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

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

Equator and pole define 0 and 90 degrees of latitude. Prime meridian ( 0 degrees) of longitude is arbitraryModern: Greenwich, Ancient: Canary Islands (Fortunate Is)

Primary motivations for latitude and longitude

Horoscopes need birth informationLat., long date, and time of birth

Face Mecca to pray (Qibla) alonggreat circle route

Gerard of Cremona – 1114-1187 translator from Arabic to Latin

Snippet of values in Marseilles Tables (From John Kirtland Wright, 1928)

Outer Ranges of Marseilles Tables Locations

Determining latitude: the sun throughout the year

Path of sunin sky

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

The problem with longitude

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”

Most precise determination of longitude in 12th century:

Timing of sunset to lunar eclipse (Roger of Hereford)

Eclipse tables used by Columbus

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)

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?

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.

Locations on an equirectangular plot

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

What on Earth is at 23 degrees W Long.?

But but but…

Cape Verde Is.discovered byPortuguese in1460.

Inconsistent withCanary Is.(16 deg. W)

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

Systematic effects?

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)

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