Prof. John Huth
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Transcript of Prof. John Huth
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Latitude and Longitude in theMiddle ages or…
what can you learn from a table of numbers and names about the world
of the 12th Century?
Prof. John Huth
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Circa 200 AD
• Ptolemy:• Inhabited world (occumene) documented• Segregated latitude regions into climes• Tables of latitude and longitude of major cities• Prime meridian = Fortunate Isles (Canaries)• Astrology• Astronomy (geocentric universe)• Works inherited by Arabs
– Copied by scribes, added to over the years
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Equator and pole define 0 and 90 degrees of latitude. Prime meridian ( 0 degrees) of longitude is arbitraryModern: Greenwich, Ancient: Canary Islands (Fortunate Is)
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Primary motivations for latitude and longitude
Horoscopes need birth informationLat., long date, and time of birth
Face Mecca to pray (Qibla) alonggreat circle route
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Gerard of Cremona – 1114-1187 translator from Arabic to Latin
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Snippet of values in Marseilles Tables (From John Kirtland Wright, 1928)
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Outer Ranges of Marseilles Tables Locations
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Determining latitude: the sun throughout the year
Path of sunin sky
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θ
Latitude is given by θ at shortest length ofshadow during the equinox
The shadow of a stick traces out the path ofa line over the course of the day at theequinox (other days are hyperbolae)
Accuracy ≈ 1 degree
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The problem with longitude
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Finding longitude
• Dead reckoning (deduced reckoning)– Travel times/distances between locations– Need radius of earth– Accurate at 10-20% level
• Clocks using a common time (eg. Greenwich mean time)– Nothing stable enough in middle ages
• Astronomical events as “clock”
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Most precise determination of longitude in 12th century:
Timing of sunset to lunar eclipse (Roger of Hereford)
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Eclipse tables used by Columbus
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City difference Long. descr Lat . descrMecca-Damascus 3.6 deg. 0.15 deg
Mecca-Baghdad 8.3 deg 0.57 deg
Damascus-Baghdad
11.0 deg 0.42 deg
Lat/long separations in Toledo tables versus modern
Longitude less precise!
Travel difficult betweenthese cities (large desert)
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Fitting Toledo/Marseilles Tables
• Goals:– Establish typical precision of latitude– Establish typical precision of longitude– Compare zero degrees for equator to table– Find “best fit” to Prime Meridian
• Canary Islands?
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Data selection
• Establish correspondence with place names– Not so easy, many names have no modern correlates
(Missera? Aranida?)• Throw out islands
– Too large for a precise target• Throw out locations where dead reckoning was
likely used for latitude (Gana, Urbs a Nuba)• Throw out entries that looked like transcription
errors.
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Locations on an equirectangular plot
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Latitude difference = -0.25 ± 0.27 degrees Consistent with equator as zero
Longitude difference = 23.0 ± 1.3 degrees Consistent with ????
Latitude standard deviation = 1.4 degrees Consistent with typical shadow stick method
Longitude standard deviation = 6.5 degrees Consistent with dead reckoning
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What on Earth is at 23 degrees W Long.?
But but but…
Cape Verde Is.discovered byPortuguese in1460.
Inconsistent withCanary Is.(16 deg. W)
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Contemporary sources
Yaqut al-Hamani: “the Fortunate Islands lie200 farsakhs west of the coast of the lands ofthe Maghrib”
600 miles consistent with Cape Verde, not Canary Is.
Roger Bacon: placed the Prime Meridian – furthest extent of terra firma - 28 degrees W. of Toledo, inconsistent with Canary Islands
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Systematic effects?
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Diameter of the Earth?
Some correlationfor cities aroundMediterranean
-10.00 0.00 10.00 20.00 30.00 40.00 50.00
-8.00
-6.00
-4.00
-2.00
0.00
2.00
4.00
6.00
8.00
10.00
12.00
Long diff
Long diff
Modern longitude
Dev
iatio
n fr
om 2
1.57
However, consistent w/ flat
Would requirea 20% underestimateof Earth’s diam.(far more precisionin Muslim world)
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Summary
• Table of latitude/longitude illustrates extent of Earth known in 12th century to the West and Muslims
• Latitude measurements consistent with shadow – stick method
• Longitude measurements consistent with dead reckoning
• Location of Prime Meridian at 23 degrees suggests that Muslims knew of Cape Verde Islands – more work would be needed to advance this