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    Re: Finding longitude in the 12th century
    From: John Huth
    Date: 2012 Sep 2, 12:45 -0400
    I've had several students who have made water clocks and test their accuracy as projects in my course.   A "very good" one was able to keep time to about 10 minutes over the course of 8 hours.    This one was a three container system.   One container puts water in a container that has an 'overflow' and keeps the depth of the water column constant, this one then drains into a cylinder that actually tracks time by the height of water accumulated.   

    These things are sensitive to things like relative humidity (evaporation from final cylinder), air pressure and temperature.   

    There are/were of course hour glasses.   According to Samuel Eliot Morrison's bio of Columbus, he timed the eclipse in St. Anne's Bay with an 'ampoletta', which was a kind of sand glass.   

    I suspect that a lack of drive for precision in longitude may have come from the lack of utility in the middle ages.   The main use of latitude and longitude tables was to make natal horoscopes and figure out how to face Mecca.    I don't know if 6 degrees is "good enough" for these purposes, but that's pretty typical for entries in tables in the 12th century.  



    On Sun, Sep 2, 2012 at 10:19 AM, Alexandre E Eremenko <eremenko@math.purdue.edu> wrote:

    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.











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