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I agree fully with Frank Reed about there being no necessity for three
simultaneous observations when taking lunars.

I imagine that this was done on Navy vessels, with a superfluity of
deck-officers and middies, and a little ceremony made of the occasion, such
as Navy vessels so enjoyed.

No doubt, an extra body would be useful to read the chronometer and make
notes, and perhaps to take a sextant to the lantern to note its reading, so
preserving the navigator's night-vision.


He added-

>You should take a
>look at some of the positions generated during Cook's first Pacific voyage
>during which lunars were used extensively (they brought an astronomer). The
>longitudes are exceptionally good. Navigators using lunars and later
>chronometers
>had no problem finding islands charted by Cook.

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

My comment here is rather tangential to the point that Frank was making.
Even though he had a chronometer on his second and third voyages, Cook
generated about as many lunar positions as on his first.

First, because he had been ordered to test out his new chronometers, and in
unknown seas there was nothing to compare them with except lunars (and
Jupiter satellites).

Second, because it was asking too much to expect a chronometer to continue
keeping good time over such long voyages, lasting for years. In fact, Cook,
using lunars, was able to allow for the accumulating error of his
chronometers, and without that, his chronometer longitudes would have been
of little use.

Third, because Cook's chronometers had their share of failings, stoppings,
and breakdowns: the final failure of the Kendall watch occurring remarkably
close to the time of Cook's own death. It was then necessary to rely on
lunars in order to get home.

It's all in "Background to Discovery", ed. Derek Howse (1990), in Howse's
chapter V, "Navigation and astronomy in the voyages".

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

Now to Frank's statement- "The longitudes are exceptionally good.
Navigators using lunars and later chronometers had no problem finding
islands charted by Cook."

That's true, though it depends what is meant by "exceptionally good". No
matter how precise the observations and calculations were, Cook was
dependent on the accuracy of the lunar distance tables, as we have been
discussing in another thread.

How good were those tables? Well, even twenty-odd years later, an analysis
of Vancouver's longitudes around Juan de Fuca Strait in 1792 shows that
predictions of the Moon's celestial longitude were often out by up to 50
arc-seconds. This followed a cyclic pattern over a lunation. Lunar
distances would show cyclic errors of a similar order. Such errors could
put a calculated longitude out by 25 arc-minutes, maybe more. With this,
any observationl error would have to be combined. Presumably the Moon
predictions were no better in Cook's time. For a lunar, accuracy to 25
minutes would be considered quite good going.

When Cook's longitudes happen to coincide rather precisely with modern
values (and indeed, many do) we have to put at least some of that down to
luck. Either Cook had, without knowing it, happened to make his
observations during that part of the lunation when the Moon prediction
error was small. Or else, some of the inevitable random error in his
observation had happened to work to cancel out some of the error in the
Moon prediction.

Even when a later navigator had a Cook position to guide him to an island,
I presume that he would still approach it along an East-West line, using
latitude sailing. To do otherwise would risk combining any error in Cook's
mapping of longitude, with any error in determining his own longitude at
sea. The island being sought could be put right below the horizon, by the
combined effect of those longitude errors.

George

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