smart also provides , in equation 32, a simpler
    expression, in which he has substituted the values of those "constants", as
    they happened to be in 1931. Douglas tells us that in his 1977 edition,
    those values had been updated to epoch 1975. It matters, to use up-to-date
    values, if any precision is being attempted.
    
    Meeus shows that over the century from 1900, the July value of EoT changed
    by all of 13 seconds of time. That would be enough to throw Sun GHA
    positions out by over 3 arc-minutes. Not a lot, perhaps, but in order to
    predict Sun positions to within "Almanac accuracy" of 0.1 arc-minutes, you
    can put up with no more that half a second of error in EoT. If you tried to
    use the Smart equation 32 for that purpose, it would already be that far out
    within 3 years of the 1975 epoch. Douglas tells us he has updated the
    parameters accordingly, which is the right thing to do. Otherwise, those
    1975 predictions would be out of date by 34 years already, in 2009.
    
    So my warning stands. Do not take the values from Smart equation 32, if you
    want precise answers for Equation of Time. Instead, go to Meeus, where you
    will find all the details to get it exactly right.
    
    ==============================
    
    The second topic relates to Charles H Cotter, and his book, "History of
    Nautical Astronomy", (1968).
    
    In an earlier posting, responding to Douglas' reference to Cotter's
    "Complete Nautical Astronomer", (1969), I wrote-
    
    "Thanks for bringing that Cotter book to my attention. I hadn't come across
    it before. Cotter also treats these questions in his "History of Nautical
    Astronomy",(1968), but some aspects are confused, and several of his
    equations are wrong. Perhaps he had got things clearer by 1969."
    
    To which Douglas Denny replied-
    
    "I have not yet looked to compare Cotter's 'History of Nautical Astronomy'
    with his 'Complete Nautical Astronomy' and check your claim that he was
    inaccurate in some way.   I have all of his books, some with personal
    annotations to me as I knew him from my Cardiff student days.  It is due to
    Charles Cotter that I have an interest in navigation and nautical astronomy
    today.  He was a most charming and generous man and an excellent teacher.
    
    I would be very surprised indeed if he is in any way "Confused" or with
    "wrong equations" as he was a recognised expert in the theroy of nautical
    astronomy."
    
    Douglas should consider the attached list of perceived errors which list
    members have discovered in "History of Nautical Astronomy", and which have
    been disseminated on this list and elsewhere. He may find it useful to keep
    as an errata list with that volume; that's what it was intended for. A few
    of those defects noted may be rather trivial, but many others are certainly
    not so. If he can shoot any down, we would be pleased to make amendments. If
    he discovers other errors, no doubt he will pass them on, and we can add
    them. As a former student of Cotter, I would be interested in any comments
    he may have about the matter.
    
    George.
    
    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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    File: 109966.cotters-errors.doc
       
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