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History of longitude
The history of longitude describes the centuries-long effort by astronomers, cartographers and navigators to discover a means of determining the longitude (the east-west position) of any given place on Earth. The measurement of longitude is important to both cartography and navigation. In particular, for safe ocean navigation, knowledge of both latitude and longitude is required, however latitude can be determined with good accuracy with local astronomical observations.
Finding an accurate and practical method of determining longitude took centuries of study and invention by some of the greatest scientists and engineers. Determining longitude relative to the meridian through some fixed location requires that observations be tied to a time scale that is the same at both locations, so the longitude problem reduces to finding a way to coordinate clocks at distant places. Early approaches used astronomical events that could be predicted with great accuracy, such as eclipses, and building clocks, known as chronometers, that could keep time with sufficient accuracy while being transported great distances by ship.
John Harrison's invention of a chronometer that could keep time at sea with sufficient accuracy to be practical for determining longitude was recognized in 1773 as first enabling determination of longitude at sea. Later methods used the telegraph and then radio to synchronize clocks. Today the problem of longitude has been solved to centimeter accuracy through satellite navigation.
Eratosthenes in the 3rd century BC first proposed a system of latitude and longitude for a map of the world. His prime meridian (line of longitude) passed through Alexandria and Rhodes, while his parallels (lines of latitude) were not regularly spaced, but passed through known locations, often at the expense of being straight lines. By the 2nd century BC Hipparchus was using a systematic coordinate system, based on dividing the circle into 360°, to uniquely specify places on Earth. So longitudes could be expressed as degrees east or west of the primary meridian, as is done today (though the primary meridian is different). He also proposed a method of determining longitude by comparing the local time of a lunar eclipse at two different places, to obtain the difference in longitude between them. This method was not very accurate, given the limitations of the available clocks, and it was seldom done – possibly only once, using the Arbela eclipse of 330 BC. But the method is sound, and this is the first recognition that longitude can be determined by accurate knowledge of time.
Ptolemy, in the 2nd century AD, based his mapping system on estimated distances and directions reported by travellers. Until then, all maps had used a rectangular grid with latitude and longitude as straight lines intersecting at right angles. For large areas this leads to unacceptable distortion, and for his map of the inhabited world, Ptolemy used projections (to use the modern term) with curved parallels that reduced the distortion. No maps (or manuscripts of his work) exist that are older than the 13th century, but in his Geography he gave detailed instructions and latitude and longitude coordinates for hundreds of locations that are sufficient to re-create the maps. While Ptolemy's system is well-founded, the actual data used are of very variable quality, leading to many inaccuracies and distortions. Apart from the difficulties in estimating rectilinear distances and directions, the most important of these is a systematic over-estimation of differences in longitude. Thus from Ptolemy's tables, the difference in Longitude between Gibraltar and Sidon is 59° 40' 0', compared to the modern value of 40° 23'0', about 48% too high. Russo (2013) has analysed these discrepancies, and concludes that much of the error arises from Ptolemy's underestimate of the size of the Earth, compared with the more accurate estimate of Eratosthenes – the equivalent of 500 stadia to the degree rather than 700. Given the difficulties of astronomical measures of longitude in classical times, most if not all of Ptolemy's values would have been obtained from distance measures and converted to longitude using the 500 value.
Ancient Hindu astronomers were aware of the method of determining longitude from lunar eclipses, assuming a spherical Earth. The method is described in the Sûrya Siddhânta, a Sanskrit treatise on Indian astronomy thought to date from the late 4th century or early 5th century AD. Longitudes were referred to a prime meridian passing through Avantī, the modern Ujjain. Positions relative to this meridian were expressed in terms of length or time differences, but degrees were not used in India at this time. It is not clear whether this method was put into practice.
Islamic scholars knew the work of Ptolemy from at least the 9th century AD, when the first translation of his Geography into Arabic was made. He was held in high regard, although his errors were known. One of their developments was to add more locations to Ptolemy's geographical tables with latitudes and longitudes, and in some cases improving the accuracy. The methods used to determine most of the longitudes are not given, but a few accounts do give details. Simultaneous observations of two lunar eclipses at two locations were recorded by al-Battānī in 901, comparing Antakya with Raqqa, determining the difference in longitude between the two cities with an error less than 1°. This is considered the best that can be achieved with the methods then available – observation of the eclipse with the naked eye, and determination of local time using an astrolabe to measure the altitude of a suitable "clock star". Al-Bīrūnī, early in the 11th century AD, also used eclipse data, but developed an alternative method involving an early form of triangulation. For two locations differing in both longitude and latitude, if the latitudes and the distance between them are known, as well as the size of the earth, it is possible to calculate the difference in longitude. With this method, al-Bīrūnī estimated the longitude difference between Baghdad and Ghazni using distance estimates from travellers over two different routes (and with a somewhat arbitrary adjustment for the crookedness of the roads). His result for the longitude difference between the two cities differs by about 1° from the modern value. Mercier (1992) notes that this is a substantial improvement over Ptolemy, and that a comparable further improvement in accuracy would not occur until the 17th century in Europe.
While knowledge of Ptolemy (and more generally of Greek science and philosophy) was growing in the Islamic world, it was declining in Europe. John Kirtland Wright's (1925) summary is bleak: "We may pass over the mathematical geography of the Christian period [in Europe] before 1100; no discoveries were made, nor were there any attempts to apply the results of older discoveries. ... Ptolemy was forgotten and the labors of the Arabs in this field were as yet unknown". Not all was lost or forgotten; Bede in his De natura rerum affirms the sphericity of the earth. But his arguments are those of Aristotle, taken from Pliny. Bede adds nothing original.
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History of longitude
The history of longitude describes the centuries-long effort by astronomers, cartographers and navigators to discover a means of determining the longitude (the east-west position) of any given place on Earth. The measurement of longitude is important to both cartography and navigation. In particular, for safe ocean navigation, knowledge of both latitude and longitude is required, however latitude can be determined with good accuracy with local astronomical observations.
Finding an accurate and practical method of determining longitude took centuries of study and invention by some of the greatest scientists and engineers. Determining longitude relative to the meridian through some fixed location requires that observations be tied to a time scale that is the same at both locations, so the longitude problem reduces to finding a way to coordinate clocks at distant places. Early approaches used astronomical events that could be predicted with great accuracy, such as eclipses, and building clocks, known as chronometers, that could keep time with sufficient accuracy while being transported great distances by ship.
John Harrison's invention of a chronometer that could keep time at sea with sufficient accuracy to be practical for determining longitude was recognized in 1773 as first enabling determination of longitude at sea. Later methods used the telegraph and then radio to synchronize clocks. Today the problem of longitude has been solved to centimeter accuracy through satellite navigation.
Eratosthenes in the 3rd century BC first proposed a system of latitude and longitude for a map of the world. His prime meridian (line of longitude) passed through Alexandria and Rhodes, while his parallels (lines of latitude) were not regularly spaced, but passed through known locations, often at the expense of being straight lines. By the 2nd century BC Hipparchus was using a systematic coordinate system, based on dividing the circle into 360°, to uniquely specify places on Earth. So longitudes could be expressed as degrees east or west of the primary meridian, as is done today (though the primary meridian is different). He also proposed a method of determining longitude by comparing the local time of a lunar eclipse at two different places, to obtain the difference in longitude between them. This method was not very accurate, given the limitations of the available clocks, and it was seldom done – possibly only once, using the Arbela eclipse of 330 BC. But the method is sound, and this is the first recognition that longitude can be determined by accurate knowledge of time.
Ptolemy, in the 2nd century AD, based his mapping system on estimated distances and directions reported by travellers. Until then, all maps had used a rectangular grid with latitude and longitude as straight lines intersecting at right angles. For large areas this leads to unacceptable distortion, and for his map of the inhabited world, Ptolemy used projections (to use the modern term) with curved parallels that reduced the distortion. No maps (or manuscripts of his work) exist that are older than the 13th century, but in his Geography he gave detailed instructions and latitude and longitude coordinates for hundreds of locations that are sufficient to re-create the maps. While Ptolemy's system is well-founded, the actual data used are of very variable quality, leading to many inaccuracies and distortions. Apart from the difficulties in estimating rectilinear distances and directions, the most important of these is a systematic over-estimation of differences in longitude. Thus from Ptolemy's tables, the difference in Longitude between Gibraltar and Sidon is 59° 40' 0', compared to the modern value of 40° 23'0', about 48% too high. Russo (2013) has analysed these discrepancies, and concludes that much of the error arises from Ptolemy's underestimate of the size of the Earth, compared with the more accurate estimate of Eratosthenes – the equivalent of 500 stadia to the degree rather than 700. Given the difficulties of astronomical measures of longitude in classical times, most if not all of Ptolemy's values would have been obtained from distance measures and converted to longitude using the 500 value.
Ancient Hindu astronomers were aware of the method of determining longitude from lunar eclipses, assuming a spherical Earth. The method is described in the Sûrya Siddhânta, a Sanskrit treatise on Indian astronomy thought to date from the late 4th century or early 5th century AD. Longitudes were referred to a prime meridian passing through Avantī, the modern Ujjain. Positions relative to this meridian were expressed in terms of length or time differences, but degrees were not used in India at this time. It is not clear whether this method was put into practice.
Islamic scholars knew the work of Ptolemy from at least the 9th century AD, when the first translation of his Geography into Arabic was made. He was held in high regard, although his errors were known. One of their developments was to add more locations to Ptolemy's geographical tables with latitudes and longitudes, and in some cases improving the accuracy. The methods used to determine most of the longitudes are not given, but a few accounts do give details. Simultaneous observations of two lunar eclipses at two locations were recorded by al-Battānī in 901, comparing Antakya with Raqqa, determining the difference in longitude between the two cities with an error less than 1°. This is considered the best that can be achieved with the methods then available – observation of the eclipse with the naked eye, and determination of local time using an astrolabe to measure the altitude of a suitable "clock star". Al-Bīrūnī, early in the 11th century AD, also used eclipse data, but developed an alternative method involving an early form of triangulation. For two locations differing in both longitude and latitude, if the latitudes and the distance between them are known, as well as the size of the earth, it is possible to calculate the difference in longitude. With this method, al-Bīrūnī estimated the longitude difference between Baghdad and Ghazni using distance estimates from travellers over two different routes (and with a somewhat arbitrary adjustment for the crookedness of the roads). His result for the longitude difference between the two cities differs by about 1° from the modern value. Mercier (1992) notes that this is a substantial improvement over Ptolemy, and that a comparable further improvement in accuracy would not occur until the 17th century in Europe.
While knowledge of Ptolemy (and more generally of Greek science and philosophy) was growing in the Islamic world, it was declining in Europe. John Kirtland Wright's (1925) summary is bleak: "We may pass over the mathematical geography of the Christian period [in Europe] before 1100; no discoveries were made, nor were there any attempts to apply the results of older discoveries. ... Ptolemy was forgotten and the labors of the Arabs in this field were as yet unknown". Not all was lost or forgotten; Bede in his De natura rerum affirms the sphericity of the earth. But his arguments are those of Aristotle, taken from Pliny. Bede adds nothing original.