Because the Heidelberg papyrus has been raised as an objection to 106 itr as a meridian measure, I added a section to my remen article about it. I also added a couple of supporting quotes from Irina Tupikova and Lucio Russo. The text is below (and hopefully an image) but if you want to read it in my PDF article (pp. 42-45), here is the link:
[home.hiwaay.net]
In 1925, Herbert Thompson stated: From the metrological statements in the papyrus at Heidelberg (dem. no. 1289), “we obtain the following table:
100 cubits = 1 h-nwh
h-nwh x 4 = 1 stadion
h-nwh x 120 = 30 stadia = 1 shfe-t
h-nwh x 240 = 60 stadia = 2 shfe-t = 1 kmy -
- It is unfortunate that the word for the highest measure is written with a single symbol only which gives no clue to the reading. The second part of the word is certainly ‘of Egypt’ and the whole must mean ‘Egyptian schoenus’. Herodotus in a well-known passage (II, 6) states that thirty stadia are equal to a parasang and sixty stadia to a schoenus. The accuracy of this statement has been severely criticized by Prof. SETHE in his Dodekaschoinos (Untersuch., II, Heft 3, 63 seq.). He refers to Artemidorus (as quoted by Strabo), a traveler of circa B.C. 100 and therefore but little later than our document...and concludes in agreement with SCHWARZ (Berl. Studien f. klass. Philologie, XV, Heft 3, 1894) that the schoenus was in later times usually equal to 30 stadia, or less often to 40.”
This statement from the Heidelberg papyrus, written in the 2nd century BC, appears to be a demotic copy of the statement by Herodotus. The only metrological difference between the two is the stadia given by Herodotus, of 600 Greek feet, or 400 Greek cubits, or 185m, versus the stadia from the demotic papyrus of 400 royal cubits, or 210m. Named ancient Egyptian multiples of the royal cubit were the Khet, of 100 royal cubits, and the itr. There was no named ancient Egyptian equivalent for Greek or Roman stadia. In 2004, Gyula Priskin stated: “The relation that one stade is made up of 400 royal cubits seems, however, evident in Papyrus Heidelberg 1289.” Priskin concluded that the stade of Eratosthenes was 400 royal cubits, and based on 5300 Eratosthenian stades as a 50x multiple of 106 itr for the length of Egypt, concluded that the length of the itr, and the Egyptian schoinos, were both 20,000 royal cubits.
In 2018, after comparing straight line distances between known locations, with the distances given in stades by ancient authors, Dmitry Shcheglov stated: “This result might have been regarded as a brilliant confirmation of the short stade hypothesis, but strangely enough, in comparing ancient and modern distances, the proponents of the itinerary stade lose sight of a crucial factor, namely measurement error. Moreover, they proceed from a tacit assumption that distances recorded in ancient sources were almost as accurate as those measured on a modern map. However, this cannot be true for two main reasons. First, with rare exception, there is no indication that distances given by ancient sources derive from actual measurements on the ground, rather than from rough estimates deduced, for example, from the duration and the average speed of travel. Second, and most importantly, even when ancient distances do derive from actual and quite accurate measurements, as is the case with the late Roman itineraries, they were certainly measured not as the crow flies, but including all numerous twists and turnings of the route. Even when ancient surveyors were able to make accurate measurements of separate road sections, they simply had no need and most probably never tried to calculate the overall straight-line distance between start and end points. This is the major reason why distances recorded in ancient sources must inevitably be over-estimated in comparison with those measured in a straight line on the modern map.”
According to Pliny 5.9 “The Nile, dividing itself, forms on the right and left the boundaries of Egypt’s lower part. By the Canopic mouth it is separated from Africa, and by the Pelusiac from Asia, there being a distance between the two of 170 (Roman) miles.” 170 × 4/5 = 136 nautical miles, × 5000 = 680,000 remen, /sq rt 2 = 480,832 royal cubits, /12,000 = 40 Egyptian schoinos. The straight line distance from Alexandria to Pelusium is 136 nautical miles, or 40 schoinos. Herodotus gave two different statements regarding the width of lower Egypt:
HERODOTUS 2.15 “If we desire to follow the opinions of the Ionians as regards Egypt, who say that the Delta alone is Egypt, reckoning its sea-coast to be from the watch-tower called of Perseus to the fish-curing houses of Pelusion, a distance of forty schoinos.”
HERODOTUS 2.6 “As to Egypt itself, the extent of it along the sea is sixty schoines, according to our definition of Egypt as extending from the Gulf of Plinthine to the Serbonian lake, along which stretches Mount Casium; from this lake then the sixty schoines are reckoned.”
HERODOTUS 2.30 “In the reign of Psammetichos garrisons were set, one towards the Ethiopians at the city of Elephantine, another towards the Arabians and Assyrians at Daphnai of Pelusion, and another towards Libya at Marea.”
Modern Kom el Nugus is the location of ancient Plenthine, on the coast of the Plenthine Gulf, at 30°58'N, 29°33'E. The location of the watch-tower of Perseus is unknown and the precise location of Marea is uncertain. In 1854, William Smith stated: “Marea, the chief town of the Mareotic Nome, stood on a peninsula in the south of Lake Mareotis, nearly due south of Alexandria, and adjacent to the mouth of the canal which connected the lake with the Nile. Under the Pharaohs, Marea was one of the principal frontier garrisons of Egypt on the side of Libya.” Heinrich Kiepert’s 1879 map of Roman Egypt gives locations for Marea, Pelusium and Mount Casium.
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Kiepert’s map places Marea, and the peninsula above Marea, slightly farther west of Alexandria, and slightly farther west of the canal that fed the lake, than the description given by Smith. Alexandria’s longitude is 29°55'E. A longitude of 29°52'E places Marea 40 schoinos due west of Pelusium. Opposite Pelusium, the location of the watch tower of Perseus may be associated with Marea, on the fortified western frontier of ancient Egypt. According to Murray and Strabo, the distance from Pelusium to Casium is 10 schoinos. Although Lake Serbonis and the Gulf of Plinthine are both diffuse locations, the given distance of 60 schoinos is also correct.
In 1882, Hultsch stated: “The fortieth of the schoinos is the Eratosthenian stadium of 300 royal cubits, or 157.5 meters.” In 1957, Ivor Thomas stated: “Heron of Alexandria (Dioptra 36), STRABO II.5.7 and Theon of Smyrna (ed. Hiller 124, 10-12), give Eratosthenes’ measurement as 252000 stades, against the 250000 of Cleomedes. ‘The reason of the discrepancy is not known; it is possible that Eratosthenes corrected 250000 to 252000 for some reason, perhaps in order to get a figure divisible by 60 and, incidentally, a round number of 700 stades for one degree. If PLINY XII.13.53 is right in saying that Eratosthenes made 40 stades equal to the Egyptian schoinos at 12000 royal cubits of .525 meters, we get 300 such cubits, or 157.5 meters, i.e., 516.73 feet, as the length of the stade. On this basis 252000 stades works out to 24662 miles, and the diameter of the earth to about 7850 miles, only about 50 miles shorter than the true polar diameter, a surprisingly close approximation, however much it owes to happy accidents in the calculation.’ (Heath -1921, H.G.M. II.107)”
In 2014, Irina Tupikova stated that given the circumference of 180,000 stadia for Ptolemy, and 252,000 stadia for Eratosthenes, and assuming both scholars used the same stadia, “The Ptolemaic earth is too small in comparison with the Eratosthenian earth (i.e. 28,305 km vs. 39,690 km, if one estimates the stadion as 157.5 m). The recalculation of spherical coordinates given on a sphere of one size to a sphere of another size is simple from the mathematical point of view, but requires some experience in the subject. The results of such a recalculation show that if Ptolemy had adopted Eratosthenes’ figure, the majority of his positions would have had coordinates which match their modern counterparts remarkably well. As a consequence, one can confirm first the very high precision of Eratosthenes’ result for the circumference of the earth and second, the near equivalence of the length of stadion used by both scholars.”
In 2013, Lucio Russo stated: “In the Greek world several different ‘stadia’ had been in use and the value of the one used by Eratosthenes is a vexata questio. Hultsch, in 1882, had determined it as 157.5m and this measure was accepted by most of the scholars till the first half of the twentieth century. Among the many other values that have been proposed it seems that the most widely accepted nowadays is 185m, which is the length of the so-called ‘Attic stadion’. This value is documented in many sources, but not explicitly referring to Eratosthenes, while Hultsch’s argument was based essentially only on a single statement by Pliny, which nevertheless refers explicitly to Eratosthenes. If we accept Hultsch’s value, the error of Eratosthenes’ measure is less than 1%, while if we assume that his stadion was the Attic one the error is about 17%. Whereas there is no general agreement on the length of the ‘stadion’ used by Eratosthenes, all scholars agree that later geographers, like Hipparchus, Strabo, Marinus and Ptolemy, used his same stadion (as shown by the fact that many distances in stadia have the same value for all of them).” Based on a statistical analysis of longitudes reported by Ptolemy, Russo stated: “We obtain for the stadion the value of 155.6m. Since 155.6 × 252,000 = 39,211,200m, this value would correspond to an error a little less than 2% on Eratosthenes’ measurement of the great circle of the earth...lending strong support to Hultsch’s determination and allowing us to exclude, in my opinion, that Eratosthenes had used the Attic stadion of 185m or the even larger stadia proposed by some scholars.”
Russo stated that while Cleomedes gave 250,000 stades for Eratosthenes’ circumference, all other ancient sources gave 252,000 for Eratosthenes’ figure, and that Eratosthenes may have given 5,250 stadia as 1/48 of the circumference, giving 252,000 for the circumference, while Cleomedes gave 5000 stadia as 1/50 of the circumference, to simply explain The Method of Eratosthenes in his short account. “In Eratosthenes’ time the angles 1/12 of a turn (corresponding to one sign of the zodiac, or 30° in our notations), 1/24 of a turn (half sign or “step”) and 1/48 of a turn (“part”), as well as sixtieths of a turn, were privileged as units of measurement, so that 1/48 of a turn was a very natural result of an angular measurement, while the angle reported by Cleomedes (1/50 of a turn) is hard to express in the units then used. 5,250 stadia is a plausible result of the measurement of Eratosthenes, because he used to express large distances as multiples of 250 stadia. An important piece of evidence is provided by Strabo, who reports that the distance between Syene and the Mediterranean was estimated by Eratosthenes as 5,300 stadia. Since Strabo always expresses large distances as multiples of 100 stadia, his figure has the best possible agreement with the value of 5,250 stadia.” The length of 5,250 stadia for 1/48 of the circumference gives 252,000 stadia for the circumference, or 700 stades per degree. The length of 5,300 stadia for 1/48 of the circumference gives 254,400 stadia for the circumference, or approximately 707 stades per degree.
The Electronic Egyptology Forum has a very long list of links for open access journal articles that are either old enough to be open access or open access to begin with. Thompson's article is JEA vol. 11 (1925):
[www.egyptologyforum.org]
Priskin: [www.academia.edu]
Shcheglov: [www.academia.edu]
Tupikova: [www.mpiwg-berlin.mpg.de]
Russo: [msp.org]
[home.hiwaay.net]
In 1925, Herbert Thompson stated: From the metrological statements in the papyrus at Heidelberg (dem. no. 1289), “we obtain the following table:
100 cubits = 1 h-nwh
h-nwh x 4 = 1 stadion
h-nwh x 120 = 30 stadia = 1 shfe-t
h-nwh x 240 = 60 stadia = 2 shfe-t = 1 kmy -
- It is unfortunate that the word for the highest measure is written with a single symbol only which gives no clue to the reading. The second part of the word is certainly ‘of Egypt’ and the whole must mean ‘Egyptian schoenus’. Herodotus in a well-known passage (II, 6) states that thirty stadia are equal to a parasang and sixty stadia to a schoenus. The accuracy of this statement has been severely criticized by Prof. SETHE in his Dodekaschoinos (Untersuch., II, Heft 3, 63 seq.). He refers to Artemidorus (as quoted by Strabo), a traveler of circa B.C. 100 and therefore but little later than our document...and concludes in agreement with SCHWARZ (Berl. Studien f. klass. Philologie, XV, Heft 3, 1894) that the schoenus was in later times usually equal to 30 stadia, or less often to 40.”
This statement from the Heidelberg papyrus, written in the 2nd century BC, appears to be a demotic copy of the statement by Herodotus. The only metrological difference between the two is the stadia given by Herodotus, of 600 Greek feet, or 400 Greek cubits, or 185m, versus the stadia from the demotic papyrus of 400 royal cubits, or 210m. Named ancient Egyptian multiples of the royal cubit were the Khet, of 100 royal cubits, and the itr. There was no named ancient Egyptian equivalent for Greek or Roman stadia. In 2004, Gyula Priskin stated: “The relation that one stade is made up of 400 royal cubits seems, however, evident in Papyrus Heidelberg 1289.” Priskin concluded that the stade of Eratosthenes was 400 royal cubits, and based on 5300 Eratosthenian stades as a 50x multiple of 106 itr for the length of Egypt, concluded that the length of the itr, and the Egyptian schoinos, were both 20,000 royal cubits.
In 2018, after comparing straight line distances between known locations, with the distances given in stades by ancient authors, Dmitry Shcheglov stated: “This result might have been regarded as a brilliant confirmation of the short stade hypothesis, but strangely enough, in comparing ancient and modern distances, the proponents of the itinerary stade lose sight of a crucial factor, namely measurement error. Moreover, they proceed from a tacit assumption that distances recorded in ancient sources were almost as accurate as those measured on a modern map. However, this cannot be true for two main reasons. First, with rare exception, there is no indication that distances given by ancient sources derive from actual measurements on the ground, rather than from rough estimates deduced, for example, from the duration and the average speed of travel. Second, and most importantly, even when ancient distances do derive from actual and quite accurate measurements, as is the case with the late Roman itineraries, they were certainly measured not as the crow flies, but including all numerous twists and turnings of the route. Even when ancient surveyors were able to make accurate measurements of separate road sections, they simply had no need and most probably never tried to calculate the overall straight-line distance between start and end points. This is the major reason why distances recorded in ancient sources must inevitably be over-estimated in comparison with those measured in a straight line on the modern map.”
According to Pliny 5.9 “The Nile, dividing itself, forms on the right and left the boundaries of Egypt’s lower part. By the Canopic mouth it is separated from Africa, and by the Pelusiac from Asia, there being a distance between the two of 170 (Roman) miles.” 170 × 4/5 = 136 nautical miles, × 5000 = 680,000 remen, /sq rt 2 = 480,832 royal cubits, /12,000 = 40 Egyptian schoinos. The straight line distance from Alexandria to Pelusium is 136 nautical miles, or 40 schoinos. Herodotus gave two different statements regarding the width of lower Egypt:
HERODOTUS 2.15 “If we desire to follow the opinions of the Ionians as regards Egypt, who say that the Delta alone is Egypt, reckoning its sea-coast to be from the watch-tower called of Perseus to the fish-curing houses of Pelusion, a distance of forty schoinos.”
HERODOTUS 2.6 “As to Egypt itself, the extent of it along the sea is sixty schoines, according to our definition of Egypt as extending from the Gulf of Plinthine to the Serbonian lake, along which stretches Mount Casium; from this lake then the sixty schoines are reckoned.”
HERODOTUS 2.30 “In the reign of Psammetichos garrisons were set, one towards the Ethiopians at the city of Elephantine, another towards the Arabians and Assyrians at Daphnai of Pelusion, and another towards Libya at Marea.”
Modern Kom el Nugus is the location of ancient Plenthine, on the coast of the Plenthine Gulf, at 30°58'N, 29°33'E. The location of the watch-tower of Perseus is unknown and the precise location of Marea is uncertain. In 1854, William Smith stated: “Marea, the chief town of the Mareotic Nome, stood on a peninsula in the south of Lake Mareotis, nearly due south of Alexandria, and adjacent to the mouth of the canal which connected the lake with the Nile. Under the Pharaohs, Marea was one of the principal frontier garrisons of Egypt on the side of Libya.” Heinrich Kiepert’s 1879 map of Roman Egypt gives locations for Marea, Pelusium and Mount Casium.
Kiepert’s map places Marea, and the peninsula above Marea, slightly farther west of Alexandria, and slightly farther west of the canal that fed the lake, than the description given by Smith. Alexandria’s longitude is 29°55'E. A longitude of 29°52'E places Marea 40 schoinos due west of Pelusium. Opposite Pelusium, the location of the watch tower of Perseus may be associated with Marea, on the fortified western frontier of ancient Egypt. According to Murray and Strabo, the distance from Pelusium to Casium is 10 schoinos. Although Lake Serbonis and the Gulf of Plinthine are both diffuse locations, the given distance of 60 schoinos is also correct.
In 1882, Hultsch stated: “The fortieth of the schoinos is the Eratosthenian stadium of 300 royal cubits, or 157.5 meters.” In 1957, Ivor Thomas stated: “Heron of Alexandria (Dioptra 36), STRABO II.5.7 and Theon of Smyrna (ed. Hiller 124, 10-12), give Eratosthenes’ measurement as 252000 stades, against the 250000 of Cleomedes. ‘The reason of the discrepancy is not known; it is possible that Eratosthenes corrected 250000 to 252000 for some reason, perhaps in order to get a figure divisible by 60 and, incidentally, a round number of 700 stades for one degree. If PLINY XII.13.53 is right in saying that Eratosthenes made 40 stades equal to the Egyptian schoinos at 12000 royal cubits of .525 meters, we get 300 such cubits, or 157.5 meters, i.e., 516.73 feet, as the length of the stade. On this basis 252000 stades works out to 24662 miles, and the diameter of the earth to about 7850 miles, only about 50 miles shorter than the true polar diameter, a surprisingly close approximation, however much it owes to happy accidents in the calculation.’ (Heath -1921, H.G.M. II.107)”
In 2014, Irina Tupikova stated that given the circumference of 180,000 stadia for Ptolemy, and 252,000 stadia for Eratosthenes, and assuming both scholars used the same stadia, “The Ptolemaic earth is too small in comparison with the Eratosthenian earth (i.e. 28,305 km vs. 39,690 km, if one estimates the stadion as 157.5 m). The recalculation of spherical coordinates given on a sphere of one size to a sphere of another size is simple from the mathematical point of view, but requires some experience in the subject. The results of such a recalculation show that if Ptolemy had adopted Eratosthenes’ figure, the majority of his positions would have had coordinates which match their modern counterparts remarkably well. As a consequence, one can confirm first the very high precision of Eratosthenes’ result for the circumference of the earth and second, the near equivalence of the length of stadion used by both scholars.”
In 2013, Lucio Russo stated: “In the Greek world several different ‘stadia’ had been in use and the value of the one used by Eratosthenes is a vexata questio. Hultsch, in 1882, had determined it as 157.5m and this measure was accepted by most of the scholars till the first half of the twentieth century. Among the many other values that have been proposed it seems that the most widely accepted nowadays is 185m, which is the length of the so-called ‘Attic stadion’. This value is documented in many sources, but not explicitly referring to Eratosthenes, while Hultsch’s argument was based essentially only on a single statement by Pliny, which nevertheless refers explicitly to Eratosthenes. If we accept Hultsch’s value, the error of Eratosthenes’ measure is less than 1%, while if we assume that his stadion was the Attic one the error is about 17%. Whereas there is no general agreement on the length of the ‘stadion’ used by Eratosthenes, all scholars agree that later geographers, like Hipparchus, Strabo, Marinus and Ptolemy, used his same stadion (as shown by the fact that many distances in stadia have the same value for all of them).” Based on a statistical analysis of longitudes reported by Ptolemy, Russo stated: “We obtain for the stadion the value of 155.6m. Since 155.6 × 252,000 = 39,211,200m, this value would correspond to an error a little less than 2% on Eratosthenes’ measurement of the great circle of the earth...lending strong support to Hultsch’s determination and allowing us to exclude, in my opinion, that Eratosthenes had used the Attic stadion of 185m or the even larger stadia proposed by some scholars.”
Russo stated that while Cleomedes gave 250,000 stades for Eratosthenes’ circumference, all other ancient sources gave 252,000 for Eratosthenes’ figure, and that Eratosthenes may have given 5,250 stadia as 1/48 of the circumference, giving 252,000 for the circumference, while Cleomedes gave 5000 stadia as 1/50 of the circumference, to simply explain The Method of Eratosthenes in his short account. “In Eratosthenes’ time the angles 1/12 of a turn (corresponding to one sign of the zodiac, or 30° in our notations), 1/24 of a turn (half sign or “step”) and 1/48 of a turn (“part”), as well as sixtieths of a turn, were privileged as units of measurement, so that 1/48 of a turn was a very natural result of an angular measurement, while the angle reported by Cleomedes (1/50 of a turn) is hard to express in the units then used. 5,250 stadia is a plausible result of the measurement of Eratosthenes, because he used to express large distances as multiples of 250 stadia. An important piece of evidence is provided by Strabo, who reports that the distance between Syene and the Mediterranean was estimated by Eratosthenes as 5,300 stadia. Since Strabo always expresses large distances as multiples of 100 stadia, his figure has the best possible agreement with the value of 5,250 stadia.” The length of 5,250 stadia for 1/48 of the circumference gives 252,000 stadia for the circumference, or 700 stades per degree. The length of 5,300 stadia for 1/48 of the circumference gives 254,400 stadia for the circumference, or approximately 707 stades per degree.
The Electronic Egyptology Forum has a very long list of links for open access journal articles that are either old enough to be open access or open access to begin with. Thompson's article is JEA vol. 11 (1925):
[www.egyptologyforum.org]
Priskin: [www.academia.edu]
Shcheglov: [www.academia.edu]
Tupikova: [www.mpiwg-berlin.mpg.de]
Russo: [msp.org]