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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

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