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    Re: Equal altitudes and double altitudes.
    From: George Huxtable
    Date: 2010 Jun 10, 23:27 +0100

    Geoffrey Kolbe had written, about equal-altitude celestial observations for
    longitude-
    
    "In fact, before the advent of GPS technology, it was probably the most
    accurate way of deriving longitude available - giving very similar
    precision."
    
    I found it hard to credit that he was claiming a similar precision to that
    of GPS, so asked for clarification-
    
    "When Geoffrey says "giving very similar precision", then I ask- similar to
    what?"
    
    The semantic differences, if any, between "accuracy" and "precision" didn't
    trouble me a bit.
    
    Geoffrey has confirmed that indeed, he was claiming " the same accuracy as
    the commonly available GPS receiver, where the circle of uncertainty in
    position has a radius about 5 metres."
    
    That claim has troubled Douglas, and troubles me too. Geoffrey has said
    nothing about the circumstances of such a measurement, but we can be clear
    he wasn't discussing a navigational exercise (certainly not one made at
    sea), but a geographical one, the sort of thing one might do to establish
    the exact position of an observatory.
    
    Presumably, it involves finding a mean time between equal-altitude
    observations of a star.
    Arbitrarily taking the latitude to be 45 degrees, an arc-minute of
    longitude is just over 1300 metres, so the target of 5 metres error
    requires the mean time to be observed to better than 15 milliseconds or so.
    Far beyond the reach of what human hand and eye can possibly manage, this
    somehow calls for the electronic measurement of the moment at which the
    star passes through a predetermined altitude. Not impossible, perhaps, but
    calling for very sophisticated equipment.
    
    And the other quantity required to high precision is the setting of the
    instrument's axis to the true local vertical, with respect to which
    longitude is determined. To reach Geoffrey's claimed 5-metre target, any
    error in setting to that vertical has to be within a quarter of an
    arc-second.
    
    All this may not be impossible, but as Douglas has correctly pointed out,
    it calls for instrumentation that's in the realm of the astronomer, not the
    navigator (not even the land-navigator).
    
    Geoffrey has said nothing at all about the context of the observations for
    which he was claiming such accuracy, and I think it's about time he did.
    
    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.
    ----- Original Message -----
    From: "Douglas Denny" 
    To: 
    Sent: Thursday, June 10, 2010 9:07 PM
    Subject: [NavList] Re: Equal altitudes and double altitudes.
    
    
    >Jim Wilson asked -
    >"I understand that the purpose of the double altitude sight is to get time
    >of meridian passage. Is there another use?"
    
    To which Geoffrey Kolbe replies: ......
    
    "What I meant was the same accuracy as the commonly available GPS
    receiver, where the circle of uncertainty in position has a radius
    about 5 metres."
    Geoffrey Kolbe
    
    =========
    
    Dear Geoffrey,
    
    Having just read this, I am dubious of the claim for accuracy of a circle
    of position of 5 Meres with anything other than observatory standards in
    equipment;  and if no radio time signals available - over a long period of
    time to establish the clock accuracy,  and only with sophisticated and
    accurately divided circles on the Zenith / altitude measuring instrument.
    
    In "ordinary" use by mariners and a sextant, I doubt this would be possible
    even with land based observations and an artificial horizon;  with
    measurements no better than say 0.2 minute of arc accuracy;  and worse,
    time only possible to within a few seconds of absolute with a chronometer.
    Even today with at least guaranteed accurate time signals;  to achieve that
    circle of position would take some doing with a sextant.  Even with a
    theodolite reading to say 20 seconds of arc I would expect it to be
    difficult exercise.
    
    I am open to correction on this of course so would like to know others'
    opinions.
    
    What would be the required accuracy of observation in time and altitude to
    achieve 5 Metre radius of position?  The experts here will post this
    quickly enough no doubt.
    
    Douglas Denny.
    Chichester.  England.
    
    
    ==============================
    Original Posting:
    
    >Jim Wilson asked -
    >
    >"I understand that the purpose of the double altitude sight is to get time
    >of meridian passage. Is there another use?"
    >
    >and Geoffrey Kolbe replied-
    >
    >".... In fact, before the advent of GPS technology, it was probably the
    >most
    >accurate way of deriving longitude available - giving very similar
    >precision.
    
    George Huxtable said
    
    >When Geoffrey says "giving very similar precision", then I ask- similar to
    >what?
    
    I am guilty of an incorrect use of the term, "precision". I should
    have said, "accuracy"
    
    What I meant was the same accuracy as the commonly available GPS
    receiver, where the circle of uncertainty in position has a radius
    about 5 metres.
    
    Geoffrey Kolbe
    
    
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