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Jim Wilson wrote-

"... But I'm a bit hazy about your reference to error and rate. I think of
error as the total change, and rate as the daily change. If the rate is
known, than the error can be calculated, and therefore eliminated. I note
that Cook's chronometer had a quite constant rate between mid-1773 and
mid-1775. Knowing that the rate of change was constant, he could have made
corrections based on elapsed time from the last calibration. I assume that
was the normal practice to minimize uncertainty."

comment by George-

Jim has it right. That's how it was done. But how accurately could it be
done? that's the question. The problem is this: you could measure the rate
before departing, ideally over a few days; a week, perhaps. All right if you
had clear skies at the right times. It was a process that could be done very
precisely on land , particularly by timing stars crossing some sight-line,
which always happened at intervals of a sidereal day, 3 minutes 56 seconds
short of a mean solar day . It needed no special equipment, Harrison timed
stars passing the edge of the window frame of his workshop to disappear
behind a neighbour's chimney. But it needed some cooperation from the
weather, unreliable in these parts. And it couldn't be done at sea.

But having got a figure for rate, how reliable would it continue to be? The
vessel is likely to be setting towards a climate that differed greatly from
the test conditions. Although chronometer makers would try to make the rate
independent of temperature, there was always some remaining effect.
Harrison, for the Barbados test, supplied with his chronometer a table
showing how a final adjustment should be made to the stated rate depending
on temperature measued in the cabin, over the voyage. That called for
regular monitoring and recording.

But it was also affected by other factors. Barometric pressure was one.
Arnold's early chronometers were found to be susceptible to corrosion, by
sea-air, of the steel balance-spring, a minute loss of metal which would
affect its stiffness and so, the rate. The natural oils that were used for
lubrication would dry out and harden, over time. Worst, a minute speck of
dust might work its way into a sensitive spot, which could make a sudden
difference, and lead a vessel into danger. After all, trusting to a
longitude that's wrong is far more dangerous than not knowing what it is at
all. That was why, from the 19th century, the standard "fit" for a
well-found vessel was to carry three chronometers. If one suddenly changed
its rate, it was obvious which was at fault.

Remember, just a second a day, over a two-month ocean passage, added up to
an error of a minute of time, or 15' of longitude: not a lot better than you
could hope for from a lunar distance. Over a long journey, precision was
vital. For an explorer, setting off away from known longitudes for years at
a time,  some way to correct for error became vital. Eventually, radio met
that need. Before then, lunar distance, at sea; perhaps Jupiter satellites,
on land.

Jim states-  "I note that Cook's chronometer had a quite constant rate
between mid-1773 and mid-1775. Knowing that the rate of change was constant,
he could have made corrections based on elapsed time from the last
calibration."

Yes, that was exactly the procedure. But there was no way to KNOW that there
had been no change since its last rateing. Cook would spend many weeks
ashore, at places such as Venus point, Tahiti, or Snip Cove, Queen Charlotte
Sound, New Zealand, and an important part of the work was a repeated
astronomical determination of longitude, averaged over many observations
over a long period. This would help to even out some of the regular monthly
cyclic errors in the almanac, about which he was at the time unaware.
Knowing a precise longitude, on a return visit it became a quick and simple
matter to deduce a new value for error of his chronometer.

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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