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1491 The year China discovered longitude.

I agree with Kieran in being suspicious of such claims about early Chinese
navigation, although I have not read the book in question and know little
about Chinese navigation and astronomy. Being in general a sceptic about
almost everything, I have some diagreements both with Menzies and with
Kieran.

Kieran quotes from Menzies-

>"Solar and lunar eclipses occur when the sun, moon and earth are in line
>with one another..."

All right so far

>...and when the moon's orbit around the earth is in the same
>plane as the earth's orbit around the sun."

The Moon's orbit round the Earth is never, ever, in the same plane as the
Earth's orbit around the Sun. There is a rather-constant tilt between them
of about 5 degrees. What Menzies should have said was that when the
Earth-Moon line crosses the plane of the Earth's orbit round the Sun,
that's when a lunar eclipse can occur (if the Sun is at the right place
then).

Further on Menzies states-

"The ability to time a lunar eclipse with absolute precision and the fact that
>the same event could be seen simultaneously from different parts of the
>globe were to prove the vital steps in Chinese attempts to find a method of
>calculating longitude."

There is no way to time a lunar eclipse with "absolute precision", as
anyone who has watched one will know. The whole event is fuzzy and
indefinite. If the Sun was a point-source of light, then the edge of the
Earth would show a sharp shadow, which we could time as it crossed the
centre of the Moon's disc, or as it covered the Noon entirely. Then (with a
timekeeper of some sort) the re-emergence could be timed in the same way,
and the midpoint between them would give what was wanted. Because the Sun
subtends half-a-degree, however, the Earth's shadow has a VERY indefinite
extent (the penumbra); the moment of the Moon entering completely into full
shadow is indeterminate, and the moment of mid-eclipse can be estimated
only within 5 or 10 minutes by human eye. It's made rather worse because
even in full umbra, light escapes round the Earth's disc through refraction
in its atmosphere, so the Moon never gets quite dark.

Kieran should remember that what was proposed in Menzies' text was not
longitudec at sea for navigation, but longitude on land for geographers, by
lunar eclipses. This was first proposed by Hipparchus about 160 BC, and
used by the Greeks for determining some  longitudes, so the Chinese were
not 300 years ahead of Europe, but 1700 years behind. Ptolemy's famous map
of 2nd century AD relied, to some extent, on longitudes determined that
way. It's true, however, that the displacement of scientific learning by
religion had then set such European knowledge back to near-zero in the
period Menzies refers to. But even in that period the Portuguese and
Spanish explorers were starting to try out eclipse observations for
longitude. Even that navigational incompetent Columbus was doing so, though
making his usual hash of it.

Once on land, it's easy to establish the direction of true North from a few
star-azimuth observations from the shore, then knock in a couple of posts
to mark a meridian line, and observe what stars were crossing that line at
the start, and end, of full umbral eclipse.

Without decent predictions of the Moon's position, which were not available
in Europe until the 18th century, Moon eclipse observations would have to
be referred back to records of simultaneous Moon measurements made back at
the base city (Cadiz or Beijing) before a longitude difference could be
deduced. That's one reason why they were useful for exploring geographers
and chart makers, but of little direct use for navigation.

Menzies tells us that the key event that had to be timed (with a star), was
what he calls U3, at the first signs of emergence from full umbra. This
seems surprising, as U2, the entry into full umbra, would have been equally
useful, and the combination of the two more useful still. Menzies' account
makes me wonder if there is some misunderstanding on his part, in that of a
translator, in that of the Chinese scribes that wrote the account, or in
that of the Chinese astronomers who developed the technique. Indeed, later,
Menzies contradicts the earlier statements, in pointing to the advantages
of averaging four eclipse-moments.

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

Kieran says-

>Ummm. I think this is a load of old cobblers for the following reasons:

Not complete "old cobblers", I suggest, but I think there's quite a bit of
cobbling in it.

>1)       How did they determine what star was crossing their local meridian
>at the time of U3? To do this they would have needed an accurate clock and
>done a double altitude shot both ante and post meridian.

Not a problem from an on-land observation, given a night's star-observing
to set up a true North-South line.

>The author
>suggested they used a clepsydras (water clock). Would this have been
>accurate enough?

Yes, I think so, on land.

>Simply recording maximum altitude would not have told them
>the time of meridian passage.

True but irrelevant.

>As an experiment I went outside with a compass and tried to visually
>ascertain true North and which star was crossing my local meridian at a
>point in time. Impossible.

But not if you had marked a meridian line with posts beforehand.

>One technique they could have used was to pick a particular star and observe
>its meridian passage (with an unknown instrument) and determine the elapsed
>time either before or after the U3 phase of the lunar eclipse. The time
>before or after the eclipse could then be compared to that back in Beijing
>at the end of the voyage. But what does that tell you? Nothing I think.

If that could be done, it would provide enough information for longitude to
be deduced, back in Beijing.

>2)       What instrument did they use to make a sufficiently accurate
>celestial observation of a star to determine its meridian passage?

Two posts in the ground: see above.

>Certainly
>not a sextant! Did they have telescopes to determine the exact moment of U3.
>I don't think so.

I don't think they did. As explained above, the different moments within a
Lunar eclipse are so fuzzy and ill-defined that a telescope would be no
better than the naked eye. A modern photometer would have been extremely
useful, however!

>3)       Could this observation have been made without a very accurate set
>of tables such as a Nautical Almanac?

Yes, the observation could, and then compared with observations back home.
But it would have been useful to know at which full Moon a lunar eclipse
was likely, and that doesn't need precise positional prediction. The
explorer would be aware that an eclipse happens (if it does happen) at the
very moment of full Moon, so he could work out which night to keep his eyes
open for it.

>4)       What happened if no star was crossing the meridian at the time of
>U3 or was so faint that it could not be observed? As suggested above they
>may have picked a star and determined the time interval between its meridian
>passage and U3.

Well, the Chinese were certainly an inventive lot. They could have made a
sketch of a constellation which spanned the meridian line, indicating just
where that line crossed it.
>
>5)       The technique requires knowledge of local magnetic variation i.e.
>the observer is trying to find out when the star crosses his local true
>meridian. The Chinese knew the difference between magnetic north and true
>north by reference to Polaris visible at Beijing. Not so once the sailed
>down into the southern latitudes. Something like a shadow stick is a
>possibility I suppose.

Kieran keeps placing the observer on board ship, but I don't think any
claim is being made that this technique was for use at sea. The magnetic
compass isn't involved.

>The technique described in the book, as I understand it, would give the
>Local Apparent Time of a Lunar Eclipse in a distant part of the world which,
>some time later, could be compared to the Local Apparent Time of a Lunar
>Eclipse in Beijing on the same day. I would appreciate any input from list
>members because if this assertion is true it requires a complete rewriting
>of history.

That assertion is quite true and has been known for over 2000 years. The
difference in longitude between two locations can be defined as the
difference in Local Apparent Times of a simultaneous event observed in
both. No rewriting of history is called for.

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

Note that one reason why lunar eclipses are so little use to mariners is
that they occur so infrequently, and presumably, by Sod's Law, never when
needed. From what I have read (with some scepticism) about Chinese
exploration, their travels, around South-East Asia, were rather leisurely
ones. The geography of the area implied that theirs were mainly coasting
passages, not great ocean travels. Here and there they would stop, to
plant, grow, and reap a crop of rice to keep them going for the next stage.
So there was plenty of time on-land to observe lunar eclipses.

Note also that in the passage quoted, Menzies makes no claim for what
accuracy the Chinese obtained for their longitudes, except for his
unjustified statements about the precise timing of an eclipse. The eclipse
method required none of the extreme precision demanded by lunar distances,
and I suggest that a careful observer might have managed to get longitudes
to a couple of degrees. It all depended on how well he could time that
fuzzy eclipse.

Thanks to Kieran for introducing an interesting topic, likely to bring out
other views than mine.

George.

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