“Why would a man think to no purpose?”
“You are a soldier, so such may seem foolish to you, but some of the greatest discoveries in history have been that way. Are you familiar with the story of how Archimedes discovered a way of measuring the volume of an irregular object?”
“No. Is it important?”
Silversmith to make a crown
Eumenius chuckled. “So important that the principle explains how a ship floats. According to the story, the king of the Greek city where Archimedes lived gave some pure silver to a silversmith to make a crown. When it was delivered, he suspected that the silversmith might have mixed base metal with the silver, keeping the rest for himself, and gave Archimedes the task of deciding the question. At first Archimedes could find no answer because he could not measure the crown. Then one day his servant filled his bath to the top of the tub and when he got in, the water ran over.” “What is so unique about that?”
“To most people nothing. But to Archimedes it meant that a body immersed in water displaces a volume equal to its own.”
“But that is obvious.”
“Perhaps, though no one had set it down as a principle before. Anyway, it told Archimedes how to measure the volume of the crown, simply by immersing it in a container filled with water and placed in a pan to catch what ran over. When he measured the amount in the pan, he knew the volume of the crown and its weight was easily determined with an ordinary pair of scales. Then by using a block of pure silver, he was able to determine the density of silver and solve his problem.”
“What was the answer?”
“The silversmith kept his head. Since then any mathematician who knows the density of an object can tell whether or not it will float. Remember when you used dry logs to cross the Rhine and capture Ascaricus and Regaisus? You were utilizing the principle Archimedes discovered.”
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