NavList:

John,

I agree that someone else probably attempted using the eclipse method prior
to Columbus, I'm just not aware of it.

I think this is an interesting question.

I've done a bit of toying around with water clocks to understand their likely accuracy.

So what is your conclusion about the accuracy?
I know that very sophisticated water clocks were built by Greek scientists
more than 2000 years ago, but I suppose this technology was
lost in the dark age. And most importantly, there was no need for it.

There are also other ways of timing, escept water clocks,
especially if you use occultations of stars instead of eclipses.
So, for exaple, if Ptolemy really wanted to determine the
difference in longitude between Alexandria and London,
and had sufficient money grants from the govmnt:-) he could send
an assistant to London to observe some occultations of stars by the Moon,
and time them (local time) by astronomical observations if they occured at night.

For this procedure, one needs neither exact Moon theory, nor exact star
catalog, one just needs accuracy sufficient for rough prediction
of occultations for few months needed for travel, to agree in advance which events to observe.

I find it amazing that we have no information of any of such experiments,
and I think the main reason was that there was no money grants for this:-)
There was just no sufficient interest.

Here is somewhat similar situation. 2000 years from now, someone asks
on the list: Could these XX century people travel to Mars?
The answer is "Yes. But they did not want to. There was no need to
justify the expense".

Alex.



    If you're trying

for an interval of, say, 6 hours, which would be necessary for the eclipse
method, I reckon that with some care, you might be able to get within about
one and a half degrees (6 minutes).

On Sun, Sep 2, 2012 at 9:48 AM, <eremenko---purdue.edu> wrote:

The earliest use that I'm aware of of using eclipses for longitude was

the

attempt by Columbus on his last voyage when marooned in St. Annes' Bay in
what is now Jamaica.   He used an ephemeris publish by Regiomontanus.

I read somewhere that the error was  18 degrees.
But it would be very interesting to know whether this was indeed
the earliest attempt in history.

I do not mean only seamen, but also geographers/astronomers.
The principle which was known for 1400 years at least was tested
by Columbus for the first time??

Alex.

On Sat, Sep 1, 2012 at 8:22 PM, Lu Abel <luabel---com> wrote:

You're right, Alex, I did substitute "latitude" for "longitude" in my
note.   Bad typo....

But the question remains.   Could someone in the 12th century, burdened
by
Roman numerals and pen-and-paper calculations, have determined his
longitude, even on land much less at sea?

Yes, Barentz did do an excellent job of determining his longitude, as
you
noted.   But what post 12th century knowledge was required to do that?


  ------------------------------
*From:* "eremenko---purdue.edu" <eremenko---purdue.edu>
*To:* NavList@fer3.com
*Sent:* Saturday, September 1, 2012 3:31 PM

*Subject:* [NavList] Re: Finding longitude in the 12th century


Dear Lu,

proves my thesis that it would have been almost impossible to produce

a

sight reduction method such as HO214 in the 12th century even if the
basics of trig were available.

I did not say anything of the sight reduction method.
"Sight reduction" is solving a spherical triangle.
This was well known to Ptolemy in II AD.

I was addressing the longitude question.

looked up "decimal numbers" in Wikipedia and it contains an almost

useless

history of them, citing obscure civilizations that might have used

them

three millenia ago, but not giving a whit of history on exactly how

and

why they displaced Roman numerals in Europe.

The article clearly and correctly says that decimal system was
introduced
in Europe by Simon Stevin in XVI century. The article on "Simon Stevin"
says in 1585. So it is quite possible that Barentsz did not use it:-)

Come to think of it, I remember decimals sometimes being
called "Arabic numerals"

Because the idea (which apparently originated in India) came to Europe
through the Arabs .

So back to the original question -- could someone have determined

their

latitude in the 12th century?

You probably mean longitude.
Latitude they could and did find. The cross-stuff was invented in
the beginning of XIV
century by Levi ben Gershon, but they had other tools like
astrolabias.

The answer seems to be a strong "no" -- at
least with respect to any subsequent technique such as lunar distances

or

the equivalent for star/planet

The answer is the "strong no" unqualified. There were no techniques
that could be used in 12 century and give sufficient precision.
On the land, the methods based on the moon could be used IN PRINCIPLE,
but I am not aware of any actual longitude determination by these
methods
until XVI century. (See my message on Barentsz).

trigonometry -- the theory may have been known, but practical use of

that

theory was impossible.

The principle was known, not the theory. The theory of the Moon motion
reached the needed degree of perfection only in XVIII century, almost
simultaneously with the invention of chronometer.

This has nothing to do with trigonometry. Trigonometry was well
established
(for calculation of things like HMO) in the Ancient Rome.

Alex.

: http://fer3.com/arc/m2.aspx?i=120527

: http://fer3.com/arc/m2.aspx?i=120530