des and the Burning Mirrors of Syracuse (D. L. Simms)

Archimedes and the Burning Mirrors of SyracuseAuthor(s): D. L. SimmsSource: Technology and Culture, Vol. 18, No. 1 (Jan., 1977), pp. 1-24Published by: The Johns Hopkins University Press on behalf of the Society for the Historyof TechnologyStable URL: http://www.jstor.org/stable/3103202Accessed: 29/11/2008 04:34

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Archimedes and the Burning Mirrors of Syracuse D. L. SIMMS

The statement that Archimedes set fire to the Roman fleet under Marcellus besieging Syracuse in 212 B.C. with burning mirrors is fre-

quently found in scientific and historical literature, and almost every generation of scientists seems challenged to prove or disprove it. A

spirited exchange of views has recently appeared in Applied Optics,' and during that same period, journals in the United States and the United Kingdom have publicized the claims of a Greek scientist that his experiments have shown that Archimedes could have succeeded.2

The balance of opinion about whether Archimedes did or did not has changed so often over the centuries that it is tempting to produce a list of distinguished scientists and scholars who have expressed an

opinion one way or the other-rather like that for or against the rotation of the earth compiled in Galileo's day. Ironically enough, in this burning mirror controversy, Galileo's name would appear on both sides.3 Belief in the Renaissance changed to skepticism at the end of the 17th century as the properties of burning mirrors became

DR. SIMMS is with the Central Unit on Environmental Pollution of the Department of the Environment of the United Kingdom; he led the U.K. delegation on marine pollution at the recent United Nations Conference on the Law of the Sea. His previous publications have been on irrigation in Great Britain and on fire research (principally on the ignition of materials by radiation). He expresses his thanks to Geoffrey Skeet for first arousing his skepticism about the burning mirrors of Archimedes.

'A. C. Claus, "Archimedes' Burning Mirrors," Applied Optics 12 (October 1973): A14; O. N. Stavroudis, "Comments," ibid. 12 (October 1973): A16; K. D. Mielenz, "That Burning Glass," ibid. 13 (February 1974): A14, A16; D. L. Simms, "More on That Burning Glass of Archimedes," ibid. 13 (May 1974): A14, A16.

2I. Sakkas, Times (London) (November 7, 1973); Washington Star News (November 13, 1973); Time (November 26, 1973); New Scientist (November 1, 1973; November 22, 1973; July 18, 1974); T. W. Africa, "Archimedes through the Looking Glass," Classical World 68 (February 1975): 305-8.

3Galileo Galilei, "The Assayer," trans. E. J. Stillman Drake, in Discoveries and Opinions of Galileo (New York, 1957), p. 246: "There they may learn that Archytas made a dove that flew, that Archimedes made a mirror which kindled fires at great distances ... and a hundred more inventions no less amazing." See also Galileo, Two New Sciences, trans. Henry Crew and Alfonso de Salvio (New York, 1914), p. 41. This, his second opinion, is based on the work of Cavalieri (B. Cavalieri, Lo Specchio ustorio, 2d ed. [Bologna, 1650]).

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better known, largely because of the influence of Descartes.4 Belief overcame skepticism in the 18th century, after the experiments of Kircher and Buffon, with Dutens's pamphlet perhaps representing its culmination, although Montucla expressed severe reservations.5 Be- lief remained in the 19th century as shown by the calculations of Peyrard and John Scott.6 There then followed the skepticism, mainly on historical grounds, of Archimedes' editors and commentators, one of whom, Dijksterhuis, also regarded the feat as technically impossible.7 Of the specific studies in this century on whether Ar- chimedes used burning mirrors, Raskin, Burger, and Schneider largely confined themselves to the historical evidence, the first two

finding in favor, the last (the most recent) against.8 Middleton considered the scientific arguments as well, but was most concerned with the work of Kircher and Buffon and the period between them.9

Ideally, the credibility of Archimedes' feat should be analyzed and discussed in terms of three questions: First, what is the historical evidence and how convincing is it? Second, did Archimedes have the knowledge and skill to design, build, and operate a burning mirror, in particular the kind of burning mirror the commentators described? And third, would Archimedes have chosen to use it in preference, or in addition, to those weapons already at his command? In earlier papers I have argued that there were good historical, scientific, and military reasons for denying that Archimedes did, could have, or indeed would have tried to set the fleet of Marcellus on fire using

4R. Descartes, Oeuvres, ed. C. Adam and P. Tannery (Paris, 1897-1913), 6:192-94. 5W. E. Knowles Middleton, "Archimedes, Kircher, Buffon and the Burning Mir-

rors," Isis 52 (1961): 170, 533-43; L. Dutens,Du Miroir ardent d'Archimede (Paris, 1775); J. E. Montucla, Histoire des mathematiques, 2 vols. (Paris, 1758; also a 2d ed. in 4 vols., much expanded, edited by Lalande [Paris, 1799-1802]).

6F. Peyrard, Le Miroir ardent d'Archimede (Paris, 1807) (in an edition of Archimedes' work and comments on the mirror by Delambre, Monge, and Charles); J. Scott, "On the

Burning Mirrors of Archimedes," Transactions of the Royal Society of Edinburgh 25 (1869): 123-49.

7J. L. Heiberg, Quaestiones Archimedeae (Leipzig, 1879), pp. 39-41, and Archimedes

(Leipzig, 1915); T. L. Heath, Works of Archimedes (1897) with The Method of Archimedes (1912) (London, 1953), pp. xxi-xxii; Paul van der Eecke, L'Oeuvres complete d'Archimede, suivies des commentaires d'Eutocius d'Ascalon, 2d ed., 2 vols. (Paris, 1960), pp. xix-xxii; E. J. Dijksterhius, "Archimedes," trans. C. Dikshoorn, Acta historica scientiarum naturalium et medicinalium 12 (1965): 28-30.

8G. Raskin, "De Brandspiegel van Archimedes," Philologische Studien 10 (1938-39): 109-18; D. Burger, "Heeft Archimedes de Brandspiegels uitgevonden," Faraday 17 (1947-48): 1-10; I. Schneider, "Die Enstehung der Legende um die kriegstechnische Anwendung von Brennspiegeln bei Archimedes," Technikgeschichte 36 (1969): 1-11.

9Middleton, pp. 533-43.

Archimedes and the Burning Mirrors

burning mirrors.10 The present paper expands those arguments, bas- ing itself upon recent studies of Greek and Byzantine geometrical optics, of the effectiveness of other Greek and Roman weapons of war, and of the use of thermal radiation to ignite materials.11

I. The Historical Evidence

The standard references to the siege of Syracuse during the Second Punic War are Polybius (?203-ca. 120 B.C.), Livy (59 B.C.-A.D. 17), and Plutarch (A.D. 45-125).12 All three gave detailed and similar accounts of the part played by Archimedes in its defense. All three emphasized that Archimedes' mechanical weapons had a devastating effect on the Romans' assault on the city by land and sea, and that as a consequence Marcellus abandoned the idea of a direct attack and settled down to a siege lasting three years. None of the three mentioned any form of fire being used as a weapon, let alone burning mirrors.

Of the three, Polybius is our most important authority. First, his histories were written within the lifetime of some of the combatants; second, he made a practice of interviewing witnesses-although we do

'0D. L. Simms, "The Legend of Archimedes and the Burning Mirrors of Syracuse," D.S.I.R. and Fire Offices' Committee, Joint Fire Research Organisation F.R. Note no. 576/1964; also "Archimedes and Burning Mirrors," Physics Education 10 (November 1975): 517-21, and "More on That Burning Glass of Archimedes" (n. 1 above), pp. A14, A16.

"A. Lejeune, "Recherche sur la catoptrique Grecque," Academie Royale de Beige, Memoires, ser. 2, vol. 52, fascicule 2 (Brussels, 1957); G. L. Huxley, Anthemius of Tralles (Cambridge, Mass., 1959); E. W. Marsden, Greek and Roman Artillery: Historical Develop- ment (Oxford, 1969); D. I. Lawson and D. L. Simms, "The Ignition of Wood by Radia- tion," British Journal of Applied Physics 3 (1952): 288-92; D. L. Simms, "Ignition of Cellulosic Materials by Radiation," Combustion and Flame 4 (1960): 293-300, and "Exper- iments on Cellulosic Materials by Radiation," Combustion and Flame 5 (1961): 369-75; D. L. Simms and Margaret Law, "The Ignition of Wet and Dry Wood by Radiation," Combustion and Flame 11 (1967): 377-88; Arvind Varma and F. R. Steward, "Spontane- ous Ignition of High Voidage Cellulosic Materials," Journal of Fire and Flammability 1 (April 1970): 154-66.

"2Polybius, The Histories, trans. W. R. Paton (London, 1923), 3:453-59 (attack by sea), 461-63 (attack by land) (8. 2. 3.2-8.4), 537-39 (capture of the city) (8. 6. 37); Titus Livius, trans. F. G. Moore (London, 1966), 6:283-87 (214 B.c. siege) (24. 34), 461 (212 B.C. death) (25. 31. 9-10); Plutarch's Lives, trans. B. Perrin (London, 1968), 5:469-79 (siege) (14. 17), 487 (death) (19.3). Fabricius (J. A. Fabricius, Bibliotheca Graeca, Lib. 3, C.22 [Hamburg, 1716], 2:551), who produced the standard list of references, added that the histories of Diodorus of Sicily and of Dionysius of Halicarnassus are incomplete. He did not include Cassius Dio in this group, but noted later than Zonaras praises Dio. Fabricius also listed Silius Italicus, Proclus, Suidas, and Zonaras, and quoted from Eustathius, Tzetzes, and the Scholiast to Lucian.

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not know whether he did this about Syracuse; third, he showed considerable interest in the technical side of war; and fourth, historiographers and historians agree that he was an outstanding historian.13 Thus to maintain the story is almost to maintain that Polybius deliber-

ately suppressed it, whereas such a suppression is contrary to our

knowledge of him and his attitude toward history. Burger's claim that we only have part of Polybius's work is not justified: the story of the

siege of the city is complete, even if there is no mention of Ar- chimedes' death in what remains of his account of its fall. Livy's historical method is open to criticism and Burger might have justification for arguing that Livy could have been silent because he had praised Archimedes enough in a work devoted to the glory of Rome.14 It is not a sustainable argument because Plutarch wrote to praise Greeks, not Romans-particularly Archimedes, whom Plutarch tended to

glorify, even deify. The silence of Plutarch is even more significant because he wrote of burning mirrors elsewhere-probably incorrectly-and because he was, as his essay "On the Face of the Moon" shows, familiar with geometrical optics.15 He would not have failed to mention the story of the burning mirror from scientific

ignorance. Schneider has recently drawn attention to a further source-a

poem by Silius Italicus (A.D. 26-101) on the Punic Wars.16 The de-

scription of Archimedes' activities at Syracuse in the poem is generally similar to that of Livy. However, Silius added a description of a

ten-story wooden tower designed by Archimedes which was used by the defenders to throw stones and lighted torches at the attackers, and which itself was destroyed by a Roman soldier throwing a firebrand. In addition, after the Romans had withdrawn from the assault, Silius Italicus described a sea battle with the Romans against the Carthaginians and the Syracusans in which fire plays a prominent role; flaming torches of pitch set fire to many ships, including

13J. B. Bury, Ancient Greek Historians (London, 1909), p. 220; M. Grant, The Ancient Historians (London, 1970), p. 164; H. H. Schullard, Scipio Africanus, Soldier and Politician (London, 1970), pp. 13, 16; M. I. Finley, The Greek Historians (London, 1959), introduction. Finley was more critical of Polybius's work, but nonetheless considered that he

belonged to the great tradition of Greek historians.

4Burger (n. 8 above), pp. 8-10; Bury, pp. 226-27; Grant, p. 225. '5Plutarch, 1:339-41 (9. 3-8); R. J. Forbes, Studies in Ancient Technology (London,

1958), 6:13; S. Sambursky, The Physical World of the Greeks, 2d ed. (London, 1963), pp. 214-17.

"'Schneider (n. 8 above), pp. 7-8; Silius Italicus, Punica, trans. K. D. Duff (London, 1934), 2:295 (14. 300-315). Duff (p. 294) commented that Archimedes' name is not mentioned in the account because it will not fit the meter of the verse.


triremes.17 Silius Italicus is not read for military history: his work is "embroidery divorced from reality."18

Both the first two pieces normally listed as secondary evidence are about a century later than Silius. Lucian, in the late 2d century A.D., provides us with the earliest record of the belief that Archimedes produced a conflagration among the ships at Syracuse; the piece is probably contemporary with that by Galen (say A.D. 160-170), with the Lucian a little earlier. Lucian did not say, as some commentators suggest, that Archimedes used burning mirrors, only that "the former burned the ships (triremes) of the enemy by means of his science."19 Lucian believed that the ships were triremes, whereas the accounts of the siege all give quinqueremes, and Casson has no doubt that quinqueremes formed the backbone of the Roman fleet at the time of the Second Punic War. It is interesting, therefore, that Silius Italicus mentioned triremes and also interesting that by Galen's and Lucian's day, the trireme was back in use in the Roman Navy.20 The piece is hearsay evidence, but such value as it has does not depend upon its being authentic Lucian, but on its being of this period.

Galen wrote: "In some such way, I think, Archimedes too, is said to have set on fire the enemy's triremes by means ofpyreia."21 There are three points to note about this sentence even in isolation from its context: first, the language implies that Galen has only heard of Ar-

17Schneider, p. 8; Silius Italicus, 2:304-5 (14. 417-22); see also 2:293 (14. 300). Livy (6:291 [24. 36. 3-4]) does not describe a battle but only movements of the Carthaginian fleet.

1J. Wright Duff, A Literary History of Rome in the Silver Age (London, 1930), p. 462. "gLucian of Samosata, Hippias, trans. A. M. Harmon (London, 1913), 1:37. The

foreword of this edition states (p. 33), "It is the general opinion that this piece is not by Lucian." H. W. and F. G. Fowler omit this piece from their edition (The Works of Lucian [Oxford, 1905], p. iii) on the grounds that both Dindorf and Jacobitz mark the passage as spurious. Chambry (E. Chambry, Lucien [Paris, 1933], p. 5) is doubtful on stylistic grounds. M. D. McLeod (University of Southampton, private communication) comments that more recent writers such as J. Bompaire (Lucien Ecrivain [Paris, 1958]) do not even consider the possibility that the piece is not by Lucian.

20Polybius, 3:453 (8. 2. 4-4.2); Livy, 6:283 (24. 34. 6); Plutarch, 5:471 (14. 3.2); L. Casson, Ships and Seamanship in the Ancient World (Princeton, N.J., 1971), p. 119; W. W. Tarn, Hellenistic Military and Naval Development (Cambridge, 1930), p. 122.

21Galen, De Temperamentis 3.2 (Bibliotheca Scriptorum Graecorum et Romanorum [Leipzig, 1969], p. 93). I have found no modern edition of this work in English. Galen noted that in bright sunlight pigeon dung has been known to self-heat and set fire to the resin- or pitch-covered woodwork of a house. "Wool, tow, wicks, pitch and anything else of a similarly dry and loose texture is readily ignited by pyreion. Also stones rubbed together kindle flame, especially if sulphur is sprinkled over them. And Medea's compound was of this kind. Everything smeared with it catches fire when heat strikes it. It is prepared from sulphur and liquid bitumen."

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chimedes' feat as a story, a tale; second, he, like Lucian, wrote "triremes"; third, the Greek word pyreia normally means "flammable materials" and not "burning mirror."22 The third point has given rise to considerable controversy, possibly to a different legend.23

Burger argued that this passage only made sense in this context if Galen were referring to a burning mirror, because the materials Galen listed ignited so quickly.24 This is not correct; burning pitch-a flame-would quickly set on fire anything that was dry and light, provided of course that it were flammable. At least one of the materials listed by Galen has a low melting point and is easier to ignite with

burning pitch than with a burning mirror, because the latter is quite as likely to melt as ignite it; in addition, ignition by a flame requires less energy than ignition without a flame!25 Moreover, the previous sentence in Galen is about self-heating materials, and the following sentence mentions Medea's compound, which, according to Galen, is made from liquid bitumen and sulfur and ignites with heat supplied by friction. It is therefore some sort of incendiary material-an in-

terpretation in line with the descriptions of its effects given in

Euripides and in Seneca.26 Thus, the text makes better sense if Galen were writing about a primitive form of Greek fire and not about

burning mirrors. Even then, Galen, like Lucian, merely provides hearsay evidence.

This analysis of Galen supports Eecke's contention that the first

22The meaning of the word 7rvpeOwv has been interpreted by Archimedes' translators and commentators either as an early version of "Greek fire" or as "burning mirrors." D.

Rivault (Archimedis Opera [Paris, 1615], pp. 546-47) concluded that the words in the

Greek text made reference to "burning stones," not to a "burning mirror." Rivault

suggested that some translators had interpreted the text incorrectly. Different editors of De Temperamentis do give conflicting interpretations.

23Petrarch said that some ascribe the invention of hurling fireballs to Archimedes

(J. R. Partington, History of Greek Fire and Gunpowder [Cambridge, 1960], pp. 103-4), and similarly there is Tartaglia's ascription of the invention of gunpowder to him

(Partington, p. 166). It may also be the source of Leonardo's story that Archimedes invented a device for spouting pitch (The Notebooks of Leonardo da Vinci, trans. Edward

MacCurdy [London, 1954], 2:209-10). Thomas Fuller (History of the Worthies of England [London, 1662], pp. 318-19) wrote of gunpowder in the first account of the Waltham

Abbey Powder Mills: "Though some suppose it is ancient as Archimedes in Europe (and ancienter in India), yet generally men behold the Friar of Mentz the first founder thereof some three hundred years since."

24Burger (n. 8 above), p. 4. 25Lawson and Simms (n. 11 above), p. 289. 26In Euripedes' Medea (trans. A. S. Way [London, 1971], 4:375-77, lines 1160-1217),

Medea gives Jason's betrothed a white robe and a golden crown; the robe bursts into flame. When her father embraces the dying bride, the witch's brew poisons him. Seneca's tragedies, Medea, trans. F. J. Miller (London, 1916), 1:279-81, 297: "fires that lurk in sulphur."


positive statement available to us that Archimedes used burning mirrors at Syracuse is that by Anthemius of Tralles.27 Nevertheless, An- themius wrote only, at least in the passages that survive, of the "unanimous tradition that Archimedes used burning mirrors to burn the enemy fleet a bowshot off." He did not know what kind of mirror Archimedes used, although he commented later that those who recall the story mention that he used several mirrors.28 We do not know how far Anthemius was able to refer to works that are now lost, but we do know that the commentary on Archimedes by Eutocius, who dedi- cated a similar work on Apollonius to Anthemius, did not include any mention of Archimedes' work on Catoptrica.29 It would appear to be legitimate to infer that it was unknown to both men, since Eutocius did refer to a work on burning mirrors by Diocles.30 Anthemius realized that a mirror in the form of conic section would be most effective, but argued that, as a single mirror of conic section would not have worked, Archimedes most probably used a speculum made from small plane mirrors. Anthemius then proceeded to design such a mirror.

The three remaining references are the Byzantine authors Eu- stathius, Zonaras, and Tzetzes of the 12th century A.D. Although Eecke translated Eustathius as referring to Archimedes using "flammable mixtures" to set fire to warships, Peyrard gave "catop- trical inventions." Eustathius is from the context (Diomedes' flashing helmet) writing about a burning mirror and not about flammable mixtures.31 Further confirmation of this interpretation comes from the reference to Anthemius's actions: we know he used mirrors to flash an intolerable light on the friends of Zeno.32 Eustathius gave no details. He merely shows that the story was widely current.

Zonaras and Tzetzes both gave circumstantial accounts of Ar-

27Eecke, L'Oeuvres complete d'Archimede (n. 7 above), p. xx. 28Huxley (n. 11 above), p. 15. 29Heath, Archimedes (n. 7 above), pp. xxxv-xxxvi. 30T. L. Heath, A History of Greek Mathematics (London, 1921), 2:200. 31Eecke, L'Oeuvres complete d'Archimede, p. xxi; Peyrard (n. 6 above), p. 561; Eu-

stathius, Commentarii ad Homeri Iliadem, ed. J. G. Stahlbaum (Leipzig, 1828; reprint ed., George Olme, 1960), 2:3 (2. 388E, verses 4-7, lines 9-14). The references in the literature are often incomplete or corrupt: "Some have been of the opinion that a sort of mirror had also been invented for Diomedes, probably fixed to his helmet or shield, so that the eyes of those who looked at him were dazzled by its brightness as it flashed when turned to reflect the rays of the sun; by which very method Archimedes, that great genius set on fire warships as though it were a sort of thunderbolt. And later a certain Anthemius, flashing one down a base (knavish) neighbor and thus terrifying him, drove him far from his own house." Astonishingly, Eustathius seems unaware of the identity of this "certain Anthemius" with the architect of Sancta Sophia.

32E. Gibbon, Decline and Fall of the Roman Empire (London, 1964), 4:184.

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chimedes using burning mirrors which they claimed to have read in earlier historians, notably Cassius Dio and Diodorus of Sicily in works now lost, and in writers on mechanics, Heron, Philon, and Pappus.33 No such passages can be found in any of the surviving works of these latter three authors.34 We know that Zonaras invented the story that Proclus used burning mirrors to destory the Gothic vessels in the harbor of Constantinople "out of his own head,"35 so that the reliabil-

ity of his account of Archimedes must also be questioned. To weight the argument against his reliability even more strongly, there is no

suggestion in Brunt's analysis that Marcellus's fleet suffered such serious losses at Syracuse as Zonaras claims. On the contrary, the evidence is that the number of Roman ships in commission in Sicily increased between 212 B.c. and 208 B.C. Livy recorded that the Roman fleet was still too large for a Carthaginian fleet with fifty-five warships.36 Finally, as Montucla long ago pointed out, Marcellus in the standard accounts withdrew his fleet.37

No one, except Scott who argued that Tzetzes could record accu-

rately since the mirror he described is capable of igniting materials, seems to have a kind word for Tzetzes. No one accuses him of poetic

33Dio's Roman History, trans. E. Carey (London, 1914), 2:171-73; Zonaras 9. 4 is given as: "At last in an incredible manner he burned up the whole Roman fleet. For by tilting a kind of mirror toward the sun he concentrated the sun's beams upon it; and owing to thickness and smoothness of the mirror he ignited the air from the beam and kindled a

great flame, the whole of which he directed upon the ships that lay at anchor in the path of the fire, until he consumed them all." Zonaras (Epitome 14.3) and Schneider ([n. 8

above], p. 9) claimed to be quoting from Dio. This, however, is in the passage where he made the unfortunate error about Proclus having used burning mirrors (see n. 35). Carey, pp. 171-72; Tzetzes Chil 2:109-28 is given as: "When Marcellus withdrew them a bow shot thence the old man constructed a kind of hexagonal mirror, and at an interval proportionate to the size of the mirror, he set similar small mirrors, with four

edges, moving by links and by a kind of hinge, and made the glass the centre of the sun's beams-its noontide beam, whether in summer or in the dead of winter. So after that, when the beams were reflected into this, a terrible kindling of flame arose upon the ships, and he reduced them to ashes a bowshot off." Peyrard (n. 6 above), pp. 562-63; Tzetzes, Chil 2, Hist. 35.

34Eecke, L'Oeuvres complete d'Archimede, p. xxii. 35Gibbon, 4:242. "That story is invalidated in the siege of Constantinople by the

silence of Marcellus and all the contemporaries of the sixth century." Gibbon (p. 183) recorded that John Malala thinks Proclus used sulfur. Proclus knew of burning mirrors from Anthemius, and Gibbon thought that his error arose from the story (p. 184) of the intolerable light flashed in the eyes of the friends of Zeno from the reflecting mirrors of Anthemius.

36P. A. Brunt, Italian Manpower, 225 B.C.-A.D. 14 (Oxford, 1971), appendices, pt. 24, pp. 666-70; table 16, p. 558. Livy, 6:291 (24. 36. 8).

37Montucla (n. 5 above), p. 247.


imagination; he did not understand how burning mirrors work.38 Nonetheless, he had read the outline of the story somewhere, although some of the details are clearly his own invention. The first part of his account of the siege must be accepted to be sufficiently similar to the general accounts to have been derived via Cassius Dio from (say) Livy. The second part, like that of Zonaras, is more than likely to have come from elsewhere. Gibbon suggested that the details of the mirror could have been taken from Anthemius's mathematical treatise where he had read it "perhaps with no learned eyes."39 In addition, Dupuy realized that the passage about the noontide sun had been incorporated from an earlier (and quite unrelated) section of Anthemius's work.40 Thus, Scott's argument is only valid insofar as Tzetzes recorded the details of Anthemius's mirror, not Archimedes. It is right to add that Kircher confirmed that ships could approach very close to the shore, as Tzetzes claimed, and the distance of thirty paces-say 30 meters-is well within a bowshot; on the other hand, this follows from the statements in Polybius and Livy that the wall of Achradina, where the assault by sea took place, was washed by the sea41 and is a necessary condition for some of the other machines to work.

38Scott (n. 6 above), p. 126; G. Sarton (Introduction to the History of Science [London, 1927], 2, pt. 1:192) noted that Tzetzes's abundant writings are superficial and mediocre. A. A. Vasiliev (History of the Byzantine Empire [Madison, Wis., 1952], p. 498) mentioned that Tzetzes constantly complained about his poverty and how he had had to sell all his books save those of Plutarch: "For me, my head is my library." Vasiliev commented, "He made in his writings a great number of elementary historical errors." Gibbon (4:364) found "the source of this idle fable ... The Chiliads of John Tzetzes." Eecke (L'Oeuvres complete d'Archimede, p. xxii) noted that Tzetzes claimed to have read the originals when in fact he had only read summaries. Tzetzes commented that such stones (hyalos) were on sale at drug sellers, "and there is no such stone, which does not have some strange uses." He goes on to suggest that this stone is a circular device of hyalos, devised for this purpose and that when it is smeared with olive oil and warmed in the sun, one may bring a wick near and set it on fire. De La Hire (1708, in E. Chambers and J. Martyn, History and Memoires of the Academie Royale des Sciences [London 1742], vol. 3 [Memoires 16:88-91, 89]) said, "We do not understand very well what he means by his oil, unless it was used to give a greater polish to the glass." Tzetzes alone gives us the age of Archimedes at his death. The vigor with which Archimedes personally defended Syracuse in the accounts of Polybius, Livy, and Plutarch does not match that of a seventy-five-year-old. Polybius (3:461 [8. 2. 7.9]) refers to him as an old man. Tzetzes may still be right, for M. Bowra (The Greek Experience [London, 1961], p. 100) points out that many of the greatest Greeks-Xenophanes, Democritus, Plato, and Sophocles -had a very long and vigorous life.

39Gibbon, 4:183, n. 3. 4'Huxley (n. 11 above), p. 37. 4Middleton (n. 5 above), p. 536; Marsden (n. 11 above), p. 72; Polybius, 3:451-52 (8.

2. 3-3.3); Livy, 6:283 (24. 34. 4).

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Nevertheless, had the relevant book of Cassius Dio survived in full and not just in the summary by Zonaras and Tzetzes, and had contained the story, the value of his account would still be doubtful. Cassius Dio (ca. A.D. 150-235) was much later than Polybius, and he is a far less reliable historian. Carey commented that he gave "a somewhat

vague, impressionistic picture of events," and other historiographers give similar appreciations of his work.42 Besides, had Cassius Dio mentioned the burning mirrors, Anthemius would surely have been more specific in his references to the story. The other historian, Diodorus of Sicily (ca. 90-20 B.c.), was much earlier than Cassius Dio, but he too is later than Polybius and, unlike him, not recognized as an authoritative source. Diodorus did intend to write about Archimedes' invention at length, but if he did mention Archimedes' use of

burning mirrors, it is strange that Plutarch did not quote from him.43 The earliest reference that we have linking Archimedes with a

burning mirror, in Apuleius's Apologia, only mentions that Ar- chimedes wrote a book which had a section on burning mirrors. He did not claim that Archimedes used the mirror to set Roman ships on fire or even that it ignited materials at a distance. He asked: "Why do concave mirrors when held at right angles to the rays of the sun kindle tinder set opposite them?" The author of the Golden Ass would not have failed to mention the story had he known of it, for he was

demonstrating his immense learning as part of his defense against the accusation of practicing sorcery. Besides, the legend would have

helped his defense in showing that that which appears miraculous is not necessarily so.44 Thus the earliest unequivocal statement available to us that Archimedes used a burning mirror to set fire to the Roman fleet is that made by Anthemius living 700 years after the event, and he only referred to a tradition. The earliest available circumstantial accounts of the use of a burning mirror are those by Tzetzes and Zonaras, nearly 1,400 years after the event. The comment of Eecke about the feebleness of the historical evidence seems fully justified.45

II. Archimedes' Knowledge

Optical and Mathematical

The next question to be considered is whether Archimedes knew

enough to design a mirror that would have worked in the way de-

42Carey (n. 33 above), l:xxiii; Grant (n. 13 above), pp. 344-45. 43Diodorus of Sicily, trans. C. H. Oldfather (London, 1939), 3:199 (5. 3.7-4). 44Apuleius, Apologia, ed. H. E. Butler and A. S. Owen (Oxford, 1914), 16.3-16. 16;

ibid., trans. H. E. Butler (Oxford, 1909), p. 42; see also p. 10 of introduction for charge of sorcery.

45Eecke, L'Oeuvres complete d'Archimede, p. xxii.


scribed by Tzetzes. It would have to have a focal length of the same order as a "bowshot," but one that could be varied, since each ship would be at a different distance from the mirror, requiring major changes, and no ship would be still, requiring minor changes. The only way of producing a mirror with a variable focus is to use pieces of flat glass which can be adjusted to lie along surfaces with different curva- tures. Although Tzetzes did not state this, the most efficient form for the mirror is a paraboloid of revolution (or a section of it, which includes the center and the axes of the mirror). All this Anthemius realized, so that he had the minimum amount of information required in order to design this kind of burning mirror: (a) a parabola has a focus; that is, parallel rays of light are concentrated at one point; (b) the mirror required has the form of the surface known as a paraboloid of revolution; (c) a sufficiently good approximation to that surface can be obtained by a set of plane mirrors: although, once the approxi- mate form has been obtained, empirical adjustments would find the most efficient shape. The actual design depends on knowing that the radiant flux at the focus produced by a given mirror decreases with increasing focal length and that there was a limiting distance beyond which ignition could not take place, and its construction depends on having some means of setting up and operating such a mirror.

It is extremely difficult to decide whether Archimedes had all this information, although we know he did have some. Archimedes wrote of conoids (paraboloids) of revolution; he may be the inventor of them. He realized that a set of lines could give as close an approximation to a parabola as one wishes; this is the essence of his method of exhaustion.46 Thus he had the basic geometrical concepts within his grasp. Archimedes' mechanical knowledge was more than sufficient to fit the mirrors together within a frame in a way that would allow him to move the plates in the way required.47 The remaining two questions, Archimedes' knowledge of the focal properties of the paraboloid and of how mirrors produced ignition, are the ones that are difficult to answer.

Very little evidence to help us with the first has survived.48 There

46Heath, Archimedes (n. 7 above), pp. 99-150 (on conoids and spheroids), and pp. 233-53 (on quadrature of the parabola).

47See n. 12 above; Marsden (n. 11 above), pp. 91 and 98; D.J. de Solla Price, "Gears from the Greeks," Transactions of the American Philosphical Society 64 (1974): 7.

48For Aristotle, see C. B. Boyer, "Aristotelian References to the Law of Reflection," Isis 36 (1945-46): 92-95; for Euclid, P. van der Eecke, Euclid's Optica and Catoptrica (Paris, 1938), p. xxxii; for Archimedes, Apuleius's Apologia (Oxford, 1914), 16.3-16.6, and Lejeune, "Recherche" (n. 11 above), pp. 142-45; for Apollonius, Diodes, and Anthemius, see T. L. Heath, "The Fragment of Anthemius on Burning Mirrors and the Fragmentum Mathematicum Bobiense," Bibliotheca Mathematica 7 (1907): 225-33, and A History of Greek Mathematics (n. 30 above), 2:201; and for Anthemius, Huxley (n. 11

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12 D. L. Simms

are some pieces by Aristotle, a text by Euclid of doubtful authenticity, the references in Apuleius about a work by Archimedes on burning mirrors and a few other notes elsewhere, scanty references to the work of Apollonius and Diodes, fragments by Anthemius, and the

Fragmentum Mathematicum Bobiense, the date and authorship of which have been the subject of considerable controversy. There seems little doubt that Euclid, Archimedes' older contemporary, could not find the focus, certainly not of a spheroidal mirror.49 However, Lejeune

above). E. Wiedemann ("Zur Geschichte der Brennspiegel," Annalen der Physik und Chimie 39 [1890]: 110-30) thought the language of the Catoptrica authentic and that it should be attributed to Euclid. A. Mieli and P. Brunet (Histoire des sciences [Paris, 1935], p. 821) said that the Catoptrica was first attributed to Euclid by Proclus, that it was not known to Pappus, and that Theon of Alexandria worked on it. G. Sarton (A History of Science [London, 1959], 2:118) thought Euclid's Catoptrica "probably apocryphal," and that we have what is called Theon of Alexandria's version from the late 4th century A.D.; but he left open the question of whether Theon was indeed the author. The work

published by A. Gogava, "Lo Specchio ustorio" (in Antiqui Scriptores [Louvain, 1548]) is not

by Archimedes. Rivault ([n. 22 above], p. 547) said that some people attributed this work to Archimedes. However, J. L. Heiberg and E. Wiedemann ("Ibn-al-Haitham's Schrift iiber Parabolische Hohlspiegel," Bibliotheca Mathematica 10 [1910]: 201-37) showed that "Lo Specchio ustorio" is an incomplete version of a work by Ibn-al-Haitham

(Alhazen). Gogava himself did not attribute the work to Archimedes. (These facts have been difficult to verify because Lalande's edition of Montucla's work [2d ed., bk. 1, p. 236 (see n. 5 above)] contains a printer's error, spelling Gogava as Gongava; a similar error occurs in Heath [Archimedes, p. xxxviii].) The date and authorship of the Frag- mentum have caused considerable controversy. Heath ("The Fragment of Anthemius," p. 233) claimed that the Fragmentum Mathematicum Bobiense must have been much earlier than Anthemius (ca. A.D. 500) both on technical and linguistic grounds. While Cantor suggested the author was Diodes (fl. 180 B.c.), Heath thought the language earlier still and, in addition, that, as its author spoke of Apollonius with great respect, a

respect not felt by later writers, it must be a young contemporary of his. Huxley ([n. 11

above], pp. 29, 32-33) did not agree with Heath's dating the Fragmentum mathematicum bobiense to between 250-180 B.c. He argued that passages in he Fragmentum are foreshadowed in the undisputed text, and that the title of Anthemlus's work suggested mechanical devices. He agreed, therefore, with Heiberg and Zeuthen (Huxley, p. 33) that Anthemius was the author of the Fragmentum. Eecke (Les Opuscules mathematique de

Didyme, Diophane et Anthemius [Bruges, 1940], p. xxix) agreed with Heath's dating but

thought the author a contemporary of Apollonius. A. Lejeune ("Euclide et Ptolomee, deux stades de l'optique geometrique grecque," Recueil de travaux a histoire et de philologie 3 [1948]: 61) offered no opinion other than its date being doubtful. Toomer (see n. 53 below) argues that he was a contemporary of Anthemius.

49Lejeune ("Recherche" [n. 11 above], pp. 180 ff.) argued that Euclid's original text could only have contained a primitive theory of mirrors and that he did not know that the incident ray, the reflected ray, and the normal to the surface were in one plane. He considered that Euclid could not construct the position of the image correctly. How- ever, he (ibid., p. 143) maintained that theorem 30 in the text was by the compiler and not by Euclid, although its errors confirmed Lejeune's conjecture that Euclid could not construct the position of the image correctly! "Theorem 30" proves, in the first place,


concluded principally from Apuleius's statements and without con-

sidering the legend of the burning mirror at all, that Archimedes knew the three laws of reflection and that he was able to construct the

position of the image correctly.50 If Lejeune were right, then in principle Archimedes could have designed a paraboloidal burning mirror. In addition, Eecke argued that the first part of theorem 30 in the "Euclidean text" was by Archimedes; that is, he could, unlike Euclid, find the focus of a spheroidal burning mirror.51 Ibn-al-Haitham believed that Archimedes, Anthemius, and others knew that the

paraboloid has a focus and that a burning mirror in that form would be the most powerful.52 It is, however, reasonable to infer that Ibn- al-Haitham assumed that Archimedes must have known this property of the paraboloid in order to have built the burning mirror that Anthemius conceived that Archimedes used.

Against these statements, there are several others to the contrary to

suggest that Archimedes did not determine the focal length of a

paraboloidal burning mirror. The strongest of these is that there is no reference to Archimedes in the newly discovered work on burning mirrors by Diodes (fl. 190-180 B.c.), whereas in its second section he solved the problem in conics left incomplete by Archimedes, to whom he referred. In addition, Diodes claimed that he was the first to prove that a parabola has a focus and that a paraboloidal mirror concentrates the sun's rays to a point. He further proved that a spheroidal mirror concentrated the rays on a straight line and therefore was less efficient than a paraboloidal one; it ignited materials less readily. Diostheus, he stated, had been the first to realize that the parabola had a focus, a fact that Archimedes might have learned from his correspondence with him. Diodes' text also suggests that contemporaries of Archi- medes had realized that a mirror with a real focus might be possible.53

Diodes would hardly have ignored even a partly successful use of

that the burning point of a concave spherical mirror, the focus, is not at the center of the mirror and that it is at a point halfway between the center and the surface of the mirror; this is correct. The second part "proves" that the burning point (image) is at the center of the mirror when the sun is the object; this is incorrect.

50Lejeune, "Recherche," particularly, pp. 142-45 and 181-82. 51Eecke, Euclid's Optica and Catoptrica, p. 123, n. 1.

52Heiberg and Wiedemann (n. 48 above), pp. 202-4. The wording of the sole English translation leaves the question obscure (H. J. J. Winter and W. Arafat, "Ibn-al-Haitham on the Paraboloidal Focussing Mirror,"Journal of the Royal Asiatic Society of Bengal 15, no. 1 [1949]: 25-40).

53Diocles, "On Burning Mirrors," annotated translation from the Arabic by G. J. Toomer, in Studies in the History of Mathematics and Physical Science (Berlin and New York, 1976) 1:2, 34, 36, 42, 140. (This work only became available to the author while this article was at proof stage.)

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14 D. L. Simms

burning mirrors made from flat plates. It is just possible that he gave Archimedes the idea of using a burning mirror and inspired a book (this could justify Apuleius's reference, which is now suspect). More- over, the Arab encyclopedist, al Singari, who referred to Diodes, believed that his predecessors had known of spheroidal burning mirrors made from flat plates.54 There are two further, though slighter, counterarguments. The Fragmentum states that Apollonius derived the correct position of the focus of a spheroidal burning mirror, but Toomer suggests that "Apollonius" was an error for "Dio- cles."55 Finally, Anthemius claimed, contradicted by Diodes, that he was the first to prove that conic sections were the most efficient burning mirrors, and that the ancients had only mechanical proofs, 56 a method which Archimedes regarded as inadequate.57

This is not conclusive evidence that Archimedes did not invent, design, and construct a paraboloidal burning mirror made from flat

plates. The basis of the invention could have been lost with his death, and Diodes reinvented it. Nevertheless, to have done so, Archimedes would probably have had to have inferred the focal properties of the

parabola. There is no doubt that the step required was within his intel- lectual capacity and well inside the paradigm of the science, or con-

ceptual framework, of his period. That he indeed did so could be inferred from the passage in Ibn-al-Haitham. But the new evidence

suggests that Archimedes was not the first to derive the theory of the

paraboloidal burning mirror, and that Diodes discovered the most efficient type. Archimedes possibly designed a spheroidal burning mirror from flat plates and might have improved its efficiency "me-

chanically," but there is nothing in Diodes to suggest this. Diodes' silence is almost as telling as that of Polybius.

Practical Application We must now examine whether Archimedes understood enough of

the way in which burning mirrors ignited materials to have conceived them to be a possible, let alone a practical, weapon of war. Lenses and mirrors may have played some part in fire making in antiquity, and

54Heath, A History of Greek Mathematics, 2:201. 55Heath, "The Fragment of Anthemius," p. 232; Huxley (n. 11 above), p. 33. 56 Heath, "The Fragment of Anthemius," pp. 228-29. Anthemius stated that "since

the ancients also mentioned the usual burning glasses (describing) how the construction of their surfaces of impact should be affected (but dealing with them) mechanically only, but not setting out any geometrical proof to this end, all of them saying that such

figures are conic sections but not specifying which, and how produced, for this reason we will try to set out some constructions for such surfaces of impact, and these not without demonstration but confirmed by geometrical methods."

57Heath, The Method of Archimedes (n. 7 above), p. 13.


concave mirrors of bronze covered with silver and lead were common.58 Indeed, Aristophanes in "The Clouds" made Strepsiades suggest to Socrates the use of a glass sphere to melt a wax writ.59 De la Hire pedantically noted that Strepsiades' trick would be very difficult to perform. Smith retorted elegantly: "Mr. Waller observes that the idea was to ridicule Socrates, it was proper to have a trick for doing what it could not perform." The pedant shows us that for the joke to have worked on the audience, the limitations of such a burning glass must have been very well known.60 There were also discussions on how they worked, notably by Aristotle and Theophrastus.61 Thus Archimedes undoubtedly had empirical knowledge of the effects of burning mirrors and was aware of discussions on how they worked.

The final difficulty is that he had no means of calculating how the radiant flux varied with distance from the mirror. Indeed, the concepts necessary to do this were not in existence. Archimedes could have assumed that the mirror would work or he could have carried out experiments to test whether it did work. Scott considered that Archimedes would have carried out experiments beforehand, and Plutarch did record that at the king's request he had prepared the artillery well in advance. Scott argued that all this knowledge must have vanished after the sack of Syracuse.62

III. Would a Burning Mirror Have Worked?

There remains the problem of whether any burning mirror could set Roman ships on fire. This question needs examining in two parts: first, under what conditions will a burning mirror ignite wood (from which ships were built) and start a continuing fire, and second, are such conditions realizable in practice? The answer to the first can be based on the results of research into the ignition of wood by radiation carried out at the British Fire Research Station and elsewhere. The answer to the second is not quite as straightforward as interpret- ers of Buffon's experiments have suggested.

The modern research work has demonstrated that many factors can affect both the time taken to ignite and the minimum radiant flux

58Forbes (n. 15 above), 5:186. The Olmecs apparently had burning mirrors much earlier still, ca. 1500-1000 B.C. (J. B. Carlson, "Lodestone Compass," Science 189 [September 1975]: 753-60).

59Aristophanes, The Eleven Comedies, trans. unknown (New York, 1936), lines 766 ff. 68De La Hire (n. 38 above), p. 89; R. A. Smith, A Complete System of Optics (Cambridge,

1738), 2:15. "6Aristotle, Posterior Analytics, trans. H. Tredennick (London, 1960), pp. 159-61 (1.

31. 88a14); Theophrastus, De Igne, trans. V. Coutant (Assen, 1971), pp. 46-47, 73. 62Plutarch, 5:473 (14. 9); Polybius (3:453 [8. 2. 3-4]) wrote only that Archimedes

acted in advance of the siege itself; Scott (n. 6 above), pp. 24-25.

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at which ignition occurs. Nonetheless, by treating wood as an inert material, the ignition time for any given radiant flux for a wide range of experimental conditions can be correlated with the thermal properties (thermal conductivity and thermal capacity). This means that

ignition may be taken to occur when the surface reaches a tempera- ture of about 545? C. This, in turn, leads to the concept of a critical radiant flux at which ignition just occurs; for oven-dry thick materials (a thick material is one in which there is no significant rise in tempera- ture of the rear surface), this value is about 0.7 cal cm-2sec-1. This

figure is a minimum, and, in practice, the flux at which ignition just occurs has been found to be much higher because the amount of volatile present in the surface region of the wood is limited and can be exhausted before the volatiles are hot enough to ignite. The smaller the area irradiated and the higher the moisture content, the higher the minimum flux and the longer the ignition time at any given flux.

Now the area irradiated by a feasible burning mirror is unlikely to exceed 25 cm square, and the wood will not be oven dry. With a moisture content of 20 percent-and ships' wood could hardly contain less-the minimum flux required to ignite a 25-cm square is about 1.5 cal cm-2sec-l, whereas a similar oven-dry specimen might be ignited by a flux of 0.8 cal cm-2sec-1. The effect of a larger area

may reduce the difference, but not below 0.7 cal cm-2sec-'. Addition-

ally, when the source of radiation is the sun, some of the incident radiation is reflected from the surface; thus the lighter the color of the wood surface, the higher the radiant flux required for ignition. The reflectivity decreases with increasing ignition time, and for short times (say 3-5 seconds) about twice as much energy is required to

ignite natural colored oak and mahogany as black, but only about 20 or 30 percent more for ignition times greater than 10 seconds.

In addition, cracks in the surface, either occurring naturally or aris-

ing from joins, tend to reduce heat losses. In some occasions, therefore, lower radiant fluxes may be sufficient to produce ignition; but the ignition times of flat plates, dihedral, and tetrahedral cones made from fiber insulating board have been found to be the same.63 Varma and Steward used poplar wood shavings compressed to give a range of materials with voids, instead of the solid surfaces used by other workers.64 They confirmed McGuire's hypothesis that such materials

might ignite at lower radiant fluxes than homogeneous solids, but the sides of a Roman ship are much more nearly a homogeneous solid than a set of voids.65

63D. L. Simms (unpublished information); Lawson and Simms (n. 11 above), p. 291. 64Varma and Steward (n. 11 above), pp. 154-55. 65Middleton (n. 5 above), p. 542.


It is, however, necessary not merely to ignite the wood but to ensure that it continues to burn. Generally, the flat thick woods were not found to continue to burn for long once the irradiating source was removed (a commonplace of observation), and the wetter the wood the shorter the length of continued burning (another common-

place of observation); dihedral angles and tetrahedral cones burned for rather longer than flat pieces under the same conditions. These were all solid materials; void materials, like those used by Stewart, normally continued to burn because the flames reinforced one another; thin ones-papers or cloths-continued to burn since the flame could penetrate to the rear surface, quickly increasing the burning surface and drastically reducing the heat loss from the flame to its sur-

roundings. Experiments using the sun as the radiation source with mirrors

made from plane glasses are in reasonable agreement with the laboratory results. Buffon constructed, from 168 plates of glass, a mirror which had a focal length of about 50 meters; it ignited wood and other materials on a sunny day in Paris. Middleton calculated that the value of the radiant flux at its focus was 0.43 cal cm-2sec-1.66 The form of the wood target is not clear from Buffon's description, nor is it certain whether the wood continued to burn. Khanna demonstrated a solar burning mirror consisting of nine plane sheets of glass that ignited wood at 15 paces, usually in a few seconds; the radiant flux was about 1.5 cal cm-2sec-l, and the wood usually continued to burn.67 At twice the distance (a bowshot), 30 paces, with the same size mirror, the flux would be about the same as that of Buffon's.

Sakkas's recent experiments appear to be similar in kind to Buffon's.68 He arranged fifty to sixty sailors, each holding a highly polished mirror about the size of a classical Greek shield along the shore at Piraeus, and had them turn their shields toward a wooden rowboat with one side covered by the outline of a galley made of tarred plywood. The boat caught fire within two minutes and continued to burn; admittedly the sun's intensity might have been stronger on a summer's day at Syracuse, and the boat might have ignited sooner there.

Although these experiments demonstrate that ignition is possible, the maximum radiant flux available from these mirrors at a bowshot

66Ibid., pp. 537-39. 67M. L. Khanna, A. L. Gardner,J. N. Davey, and S. P. Suri, "Plane Glass Mirror Solar

Energy Concentrate for Concentrating Sugar Cane and Palm Juices,'journal of Scientific and Industrial Research 18A (1959): 212-17; M. L. Khanna, "The Sun at Work," Associa- tion for Applied Solar Energy 1 (June 1956): 4; Khanna (private communication).

68Sakkas (n. 2 above), p. 9.

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distance is very little, if at all, above the critical flux for oven-dry wood, let alone wet wood. Since the radiant flux is lower away from the focal plane, the time taken to ignite is greater, and it is less likely that ignition would occur. Thus it is critically important to ensure that the wood is at the focus, and even then, under the most favorable conditions, wood is unlikely to be ignited in less than 30 seconds. We

may reasonably conclude that only carefully arranged targets of materials at the focus can be ignited and made to continue to burn by these mirrors.

We now consider the second of the two questions-the relevance of Buffon's and Sakkas's experiments to the actual situation. All their

experiments were carried out under static conditions-that is, the

target was still and at a known distance from the focus. Buffon moved a piece of wood until signs of burning, such as smoke and a darkening of the surface, showed that the specimen was at or near the focus. His mirrors were carefully adjusted by experimental assistants beforehand to ensure that the focus was at a previously defined place. Although the focal length could be adjusted, this could only be done slowly and required his being able to observe the effects on the target. Peyrard proposed overcoming this long time delay by using a tele-

scopic sighting device, something certainly not available to Archimedes.69 Scott, however, pointed out that a few large mirrors, rather than Buffon's 168 small ones, and much closer to the mirror described by Tzetzes, would be just as efficient as a large number of small ones; the task of adjusting its focus would be much simpler and well within the bounds of technical possibility for one man, as Khanna found, although not as Anthemius apparently believed. Nonetheless, Khanna too had an easily observable target.70

Difficult though it is to adjust the focus when the distance is known and the target under close observation, the task in practice is much more difficult. First, the Roman ships were at an unknown distance. Archimedes had no means of determining how far any ship was from the burning mirror, and he needed to have the distance precisely, because as we have noted the radiant flux falls off rapidly away from the focus. Second, the ships were not still. It is, therefore, not enough to alter the mirror's focus in order to attack different ships, that is, make major adjustments; it is also necessary to keep the focus at the same place on an individual ship for long enough to start a fire. For the same spot 30 meters away to be irradiated continuously, the

operator would have to be able to adjust the focal length and hold the focus onto the target to closer than 1/20 for at least 30 seconds.

69Peyrard (n. 6 above), pp. 554-55. 70Scott (n. 6 above), p. 126.


Sakkas is recorded as recognizing that the target must be static in order for the ship to be ignited and as believing that Archimedes would have relied on the element of surprise to ensure that the commanders were unable to move their ships. This hypothesis is not credible. Even with the reasonably efficient Greek anchor, ships would drift, pitch, and roll. Furthermore, some of the Roman ships were

certainly topheavy,71 as Montucla realized, so that it would have been

extraordinarily difficult to keep the focal spot in the same position, supposing it possible to detect whether that position actually was the focus.72 In order to meet this last point Claus has suggested the in-

genious idea of using a double-sided mirror with a small hole for

sighting purposes.73 He argued that by looking through the hole at the ship, the operators would be able to tell that the mirror was on target when they could no longer see the reflection of the ship in their mirror. The idea might work with a static ship with a target marked on it (provided that the sun did not blind its operators) but leaves

open the question of how the operators would know they were all

aiming at the same place. Thus, those who have argued in favor of Archimedes' feat on the basis of Buffon's experiments, or like Sakkas on the basis of his large-scale variations, have failed to realize that these experiments and the practical conditions are different. They have been deceived into believing that an experiment based on a static situation that is a fixed target under close observation resembles a

dynamic one, a ship (moving in three directions) at an unknown distance.

The difficulty of predicting whether a burning mirror would set a

moving ship on fire, as opposed to a moving block of wood, from Buffon's experiments is increased by the fact that we do not know with any certainty what a Roman ship of a period looked like. Casson considered that the ships in Rome's fleet in 200 B.C. were quinqueremes, that is, five men to an oar, and similar to the galleys of the Middle Ages; there would be about 300 rowers with a marine force of 120, but only eighty first-line troops if the corvus or "ram" were employed. However, Anderson argued that a quinquereme may not be five men to an oar but three men to one and two to another. With the latter design the men and the ship were a little more exposed to radiation. In either system, soldiers, and sailors at the oars, might have been in direct line of sight of the mirror, although this was

71Polybius, 3:453-5 (8. 2. 4.2-4.11). Eight ships were lashed together to form a base for a "sambuca." Huxley (n. 11 above), p. 13: "The result can be obtained by several men holding mirrors in the required position."

72Montucla (n. 5 above), 1st ed., p. 247. "Claus (n. 1 above), p. A14.

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unlikely since the rowers were shielded by the sides of the ships and, if Adcock is right, shielded by the deck as well, with the soldiers stand-

ing well back.74 With these conditions the mirror could possibly inflict burns to the skin very quickly indeed even at low radiant fluxes.75 Thin materials might be ignited; these could include the sails, if these were not furled76 as they normally were in battle, and any clothing the Romans were wearing, but this is doubtful.

Thus an examination of the experimental evidence demonstrates that a burning mirror is unlikely to produce ignition on a moving ship and even more unlikely to produce a continuing fire. Since the fire would have a small beginning and spread slowly, there would be ample time to extinguish it. The most one can argue is that the mirror de-

signed by Anthemius might have been used as a weapon against per- sonnel and possibly to dazzle people. Moreover, a burning mirror is

heavily dependent on the weather-generally reliable though the weather may be in the Sicilian summer-the time of day, and the position of the sun relative to the ships to the mirror as Anthemius realized.77 To overcome this last problem a whole battery of mirrors would have been required. Thus as a weapon of war the burning mirror was of little value, and the probability of being able to use it was far too low for any mathematician to risk.

IV. Would Archimedes Have Tried?

Disregarding the evidence that, in principle, the weapon was use- less, we must now ask whether the description of its use makes mili-

tary sense. If Tzetzes or Zonaras is to be believed, Archimedes first allowed

the ships of Marcellus to come within reach of grappling machines; then, after the ships had had to withdraw a little, he used hurling slings to throw stones at them and then, and only then, when they had

74L. Casson, The Ancient Mariners (London, 1959), pp. 145-46; and Ships and Seaman-

ship (n. 20 above), pp. 99-102, 116, 143-44; R. C. Anderson, Oared Fighting Ships (Lon- don, 1962), p. 25.

75F. E. Adcock, The Greek and Macedonian Art of War (Berkeley, Calif., 1959), pp. 39-40. Pictures do not help. Artists have always earned the scorn of sailors. Jane Austen, the sister of two admirals, must have echoed her brothers' opinion of "what

queer fellows your fine painters be to think anybody would venture their lives in such a

shapeless old cockleshell as that" (Persuasion [London, 1965], p. 179). 76T. C. Letherbridge, "On Shipbuilding," in History of Technology, ed. C. Singer, E. J.

Holmyard, et al. (Oxford, 1956), 2:570. 77Huxley (n. 11 above), p. 14: "Moreover it is possible to blind the sight of an enemy."

Anthemius of course used them for this purpose himself (see nn. 31, 35); see also p. 12: "For whenever conflagration occurs, the mirrors are always turned towards the sun."


withdrawn a bowshot away, did he use the burning mirror. This order is itself curious. Why not use the mirror first, since normal tactics are to keep the enemy as far away as possible and the one, according to

Polybius, that Archimedes adopted with his other weapons. It

perhaps might be argued that this was the necessary order, because unless the ships were in complete confusion, a bowshot or stone from one of the Roman slingers could have disabled the operators.78 It might be argued further that the Romans were more terrified by this device than by the others, although Livy and Plutarch leave no doubt of their terror of all Archimedes' devices-in spite of the fact that they were familiar with the burning glass. But, if they were only a bowshot away, it is unlikely that every man was so paralyzed that he was unable to use his bow or his sling to attack Archimedes and the operators. And it is difficult to believe that all the ships (for Zonaras leaves none to survive) were within the range and operating angle of the mirrors and that all the commanders were so stunned that none attempted to escape or could escape in time. Thus their descriptions hardly make military sense and are further evidence that the story they tell derived from two separate sources.

We must now ask how the burning mirror compared with the other weapons of war of the period. Archimedes could have thrown pots containing flammable materials at naval or military targets. Their earliest recorded use at sea is by the Rhodians in 190 B.C. which is only a little later than the siege of Syracuse, but Partington gives examples of the use of fire pots in battles as early as 360 B.C.79 These fire pots were much more likely to start a fire than a burning mirror; moreover, they could only be extinguished by vinegar or a similar compound, whereas seawater can be used to extinguish a fire started by a burning mirror. The energy they contained was far greater than that available from a burning mirror, their accuracy of delivery was more precise, and the weapon was independent of the position and

angle of the ships to a much greater extent than the burning mirror. Moreover, artillery is independent of the weather and time of day, and fire pots could have been aimed to fall inside the ships where the fighting men were crowded together. If Archimedes were to have used fire as a weapon, there is little reason to doubt that he would have chosen fire pots rather than burning mirrors.

But did Archimedes need to employ fire pots? Marsden has no doubt of the effectiveness of Archimedes' artillery at both long and short range; the large double-purpose engine could hurl a 3-

78Livy, 6:283 (24. 34. 5-6): "Most of the ships' archers and slingers." 79Partington (n. 23 above), p. 1.

21

22 D. L. Simms

talent shot or a 12-cubit bolt 200 yards.80 The descriptions of the battle by Polybius, Livy, and Plutarch show that with the great resources of Hiero of Syracuse available to him and with Syracuse al-

ready an immensely strong fortress, Archimedes had devised, produced, and organized a comprehensive defensive system capable of

dealing with any form of assault both by land and sea, by day and by night.81 This was his real contribution to the art of warfare. It is

legitimate to infer that he did not create a new weapon of fire and that we can disregard Galen and Lucian as providing uninformed gossip.

Finally, if burning mirrors had been so very effective, it is difficult to believe that no one would have tried to recover this weapon of war.

Apollonius was still alive, and so was Diodes. In many centuries of almost continuous warfare that faced Byzantium, successful burning mirrors would have been a useful weapon to supplement Greek fire. Once Anthemius had designed a working system, why did not his

patron, Justinian, have him build one? No later inventor from Napier onward has ever persuaded anyone to use it.

V. Summary of Conclusions

The historical evidence for Archimedes' burning mirrors is feeble, contradictory in itself, and the principal and very late authorities for the story are unreliable, while the standard and contemporary au-

thority was silent. There is conflicting evidence about whether Ar- chimedes could have designed a paraboloidal burning mirror and some evidence to suggest he did not, although there is Diodes' sub- stantial evidence that he wrote about burning mirrors and knew

something of what they could do. Modern experiments suggest a

burning mirror is highly unlikely to produce ignition on a moving ship, let alone a continuing fire, and any reasonable comparison suggests that a burning mirror is much less effective and reliable than

throwing the predecessor of Greek fire or even stones. Thus there are

ample historical, scientific, and military grounds for concluding that Archimedes did not use a burning mirror as a weapon of war.

80 Marsden (n. 11 above), pp. 91, 98; Reading University students of classics and of

engineering have constructed the Greek catapult or palintenon: one built with modern materials hurled a 5 1-pound shot 300 feet (Observer Magazine [London] [November 10, 1974], p. 86).

81A. W. Lawrence ("Archimedes and the Design of the Euryalus Fort,"Journal of Hellenic Studies 66 [1946]: 99-107) suggested that Archimedes may have redesigned the fortifications as the quality of the work is so high. Lawrence's wartime experience with

operational research workers suggested that this accorded with accounts of Ar- chimedes' brilliance in operational research in the standard references "even if these are partly fabulous." This is not to deny that fire was used as a weapon (its use was standard practice), only that Archimedes made no special use of it.

Archimedes and the Burning Mirrors 23

VI. Possible Origins of the Legend

How, then, did the story originate? Montucla suggested the belief that Archimedes used "fire," and the knowledge that he had written on burning mirrors, led later writers to combine the two stories.82 Schneider, in effect, elaborated on this idea, at least as far as the "fire"

part of the story is concerned. He argued that Lucian and Galen were recalling the verses of Silius Italicus and not the histories of Polybius, Livy, and Plutarch. (They are both later than Apuleius who did not know the story.) Because Lucian and Galen had written the "story" down, Schneider considered they provided a solid basis for what reached the Byzantines.83 Finally, he commented, that belief was

strengthened by the semideification of Archimedes already recogniz- able in Plutarch's record; indeed, it became almost explicit in Anthemius's reference to the "god-like" Archimedes.84

Some futher confirmation for Schneider's hypothesis is that Lucian and Galen called the ships triremes as did Silius, and not quinqueremes as did the historians; this may be because by their day the trireme had regained its place as the principal ship in the Roman fleet. Lucian could also have provided the kind of link that Montucla looked for. The reference to Archimedes in Hippias could have been extended without warrant to another passage in the essay.85 "It would take no little time to sing his [i.e., Hippias's] praises in the doctrine of rays, refractions, and mirrors."

But where did Silius Italicus find the story of the tower and the fire? One might argue that their introduction into the Punica was poetic license since the use of the tower at sieges was well-established practice. Or, since fire had been used as a weapon at Syracuse before, Silius might just have borrowed the story from Thucydides or some chronicler of the Peloponnesian War; he mentioned the pride of the Syracusans in their destruction of the Athenian fleet in the previous lines.86

We must also recognize that Galen and Lucian may not have been

82Montucla (n. 5 above), 1st ed., p. 247. 83Schneider (n. 8 above), pp. 5, 6, 7, 11.

84Huxley (n. 11 above), p. 15. 85Lucian (n. 19 above), p. 39. 86Tarn (n. 20 above), pp. 110, 116: "The tower at Rhodes ... was about 60 feet high.

... The old protection against fire, raw hides, . . . had been replaced by an armouring of iron plates, .... But when it went into action the Rhodian stone-throwers knocked off some of the armour plates, and it was then set on fire by flame-carriers.... Its base was oil or naptha in some form enclosed by a cylinder fired from the stone-throwing catapult." Thucydides, History of the Peloponnesian War, trans. C. F. Smith (London, 1965), 4:105-7 (7. 53. 4 ff.); Italicus (n. 16 above), p. 293 (14. 280-85).

24 D. L. Simms

the sole "authorities" for the story, so that what reached the Byzan- tines may have been more detailed; for example, Tzetzes and Zonaras both claim to have read the story in Cassius Dio, although whether

they did so is doubtful. We can identify Anthemius's contribution, which was to "prove" that a burning mirror could be used.87 Finally, his guess as to what kind of burning mirror Archimedes could have used was incorporated into Tzetzes's account as the actual mirror that Archimedes did use. The story would thus be assembled by a se-

quence of misunderstandings, and there is no need to pray in aid "an

antique Munchausen."88 When Gibbon said, "I am more disposed to attribute the art to the

greatest mathematician of antiquity than to give the merit of the fiction to the idle fancy of a monk or a sophist," one remembers that he was not always so kind to their idle fancies, and that with the very same story in Byzantine times he made allowances for sheer confusion.89 The legend was invented "out of someone's head," but its

long history is worth a separate paper.

87The pattern in the history of the legend is that revival of belief follows a scientist

discovering that burning mirrors can be made to ignite materials at a distance. P. E. Ariotti ("Bonaventura Cavalieri, Marin Mersenne, and the Reflecting Telescope," Isis [1975], pp. 66, 233, n. 307, as opposed to his comment facing 303) appears to be the latest victim.

88Africa (n. 2 above), p. 305. This is not, however, intended as a testimonial to the

veracity of Lucian or Apuleius, both of whom could fit the description. 89Gibbon (n. 32 above), pp. 83-84.

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des and the Burning Mirrors of Syracuse (D. L. Simms)