NavList:

I had posed this question [Navlist 188].

> Departing from Shetland, with its Northerly point in sight, at a
> certain time-by-chronometer, an alt. of the Sun (supposing the N.
> end
> of Shetland to lie in long. 38'W) gave the Chronometer slow of
> Greenwich 3 minutes 39 seconds ...
>
> However, even in British home waters, the less-frequented parts had
> not all been well surveyed by 1818, and the charts carried may have
> been somewhat defective. Anyway, a modern atlas puts the N end of
> Shetland at about 0 deg 50' W, rather than 0 deg 38' W as had been
> assumed; quite a difference.
>
> In the light of that information, what should the chronometer error
> have really been?

Thanks to Lars Bergman and Fred Hebard, who agreed (after an initial
difference about the amount) that in the light of knowing the true
longitude of the North of Shetland, the chronometer would actually
have been slow, on Greenwich, by 4 minutes 27 seconds, rather than by
3 minutes 39 seconds as presumed.

That mattered a bit more than it might seem, because the RATING of the
chronometer, the daily loss or gain with respect to Greenwich, had
been based on that Shetland observation, taken along with some earlier
determination. We are not given any information about that previous
timing, but the ship had been lying in the Mersey, at Liverpool, on
April 1st, departing early on the 2nd. So it's most likely, then that
the chronometer had been checked by a port time-signal around noon on
April 1st, which was 19 days before that Shetland observation. From
the change in its time with respect to Greenwich, over that 19-day
interval, it had been deduced to be gaining at 10 seconds per day. In
which case, on April 1st it must have been slower on Greenwich, by 19
x 10 seconds, so must have then been slow by 6 minute 49 seconds ( 190
seconds plus 3 min 39 sec)

Now, knowing more about the Shetland longitude, we can reassess that
chronometer rate. If it was actually slow, off Shetland, by 4 minutes
27 seconds (and not 3 minutes 39 seconds as had been deduced), then it
had gained, in the 19 days since Liverpool,  2 minutes 22 seconds, or
7.5 seconds a day, not 10 seconds a day as previously thought.

As the vessel would be away from well-charted landmarks until her
return, 4 months later, any such error of 2.5 seconds per day in the
assumed chronometer rate would accumulate, and on returning to
Shetland waters (when longitude REALLY mattered) could be out by some
300 seconds, or 5 minutes of time, or 1 degree 15 minutes of
longitude, or 37 miles. More than enough to make all the difference
between safety and disaster, in such rock-strewn and unlit waters.

All this assumes a perfect chronometer; one for which the rate isn't
zero but stays absolutely constant over the Summer voyage. It goes to
show that the chronometer did not always provide the complete answer
to a navigator's needs, when the voyage was a prolonged one.

Using that chronometer the navigator was able, 8 days after leaving
Shetland, to deduce a longitude for Beerenberg Mountain, on Jan Mayen
island, to be within a minute of its modern value, so in practice his
chronometer was behaving well (or else his errors were cancelling
out).

================================

Fred wrote "I'm not sure what slow of Greenwich means", and it's true,
our choice of words about timing, is rather illogical, and confusing.

When we refer to a clock as being "slow", we don't necessarily mean
that it's "going" slowly at all. We mean that it's late, behind the
true time. It might easily be "gaining", getting ahead, or "losing",
falling back, on true time, and logically, those rates are what the
words fast and slow should refer to. But it's far too late to change
common usage now, and we just have to go along with it.

George.

contact George Huxtable at george@huxtable.u-net.com
or at +44 1865 820222 (from UK, 01865 820222)
or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.


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