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Hydrostatic Balance

The "Eureka" story about Archimedes and the bath tub was as well known in Galileo's day as it is in ours. Galileo, who was a great admirer of Archimedes and adopted many of his methods, probably read it in one of the editions of Vitruvius's The Ten Books on Architecture,[1] which was very popular in Renaissance Europe.

Supposedly, it was in the bath tub that Archimedes figured out the solution to the problem posed to him by the king of Syracuse: was a crown (or wreath) supposedly made of pure gold in fact entirely gold?

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He measured the amount of water displaced by the crown and by an equal weight of gold, and found that the crown displaced more water. Its specific gravity was thus less than that of gold, and therefore it had been adulterated with another metal.

Weighing precious metals in air and then in water was presumably a practice that was common among jewelers in Europe. Galileo had some ideas for refining the practice and, at the age of 22, he wrote