Archimedes' name is forever embedded in the history of scientific discovery. His various contribution to the fields of both science and advanced mathematics have made his name renowned as a pioneer of modern science. The most famous tale of Archimedes is, without a doubt, the tale of him dashing madly through the streets of the Sicilian city Syracuse, screaming "Eureka!" (or in English, "I have found it!").
How Archimedes got to be screaming down the streets without any sort of clothing has been debated over the years, but historians have managed to get a good idea of what probably occurred. It is believed that King Heiro II (a friend of Archimedes) had ordered a new crown to be made of solid gold. For whatever reason, the king began to suspect the goldsmith that had forged the crown of adding in trace amounts of silver to cut costs. Unable to know for certain, the king asked Archimedes for help.
After giving the matter serious thought, Archimedes attention to his friend's problem began to fade, and the tale goes that he went for one last thinking session to see if he could resolve the problem once and for all. He went to the Syracuse public bath house (which were common in ancient times) with the intent of muling the problem over in his head while bathing. Archimedes filled the tub with water, and let his naked form into the warm body of water. Immediately, he noticed that some excess water spilled out of the tub.
This sparked a revelation for Archimedes, and he began his famous race across Syracuse with those famous words on his lips and wearing his even more famous attire (or lack thereof). What Archimedes had realized was that amount of water that splashed out of the tub was equal to his volume, that is assuming that the tub was filled to the top and that Archimedes slipped into the tub at a slow pace. This also banks on the principal that water is cannot be compressed except under certain circumstances, and simply dropping an object (whether living or inanimate) is not enough to compress water.
After Archimedes return to his place of dwelling and put some clothes on, he filled a bowl with water and placed it in a larger bowl. The he gently let down the crown, and as expected, some water spilled out. Archimedes quickly measured the volume of displaced water and calculated the density. By taking the weight of the crown and dividing it by the volume of excess water, Archimedes got a figure that represented the density of the crown. When compared to the known density of an equal amount of gold, Archimedes noticed that the crown was less dense than the gold. This led him to believe that the king had been cheated, and cheaper, less expensive metals we used to cut expenses on the part of the goldsmith.
The famous discovery made that day by Archimedes revolutionized the science of fluid dynamics, and the principals governed by his bathtub mishap are still applicable today. For it is often at the most unaware times when most great discoveries are made, and the tale of Archimedes is no exception.