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    Re: Lunars: Jupiter's BIG.
    From: Fred Hebard
    Date: 2003 Dec 24, 11:51 -0500

    I also must thank George for his expansion of his point that lunars
    would be inadequate for rating chronometers.  I agree with his
    conclusion.
    
    On Dec 24, 2003, at 11:14 AM, George Huxtable wrote:
    
    > Fred Hebarf wrote-
    >> In answer to various claims about the accuracy of lunars, it would
    >> seem
    >> to me that the error in lunars should approach the precision of the
    >> sextant, given enough measurements of decent quality and decent
    >> reduction procedures.  That would be 0.1 to 0.2' of arc, or 12-24
    >> seconds.
    >
    > That may be what Fred can reliably achieve on land, with a stable
    > platform
    > beneath his feet. It's rather better than could be expected at sea, in
    > the
    > size of vessel that was used in the heyday of lunars.
    >
    >
    > Replying to Fred's comment that-
    >
    >>> "I believe that to _rate_ a chronometer one needs at least three
    >>> lunars spread over at least three days. "
    >
    > Frank Reed replied-
    >
    >>> Just one lunar will do. When you leave port, you know your
    >>> chronometer's error (assuming it's a port with a well-established
    >>> longitude). Let's suppose it's sixty seconds slow as you depart.
    >>> After
    >>> five months at sea, you get some measure of your longitude. This
    >>> could
    >>> be from speaking another ship, from visiting a port, OR from shooting
    >>> a lunar. Suppose your chronometer now appears to be 4 minutes fast.
    >>> That means it's gaining 1 minute per month. That's the rate.
    >
    > Finding the current rate isn't quite as simple as that. Let's say that
    > at
    > departure the rate had been determined to be zero; neither gaining nor
    > losing, on the basis of, say, time-gun signals over a day or perhaps a
    > few
    > days. And the error in the chronometer time, at departure, happened to
    > be
    > 60 seconds behind Greenwich. And after five months, as Frank presumes,
    > the
    > time error is found to be 4 minutes ahead of Greenwich. We can agree,
    > then,
    > that the AVERAGE rate over that 5-month period has been 1 minute per
    > month,
    > gaining. But that's no more than history, water under the bridge. What
    > we
    > need to know is what is the rate NOW, in order to extrapolate
    > chronometer
    > error into the future.
    >
    > If the rate had been changing smoothly and steadily, from zero at
    > departure, and the average rate over the period was 1 minute per month
    > (gaining), then its current rate at the end of the period would be 2
    > minutes per month (gaining). It's a big assumption, of course, that the
    > rate would change smoothly and steadily.
    >
    > The point I am trying to make is that in order to RATE a chronometer,
    > rather than simply establish its error, one needs to find the rate AT
    > OR
    > NEAR THAT MOMENT, not what it has been averaging over a previous
    > passage.
    > For this to be done, one needs to be back in harbour, with a
    > time-source
    > that's precise to the second or better, and the longitude held
    > constant. It
    > doesn't even require a harbour with known longitude:just any old
    > anchorage
    > will do, using successive time-sights over a day or days, to determine
    > the
    > RATE, though to find the clock-error then requires a spot with known
    > longitude.
    >
    > The trouble with using a lunar to determine rate is that because each
    > measurement is so inaccurate (to a minute or two of time) then any
    > determination of rate over a short interval is hopelessly imprecise.
    >
    > George
    >
    > ================================================================
    > contact George Huxtable by email at george---.u-net.com, by
    > phone at
    > 01865 820222 (from outside UK, +44 1865 820222), or by mail at 1 Sandy
    > Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
    > ================================================================
    >
    
    
    

       
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