The Accuracy of Ancient Cartography Reassessed: The Longitude Error in Ptolemy’s Map
Dmitry A. Shcheglov, S. I. Vavilov Institute for the History of Science and Technology
Abstract: This essay seeks to explain the most glaring error in Ptolemy’s ge- ography: the greatly exaggerated longitudinal extent of the known world as shown on his map. The main focus is on a recent hypothesis that attributes all responsibility for this error to Ptolemy’s adoption of the wrong value for the circumference of the Earth. This explanation has challenging implications for our understanding of ancient geography: it presupposes that before Ptolemy there had been a tradition of high-accuracy geodesy and cartography based on Eratosthenes’ measurement of the Earth. The essay argues that this hypothesis does not stand up to scrutiny. The story proves to be much more complex than can be accounted for by a single-factor explanation. A more careful analysis of the evidence allows us to assess the individual contribution to Ptolemy’s error made by each character in this story: Eratosthenes, Ptolemy, ancient survey- ors, and others. As a result, a more balanced and well-founded assessment is offered: Ptolemy’s reputation is rehabilitated in part, and the delusion of high- accuracy ancient cartography is dispelled.
he most striking feature of Ptolemy’s map is the greatly exaggerated longitudinal extent Tof the known world (see Figure 1).1 In comparison with modern maps, Ptolemy’s map
Dmitry A. Shcheglov is a senior research fellow at the St. Petersburg Branch of the S. I. Vavilov Institute for the History of Sci- ence and Technology of the Russian Academy of Sciences. His area of research is the history of ancient science, in particular mathematical geography and cartography. His current research project focuses on Ptolemy’s map and historical metrology. St. Petersburg Branch of the S.I. Vavilov Institute for the History of Science and Technology, Russian Academy of Sciences, Saint Petersburg, Russian Federation; [email protected]. Acknowledgements: I would like to thank Luis Robles Macías, Sorin Forţiu, and the Isis referees and editors for their helpful comments and suggestions. This article is a part of the research project “Internal Structures of Ptolemy’s Map,” supported by the Russian Foundation for Humanities (grant 15-01-00005). 1 By “Ptolemy’s map” I mean, first of all, not the surviving medieval copies thereof but a digital map composed mostly from the text of his Geography (written ca. 150 c.e.). For the text see the newest edition: Alfred Stückelberger and Gerd Graßhoff, eds., Klaudios Ptolemaios: Handbuch der Geographie: Griechisch–Deutsch, Einleitung, Text und Übersetzung, Vols. 1 and 2 (Basel: Schwabe, 2006).
Isis, volume 107, number 4. © 2016 by The History of Science Society. All rights reserved. 0021-1753/2016/0107-0001$10.00. 687
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Figure 1. Ptolemy’s map superimposed over a modern map with Calpe/Gibraltar as a reference point. Isis—Volume 107, Number 4, December 2016 689 appears stretched almost uniformly from east to west by a factor of 1.4.2 Thus, the longitudinal distance between its extreme points, the Fortunate (Canary) Islands in the west and the Sera Metropolis (the capital of China) in the east, is ≈180°3 instead of the actual ≈125º.4 This error has profoundly influenced the history of cartography up to the eighteenth century.5 But how can it be explained?6 Was it due to Ptolemy himself, or to his predecessors with their precon- ceptions about the size of the Earth, or to some errors in distance measurements? Answering this question is crucial for a better understanding both of ancient “scientific” geography that preceded Ptolemy and of his own place in the history of science. First of all, to assess the accuracy of Ptolemy’s map we should bear in mind that he was the first geographer who presented all material solely in terms of spherical coordinates (degrees of latitude and longitude). His predecessors described space mostly in terms of distances stated in customary units (Greek stades, Roman miles, Egyptian schoeni, Persian parasangs, etc.). In this regard, the difference between how latitude and longitude were determined is crucially important. Methods for determining latitude, being rather simple, had been known in Greece since at least the fourth century b.c.e. By Ptolemy’s time, latitudes of a number of the most important cities had been determined (e.g., Alexandria, Rhodes, Athens, Rome, Massalia). In Geography 1.4 Ptolemy calls such cities θεμέλιοι—that is, the “foundations” that should be used as reference points for developing the rest of his map. The problem of determining geographical longitude was efficiently solved only in the eighteenth century with the invention of the marine chronometer. Ancient geographers knew
2 Of course, 1.4 is an averaged value for the whole map. For its different parts, the stretching factor varies from 1.2 for the Eastern Mediterranean to 1.8 for the Western Mediterranean and even to 2.1 for India. For a more detailed analysis see Dmitry A. Shche- glov, “The Error in Longitude in Ptolemy’s Geography Revisited,” Cartographic Journal, 2016, 53:3–14, http://www.tandfonline .com/doi/abs/10.1179/1743277414Y.0000000098. A good illustration of this stretching is given by the maps prepared by Heinrich Kiepert (in The Encyclopaedia Britannica, 9th ed., Vol. 15 [London: Adam & Charles Black, 1898], Plate VII) and by Elisabeth Rinner (in Zur Genese der Ortskoordinaten Kleinasiens in der Geographie des Klaudios Ptolemaios [Bern: Sauer, 2013], p. 12, fig. 1, http://repository.topoi.org/BACP/BACP0066/BACP0066a.pdf ). See also Alfred Stückelberger and Florian Mittenhuber, eds., Klaudios Ptolemaios: Handbuch der Geographie: Ergänzungsband mit einer Edition des Kanons bedeutender Städte (Basel: Schwabe, 2009), p. 267. 3 More precisely, Ptolemy locates the Fortunate Islands either on the zero meridian (in a unique codex Vaticanus graecus 191) or on the meridian of 1° (in other MSS descending from the archetype Ω). At the eastern limit of the known world, Ptolemy places Sera (either Chang’an—i.e., modern Xi’an—or Luoyang) at 177º15′ long and Sina (a city in South China) at 180º long (1.11.1, 15.9–10). 4 Modern longitudes of the aforementioned points are the following: Xi’an at ˗108°54′; Luoyang at ˗112°27′; the Canary Islands lie between ˗18°9′ and ˗13°25′. Accordingly, the longitudinal interval between the extreme points varies from 122°19′ to 130°36′. 5 See, e.g., Gustav Forstner, Längenfehler und Ausgangsmeridiane in alten Landkarten und Positionstabellen (Studiengang Geodäsie und Geoinformation, Universität der Bundeswehr München, 80) (Neubiberg: Univ. Bundeswehr München, 2005), http://www.unibw.de/bauv9/Org/schriftenreihe/pdf-ordner/heft-80/heft-80.pdf; and Luis A. Robles Macías, “The Longitude of the Mediterranean throughout History: Facts, Myths, and Surprises,” e-Perimetron, 2014, 9:1–29, http://www.e-perimetron.org /Vol_9_1/Robles.pdf. 6 Strangely enough, all standard works on Ptolemy’s Geography remain silent on this question: Erich Polaschek, “Klaudios Ptol- emaios: Das geographische Werk,” in Paulys Real-Encyclopädie der classischen Alterthumswissenschaft, Suppl.-Vol. 10 (Stuttgart: Metzler, 1965), cols. 680–833; Germaine Aujac, Claude Ptolémée, astronome, astrologue, géographe: Connaissance et repré- sentation du monde habité (Paris: CTHS, 1993); John L. Berggren and Alexander Jones, Ptolemy’s “Geography”: An Annotated Translation of the Theoretical Chapters (Princeton, N.J.: Princeton Univ. Press, 2000); and Stückelberger and Mittenhuber, eds., Klaudios Ptolemaios (cit. n. 2). Even more strangely, this question has also been neglected in the recent studies aimed at com- paring Ptolemy’s map with a modern one: Andreas Kleineberg, Christian Marx, Eberhard Knobloch, and Dieter Lelgemann, Germania und die Insel Thule: Die Entschlüsselung von Ptolemaios’ “Atlas der Oikumene” (Darmstadt: WBG, 2010); Kleineberg, Marx, and Lelgemann, Europa in der Geographie des Ptolemaios: Die Entschlüsselung des “Atlas der Oikumene”: Zwischen Orkney, Gibraltar und den Dinariden (Darmstadt: WBG, 2012); Marx and Kleineberg, Die Geographie des Ptolemaios: Geogra- phike Hyphegesis Buch 3: Europa zwischen Newa, Don und Mittelmeer (Berlin: epubli GmbH, 2012); and Rinner, Zur Genese der Ortskoordinaten Kleinasiens (cit. n. 2).
This content downloaded from 128.220.159.005 on April 26, 2017 08:50:36 AM All use subject to University of Chicago Press Terms and Conditions (http://www.journals.uchicago.edu/t-and-c). 690 Dmitry A. Shcheglov The Accuracy of Ancient Cartography Reassessed just one rigorous method for determining longitude: measuring the difference in local time between two places through simultaneous observations of a lunar eclipse. This method was pioneered by Hipparchus of Nicaea (ca. 162–127 b.c.e.) but was too impractical to become widely used.7 Ptolemy (Geography 1.4.2) complains openly about the paucity of such observa- tions, giving only one example.8 We may reasonably suppose, therefore, that the longitudes on his map were, with few exceptions, derived from distances measured in customary units.9 Therefore, there are only three factors that can account for the east–west stretching of Ptol- emy’s map:
1. an underestimated value for the circumference of the Earth, which makes all distances projected on its surface (i.e., converted to degrees) proportionally overesti- mated in angular terms;10 2. a systematic overestimate of the distances themselves; 3. a mix-up between different units of distance: Ptolemy might have been unaware that his sources had used a shorter unit than he did. As a result, distances originally expressed in shorter units would have been considered to be longer than they actu- ally were.
None of these factors could significantly affect the latitudinal framework of Ptolemy’s map, because it was firmly referenced to the key points whose latitudes had been determined astro- nomically.11 This is why Ptolemy’s map is stretched mostly in the east–west direction. The ultimate goal of this essay is to evaluate the contribution of each factor to the longi- tudinal distortion of Ptolemy’s map. This problem has far-reaching implications for our un- derstanding of ancient geography in general and for assessing the accuracy of its methods in particular. As the starting point in this investigation, we can take a recent hypothesis addressing the same problem.
I. THE “ WRONG CIRCUMFERENCE HYPOTHESIS” In recent years a number of researchers—Dennis Rawlins (Baltimore), Lucio Russo (Rome), Irina Tupikova (Dresden), and Klaus Geus (Berlin)—have independently proposed essentially the same hypothesis. They all suggest that the longitudinal stretching of Ptolemy’s map can be
7 Hipparchus, frag. 11 Dicks = Strabo, Geography 1.1.12 C7. For more details on and discussion of the pitfalls of this method see Otto Neugebauer, A History of Ancient Mathematical Astronomy, Pts. 1–3 (Berlin: Springer, 1975), pp. 668, 845–848; and Berggren and Jones, Ptolemy’s “Geography,” pp. 29–30. 8 A famous lunar eclipse of 20 Sept. 331 b.c.e. was observed, according to Ptolemy, at Arbela in Assyria and at Carthage (cf. Ar- rian, The Anabasis of Alexander 3.7.6), which gave a three-hour difference between them—i.e., 45º of longitude. This result is overestimated by 1.34 times: the actual distance between Arbela (modern Erbil, 44º long) and Carthage (10º20′ long) is 33º40′. Four similar observations are mentioned by other sources, and three of them also give badly overestimated results: Cleomedes, Caelestia 1.8 (a four-hour difference between Spain and Persia); Hero, Dioptra 35 (two hours between Rome and Alexandria); and Pliny, Natural History 2.180 (two hours between Sicily and Arbela; three hours between Campania and Armenia). 9 Ptolemy himself points this out in Geography 1.4.2. For similar opinions see Konrad Miller, Die Erdmessung im Altertum und ihr Schicksal (Stuttgart: Strecker & Schröder, 1919), p. 42; Otto Cuntz, Die Geographie des Ptolemaeus: Galliae, Germania, Rae- tia, Noricum, Pannoniae, Illyricum, Italia: Handschriften, Text und Untersuchung (Berlin: Weidmann, 1923), p. 110; J. Oliver Thomson, History of Ancient Geography (Cambridge: Cambridge Univ. Press, 1948), p. 343; and Neugebauer, History of Ancient Mathematical Astronomy (cit. n. 7), pp. 667–668, 938. 10 For the mathematics underlying this transformation see Irina Tupikova, Ptolemy’s Circumference of the Earth (Berlin: Max- Planck-Institut für Wissenschaftsgeschichte, 2014), https://www.mpiwg-berlin.mpg.de/Preprints/P464.pdf. 11 Cf. Miller, Die Erdmessung im Altertum und ihr Schicksal (cit. n. 9), pp. 47–48; and Alfred Stückelberger, “Masse und Mes- sungen,” in Klaudios Ptolemaios, ed. Stückelberger and Mittenhuber (cit. n. 2), pp. 241–244.
This content downloaded from 128.220.159.005 on April 26, 2017 08:50:36 AM All use subject to University of Chicago Press Terms and Conditions (http://www.journals.uchicago.edu/t-and-c). Isis—Volume 107, Number 4, December 2016 691 explained completely by a single factor: using the wrong value for the circumference of the Earth.12 This essay presents a critical response to this hypothesis. The hypothesis proceeds from a remarkable coincidence between the average stretching factor of Ptolemy’s map (see above) and the ratio between the two best known ancient estimates of the circumference of the Earth: 252,000 stades calculated by Eratosthenes (ca. 276–194 b.c.e.) and 180,000 stades adopted by Ptolemy—namely, 252/180 = 1.4.13 This coincidence means that if we place Ptolemy’s map, or any part of it, with its linear distances remaining un- changed, onto a sphere with Eratosthenes’ circumference, then all its outlines will turn out to be pretty accurate in comparison with modern maps (numerous examples have been discussed by Tupikova and Geus). Meanwhile, there was a crucial difference between Eratosthenes’ and Ptolemy’s estimates. Whereas the former was almost universally accepted in antiquity,14 including by Ptolemy him- self in his main lifework, the Almagest,15 the latter had been almost unknown before Ptolemy
12 Dennis Rawlins, “Ancient Geodesy: Achievement and Corruption,” Vistas in Astronomy, 1985, 28:255–268; Rawlins, “The Ptolemy GEOGRAPHY’s Secrets,” DIO, 2008, 14:33–58; Lucio Russo, “Ptolemy’s Longitudes and Eratosthenes’ Measurement of the Earth’s Circumference,” Mathematics and Mechanics of Complex Systems, 2013, 1:67–79, http://msp.org/memocs/2013/1-1 /p04.xhtml; Klaus Geus and Irina Tupikova, “Von der Rheinmündung in den Finnischen Golf . . . Neue Ergebnisse zur Weltkarte des Ptolemaios, zur Kenntnis der Ostsee im Altertum und zur Flottenexpedition des Tiberius im Jahre 5. n. Chr.,” Geographia Antiqua, 2013, 22:125–143; Tupikova and Geus, The Circumference of the Earth and Ptolemy’s World Map (Berlin: Max-Planck- Institut für Wissenschaftsgeschichte, 2013), https://www.mpiwg-berlin.mpg.de/Preprints/P439.pdf; Tupikova, “Ptolemy’s World Map and Eratosthenes’s Circumference of the Earth,” Proceedings of the Twenty-sixth International Cartographic Conference, 25–30 Aug. 2013, Dresden, http://icaci.org/files/documents/ICC_proceedings/ICC2013/_extendedAbstract/442_proceeding .pdf; Tupikova, Ptolemy’s Circumference of the Earth (cit. n. 10); and Tupikova, Matthias Schemmel, and Geus, Travelling along the Silk Road: A New Interpretation of Ptolemy’s Coordinates (Berlin: Max-Planck-Institut für Wissenschaftsgeschichte, 2014), https://www.mpiwg-berlin.mpg.de/Preprints/P465.pdf. It should be emphasized that in this section I give only a summary of the common position shared by these scholars. Aside from this common denominator, their positions differ in many details. For example, Russo clarifies his position in later works. He argues that both of Ptolemy’s errors—his underestimated value for the Earth’s circumference and the east–west stretching of his map—resulted from a combination of some accurate distance measure- ments in the east–west direction with the preconceived idea shared by ancient geographers that the whole of the oikoumene must fit inside 180º longitude: Russo,L’America dimenticata: I rapporti tra le civiltà e un errore di Tolomeo, 2nd ed. (Milan: Feltrinelli, 2013); and Russo, “Far-Reaching Hellenistic Geographical Knowledge Hidden in Ptolemy’s Data,” 2016,
This content downloaded from 128.220.159.005 on April 26, 2017 08:50:36 AM All use subject to University of Chicago Press Terms and Conditions (http://www.journals.uchicago.edu/t-and-c). 692 Dmitry A. Shcheglov The Accuracy of Ancient Cartography Reassessed accepted it in the Geography,16 one of his later treatises.17 It is reasonable to assume, therefore, that early versions of Ptolemy’s map or its sources were also initially based on Eratosthenes’ value. On the basis of these observations, it has been argued that the east–west stretching of Ptol- emy’s map was caused by a change in the proposed value of the Earth’s circumference. This means that all the linear distances (in stades, miles, etc.) underlying his map had initially been supposed to be measured on a sphere with Eratosthenes’ circumference, but eventually were converted to angular units (degrees) on a much smaller sphere. As a result, all the distances when expressed in angular units increased by a factor of 1.4. This hypothesis implies that Ptolemy’s sources—or, to put it differently, the early version of his map—were uncannily accurate in terms of spherical coordinates. From this fact, the advo- cates of the hypothesis draw two far-reaching conclusions. The first is that distance measure- ments underlying Ptolemy’s map and Eratosthenes’ value for the circumference of the Earth were equally accurate. This, in turn, implies that the length of the stade used by Eratosthenes must have been close to the 1/252,000 part of the actual circumference of the Earth—that is, close to 158.8–159 m.18 The latter conclusion finds strong support in a long-standing and widely accepted view that Eratosthenes and many other Greek authors of the pre-Roman period used a stade of about 157.5 m, instead of the 185 m accepted after the Roman conquest (see Sect. V for details).
.pdf; Polaschek, “Klaudios Ptolemaios” (cit. n. 6), col. 682; Neugebauer, History of Ancient Mathematical Astronomy (cit. n. 7), p. 939; Berggren and Jones, Ptolemy’s “Geography” (cit. n. 6), p. 20; and Rawlins, “Ptolemy GEOGRAPHY’s Secrets” (cit. n. 12), p. 37 n 13. 16 Before Ptolemy this value was used only twice: by Marinus of Tyre, Ptolemy’s immediate predecessor in geography, and by the Stoic philosopher Posidonius (ca. 135–51 b.c.e.). Therefore, at least two reservations are needed here. First, for the purposes of our study, the question of the relations between Ptolemy and Marinus may be set aside because in the eyes of modern historians they are inseparable, like Siamese twins: Edward H. Bunbury, A History of Ancient Geography: Among the Greeks and Romans, from the Earliest Ages till the Fall of the Roman Empire, 2nd ed., Vol. 2 (New York: Dover, 1959), pp. 520–521, 541–542, 544, 560; Hugo Berger, Geschichte der wissenschaftlichen Erdkunde der Griechen, 2nd ed. (Leipzig: Veit, 1903), pp. 644–647; Ernst Honigmann, “Marinos 2,” in Paulys Real-Encyclopädie der classischen Alterthumswissenschaft, Vol. 14.2 (Stuttgart: Metzler, 1930), col. 1789; and Antonin Wurm, Marinus of Tyre (Some Aspects of His Work) (Choteˇborˇ: Stýblo, 1931), p. 30, http:// ihst.nw.ru/images/geography/Wurm/Wurm_Marinus_of_Tyre_1931.pdf. Marinus and his relations to Ptolemy deserve to be the subject of a separate study. Second, the widespread assumption that Ptolemy (and Marinus) owed the value of 180,000 stades to Posidonius has no basis other than the very fact that they used the same value, which may have been a pure coincidence, as was noted by Berggren and Jones, Ptolemy’s “Geography,” p. 21 n 21. In his reasoning about the measurement of the Earth (frag. 202 Edelstein-Kidd = Cleomedes, Caelestia 1.10.50–2), Posidonius did not aim to achieve accurate results but only wanted to illus- trate the method as such, and this is why he was extremely careless in handling figures: Berger, Geschichte der wissenschaftlichen Erdkunde der Griechen, pp. 577–582; Christian M. Taisbak, “Posidonius Vindicated at All Costs? Modern Scholarship versus the Stoic Earth Measurer,” Centaurus, 1974, 18:253–269; and Ian G. Kidd, Posidonius, Vol. 2: The Commentary, Pt. 2: Testimonia and Fragments 150–293 (Cambridge: Cambridge Univ. Press, 1988), pp. 726–728. In view of this, it seems highly doubtful that an experienced cartographer—Marinus— and an astronomer—Ptolemy—would have uncritically borrowed results from a dilet- tante Posidonius; cf. David Dicks, The Geographical Fragments of Hipparchus (London: Athlon, 1960), pp. 150–151. There are also good reasons to suppose that Ptolemy’s value for the Earth’s circumference was obtained by a method quite different from that used by Posidonius. See Michael J. T. Lewis, Surveying Instruments of Greece and Rome (Cambridge: Cambridge Univ. Press, 2001), pp. 148–155; and Klaus Geus and Irina Tupikova, “Historische und astronomische Überlegungen zur ‘Erdmes- sung’ des Ptolemaios,” in Vermessung der Oikumene, ed. Geus and M. Rathmann (Berlin: De Gruyter, 2013), pp. 171–184. 17 On the chronology of Ptolemy’s works see Schnabel, “Die Entstehungsgeschichte des kartographischen Erdbildes des Klau- dios Ptolemaios” (cit. n. 15); Neugebauer, History of Ancient Mathematical Astronomy (cit. n. 7), pp. 835, 934, 939; and Renate Burri, Die “Geographie” des Ptolemaios im Spiegel der griechischen Handschriften (Berlin: De Gruyter, 2013), pp. 30–33, 45–48. 18 Russo, “Ptolemy’s Longitudes and Eratosthenes’ Measurement of the Earth’s Circumference” (cit. n. 12), p. 70; Tupikova and Geus, Circumference of the Earth and Ptolemy’s World Map (cit. n. 12), p. 21; Geus and Tupikova, “Von der Rheinmündung in den Finnischen Golf . . . Neue Ergebnisse zur Weltkarte des Ptolemaios (cit. n. 12), p. 127 n 7; Tupikova, Ptolemy’s Circumfer- ence of the Earth (cit. n. 10), pp. 5, 22–23; and Tupikova et al., Travelling along the Silk Road (cit. n. 12), pp. 58–62.
This content downloaded from 128.220.159.005 on April 26, 2017 08:50:36 AM All use subject to University of Chicago Press Terms and Conditions (http://www.journals.uchicago.edu/t-and-c). Isis—Volume 107, Number 4, December 2016 693
When using these “short” stades, Eratosthenes’ value for the Earth’s circumference works out to be 39,690 m—that is, an error of less than 1 percent.19 Similarly, many other distances quoted by ancient sources become surprisingly accurate when expressed in the “short” stades (see Sect. VI). As a result, a fascinating prospect opens before us. It turns out that in antiquity there was a tradition of “thrice” highly accurate geodesy and cartography: first, unknown surveyors mea- sured distances with high accuracy; second, Eratosthenes calculated the circumference of the Earth to within 1 percent of the true value; third, on the basis of his calculation unnamed successors drew so accurate a map that it could even compete with the maps of the Age of Dis- covery. But then Ptolemy committed the same “crime” that was imputed to his astronomical works by Robert Newton: he not only appropriated the achievements of his predecessors but also perverted them completely.20 That is the picture that ultimately emerges from the works of Rawlins, Russo, Tupikova, and Geus.21 It is fair to add that exactly the same idea had already been proposed as far back as the eighteenth century by a French historian of geography, Pascal- François-Joseph Gossellin.22 It has to be stressed that there is much that is attractive in the hypothesis described—not least its elegance and explanatory power. On closer examination, however, its charm proves deceptive. On the one hand, the hypothesis as presented by its advocates contains numerous logical fallacies. On the other, it is contradicted by other evidence. In the next section, I outline its main flaws and briefly present my own arguments.
II. PROBLEMS AND POSSIBLE SOLUTIONS In fact, at the very basis of the “wrong circumference hypothesis” there lies a patently false de- duction. It is true that Gossellin, Russo, Tupikova, and Geus have convincingly demonstrated that Ptolemy’s coordinates, recalculated for a sphere with Eratosthenes’ circumference, turn out to be highly accurate. But the further conclusions that they draw from this observation do not necessarily follow. First of all, the match between the recalculated Ptolemy coordinates and the modern ones, however close, does not in itself mean that the longitudinal distortion in Ptolemy’s map was due entirely to a single cause—namely, the wrong value for the Earth’s circumference. Nor does it warrant discarding two other possible causes: the exaggeration of distances and the lengthening of the stade. Another crucial point to stress is that Ptolemy’s recalculated map turns out to be accurate only in terms of spherical coordinates. This does not mean that the actual distance measurements underlying it and Eratosthenes’ value for the Earth’s circumfer- ence were equally accurate. In fact, we cannot ascertain the accuracy of these two factors sepa- rately, but only the accuracy of their quotient (that is to say, the accuracy of distances converted
19 An alternative and less popular value ascribed to Eratosthenes’ “short” stade is 148 m, which gives 37,296 km for the cir- cumference of the Earth. I shall not linger on this idea because it has already been severely criticized in Dicks, Geographical Fragments of Hipparchus (cit. n. 16), pp. 43–45; and Donald Engels, “The Length of Eratosthenes’ Stade,” American Journal of Philology, 1985, 106:299–304. 20 Robert R. Newton, The Crime of Claudius Ptolemy (Baltimore, Md.: Johns Hopkins Univ. Press, 1977). 21 Rawlins, however, does not support the idea of Eratosthenes’ “short” stade: Dennis Rawlins, “The Eratosthenes-Strabo Nile Map: Is It the Earliest Surviving Instance of Spherical Cartography? Did It Supply the 5000 Stades Arc for Eratosthenes’ Experi- ment?” Archive for History of Exact Sciences, 1982, 24:211–219, esp. p. 218. 22 P. F. J. Gossellin, Géographie des Grecs analysée (Paris: Didot l’Aîné, 1790), pp. 118–124, Tables VII–VIII; and Gossellin, Observations sur la manière de considérer et d’évaluer les anciens Stades itineraries (Paris: Imprimerie Imperiale, 1805). His opinion was accepted by James Bell, “Supplement by the Editor,” in The History, Arts, and Sciences of the Ancients, ed. Charles Rollin (Glasgow: Blacke, Fullarton, 1829), p. 599. Independently, the same idea was briefly stated by Miller, Die Erdmessung im Altertum und ihr Schicksal (cit. n. 9), p. 41.
This content downloaded from 128.220.159.005 on April 26, 2017 08:50:36 AM All use subject to University of Chicago Press Terms and Conditions (http://www.journals.uchicago.edu/t-and-c). 694 Dmitry A. Shcheglov The Accuracy of Ancient Cartography Reassessed into degrees). This uncertainty suggests an alternative and more plausible explanation for the spectacular accuracy of Ptolemy’s coordinates recalculated for Eratosthenes’ Earth, as I shall show below. Finally, all three main points of the hypothesis in question—the incorrect value for the Earth’s circumference as the only cause of the stretching of Ptolemy’s map, the high accuracy of ancient distance measurements, and the use of the “short” stade (which is implied by the high accuracy of Eratosthenes’ value for the circumference)—conflict with the evidence from other sources. And the conflict is so serious that either it entails a radical revision of our con- ventional views on ancient geography or (as is more likely) destroys the hypothesis itself. First, there are good reasons to conclude that both Ptolemy and Eratosthenes used stades close to 185 m in length, which was commonly accepted in the Roman period, whereas the “short” stade of 157.5 m seems rather like a scholarly fiction (see Sects. III–V). Expressed in these “common” stades, Eratosthenes’ value for the Earth’s circumference turns out to be overestimated by 16.5 percent (252,000 x 185 m = 46,620 km) compared with the true size, whereas Ptolemy’s value proves to be underestimated by 16.7 percent (180,000 x 185 m = 33,300 km). Second, it is highly doubtful that Greek geographers ever had really accurate distance mea- surements at their disposal. Both of our main authorities on ancient geography, Ptolemy and Strabo, emphasize repeatedly that distances reported by travelers are considerably exaggerated: by a third or even by half, according to Ptolemy, and Strabo’s estimates are similar.23 More thorough comparison with modern data shows that on average ancient distances were overesti- mated by approximately 20–25 percent (see Sect. VI). These results have an interesting corollary: if overestimated distances are expressed in de- grees of the almost equally overestimated great circle of Eratosthenes’ Earth, then the two er- rors cancel each other. A map constructed on this basis turns out to be quite accurate in terms of spherical coordinates. This explains why Ptolemy’s map, placed on Eratosthenes’ Earth, matches modern maps remarkably closely. If the same distances, overestimated by at least 20 percent, are converted to degrees according to Ptolemy’s value for the Earth’s size, which was underestimated by about 17 percent, then the resulting map becomes stretched by approx imately 40 percent in angular terms. My main contention in this essay is that of two alternatives—either incredibly accurate dis- tance measurements in “short” stades or exaggerated measurements in “common” stades—the latter is much better supported by the evidence and, therefore, more plausible. In the following sections I shall put this thesis on a more solid footing. In order to do that, we need to find three “unknowns”: the length of Ptolemy’s stade (Sect. IV), the length of Eratosthenes’ stade (Sect. V), and the average accuracy of ancient measurements of distances (Sect. VI).
III. THE LENGTH OF THE STADE The length of the stade is of crucial importance when evaluating the accuracy both of Ptol- emy’s map and of Eratosthenes’ measurement of the Earth. Contrary to the claims made by the advocates of the “wrong circumference hypothesis,” we have to reiterate that, in the absence of a firmly defined stade, the agreement between the recalculated Ptolemy coordinates and the modern ones, however close, in itself tells us nothing about the accuracy of Ptolemy’s sources. Therefore, we need to take at least a brief excursion into the field of historical metrology.
23 Ptolemy, Geography 1.13.2, 1.13.5, 1.13.7, 1.13.8, 11.4, 12.1; and Strabo, Geography 2.4.4 C106–107, 3.3.3 C193, 8.2.1 C335, 14.1.9 C636, 14.1.28 C643, 11.13.4 C524, 14.1.2 C632.
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“Few problems of Greek and Roman metrology are as tantalizing as the problem of the length of the various stades.”24 The crux of the problem is that, as a rule, ancient sources are silent about the length of the stade. All the evidence comes from a couple of accidental asides and from a few entries in late lexicons and handbooks (see below). Usually, ancient au- thors, unlike modern scholars, betray no sign of uneasiness about the uncertainty of the stade’s length. Strictly speaking, therefore, we are left in complete ignorance as to what distance each author had in mind when using this term in each particular case. This “silence of sources” is fertile ground for various conjectures, some of them diametri- cally opposed to others. The main controversy is between two general considerations. Some scholars infer from this silence that most of the ancient authors used, or at least believed that they used, nearly the same stade.25 Seen in this light, it seems highly improbable that Eratos- thenes, or any other Greek geographer, would have invented a stade completely different from the “common” one without voicing clear reservations. Other scholars argue that standardiza- tion of distance units was simply impossible in ancient Greece.26 Instead, different authors at different times and in different places could have and indeed must have, wittingly or unwit- tingly, applied the term “stade” to different units without worrying too much about accuracy. Both positions somewhat simplify the situation. To steer a sensible course between these two extremes, the only thing we can do is to stick as closely as possible to the known facts. The only reliable way to determine the length of the stade is to express it through units reliably attested by archaeological evidence. Such evidence includes the Roman foot, different feet used by the Greeks, and the racetracks of the Greek stadiums, which represent a direct material equivalent of the stade as a unit of distance. Below I consider these three groups of sources in detail. Written sources express the stade through the Roman mile, which equals 5,000 Roman feet. Since the length of the Roman foot is amply attested, the Roman mile—unlike the Greek stade—may also be considered a firmly defined value. Modern textbooks usually state the length of the mile within the range 1,478–1,482.5 m, with 1,480 m as an average value.27 Ancient sources mention four possible ratios between the mile and the stade: 8⅓, 8, 7½, or
24 Israel E. Drabkin, “Posidonius and the Circumference of the Earth,” Isis, 1943, 34:501–512, on p. 510. For a good introduction to the problem see Ludwig Fenner von Fenneberg, Untersuchungen über die Längen-Feld- und Wegemaasse des Völker des Al- terthums insbesondere der Griechen und der Juden (Berlin: Dümmler, 1859); Friedrich Hultsch, Griechische und römische Metrolo- gie, 2nd ed. (Berlin: Weidmann, 1882); and Carl Friedrich Lehmann-Haupt, “Stadion (Metrologie),” in Paulys Real-Encyclopädie der classischen Altertumswissenschaft, Vol. 3A2 (Stuttgart: Metzler, 1929), cols. 1930–1962. For a valuable criticism of previous scholarship see also Engels, “Length of Eratosthenes’ Stade” (cit. n. 19). 25 For this opinion see William Falconer, Arrian’s Voyage Round the Euxine Sea, Translated and Accompanied with a Geographi- cal Dissertation and Maps (Oxford: Cooke, Cadell & Davies, 1805), pp. 137–164; W. Martin Leake, “On the Stade, as a Linear Measure,” Journal of the Royal Geographical Society of London, 1839, 9:1–25; Bunbury, History of Ancient Geography (cit. n. 16), pp. 209–210; Gaetano M. Columba, Eratostene e la misuratione della meridiane terrestre (Palermo: Clausen, 1895), pp. 64, 66–69; Dicks, Geographical Fragments of Hipparchus (cit. n. 16), pp. 42–46; Engels, “Length of Eratosthenes’ Stade”; Sarah Pothecary, “Strabo, Polybios, and the Stade,” Phoenix, 1995, 49:49–67; Berggren and Jones, Ptolemy’s “Geography” (cit. n. 6), p. 14 n 10; and Duane W. Roller, Eratosthenes’ “Geography”: Fragments Collected and Translated, with Commentary and Additional Material (Princeton, N.J.: Princeton Univ. Press, 2010), pp. 271–273. 26 Aubrey Diller, “The Ancient Measurements of the Earth,” Isis, 1949, 40:6–9, on p. 8; Dicks, Geographical Fragments of Hip- parchus, p. 43; and Klaus Geus, “A ‘Day’s Journey’ in Herodotus’ Histories,” in Features of Common Sense Geography: Implicit Knowledge Structures in Ancient Geographical Texts, ed. Geus and Martin Thiering (Berlin: LIT, 2014), pp. 148–156, esp. p. 148. 27 To proceed from the length of the Roman foot, determined to be between 294 and 298 mm, the Roman mile must have varied even more widely: within 20 m, from 1,470 to 1,490 m. But even this range amounts to only 1.35 percent of the average value of 1,480 m, which corresponds to 5,000 x 296 mm, the most often-cited value for the Roman foot. On the Roman foot see Kon- rad Hecht, “Zum römischen Fuß,” Abhandlungen der Braunschweigischen Wissenschaftlichen Gesellschaft, 1979, 30:107–108. Lehmann-Haupt (“Stadion” [cit. n. 24], cols. 1961–1962) gives for the Roman mile the maximum range of 1,471.23–1,494 m
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7 stades to the mile. The majority of sources from the late second century b.c.e. to the second century c.e., among them the most trustworthy ones, used a ratio of 1:8.28 That of 1:8⅓ is men- tioned only twice.29 The ratio of 1:7½ is attested from the third century c.e. onward30 and that of 1:7 only in the Byzantine period.31 The amount of evidence in favor of the ratio 1:8 leaves little doubt that under the Romans it was accepted as a standard. The real problem, therefore, concerns the pre-Roman stade. On the one hand, written sources of the Roman period repeatedly borrow distances from earlier geographers without the slightest hint that they might have used different stades.32 On the other hand, however, skeptics rightly point out that these sources are not reliable for the earlier period. Archaeological sources, meanwhile, suggest that the length of the Greek stade could vary considerably. The Greek word στάδιον means simply a stadium—that is, a sports facility in the modern sense. It is likely correct to say that the ancient Greeks measured space in terms of stadiums just as our contemporaries sometimes measure it in terms of football fields.33 Taking into account how much the Greeks were obsessed with sports competitions, and that almost every Greek state had its own stadium, it is unsurprising that it could be used as a conventional standard for measuring distance.34 More specifically, the stade as a unit of distance corresponded to the length of a stadium’s racetrack (δρόμος). At present, we know of at least twelve ancient stadi- ums with extant racetracks. They cluster around five lengths: 165–166 m (Corinth, Halieis), 176–178 m (Delphi, Nemea, possibly Miletus), 181–182 m (Isthmia II, Epidaurus, Delos), 185 m (Athens), and 191–192 m (Olympia, Priene, Isthmia I, possibly Miletus).35 Some of the
and the average value of 1,485 m. Omert J. Schrier (“Hannibal, the Rhone, and the ‘Island’: Some Philological and Metrological Notes,” Mnemosyne, 2006, 59:507–509) calculates a range of 1,471–1,485 m. 28 Polybius, History 3.39.8; Strabo, Geography 7.7.4 C322 (he cites this opinion as that of the “many”: ὡς μὲν οἱ πολλοί), frag. 56; Vitruvius, On Architecture 1.6.9; Pliny, Natural History 2.85, 2.247, 5.26, 6.108; Columella, On Agriculture 5.1; Censorinus, The Birthday Book 13.2; and Isidore of Seville, Etymologies 15.15.6, 15.16.3. Other sources converted distances from stades to miles at the rate of 8 to 1: Titus Livius, History of Rome 21.27, 25.9, 30.5, 30.8 (figures borrowed from Polybius,History 3.101, 14.4, 14.8); Agrippa, frag. 56 Klotz = Pliny, Natural History 5.65; Diodorus, The Library of History 4.56, 20.36; and Appianus, Roman History 12.94. To this list one should add the so-called Stadiasmus of Patara, a unique epigraphic document stating some distances in Asia Minor; see Mustafa Adak and Sencer Şahin, Stadiasmus Patarensis: Itinera Romana Provinciae Lyciae (Istanbul: Ege Yayinlari, 2007), pp. 107, 120. 29 The sources are Polybius (according to Strabo, Geography 7.7.4 C322, frag. 56) and Censorinus (The Birthday Book 13.2). 30 Hero of Alexandria (Geometria 106.24; see Friedrich Hultsch, ed., Metrologicorum scriptorum reliquae, Vol. 1 [Leipzig: Teub- ner, 1864], p. 183–184, 186), Hesysius (s.v. μίλιον), Suda (s.v. στάδιον), Scholia to Lucian (24 Rabe 99), and Leo the Wise (Tactica 17.89). Dio Cassius (38.17.7, 39.50.2, 46.44.4, 48.14.6, 48.43.3, 52.21.2, 52.22.1, 55.26.1, 58.21.1, etc.) and the sixth- century anonymous Periplus of the Euxine Sea (passim) use this rate to convert stades to miles. 31 Epiphanius of Cyprus (On Measures and Weights, frag. 12; see Hultsch, ed., Metrologicorum scriptorum reliquae, p. 275), Suda (s.v. μίλιον), Scholia to Lucian (24 Rabe 99), and a seventh-century Armenian geographer Anania Shirarkatsi. On the latter see Hans von Mžik, Erdmessung, Grad, Meile und Stadion nach den altarmenischen Quellen: Ein Beitrag zur Geschichte der Erdkunde und der Kulturbeziehungen zwischen Hellenismus und Armeniertum (Vienna: Mechitharisten, 1933), p. 110. Hultsch, Griechische und römische Metrologie (cit. n. 24), p. 569 n 2, argues that the same ratio may have been used by Procopius of Caesarea (History of the Wars 5.11.2). 32 For example, Eratosthenes’ distances were extensively used by Strabo (passim), Hipparchus (passim; see Dicks, Geographical Fragments of Hipparchus [cit. n. 16]), Polybius (in Pliny 5.40), Artemidorus (in Pliny 2.244–245; Strabo 14.2.29 C663), and Agathemerus, Sketch of Geography 3.14, 4.15, 4.18. They were also converted to Roman miles at the rate 8:1 by Vitruvius, On Architecture 1.6.9; and Pliny, Natural History 2.247, 5.40, 5.132, 6.36, 6.56, 6.108; cf. also 6.61–62. 33 According to a legend referred to by Isidore of Seville (Etymologies 15.16.3), the length of the stadium was established by Hercules and derived from a distance that he was able to run without taking a breath. 34 See similarly Leake, “On the Stade” (cit. n. 25), p. 3; and Edward Gulbekian, “The Origin and Value of the Stadion Unit Used by Eratosthenes in the Third Century B.C.,” Arch. Hist. Exact Sci., 1987, 37:359–363, esp. p. 360. 35 Hultsch, Griechische und römische Metrologie (cit. n. 24), p. 530; E. Fiechter, “Stadion (der Bau),” in Paulys Real- Encyclopädie der classischen Alterthumswissenschaft, Vol. 3A2 (cit. n. 24), col. 1969; William B. Dinsmoor, The Architecture of
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Hellenistic and Roman stadiums in Asia Minor are considerably longer than those in Greece proper, although the lengths of their racetracks cannot always be measured accurately.36 The stade is unanimously defined as a distance of 600 feet.37 Nowhere is the length of the Greek foot attested directly in written sources. What is often presented in modern scholarship as a “common Greek foot” of circa 308.3 mm in length38 is merely deduced from the length of the “common” stade (that is to say, by calculating 185 m/600). The same length of 25/24 of a Roman foot is attributed by a field measurer, Hyginus, to the foot used in Cyrenaica and called the “Ptolemaic.”39 Another “Ptolemaic” foot, which related to the Roman one in the ratio 6 to 5 and was, therefore, about 355.2 mm, is mentioned by a certain Didymus.40 Since written evidence is limited to these few scraps,41 the only available method for deter- mining the length of the Greek foot is to deduce it from the measurements of ancient build- ings. Numerous observations accumulated over time demonstrate the high variability of Greek metrological practice.42 There seems, however, to be scholarly consensus about the coexistence in classical Greece of at least three different feet: the Attic foot equal to the Roman one of circa 294–296 mm, the Doric or Pheidonic foot of circa 325–328 mm, and the Ionic or Samian foot of circa 348–350 mm (which is close to Didymus’s “Ptolemaic” foot).43 These feet imply the following values for the length of the stade: 176.4–177.6 m, 195–196.8 m, and 208.8–210 m, respectively, which roughly correspond to the aforementioned ratios of 8⅓, 7½, and 7 stades per Roman mile. The 308-mm foot corresponding to the “common” stade of 185 m is so poorly attested that Wilhelm Dörpfeld and William Bell Dinsmoor, the most authoritative experts in classical architecture, even called it the foot “which no Greek ever employed.”44 Some scholars
Ancient Greece, 3rd ed. (London: Biblo & Tannen, 1950), p. 251; and David G. Romano, Athletics and Mathematics in Archaic Corinth: The Origins of the Greek Stadion (Philadelphia: American Philosophical Society, 1993), pp. 17, 43, 50 n 21. I deliber ately omit the many technical difficulties posed by each of the stadiums; for more details see Oscar Broneer, Isthmia, Vol. 1: The Temple of Poseidon (Princeton, N.J.: Princeton Univ. Press, 1971), pp. 174–176. 36 Pergamon (210 m), Perge in Pamphylia (234 m), Aizanoi (212.3 m), Aphrodisias in Caria (total length 227.3 m; the racetrack is 180–188 m without bends), Laodicaea (at least ca. 280 m). Various numerical data are collected in Michael Stubenrauch, Unterhaltungsarchitektur im Kontext kleinasiatischer Städte: Das Stadion in römischer Zeit zwischen Sport und Spektakel, Pt. 1: Text und Katalog (Magisterarbeit Ludwig-Maximilians-Universität München, 2006), pp. 32–33, 52, 80, 105. Cf. also Leake, “On the Stade” (cit. n. 25), p. 4; Romano, Athletics and Mathematics in Archaic Corinth, pp. 586–587; and Katherina Welch, “The Stadium at Aphrodisias,” American Journal of Archaeology, 1998, 102:548–550. 37 Herodotus, History 2.149.3; Censorinus, The Birthday Book 13.2; Aulus Gelius, Attic Nights 1.1.2; Hero 1.21 (see Hultsch, ed., Metrologicorum scriptorum reliquae [cit. n. 30], p. 183); and Suda (s.v. μίλιον, s.v. στάδιον, etc.). 38 See, e.g., Falconer, Arrian’s Voyage Round the Euxine Sea (cit. n. 25), pp. 140–141, 147–148; Robert Hussey, An Essay on the Ancient Weights and Money, and the Roman and Greek Liquid Measures, with an Appendix on Foot (Oxford: Collingwood, 1836), p. 234; Algernon E. Berriman, Historical Metrology (London: Dent, 1953), pp. 117–119; Engels, “Length of Eratosthenes’ Stade” (cit. n. 19), p. 298; and Pothecary, “Strabo, Polybios, and the Stade” (cit. n. 25), p. 58. 39 Carl Thulin, ed., Corpus agrimensorum Romanorum, Vol. 1, Fasc. 1: Opuscula agrimeinsorum veterum (Leipzig: Teubner, 1913), pp. 85–86. 40 Hultsch, ed., Metrologicorum scriptorum reliquae (cit. n. 30), p. 180. 41 I leave aside the vexed question of the Italic and Phileterian feet mentioned by Hero of Alexandria. 42 Scholarly opinion has tended to polarize between two positions. The “reductionist” school assumes that the apparent diversity of Greek metrological practices can be reduced to a combination of local standards related to one another by simple arithmetical ratios (as, for example, 24/25 or 5/6). The “permissive” school suggests that there was no general system at all in Greece but that almost every state could use its own unique standard. See Mark Wilson Jones, “Doric Measure and Architectural Design, 1: The Evidence of the Relief from Salamis,” Amer. J. Archaeol., 2000, 104:73–93, esp. p. 75. 43 Broneer, Isthmia (cit. n. 35), pp. 174, 177; Burkhardt Wesenberg, “Zum metrologischen Relief in Oxford,” Marburger Winck elmann Programm, 1975/1976, p. 16; Hermann H. Büsing, “Metrologische Beitrage,” Jahrbuch des Deutschen Archäologischen Instituts, 1982, 97:1–45; Hansgeorg Bankel, “Zum Fussmass attischer Bauten des 5. Jahrhunderts v. Chr.,” Athenische Mitteilun- gen, 1983, 98:89, 93–95; and Wilson Jones, “Doric Measure and Architectural Design, 1,” p. 75. 44 Wilhelm Dörpfeld, “Beiträge zur antiken Metrologie,” Mittheilungen des Institutes in Athen, 1882, 7:277–290; and Dinsmoor, Architecture of Ancient Greece (cit. n. 35), p. 161 n 1. The only clear evidence for this foot comes from a sixth-century c.e. relief from
This content downloaded from 128.220.159.005 on April 26, 2017 08:50:36 AM All use subject to University of Chicago Press Terms and Conditions (http://www.journals.uchicago.edu/t-and-c). 698 Dmitry A. Shcheglov The Accuracy of Ancient Cartography Reassessed argue for the existence of other feet: the so-called Oscan-Italian foot of 275–278 mm,45 the Isth- mian foot of 302 mm,46 and the Olympic foot of 320.4–321 mm.47 These three feet, however, are far from being widely accepted among classical metrology and architecture experts. The results of this survey are summarized in Table 1. Interestingly, the table shows that all groups of sources give us nearly the same set of values. The main question raised by this survey is how to reconcile the prevalence of the 185-m stade in written sources with the wide diversity of other attested values. A simple clue to this question may be suggested by the fact that 185 m is close enough to the mean between other values: 176–178 m and 195–198 m, 165–166 m and 210–213 m. This fact, together with the simplicity of the ratio 1:8, could have played a part in its acceptance as the best compromise value. To conclude, it seems doubtful that all distances recorded by ancient sources, even in the Roman period, could always have been measured in the same standard stades. Mere doubt, however, is not enough to outweigh concrete evidence. Meanwhile, the evidence allows us to draw quite definite conclusions. First, if the length of the stade did vary, it most probably varied within the range between the extreme attested values, 165–213 m. Second, if an aver- age length of the stade, or the most widely used one, is to be found, then the “common” stade of 185 m is the most plausible candidate for that role. Finally, the most evident conclusion is that the “short” stade of 157.5 m is nowhere attested: we have neither reliable written evidence for it, nor stadiums of this length, nor feet equal to 1/600 of this stade (which would equal ca. 262.5 mm).
IV. THE LENGTH OF PTOLEMY’S STADE What the length of the stade used in Ptolemy’s geography was is a difficult question. Many scholars have believed that it was a “long” stade equal to 1/7.5 or 1/7 of a Roman mile—that is, 197–198 m or 210–213 m. Combined with the hypothesis that earlier geographers used a “short” stade (of 148 m or 157.5 m), this assumption can explain the east–west stretching of Ptolemy’s map without resorting to the “wrong circumference hypothesis.”48 These two expla- nations are, therefore, essentially similar but mutually exclusive.
Palestine; see Félix-Marie Abel, “Chronique, I: Inscription grecque de l’Aqueduc de Jérusalem avec la figure du pied byzantin,” Revue Biblique, 1926, 35:284–288. Apart from this relief, the 308-mm foot was deduced from the length of the Parthenon’s stylobate. See Hussey, Essay on the Ancient Weights and Money (cit. n. 38), pp. 220, 232; Fenneberg, Untersuchungen über die Längen-Feld- und Wegemaasse (cit. n. 24), pp. 7–8; and Hultsch, Griechische und römische Metrologie (cit. n. 24), pp. 66–67. However, the validity of these calculations has long been contested; see, e.g., Dörpfeld, “Beiträge zur antiken Metrologie,” pp. 294–302. 45 It was derived by Heinrich Nissen from buildings excavated at Pompeii; see Nissen, Pompejanische Studien zur Städtekunde des Altertums (Leipzig: Breitkopf & Härtel, 1877), pp. 70–90. See also Wilhelm Dörpfeld, “Der Römische und Italische Fuss: Schreiben an Herrn Professor Mommsen,” Hermes, 1887, 22:79–85; Lehmann-Haupt, “Stadion” (cit. n. 24), cols. 1934, 1942; and Robert R. Stieglitz, “Classical Greek Measures and the Builder’s Instruments from the Ma’agan Mikhael Shipwreck,” Amer. J. Archaeol., 2006, 110:200–203. 46 It was identified in the temples at Corinth, Isthmia, Olympia, and Aegina by Broneer, Isthmia (cit. n. 35), pp. 176–181. 47 It was derived from measurements of the temples of Zeus and Hera in Olympia by Hultsch, Griechische und römische Metrologie (cit. n. 24), pp. 496, 526, 529–533; his conclusions have been contested by Lehmann-Haupt, “Stadion” (cit. n. 24), cols. 1942–1943. 48 On the stades of 157.5 m and 210 m ascribed to Eratosthenes and Ptolemy, respectively, see Paul Tannery, Recherches sur l’histoire de l’astronomie ancienne (Paris: Gauthier-Villars, 1893), pp. 109–110; Thomas Heath, Aristarchus of Samos (Oxford: Oxford Univ. Press, 1913), pp. 339, 346; Oskar Viedebantt, “Eratosthenes, Hipparchos, Poseidonios: Ein Beitrag zur Geschichte des Erdmessungsproblems im Altertum,” Klio, 1915, 14:207–256, esp. pp. 209, 212–215, 232, 252–256, 1920, 16:96–100; Miller, Die Erdmessung im Altertum und ihr Schicksal (cit. n. 9), pp. 6–7, 10–14, 17; Mžik, Erdmessung, Grad, Meile und Stadion nach den altarmenischen Quellen (cit. n. 31), pp. 105–112; and Christian Meuret, “Outils mathématiques et données itineraires: Re- flexions sur evaluation de la circonférence terrestre chez Ptolémée,” in Geographica Historica, ed. P. Arnaud and P. Counillon (Bordeaux: Ausonius, 1998), pp. 160–165. On the alternative values of 148 m and 198 m see Diller, “Ancient Measurements
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Table 1. The Length of a Stade as Attested by Different Groups of Sources
As Attested by Length of a Stade Written Sources (in meters) (stades per mile) Greek Stadiums in Feet
165–166 – Corinth, Halieis Oscan-Italian (?) 176–178 8⅓ Delphi, Nemea, Miletus (?) Attic 181–182 – Isthmia II, Epidaurus, Delos Isthmian (?) 185 8 Athens “Common” (?) 191–192 – Olympia, Priene, Isthmia I, Olympic (?) Miletus (?) 195–198 7½ – Doric 210–213 7 Pergamon, Aizanoi, Laodicaea, Ionic etc. (?)
But in fact the attribution to Ptolemy of a “long” stade is not supported by any analysis of his map. The only basis for this opinion is a rather shaky interpretation of the fact that Posido- nius (ca. 135–51 b.c.e.) is credited with two different estimates of the Earth’s circumference: 240,000 stades, according to Cleomedes,49 and 180,000 stades, according to Strabo,50 which is the same as was adopted by Ptolemy. There are two possible explanations of this discrepancy. The first one assumes that both figures represent the same value expressed in different stades, “short” and “long”: either 157.5 m and 210 m, or 148 m and 198 m, respectively.51 Accordingly, only if this explanation is correct, and if Ptolemy has really borrowed his estimate of the Earth’s circumference from Posidonius, then Ptolemy’s stade could have been a “long” one. There are, however, serious reasons to doubt, first, that Ptolemy’s estimate had anything to do with Posidonius (see note 16, above) and, second, that a “short” stade is not a scholarly myth (see the next section). Besides, Strabo evidently does not admit the possibility that Eratosthenes and Posidonius may have expressed distances in different stades.52 An alternative explanation is that the two figures credited to Posidonius are based on differ- ent estimates of the distance between Alexandria and Rhodes: 5,000 stades (a rough estimate
of the Earth” (cit. n. 26), pp. 8–10; Polaschek, “Klaudios Ptolemaios” (cit. n. 6), cols. 694, 800; Irene Fischer, “Another Look at Eratosthenes’ and Posidonius’ Determinations of the Earth’s Circumference,” Quarterly Journal of the Royal Astronomical Society, 1975, 16:159–160, 163, 165; Annemarie Bernecker, Die Feldzüge des Tiberius und die Darstellung der unterworfenen Ge- biete in der “Geographie des Ptolemaeus” (Bonn: Habelt, 1989), pp. 331–374; and Hugh Thurston, Early Astronomy (New York: Springer, 1994), p. 121. A compromise solution, combining the stades of 148 m and 210 m, is proposed by Eberhard Knobloch, Dieter Lelgemann, and Andreas Fuls, “Zur hellenistischen Methode der Bestimmung des Erdumfanges und zur Asienkarte des Klaudios Ptolemaios,” Zeitschrift für Geodäsie, Geoinformation und Landmanagment, 2003, 128:211–217. 49 Caelestia 1.10.50–52 = frag. 202 Edelstein-Kidd. 50 Geography 2.2.2 C95 = frag. 49 Edelstein-Kidd. 51 Viedebantt, “Eratosthenes, Hipparchos, Poseidonios” (cit. n. 48), pp. 94, 99; Miller, Die Erdmessung im Altertum und ihr Schicksal (cit. n. 9), pp. 12–13, 15–16; Aubrey Diller, “Geographical Latitudes in Eratosthenes, Hipparchus, and Posidonius,” Klio, 1934, 27:258–269, esp. p. 259; Diller, “Ancient Measurements of the Earth” (cit. n. 26), pp. 8–10; and Thomson, History of Ancient Geography (cit. n. 9), p. 212. 52 For similar criticism of this explanation see Drabkin, “Posidonius and the Circumference of the Earth” (cit. n. 24), pp. 510–511; and Dicks, Geographical Fragments of Hipparchus (cit. n. 16), pp. 150–152.
This content downloaded from 128.220.159.005 on April 26, 2017 08:50:36 AM All use subject to University of Chicago Press Terms and Conditions (http://www.journals.uchicago.edu/t-and-c). 700 Dmitry A. Shcheglov The Accuracy of Ancient Cartography Reassessed used in Cleomedes’ account) and 3,750 stades (a value calculated by Eratosthenes: frag. 128 = Strabo 2.5.24 C126).53 If Posidonius substituted the more accurate Eratosthenic value in his calculations, he would have reached the result of 180,000 stades. However that may be, the only reliable way to determine the length of Ptolemy’s stade is to find close enough and statistically significant correspondences between his map and distances recorded by other sources in Roman miles, which would give us the ratio between Ptolemy’s stade and the mile. I know of only a few attempts at such comparison.54 All of them, indepen- dently of one another, demonstrate that in most cases distances derived from Ptolemy’s map and those given in the Roman itineraries agree closely enough at the rate of 8 stades to a mile— a predictable result in light of what has been said in the previous section. This result implies that Ptolemy’s value for the circumference of the Earth was underes- timated by only 16.7 percent (180,000 x 185 m = 33,300 km). This underestimation, there- fore, could be responsible for only half of Ptolemy’s error in longitude: it could have caused a stretching of his map by only 1.2 times instead of the 1.4 times actually observed.
V. THE “ SHORT STADE HYPOTHESIS” The idea that Eratosthenes and some other Hellenistic geographers used a “short” stade is both the cornerstone and the Achilles heel of the “wrong circumference hypothesis.” This idea has been repeatedly criticized and rejected as unfounded, but it is still revived time and again, with enviable persistence. I hope this article can contribute to sorting the wheat from the chaff in this controversy. The starting point for any discussion about a “short” stade, and the only direct evidence for it, is a brief remark in Pliny (Natural History 12.53) that “by the calculation of Eratosthenes, a schoenus measures 40 stades, that is 5 miles, but some authorities have made the schoenus 32 stades.”55 It may seem clear that Pliny is talking here about the well-known “common” stade equal to ⅛ of a Roman mile. But the advocates of the “short stade hypothesis” discard Pliny’s reference to the mile and try to determine Eratosthenes’ stade through the schoenus. The Greek term σχοῖνος literally means “rush” or “a rope twisted of rushes” and refers, primar- ily, to a local Egyptian unit of distance but also to similar units used in Mesopotamia and Persia. Our main sources emphasize that the schoenus, unlike the stade, was a very vague measure:56 it could vary fourfold, from 30 to 120 stades.57 Therefore, it would be reasonable to define the
53 Berger, Geschichte der wissenschaftlichen Erdkunde der Griechen (cit. n. 16), p. 580; and Kidd, Posidonius (cit. n. 16), pp. 722– 725. Cf. Lewis, Surveying Instruments of Greece and Rome (cit. n. 16), pp. 146–148. 54 On Gallia, Italy, and the provinces of the mid-Danube see Cuntz, Die Geographie des Ptolemaeus (cit. n. 9), pp. 110–111, 119–121; on Mauretania see John E. H. Spaul, “Studies in the Roman Province of Mauretania Tingitana” (Ph.D. diss., Durham Univ., 1958), http://etheses.dur.ac.uk/10374; on Spain see Jose Maria Gómez Fraile, “Sobre la antigua cartografía y sus métodos: Los fundamentos numéricos de la Hispania de Claudio Ptolomeo,” Iberia, 2005, 8:35–64; Javier Urueña Alonso, “El item ab Hispali Cordvbam en la Geographia de Ptolomeo: Una propuesta de interpretación del método cartográfico Ptolemaico,” Habis, 2014, 45:137–150; and Urueña Alonso, “El método cartográfico de Ptolomeo: Análisis del sistema de localización utilizado en la Geographia para la ubicación de las poblaciones del interior de la península Ibérica,” Palaeohispanica, 2014, 14:153–185. 55 “schoenus patet Eratosthenis ratione stadia XL, hoc est p. V, aliqui XXXII stadia singulis schoenis dedere.” 56 Strabo (17.1.24 C804; cf. similarly about the parasang, 15.11.5 C518) and Pliny (6.125: “cum Persae quoque schoenos et parasangas alii alia mensura determinant”). 57 Our sources quote the following values for one schoenus: Herodotus (2.6.149)—60 stades; Strabo—normally 30 stades (fol- lowing Artemidorus: Geography 17.1.24 C804), but also 40 (following Theophanes of Mytilene: 11.14.11 C530), 60, and even 120 stades (17.1.24 C804); Pliny (5.11, 5.63, 12.52)—30 or 32 stades; Ptolemy (Geography 1.11.4, 1.12.4)—30 stades; Hero of Al- exandria (Definitions 131–132; Geometria 106.24; see Hultsch, ed., Metrologicorum scriptorum reliquae [cit. n. 30], p. 140)—nor- mally 30 stades, but there is also a “barbarian schoenus” of 45 stades and a “Persian” one of 60 stades. See also Hero’s fragments in Hultsch, ed., Metrologicorum scriptorum reliquae, pp. 183–184, 186. The 30-stades schoenus is also mentioned in the Heidelberg papyrus 1289. See Henri Sottas, “Les mesures itinéraires ptolémaïques et le papyrus démotique 1289 de Heidelberg,” Aegyptus,
This content downloaded from 128.220.159.005 on April 26, 2017 08:50:36 AM All use subject to University of Chicago Press Terms and Conditions (http://www.journals.uchicago.edu/t-and-c). Isis—Volume 107, Number 4, December 2016 701 schoenus through the stade, as Pliny clearly does in the quoted passage, and not vice versa.58 But this has not stopped the advocates of the “short stade hypothesis.” They make the following calculations. One schoenus is most often defined as 30 stades. One stade traditionally consists of 400 cubits. The royal Egyptian cubit has been firmly deter- mined on the basis of archaeological evidence as circa 525 mm.59 Therefore, one schoenus is 1 equal to 6,300 m, while Eratosthenes’ stade, equal to /40 of a schoenus, works out at 157.5 m. This result, with minor variations, was first suggested by P. S. Girard, J. A. Letronne, and Frie drich Hultsch60 and remains very popular to this day.61 These considerations suffice to show how precarious is the proposed interpretation of Pliny’s remark: it is based on a combination of different testimonies, none of which is reliable enough by itself. This construction can hardly be regarded as a firm basis for far-reaching conclusions about Eratosthenes’ stade, nor can it alone outweigh ample evidence for the common use of the 185-m stade.
VI. THE ACCURACY OF ANCIENT DISTANCE MEASUREMENTS Perhaps the main argument for the “short” stade is based on comparison between ancient and modern distances: those measured on a modern map are divided by their ancient counterparts in stades, giving the length of an average stade. This comparison has been undertaken repeat- edly, from James Rennell (1800) and P. F. J. Gossellin (1819) to the most recent studies, and invariably the average stade comes out to be much closer to the “short” value of 157.5 m than to the “common” one of 185 m.62 On this basis, many researchers suggest that for practical pur-
1926, 7:237–242, esp. p. 238; S. Vleeming, “Maße und Gewichte in den demotischen Texten (insb. aus der ptol. Zeit),” in Lexikon der Ägyptologie, eds. W. Helck, E. Otto, and W. Westendorf, Vol. 3 (Wiesbaden: Harrassowitz, 1980), cols. 1209–1212; and Gyula Priskin, “Reconstructing the Length and Subdivision of the Iteru from Late Egyptian and Graeco-Roman Texts,” Discussions in Egyptology, 2004, 60:57–71. 58 This was noted by Gulbekian, “Origin and Value of the Stadion Unit” (cit. n. 34), p. 360; and Engels, “Length of Eratosthenes’ Stade” (cit. n. 19), pp. 300–301. 59 Richard Lepsius, Die alt-aegyptische Elle und ihre Eintheilung (Berlin: Dümmler, 1865). According to recent research, the royal Egyptian cubit varies within 521–529 mm, with the average value of 525 mm: Antoine Pierre Hirsch, “Ancient Egyptian Cubits—Origin and Evolution” (Ph.D. diss., Univ. Toronto, 2013), https://tspace.library.utoronto.ca/bitstream/1807/35848/10 /Hirsch_Antoine_P_201306_PhD_thesis.pdf. An alternative estimate is 523.7 mm: W. M. Flinders Petrie, The Pyramids and Temples of Gizeh (London: Field & Tuer, 1883). 60 Pierre Simon Girard, “Sur la coudée septennaire des anciens Égyptiens et les différents étalons qui en ont été retrouvés jusqu’à présent,” Mémoires de l’Académie des Sciences de l’Institut de France, 1830, 9:591–608; Jean Antoine Letronne, Recherches critiques, historiques et géographiques sur les fragments d’Héron d’Alexandrie, ou du système métrique égyptien (Paris: Imprimerie Nationale, 1851), pp. 110–130; and Hultsch, Griechische und römische Metrologie (cit. n. 24), pp. 54, 60–63, 363–364. 61 Wolfgang Kubitschek, “Karten,” in Paulys Real-Encyclopädie der classischen Alterthumswissenschaft, Vol. 10.2 (Stuttgart: Metzler, 1919), cols. 2080–2081; Cuntz, Die Geographie des Ptolemaeus (cit. n. 9), pp. 111, 120–122; August Oxé, “Die Massta- fel des Julianus von Askalon,” Rheinisches Museum für Philologie, 1963, 106:264–286; Germain Aujac and Fançois Lasserre, eds., Strabon, Géographie, Vol. 1, Pts. 1–2 (Paris: Les Belles Lettres, 1969), Pt. 1, p. 53, Pt. 2, pp. 190–191; Pascal Arnaud, Les routes de la navigation antique: Itinéraires en Méditerranée (Paris: Errance, 2005), p. 85; and Stückelberger, “Masse und Messungen” (cit. n. 11), pp. 223–224, 259. For further references see note 48, above. 62 James Rennell, The Geographical System of Herodotus (London: Bulmer, 1800), pp. 13–34; Gossellin, Observations sur la manière de considérer et d’évaluer les anciens Stades itineraries (cit. n. 22); P. F. J. Gossellin, Recherches sur le principe, les bases et l’évaluation des différens systemes métriques linéaires de l’antiquité (Paris: Imprimerie Royale, 1819), pp. 21–22, 25–26, 46, 53; Edme F. Jomard, Mémoire sur le système métrique des anciens Égyptiens, contenant des recherches sur leurs connoissances géomé- triques et sur les mesures des autres peuples de l’antiquité (Paris: Imprimerie Royale, 1817), pp. 8, 16; Christian L. Ideler, “Über die Längen- und Flächenmaße der Alten: Über die von d’Anville in die alte Geographie eingeführten Stadien,” Abhandlungen der Königlichen Akademie der Wissenschaftenzu Berlin: Philosophisch-Historische Klasse, 1826, pp. 9–12, 1827, pp. 113–118, 126–127; Leake, “On the Stade” (cit. n. 25), pp. 11–12 (obtains 137.4–154.5 m for the average stade); Viedebantt, “Eratosthe- nes, Hipparchos, Poseidonios” (cit. n. 48), pp. 214–216; Jacques Dutka, “Eratosthenes’ Measurement of the Earth Reconsid- ered,” Arch. Hist. Exact Sci., 1993, 46:55–66; David French, “Pre- and Early-Roman Roads of Asia Minor: The Persian Royal
This content downloaded from 128.220.159.005 on April 26, 2017 08:50:36 AM All use subject to University of Chicago Press Terms and Conditions (http://www.journals.uchicago.edu/t-and-c). 702 Dmitry A. Shcheglov The Accuracy of Ancient Cartography Reassessed poses ancient surveyors used a special short stade, one never directly attested in extant sources. Following Rennell, this stade is often termed the “itinerary stade.” This result might have been regarded as a brilliant confirmation of the “short stade hypoth- esis” were it not for one “but”: strangely enough, in comparing ancient and modern distances, a crucial factor has been lost sight of—namely, “measurement error.” The proponents of the “itinerary stade” proceed from a tacit assumption that ancient distances were measured almost as accurately as modern ones. However, this cannot be true, for two main reasons.63 First, with rare exceptions, there is no indication that distances given by ancient sources were actual mea- surements on the ground, rather than rough estimates deduced, for example, from the duration and the average speed of travel.64 Second, and most important, even when ancient distances do derive from actual and quite accurate measurements, they were certainly measured not as a crow flies but including all the twists and turns of the route, about which we have no infor- mation. This is why ancient distances tend to be exaggerated, even when we try to reconstruct ancient routes.65 As applied to our problem, this means that in most cases the average length of the stade derived from a comparison of ancient and modern distances is inversely proportional to the degree of accuracy we can assign to ancient distances: the higher the accuracy, the shorter the stade. In other words, the results of any comparison of distances can be treated in two ways: if ancient measurements were accurate, this inevitably leads us to a “short” stade; if they were considerably overestimated, this is more consistent with the assumption that a “common” stade was used.66 To make a reasoned choice between these options, we can apply a simple test: the same comparative approach may be used to determine the length of the Roman mile. Since it has been firmly established as equal to 1,480 m, such comparison will yield the average accuracy of Roman distance measurements. On the assumption that the average accuracy of Greek distance measurements could not be greater than that of Roman ones, we can calculate an average length for the stade. It should be stressed that this method is, of course, not rigorous enough to yield a precise result. But if we only have to choose between two possibilities—either
Road,” Iran, 1998, 36:15–43, esp. p. 20 (he obtains 152 m for the average Xenophon’s stade); Michael J. Ferrar, Eratosthenes, Hipparchus, and Strabo: Geographia: The Length of the Oikoumene Measured on an Aslant Alignment, 2010, www.cartogra phyunchained.com/es1.html; Christian Marx, “Lokalisierung von Pytheas’ und Ptolemaios’ Thule,” Z. Geodäsie, Geoinforma- tion Landmanagement, 2014, 139:1–7; and Marx, “Analysis of the Latitudinal Data of Eratosthenes and Hipparchus,” Math. Mechan. Complex Syst., 2015, 4:309–339, esp. p. 318. The most thorough comparison of distances reported by Strabo with their modern counterparts has been undertaken by Leonid V. Firsov, “Ob Eratosfenovom ischislenii okruzhnosti Zemli i dliny ellinisticheskogo stadiia [On Eratosthenes’ Calculation of the Circumference of the Earth and of the Length of the Hellenistic Stade],” Vestnik drevnei istorii [Journal of Ancient History], 1972, 3:163–168 (in Russian with English abstract). As a result, he has obtained 154.4–157.8 m for the weighted mean length of the stade. 63 For a similar opinion see Rennell, Geographical System of Herodotus, pp. 22–23; Leake, “On the Stade,” p. 13; Hultsch, Grie- chische und römische Metrologie (cit. n. 24), pp. 50–51; Thomson, History of Ancient Geography (cit. n. 9), p. 161; Engels, “Length of Eratosthenes’ Stade” (cit. n. 19), p. 307; and Geus, “A ‘Day’s Journey’ in Herodotus’ Histories” (cit. n. 26), p. 148. 64 On ancient techniques of measuring distances see Lewis, Surveying Instruments of Greece and Rome (cit. n. 16), pp. 13–35, 217–245. 65 This was noted, for example, by Bunbury, History of Ancient Geography (cit. n. 16), p. 210; Miller, Die Erdmessung im Alter- tum und ihr Schicksal (cit. n. 9), p. 43; and Engels, “Length of Eratosthenes’ Stade” (cit. n. 19), p. 307. For similar criticisms of Rennell’s reasoning see Falconer, Arrian’s Voyage Round the Euxine Sea (cit. n. 25), pp. 149–164. The late Roman itineraries are usually very accurate for short distances. However, for long distances composed of a series of short segments their data, too, are considerably in excess of the respective shortcut distances on a modern map owing to the sinuosity of roads. 66 Similarly, Dörpfeld (in “Beiträge zur antiken Metrologie” [cit. n. 44], pp. 303–304) argued for 178 m as the “common” length of the pre-Roman stade and thus came to the conclusion that distances measured in these stades were overestimated by 25 percent on average.
This content downloaded from 128.220.159.005 on April 26, 2017 08:50:36 AM All use subject to University of Chicago Press Terms and Conditions (http://www.journals.uchicago.edu/t-and-c). Isis—Volume 107, Number 4, December 2016 703 the “short” or the “common” stade as the one used by Hellenistic geographers—then this method seems efficient enough to tip the scales in one direction or the other. For this purpose I have examined more than 160 distances given in Pliny’s Natural History (ca. 79 c.e.) and obtained the following results.67 If these distances are believed to be accurate, then, by the same logic that has led us to the “itinerary stade,” we have either to conclude that Pliny’s mile was equal to circa 1,190 m,68 which is impossible, or to assume that Roman measurements of distances were much less accurate than Greek ones, which is hard to believe. Otherwise, we have to conclude that Pliny’s distances were overestimated by 25 percent on average—that is, by approximately the same amount that Eratosthenes’ and Strabo’s distances must have been if they were expressed in the “common” stades of 185 m.69 This argument, of course, needs further elaboration and testing, but in any case it seems to undermine the “short stade hypothesis.” It remains to add that, as applied to Eratosthenes’ measurement of the Earth, the idea of the “itinerary stade” creates an obvious vicious circle. If the “short” stade is deduced from a tacit as- sumption of highly accurate ancient distance measurements, then it is unsurprising that, when substituted into Eratosthenes’ calculations, it makes his result amazingly accurate as well.
VII. THE EARLY VERSION OF PTOLEMY’S MAP In this section I try to show that the interplay of different factors behind the longitudinal defor- mation of Ptolemy’s map was even more complicated than it may appear from what has been said so far. In spite of the criticisms of the “wrong circumference hypothesis” I have presented, its core assumption that the early version of Ptolemy’s map was based on Eratosthenes’ value for the circumference of the Earth receives strong confirmation from a different side. Thus, a number of researchers—Ernst Herzfeld, Antonin Wurm, and I—have independently demon- strated that a large part of Ptolemy’s map represents with high accuracy the main parameters of Eratosthenes’ geographical system translated into degrees according to Eratosthenes’ scale (where 1° of the meridian is 700 stades, and not 500 as in Ptolemy).70 Let us consider this point briefly. The framework of Eratosthenes’ “world map” was based on the system of so-called sphragides or “seals”: large regions shaped like quadrangles bounded by parallels and meridians.71 Strabo, our sole source on this subject, describes only four sphragides in Asia. In the north all of them were bounded by the Taurus range. In the west and east they were delimited by meridians: one passed along the Indus and separated India from Ariana; another passed through the Caspian
67 This section is an extract from my forthcoming paper “The So-Called ‘Itinerary Stade’ and the Accuracy of Eratosthenes’ Measurement of the Earth.” 68 More precisely, the result falls within the range of 1,123–1,196 m for different groups of distances: overland, across the open sea, along the seacoast, etc. 69 Similar observations have been made by Leake, “On the Stade” (cit. n. 25), p. 25; and Konrad Miller, Itineraria Romana: Römische Reisewege an der Hand der Tabula Peutingeriana dargestellt (Stuttgart: Strecker & Schröder, 1916), pp. 470, 516, 555–556, 663, 712. 70 Friedrich Sarre and Ernst E. Herzfeld, Archäologische Reise im Euphrat- und Tigris-Gebiet, Vol. 1 (Berlin: Reimer/Vohsen, 1911), pp. 143–153; Antonin Wurm, Mathematické základy mapy Ptolemaiovy [Mathematical Foundations of Ptolemy’s Map] (Choteˇborˇ: Stýblo, 1937), http://ihst.nw.ru/images/geography/Wurm/Wurm_Mathematicke_zaklady_mapy_Ptolemaiovy_1937. pdf; Wurm, O vzniku a vývoji mapy Ptolemaiovy (cit. n. 15); and Dmitry A. Shcheglov, “Ptolemy’s System of Seven Climata and Eratosthenes’ Geography,” Geog. Antiqua, 2004, 13:21–37, esp. pp. 30–31. 71 Of course, by “Eratosthenes’ map” I mean only an intelligible geometric construction or a “mental map.” There is no evidence that he ever created a map as a material artifact. On sphragides see Klaus Geus, “Measuring the Earth and the Oik- oumene: Zones, Meridians, Sphragides, and Some Other Geographical Terms Used by Eratosthenes of Kyrene,” in Space in the Roman World: Its Perception and Presentation, ed. Richard Talbert and Kai Brodersen (Münster: LIT, 2004), pp. 11–26.
This content downloaded from 128.220.159.005 on April 26, 2017 08:50:36 AM All use subject to University of Chicago Press Terms and Conditions (http://www.journals.uchicago.edu/t-and-c). 704 Dmitry A. Shcheglov The Accuracy of Ancient Cartography Reassessed
Figure 2. Eratosthenes’ distances underlying Ptolemy’s map.
Gates (the Sirdar Pass in Iran) and separated Ariana from the third sphragis. The western boundary of the third sphragis was the Euphrates. Already, at first sight, the outlines of the second and the third sphragides are clearly visible on Ptolemy’s map (see Figure 2). More important, about twenty distances given by Eratosthe- nes for this area fit closely with Ptolemy’s map (they are shown by the arrows on Figure 2).72 As an illustration, I will consider only the two most important examples concerning the longitu- dinal extent of these sphragides. The length of Ariana (from the Caspian Gates to the Indus) was, according to Eratos- thenes, 14,000 stades at about the latitude of Rhodes (36º on Ptolemy’s map).73 In Ptolemy, Ariana lies between the meridians of 94º (through the Caspian Gates) and 119º (the bound- ary of India), which equals about 14,000 stades at the latitude of Rhodes (where 1º long = 700 stades x cos 36º = 566 ≈ 560 stades).74 The length of the third sphragis from Babylon to
72 For a detailed argument see my forthcoming paper “Eratosthenes’ Contribution to Ptolemy’s Map,” Imago Mundi (in press). 73 Eratosthenes, frag. 37, 78 Roller = Strabo, Geography 1.4.5 C64, 15.2.8 C724. 74 Antonin Wurm, Mathematické základy mapy Ptolemaiovy (cit. n. 70), pp. 7–8, 4, 12; Wurm, O vzniku a vývoji mapy Ptole- maiovy (cit. n. 15), pp. 7–8, 11; and Shcheglov, “Ptolemy’s System of Seven Climata and Eratosthenes’ Geography” (cit. n. 70), p. 31. Ptolemy usually rounded all coordinates and values of a degree of longitude at different latitudes. See Wurm, Marinus of Tyre (cit. n. 16), pp. 25–27; Leif Isaksen, “Lines, Damned Lines, and Statistics: Unearthing Structure in Ptolemy’s Geographia,” e-Perimetron, 2011, 6:254–260, www.e-perimetron.org/ Vol_6_4/Isaksen.pdf; and Christian Marx, “On the Precision of Ptolemy’s
This content downloaded from 128.220.159.005 on April 26, 2017 08:50:36 AM All use subject to University of Chicago Press Terms and Conditions (http://www.journals.uchicago.edu/t-and-c). Isis—Volume 107, Number 4, December 2016 705 the eastern boundary is stated to be 9,000 stades at about the latitude of Alexandria (31º on Ptolemy’s map).75 In Ptolemy, the longitudinal interval between Babylon (79º) and the eastern boundary of the sphragis (94º) is precisely 9,000 stades at the latitude of 31º (where 1º long = 700 stades x cos 31º = 600 stades).76 These and other similar observations suggest that the whole area of Ptolemy’s map, at least between Babylon and the Indus, has been based on a set of distances expressed in Eratosthenes’ degrees. This, on the one hand, confirms that the early version of Ptolemy’s map may have been based on Eratosthenes’ value for the Earth’s circumference. But, on the other hand, it undermines the idea that Ptolemy’s adoption of a smaller value was the main factor responsible for the stretching of his map: a part of his map was not recalculated to the 500-stade degrees but nevertheless has almost the same stretching factor as the other parts.77
CONCLUSIONS The general impression gained from this investigation is that the “wrong circumference hy- pothesis” attempts to cut the Gordian knot at one stroke, whereas it should be disentangled carefully. The reality proves to be more complex and intricate than can be accounted for with a single-factor explanation. The results of the investigation are twofold. On the one hand, we have merely reaffirmed, albeit on a more solid footing, an opinion more than two centuries old.78 It may be summa- rized as follows. Ancient surveyors usually overestimated distances, which was inevitable for that time. It is hardly surprising that Eratosthenes’ measurement of the Earth, based on one of these distances, came to be overestimated as well. Interestingly, the errors in Eratosthenes’ and Ptolemy’s estimates of the Earth’s circumference were almost equal in magnitude, but opposite in sign. Consequently, distances projected on Ptolemy’s Earth become still more exaggerated in angular terms than they were to begin with. Therefore, only about half of Ptolemy’s error in longitude can be attributed to his incorrect value for the Earth’s size. In contrast, when pro- jected on Eratosthenes’ Earth the same distances come to be quite accurate in angular terms. The incredible accuracy of the reconstructed early Ptolemaic map, therefore, proves to be a quaint illusion produced by a superposition of two opposite errors. In these circumstances, it would be unfair to blame Ptolemy for his errors, because the whole tradition he relied on was a chain of errors. On the other hand, two other observations are more important. First, we have defined the range in which the length of the Greek stade could vary and, therefore, the extent to which this
Geographic Coordinates in His Geographike Hyphegesis,” History of Geo- and Space Sciences, 2011, 2:29–37, http://www.hist- geo-space-sci.net/2/29/2011/hgss-2-29-2011.pdf. For example, 1º of longitude at the latitude of Rhodes (36º) equals 500 stades x cos 36º = 404.5 stades, but Ptolemy always rounds it to 400 stades. 75 Eratosthenes, frag. 60 Roller = Strabo, Geography 2.5.38 C133. 76 This was noted by Sarre and Herzfeld, Archäologische Reise im Euphrat- und Tigris-Gebiet (cit. n. 70), pp. 151–152; and Shcheglov, “Ptolemy’s System of Seven Climata and Eratosthenes’ Geography” (cit. n. 70), pp. 30–31. 77 The stretching factor for Ptolemy’s map between Babylon and the Indus (at the mouth of the Kabul where it was crossed by Alexander’s army) is equal to the quotient of division of Ptolemy’s longitudinal difference between them by the difference between their modern longitudes: (119°˗ 79)/(72.23°˗ 44.42) = 1.43. For more details see Shcheglov, “Error in Longitude in Ptolemy’s Geography Revisited” (cit. n. 2). 78 For this opinion see, e.g., Konrad Mannert, Geographie der Griechen und Römer auf ihren Schriften dargestellt, 2nd ed., Pt. 1: Allgemeine Einleitung (Nürnberg: Grattenauer, 1799), p. 141; Albert Forbiger, Handbuch der alten Geographie, Vol. 1 (Leipzig: Mayer & Wigand, 1842), p. 413; Bunbury, History of Ancient Geography (cit. n. 16), pp. 568–569; and Carmody, “Ptolemy’s Triangulation of the Eastern Mediterranean” (cit. n. 13), p. 604. Cf. John L. Berggren, “Ptolemy’s Maps as an Introduction to Ancient Science,” in Science and Mathematics in Ancient Greek Culture, ed. C. J. Tuplin and T. E. Rihll (Oxford: Oxford Univ. Press, 2002), pp. 36–55, esp. p. 50.
This content downloaded from 128.220.159.005 on April 26, 2017 08:50:36 AM All use subject to University of Chicago Press Terms and Conditions (http://www.journals.uchicago.edu/t-and-c). 706 Dmitry A. Shcheglov The Accuracy of Ancient Cartography Reassessed variation could have contributed to Ptolemy’s cartographic errors. Second, we have found that a large part of Ptolemy’s map was expressed in degrees according to Eratosthenes’ rate of 1º = 700 stades, but nevertheless it exhibits the same longitudinal error as other parts. The combina- tion of all these factors must inevitably have produced a rather confused picture. At the same time, I believe, these findings provide us with a new and powerful tool to investigate Ptolemy’s map and thereby open promising perspectives for further studies.
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