Searching through old journals results in wonderfully serendipitous moments.  I originally started searching through the Proceedings of the Royal Society of Edinburgh for articles by Lord Kelvin, but along the way have found all sorts of interesting and thought-provoking papers.

A few weeks ago I noted that one article, “On the bursting of firearms when the muzzle is closed by snow, earth, grease, &c.”, foreshadowed later attempts by the MythBusters to test whether the barrel of a gun will “banana peel” when fired with a plug in it.  About the same time, however, and in an earlier volume of the Proceedings, I found an article with the title, “On the burning mirrors of Archimedes, and on the Concentration of light produced by reflectors,” by John Scott.  This article is also an investigation of a myth that would be tackled some 130 years later by the MythBusters!  Apparently the 1870s-1880s were a good era for ‘busting!

The myth in question concerns the brilliant Greek intellectual Archimedes (287 BC – 212 BC), who made amazing discoveries in science, mathematics and engineering, and produced a number of groundbreaking inventions*.  His final inventions were developed to protect his home city of Syracuse from a Roman siege; Archimedes himself was slain at the end of the siege by a Roman soldier.  Tales of his siege-breaking inventions spread, however, and became the stuff of legend.  One reported device was a crane with a claw-like attachment used to capsize ships, known as the Claw of Archimedes; modern tests have shown the device to be feasible.  More intriguing, and more controversial, is the report that Archimedes developed a giant mirror or collection of mirrors that could focus the Sun’s rays and set ships on fire!

I should note right off the bat that the article by Scott to be discussed here is not the only historical attempt to evaluate the plausibility of the Archimedes story, and the Mythbusters’ attempts not the only modern attempts to test it.  There was a test in 1973, for instance , as described on an interesting page by Michael Lahanas dedicated to the Archimedes mirror,

A Greek scientist, Dr. Ioannis Sakkas, curious about whether Archimedes could really have used a “burning glass” to destroy the Roman fleet in 212 BC lined up nearly 60 Greek sailors, each holding an oblong mirror tipped to catch the Sun’s rays and direct them at a wooden ship 160 feet away. The ship caught fire at once…..Sakkas said after the experiment there was no doubt in his mind the great inventor could have used bronze mirrors to scuttle the Romans.

The site also links to an image of the experiment:

Scott’s 1867 paper is itself mainly a summary and critique of earlier attempts to test the “burning mirror” story.  He begins by pointing out the weakness of the historical record:

That the Roman ships were destroyed by burning glasses invented by Archimedes, is mentioned as a fact by most of the ancient writers, especially those who treat on mechanics, and their statements have been repeated by succeeding authors, without any doubts having suggested until comparatively recent times.  The earliest authorities on the subject are Diodorus Siculus, Lucian, Galen, Dion Cassius, and Pappus.  It is much to be regretted that a work by the last named author on the Siege of Syracuse is now lost; but Zonares and Tzetzes, writers of the 12th century, in whose time it was extant, give quotations from it.  That of the latter, translated pretty literally, runs thus:–“When Marcellus had placed the ships a bow shot off, the old man (Archimedes) constructed a sort of hexagonal mirror.  He placed at proper distances from the mirror other smaller mirrors of the same kind, which were moved by means of their hinges and certain plates of metal.  He placed it amid the rays of the sun at noon, both in summer and winter.  The rays being reflected by this, a frightful fiery kindling was excited on the ships, and it reduced them to ashes, from the distance of a bow shot.  Thus the old man baffled Marcellus, by means of his inventions.”

Scott then notes that plenty of other inquisitive minds have tested the burning mirror idea:

At a later period, mirrors similar to that of Archimedes, appear to have engaged the attention of Baron Napier of Merchiston, and other mathematicians; but strange enough, the famous naturalist, Buffon, was the first to establish the practicability, and therefore the probability, of the achievement.  He employed a combination of plane reflectors, consisting of ordinary looking-glasses, eight inches by six, attached to a single frame.  With forty of these glasses he set on fire tarred beech at a distance of 66 feet.  A plank smeared with tar and brimstone, was ignited at 126 feet, by 98 glasses.  A combination of 128 glasses, with a clear sun, inflamed very suddenly a plank of tarred fir at 150 feet.  In addition to these experiments made at Paris, about the beginning of April, others were made in summer, by which wood was kindled at 200 and 210 feet, and silver and other metals were melted at distances varying from 25 to 40 feet.

Buffon’s work is difficult to discount, as he was no idiot!  The Comte de Buffon (1707-1788) was the most influential naturalist of his time, and also made important contributions to other fields.  Prior to writing his 36 volume Histoire naturelle, générale et particulière over the years 1749-1788, he also did significant research in physics and mathematics.  His studies of Archmedes’ mirrors formed part of his Mémoires de mathématique et de physique, circa 1747**, entitled, “Invention de miroirs ardens, pour brusler a une grande distance”; they can be read online here.  I’ll have to return to his analysis in a future post, after a bit of translating!  It is worth emphasizing that Buffon’s results are well-documented experimental research, not hearsay like the earlier discussions of the historians.

But even Scott, in his 1867 paper, realizes that the question is more complicated than the tests of Buffon could address,

So much for the positive side of the question, let us now briefly consider the negative side.

Descartes and others treated the whole affair of the burning mirrors as a fiction, on the gratuitous assumption that the specula employed were single parabolic reflectors.  A different and more valid reason for doubt has arisen from the circumstance, that Polybius, Livy, and Plutarch, are silent respecting the burning mirrors, although they describe some of the other contrivances employed by Archimedes against the assailants.  In reply to this objection, it has been stated, as an admitted axiom in estimating historical evidence, that the silence of one author is not sufficient to disprove an event of which another, even subsequent in point of time, has given a plain and consistent narrative.  Besides, similar omissions by ancient historians are not unfrequent; and in this instance, it is the less surprising, since the invention had perished with the fall of Syracuse, and the death of the illustrious inventor, who, in the peculiar circumstances, must have endeavoured to keep from his contemporaries the secret of its construction.

So one of the biggest arguments against the Archimedes mirrors is that plenty of contemporary historians didn’t bother to mention them.  I agree that this is hardly conclusive evidence against their existence — in the heat of battle, Archimedes’ gizmos probably seemed a rather inconsequential footnote to the carnage.

Returning to Buffon’s experiments, Peyrard appends to his translations of the works of Archimedes a memoir of his own, pointing out the defects of Buffon’s combination of reflectors, viz.:–That the number of assistants required to adjust so many mirrors were apt to confuse one another– the operation itself was a tedious one, taking about half an hour for one hundred and sixty-eight mirrors — and, after all, the superposition of the light was imperfect.  Again, after a short interval, a readjustment would be rendered necessary by the angular deviation of the rays, arising from the varying position of the sun.  Peyrard suggests “that each mirror should be furnished with a telescope, and a somewhat complex apparatus, to render the adjustment more speedy and accurate, and by this means to diminish the number of assistants required.  This remedy is admitted to be only partial.  It is proposed, in what follows, to obviate the forementioned defects, by producing a solar reflecting machine, capable of being directed by one eye, guided by a single hand, and coinciding in its construction with the description in the fragment preserved by Tzetzes from Pappus.

François Peyrard was a scholar who in 1807 provided a French translation of Archimedes’ works, “Œuvres d’Archimède,” which can be read at archive.org.  He also did his own investigations on the possibility of burning mirrors, starting on page 539 of the translated works, titled, “Miroir Ardent”.  There’s another blog post in dissecting Peyrard’s work, but he primarily points out that Buffon’s contraption was too time-consuming to be effective, and suggests improvements.  This leads Scott to conclude,

It is stated that Archimedes contrived a hexagonal mirror, and placed at proper distances from it other smaller ones of the same kind.  This peculiarity has no parallel in that of Buffon.  Articles 11, 12, and 13, in the memoir, show how burning mirrors can be constructed, corresponding to the above description, free from the defects of Buffon, and capable, moreover, of darting the consuming rays instantaneously in any given direction, thereby affording a strong presumption that the accounts respecting the Archimedian Mirror are in the main authentic.

So Scott concludes from the prior experiments of Buffon and Peyrard*** that the Archimedes story is true; the Mythbusters, however, came to a very different conclusion.  In episode 16 in their 2004 season, they tested the myth and concluded, as summarized by Wikipedia,

In order to have any effect, the mirror would have to be impractically large, and even then, the temperature of wood only raised a few degrees. On the Discovery website, however, a challenge was thrown out to the viewers to come up with an experiment to prove it plausible, and so far, a few of the entries seem to have done so. When all the tests were completed the myth was conclusively busted.

This didn’t satisfy viewers entirely, so in episode 46 of their 2006 season, the Mythbusters revisited the myth, teaming up with a group from MIT that had also tested the “death ray”:

The large scale array simply took too long to light the ship on fire. On top of that the ship only ignited when it was stationary and positioned at less than half the distance described in the myth. The myth was plausible at a smaller scale, however. Flaming arrows were fired from a ballista at the ship, but to little effect. The most effective (and plausible with Archimedes-era technology) method of lighting the ship ablaze was through the use of Molotov cocktails.

It is rather fascinating to see that different experimentalists testing the myth can come to very different conclusions about its validity!

This highlights, however, part of the challenge that the Mythbusters, and indeed any skeptics, face when attempting to investigate historical claims: the myths themselves are typically ill-posed in the sense of a scientific problem.  In other words, there are many different questions one can ask about the validity of a myth, and it can be very difficult to reduce a given myth to a single yes-or-no question.  To illustrate this, consider the Wikipedia summary of the Mythbusters’ second test:

All in all, the MythBusters concluded that the Archimedes Death Ray was too complicated and impractical to be a viable weapon for its time.

Emphasis mine.  The Mythbusters considered the myth busted because the weapon is impractical, though that doesn’t mean that it isn’t possible — and neither conclusion excludes the possibility that Archimedes tried it at Syracuse!  Thinking for a few minutes, I was able to come up with a large list of quasi-independent questions, each of which could be said to reflect upon the truth/falsity of the Archimedes burning mirrors:

• Is the Archimedes weapon practical? “Practical” in this sense means that the weapon would be worth the effort compared to other weapons of the time.  This question was (almost) conclusively busted by the Mythbusters.
• Is the Archimedes weapon possible? In other words, can one set ships on fire with burning mirrors?  The Mythbusters also showed that this is plausible.
• Did Archimedes set ships on fire at Syracuse with mirrors? Even if the weapon isn’t practical, that doesn’t mean that Archimedes didn’t manage, perhaps through pure luck, to set ships on fire.  This question can be asked as long as it is possible to set ships on fire.
• Did Archimedes try to set ships on fire? Even if he didn’t succeed, that doesn’t mean that Archimedes didn’t actually try to set ships on fire during the battle.  Given his stature in Syracuse, I could well imagine military leaders giving him free rein to try his crazy ideas.  After all, it’s not like modern armies dump tons of resources into pie-in-the-sky, even idiotic ideas (see, for instance, here and here).  The generals of Archimedes’ era may also have appreciated the psychological effect that strange new weapons might have on the enemy, even if they didn’t work.
• Did Archimedes try to burn sailors? The actual target of the mirrors might not have been the ships, but the sailors on those ships.  Again, the generals might have decided that the psychological impact of soldiers being burned from afar was worth the effort.
• Did Archimedes employ mirrors at the siege of Syracuse? Even if he didn’t use mirrors for burning ships, Archimedes might have employed mirrors for other reasons.  Imagine giving soldiers on the walls highly polished shields, and training them to direct the reflections onto the eyes of sailors in the invading fleet.  Such “dazzler” techniques are a viable strategy in modern warfare.  In Archimedes’ time, it might have been necessary to distract the sailors from the big, ship-destroying claws on the shores.  Furthermore, if the ships were set on fire through other means, such as Molotov cocktails, eyewitnesses might have been confused into thinking the ships were ignited by the sun’s rays.

Only the first two of these questions are directly answerable through experimental testing, but those tests do not exclude the possibility of the other questions being true.  There are other subtleties**** related to the “burning mirrors” question that can also have a big impact on the answer:

• How much were the mirror-workers trained? The difference between “practical” and “impractical” often has to do with the amount of training one has.  Anyone who has watched the X-Games should realize that human beings can perform seemingly impossible feats with the right training.  Similarly, after years of experience, scientists know their lab equipment well enough to do things that seem like magic to the untrained eye.  Similarly, Archimedes may have worked with his own mirror contraption long enough — or trained other to do so — to an extent that setting the right focus became a matter of minutes or seconds instead of hours.
• What were the ships made out of? It is telling that Buffon was using tarred wood as his target material.  Sailing ships of antiquity were treated with a number of substances to protect from the elements.  Even in the Age of Sail, ships had seams caulked with tar, and ropes greased with fat, making them highly combustible.  Ships were so combustible, in fact, that the use of “fire ships” — ships loaded with flammable materials and steered deliberately into crashing into the enemies’ fleet — was a valid and very successful military tactic.  A burning mirror may have been intended to burn the flammable coatings of the ship, rather than the wood of the ship.

With all these questions, it is probably not surprising that there have been a large number of tests and speculations on the subject, including a paper by A.C. Claus in Applied Optics 12 (1973), A14, and a flurry of letters in response (subscription required).  A historical review and analysis of experiments up to 1977 are given in D.L. Simms, Technology and Culture 18 (1977), 1-20 (subscription required, again).  Even with the Mythbusters’ excellent test of the Archimedes myth, I have a suspicion that we haven’t heard the last of this one…

But wait! I’ve got more historical mythbusting to review!  Sometime soon I’ll post a review of a paper on the “secrets of the pyramids”!

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J. Scott, Esq., “On the burning mirrors of Archimedes, and on the concentration of light produced by reflectors,” Proceedings of the Royal Society of Edinburgh 6 (1867-1868), 232-235.

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* I emphatically DO NOT, I repeat, DO NOT recommend watching the video at this link for more information about Archimedes.  Don’t do it.  You have been warned…

** So, technically, the title of this post should be, “Mythbusters were scooped — by 250 years!”

*** What is it with the French and Archimedes’ mirrors?  We have Buffon, Descartes, and Peyrard all weighing in on the matter.

**** Some of these were probably addressed by the Mythbusters, but I haven’t seen the episodes for a while and can’t be sure.