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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@huxtable.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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