Posidonius and the Circumference of the Earth

Posidonius and the Circumference of the EarthAuthor(s): I. E. DrabkinSource: Isis, Vol. 34, No. 6 (Autumn, 1943), pp. 509-512Published by: The University of Chicago Press on behalf of The History of Science SocietyStable URL: http://www.jstor.org/stable/225895 .

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The Origin and Earliest History of Falconry 509

have learned hawking from them. We know that they did introduce stirrups and spurs into Europe, so why might they not have brought falconry with them also? Or again the Huns and Alans, both peoples of Oriental origin and inhabitants of steppes, born riders and huntsmen, might have spread the sport, or at least given it an impetus when they reached Italy in the 5th century. In any case, it will be granted as more likely that either the Romans-through service in their eastern colonies-or the Germans-through contact with eastern peoples on their migrations-learned and copied the sport from Orientals, than that the

Germans invented and fostered hawking during this period.2 The Society of Fellows Harvard University

92I ask my readers who are able to contribute any new material in the subject covered in this paper, to send it to the Editor of Isis, for publication among the Notes. I have gathered material for another paper on "Falconry during the early Middle Ages," which will deal with Central Europe (the Church and falconry; Carolingian falconry, etc.), with England before the Norman Conquest, Scandinavia, Russia and the Near East up to the 12th century; I hope to publish it after the war. I would appreciate any contributions and suggestions sent to me at: 42 East Manning Street, Providence, R. I.

POSIDONIUS AND THE CIRCUMFERENCE OF THE EARTH

By I. E. DRABKIN

IN a well-known passage (I.10) CLEOMEDES ex- plains the methods used by ERATOSTHENES and POSIDONIUS for the determination of the circumference of the earth. The procedure is to find the difference in latitude between two places on the same meridian, measure the terrestrial distance between these places, and thus find the measure of 10 and of the whole circumference.

Whether the heavenly body used for the determination of the difference in latitude be the sun, as it was in ERATOSTHENES' procedure, or some other star-PosIDONIUS used the star Ca- nopus-the method is fundamentally the same. In all probability a similar procedure had been used by "the mathematicians" who, ARISTOTLE tells us (De Caelo 298a16), arrived at the figure 400,000 stades, and by those who, according to ARCHIMEDES (Sand Reckoner I.8), made the circumference 300,000 stades.

Now, in the passage to which we have referred, CLEOMEDES asserts that ERATOSTHENES reached the result 250,000 stades' on the basis of a difference of latitude of 7%Y (or %0 of a circumference) between Alexandria and Syene and a terrestrial distance of 5000 stades between these two cities.

In the same passage we are told that Posi- DONIUS, on the basis of a difference of latitude of 7%0 (%8 of a circumference) between Rhodes and Alexandria, concluded2 that "the circumference of the earth is 240,000 stades, if the distance from Rhodes to Alexandria is 5000 stades; but if this distance is different, the circumference will also be proportionately different." (CLEO- MEDES, p. 94.19 ZIEGLER.)

lThe question of the origin of the correction to 252,000 stades does not concern our present inquiry.

2Te words of CLEOMEDEs are not a direct quotation from POSIDONIUs but seem to represent the latter's argument.

Now STRBo, whose temporal relation to CLEO- MEDES cannot be determined, tells us (p. 95 CA- SAUBON; cf. p. 102) that POSIDONIus estimated the circumference of the earth at about 180,000 stades. STRBo speaks of this estimate as "one of the more recent measurements, the one that makes the earth smallest."

There has been much discussion of these two divergent measurements ascribed to POSIDONIUS and attempts have been made to explain the discrepancy on the basis of (1) two different measurements for the distance from Rhodes to Alexandria, or (2) two different measurements of the stade.

The first explanation supposes that the circumference of 240,000 stades is based on a measurement of 5000 stades for the distance from Rhodes to Alexandria, while that of 180,000 stades is based on a measurement of 3750 for this distance, the difference in latitude being 7%O. Certainly some color is lent to this line of explanation by the words of CLEOMEDES quoted above: "but if this distance is different, the circumference will also be proportionately different."

There is, however, at least a prima facie difficulty with this explanation. The figure 3750, if it is derived from ERATOSTHENES, is a deduction from an observed difference in latitude of 5 % 0 or 5 5/1 0, taken in conjunction with ERATOSTHENES'

measure of the circumference, 250,000 or 252,000 stades.8 POSIDONIUS would, in this case, be assert- ing a measurement of the circumference (180,000

3 STRABO, P. 125 CAS.: "The voyage from Rhodes to Alex- andria with the north wind is about 4000 stades, while the voyage along the coast is twice as long. Now ERATOSTHENES tells us that this is a sailor's estimate of the length of the trip, some giving the aforesaid figure, and others not hesitating to put the figure at 5000 stades. But he says that by using0 sundials he found the distance to be 3750 stades."



510 I. E. Drabkin

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stades) on the basis of a figure itself based on an entirely different measurement of the circumference (250,000 or 252,000 stades).

Now a very plausible answer was given to this objection.' It was held that POSIDONIUS was not attempting to give definitive geographical results but merely hypothetical examples of method, that his interest was not that of the professional geog- rapher seeking the most precise measurement, but rather that of the teacher of philosophy and science demonstrating the basic methodology involved. If this is the case, it would be quite in order for him to say that, on the assumption of a difference of 7% 0 in latitude between Rhodes and Alexandria, the circumference of the earth is 240,000 stades if the distance between the two cities is 5000 stades, while the circumference is 180,000 stades if the distance between the cities is 3750 stades. There is, in this view, no reason to reconcile the two divergent estimates of the circumference ascribed to POSIDONIus nor to re- quire that he use the data of his examples (e.g., the distance of 3750 stades between Rhodes and Alexandria) in the same framework in which they happen to have been historically discovered.

ERATOSTHENES and HIPPARCHUS had, to be sure, reached a far more accurate determination of the difference in latitude between the two cities. But those who view the problem in the manner I have indicated might hold that it was precisely in order to give a simple example of method for non-specialists that POSIDONIUS, sacrificing astronomical accuracy, took the elevation of Canopus at Rhodes to be zero." For in estimating the dif-

4Perhaps first by J. A. LETRONNE. See H. BERGER, Gesch. d. wiss. Erdkunde d. Griechen, 577-582; T. L. HEATH, Aris- tarchus, 345 f; 0. VIEDEBANrr, Klio XIV (1915), 221-232.

5 Even if allowance is made for the effect of refraction, the star Canopus in POSIDONIUs' time attained an elevation of more than 1? above the horizon in the city of Rhodes (and more on the rest of the island). Actually it was visible for about 2? hours. It is unnecessary for our purpose to go

ference in latitude between the two cities he would, consequently, not have to subtract anything from the observed elevation of the star at Alexandria.

Those who are dissatisfied with the approach just outlined generally adopt what I have called the second explanation. They hold that the circumference of 240,000 stades is based on a stade of 1/% of a Roman mile, which we may call the Eratosthenean stade, while the figure 180,000 is based on a stade four-thirds as long, i.e. a stade of 2//'5 of a Roman mile, the so-called Philetaerian stade, and that consequently the two measurements are really one.'

Now few problems of Greek and Roman metrology are as tantalizing as the problem of the length of the various stades. LEHMANN-HAUPT in his article "Stadion" in PAULY-WISSOWA'S Real-Encyclopddie (III [Second Series], 1930- 1963) has shown that at least seven different stades were in use at various times and places, measuring, respectively, 5, 7, 7%, 8, 8%, 9, and 10 to the Roman mile. Without going into any of the complicated problems involved, let me say at the outset that' it is metrologically possible that POSIDONIUS wittingly or unwittingly used the Philetaerian stade (7? to the mile). I suspect, however, that were it not necessary to account for the figure 180,000, the natural assumption would be that POSIDONIUS used the same stade as POLY- BIUS (the so-called Olympic stade, 8% to the mile), or the Italian stade (8 to the mile).'

But quite apart from this there is a serious difficulty with the assumption that the two figures ascribed to POSIDONIus represent the same measurement in alternative standards. For both STRABO and CLEOMEDES seem to indicate otherwise.

into the question of POSIDONIus' dependence on EUDOXUS or anyone else for the data about Canopus.

" See e.g. H. VON MZIK, Mitteil. Geogr. Ges. Wien LVI1I (1915), 175; F. WESTBERG, Klio XIV (1915), 344 n.; 0. VIEDEBANTT, Klio XVI (1920), 94-100; AuBREY DILLER, Klio XXVII (1934), 258-259.

7 STRABO tells us (p. 322 CAB., cf. VII frag 56 [57J) that most people take 8 stades to the mile, but that POLYBIUS took 8%. See W. KUBITSCHEK, art. "Karten," R.E. X.2081. art. "Erdmessung," Suppl. VI.51.

The connection of POSIDONIus' estimate with the sub- sequent adoption by MARINUS and PTOLEMY of a circumference of 180,000 stades, and the effect of that choice on later geographers including COLUMBUS, are matters that lie outside the scope of this paper. Two points may, however, be noted. (1) The figure 180,000, however it was arrived at by POSIDONIUS, certainly did not involve for MARINUS and PTOLEMY a difference of 7%? in latitude between Rhodes and Alexandria. (2) While 0. CUNTZ (Die Geographie des Ptolemaeus, 110-112, 120) has made out a strong case for PTOLEMY'S use of the Italian stade (8 to the mile), the pos- sibility of his having used the Philetaerian stade cannot be summarily dismissed. See Geog. I. 11. 3, 12.3, and the paper of MZIK cited above. Again, it may be asked to what extent, if any, we are dealing here with a hypothetical stade of !Aoo of a terrestrial degree.



Posidonius and the Circumference of the Earth 511

STRABO, as we have seen, speaks of the Posi- donian estimate of 180,000 stades as "making the earth smallest." Again, when CLEOMEDES says, in the passage quoted above, wrpo ?oyov TO'V

8M7vT?a/rTOS, he can only be referring to a difference in distance, not to a difference in standard. Though this difficulty may not be fatal to the theory proposed, for confusions in metrology are not uncommon in ancient authors, it certainly prevents us from accepting the theory with com- plete confidence.

I believe that still another approach to the problem is possible. While CLEOMEDES tells us how the estimate of 240,000 stades was arrived at, STRABO gives us no such information about the figure 180,000. Now it has always been as- sumed that the general method employed was the same in both cases. But may not this very assumption, from which all the difficulties arise, be unnecessary?

I should like to suggest that POSIDONIUS may have combined (1) a proposition of ERATOS- THENES well known to him, that the sun at the zenith casts no shadow over a circle 300 stades in diameter (CLEOMEDES, pp. 98.5, 140.7, 144.24 ZIEGLER), with (2) an estimate of %0o of the circumference, i.e. 36', as the apparent diameter of the sun. These data would give a terrestrial circumference of 180,000 stades (300X600).8

CLEOMEDES tells us (p. 144.24)9 that Posi- DONIUS used the first proposition in combination with an assumption that the sun's orbit was 10,000 times the earth's circumference, to arrive at an estimate of 3,000,000 stades (300X10,000) for the diameter of the sun.

As for the second proposition, that concerned with the sun's angular diameter, it is perhaps on the authority of POSIDONIUS' pupil, VARRo, that MARTIANUS CAPELLA gives (VIII, p. 860) 36' as the apparent diameter of the moon.10 Better ap- proximations had, indeed, been given by ARIS- TARCHUS (% 1) and ARCHIMEDES (between 1%64

8 According to my conjecture, AB in the figure is 300 stades and ACB = 36'. Solar parallax is neglected, as regularly in antiquity, the angular diameter of the sun as seen from the surface of the earth being used for the central angle.

I Te words of CLEOMEDES, C;,v OTrws Jp TO&s 4acZol,dPOLs

JX6rrcPJP (27), would seem to indicate that POSIDONIUS under- stood this figure as a datum of observation rather than as a convenient lower limit for observable differences of latitude, derived from the Eratosthenean measure of a degree (700 stades) and an approximation of 20 for the angular diameter of the sun. ERATOSTHENES seems to have taken 400 stades as a general limit of such observability (STRAmo, p. 87 CAS.). But see H. BERGER, op. cit., 410.

10 For practical purposes the angular diameters of the sun and moon were considered equal (CLEOMEDES, P. 178.24). More precise determinations were required for astronomical work (see PTOLEMY, ilmagest V. 14).

and %0o of a right angle) but this would not con- stitute a bar to the present conjecture."1

It has been suggesed"2 that POSIDONIUS may have proposed or made use of a third figure for the circumference of the earth, 300,000 stades."3 There is no direct evidence for this and the deduction depends on a combination of two propositions of POSIDONIUS: (1) the proposition just referred to, that the orbit of the sun is 10,000 times the circumference of the earth (CLEOMEDES, pp. 144-146), and (2) the proposition that the sun is, roughly, 500,000,000 stades distant from the earth."4

These propositions taken together would involve a measure of approximately 50,000 stades for the radius of the earth, and, by a rough approximation common in non-technical work, a circumference of 300,000 stades.

But did POSIDONIus deduce the measure of the circumference by using these propositions, or was the measure of the circumference one of his as- sumptions? May he, indeed, have used the propositions referred to quite independently of each other as informal examples in his teaching? I cannot answer these questions, but the fact that the various possible combinations involve figures in conflict with others that are ascribed to Posi- DONIUS would not, in itself, necessitate an outright rejection of any of the possibilities. For Posi- DONIUS seems to me to have been at least as interested in giving examples of the methods of mathematical geography and perhaps suggesting wide limits within which a true measure falls, as in seeking a definitive determination of that true measure. It must be said, however, that the ancient geographers were quite aware that their methods were at best approximative. The use of round numbers is but one indication of this.

In this connection it should be pointed out that shortly before the time of MARINUS and PTOLEMY there were current, apparently, estimates of the

11 ARCHIMEDES, Sand Reckouner I. 10, 16. 12 F. HULTSCH, Poseidonios iiber d. Grosse u. Entfernung

d. Sonne, Abh. Ges. Wiss. Gattingen, N.F. I.5 (1897), 11- 32. See also T. L. HEATH, Aristarchus, 344-347.

"'This measurement was current, as we have seen above, in the time of ARCHIMEDES. See W. KUBITSCHEK, art. "Erd- messung," R.E. Suppl. VI.33-35. There is no compelling reason to follow BERGER in his ascription of the result to DICAEARCHUs. See W. A. HEIDEL, The Frame of the Ancient Greek Maps, 113-117; 0. NEUGEBAUER, Amer. bourn. Phil. LXII (1941), 344-347.

14 More exactly 502,000,040. "POSIDONius holds that the height to which mists and winds and clouds reach is no less than 40 stades from the earth's surface, that then the air becomes pure, serene, and of undisturbed brightness, that the distance from the layer of clouds to the moon is 2,000,000 stades, and from there to the sun 500,000,000 stades." PLINY, Nat. Hist. II.85.



512 I. E. Drabkin

circumference of the earth that varied consid- erably. PLUTARCH refers to the estimate of the earth's radius at 40,000 stades as a sort of mean estimate." And we have seen that STRABO speaks

15 Ka-& TOtJs Auws dvacerpovh'ras, On the Face in the Moon 925D. The rough approximation to the circumference, 240,000, would actually be midway between the attested estimates, 180,000 and 300,000. In the more accurate working out the "mean') estimate is practically the same as that of ERATOSTHENES.

of "more recent estimates" of which that of PosI- DONIUS is only one.

It must be remembered, however, that no estimate of 300,000 stades of POSIDONIUS is actually attested. It is the figure 180,000 that in the first instance requires clarification and it is to this end that my conjecture is directed.

Institute of the History of Medicine The Johns Hopkins University

QUERIES AND ANSWERS

QUERY No. 104. What is lucerrage?

The Augustinian monk, SEBASTI'AO MANRIQUE, was born in Oporto, took orders at Goa in 1604, was sent as a missionary from Goa to Arakan (NE part of the Bay of Bengal) in 1629, travelled ex- tensively in India and the Far East, returned to Rome in 1643 and wrote there in Spanish an account of his adventures; in 1669 he was mur- dered in London by his own Portuguese servant. His work was written in a very poor language (castellano desastroso) but is of considerable interest. The first edition of Itinerario de las Mis- siones que hizo el Padre F. Sebastian Manrique

appeared in Rome in 1649; the text was re-

chittagon

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l > WEgPc lul~~~l er (Paragri (Psy ai)l

Buthidau~~~F d:u thai

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A'~~~k

appoximat route being agiven

printed in Rome in 1653. Both editions seem to be very rare. However, the text is easily available in the excellent translation made by Lt. Col. C. ECK- FORD LUARD (d. 1927) and Father H. HOSTEN, S.J. (Hakluyt Society, 2 vols., Oxford 1927).

In 1630 Father MAN-RIQUE travelled from Dianga, in the northern part of the Arakan king- dom, to the capital Mrauk-u (see map borrowed with kind permission from the Hakluyt edition) where he fell gravely ill. His illness lasted five months; finally the king sent him his tabibo, or doctor (Arabic tabib) who cured him with lucerrage. Says Father MANRIQUE (vol. 1, 165):

As we are now on the subject of this admirable root it will not be out of place to give an account of it, first informing the, curious reader that what we say about it we learnt from what we saw and experienced and not from hearsay.

The Lucerrage is similar in appearance to the Tamarisk, differing, however, in its leaves, which are broader and a dull green below and shining green above. The plants are from four to six palms in height, the whole plant, including the root, being covered with a bark that looks like white poplar. This wonderful plant grows wild in the Macassar islands [in Celebes] and Bima [Sumbawa, near Java], whence the best are obtained. The plant's whole value lies in its root, which strikes always towards the north. In this the' Divine Creator has placed such virtues as to make it as it were a supernatural plant. For it can be used in any kind of fever, any case of poisoning, and for the bite from any poison- ous animal. This root is used by grinding it up with water on a stone. It is then either drunk or placed on the lachrymal gland of the eye, when it causes an expulsion of the poison. It produces such miraculous results as to be incredible, and I should never have dared to mention them if I had not actually seen an experiment made. A warning must be given that all the Lucerrage which the people of Macassar and Bima sell secretly is not good, for good Lucerrage is only collected on an order from the Sumbanco, a title correspond- ing to "Great King and Lord ruling over lesser kings."

Whenever the Sumbanco proposes to give one of these plants to any stranger or Ambassador, he first has an example of its effects shown to him as he did to Don PHELIPE LOBO. This nobleman had completed the tenure of his office as Commander-in-chief in China, and was returning via Goa, when he was forced to take refuge at Macassar with several ships and galleons belonging to the fleet. He was received by the Sumbanco with the greatest pomp and ostentation, as was his usual custom, because His Highness had always been much attached to the Portuguese nation, with whom he had



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Posidonius and the Circumference of the Earth