Cooke, Roger M. (Author)
Notices of the American Mathematical Society
Volume: 57, no. 4
Issue: 4
Pages: 464-475
How much should one be willing to bet on the historical truth of this story? It seems doubtful that Archimedes could have weighed gold and silver and measured the amount of water they displace so precisely as to solve the problem he had been challenged with. The di erence in the amount of water displaced must have been very small. Moreover, Vitruvius claims that Archimedes performed a quantitative analysis of the crown, determining the exact amount of silver that had been used to replace the gold. That would have been unnecessary if his only task had been to determine whether the gold had been alloyed with silver, which is probably all the king would have wished to know. And again, although the physical principle involved in the analysis is correct, the practical application of it appears to be much more challenging. As is the case with other stories told of Archimedes by Vitruvius' contemporary Plutarch, such as the story that he designed a claw to be attached to a crane that could snatch Roman ships out of the water during the siege of Syracuse (Life of Marcellus, Ch. 15, 3), there seem to be some practical di culties. Although engineers working with both the BBC and the Discovery Channel have constructed machines that are capable of upending a Roman ship from shore, it is di cult to believe the ships could not have maneuvered out of reach. It has been conjectured that the claw was used at night, when the sailors could not see it approaching. But perhaps the main purpose of the claw was to keep the ships from attempting to land at all. In that case, it would indeed have been a practical defensive weapon that needed only to be demonstrated once, not regularly used. The same explanation would apply to Archimedes' supposed use of burning mirrors to set the Roman ships on re. Revolved conic sections were well enough understood in his day to allow the design of such mirrors. Modern experimenters have found it di cult to set wood on re in this way, but it is not necessary to set a ship on re to make it unbearably hot for its human occupants. Thus, these two stories merit a somewhat higher degree of con dence than the story of the crown. If indeed these stories are only legends and not true reports, one can imagine how they may have arisen, since Archimedes wrote treatises on oating bodies, the lever, and the parabola.
...MoreDescription On the mathematical work of Archimedes.
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