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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,  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  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" 
>>>> *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
>
>
>

   

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