While pausing to think about that, he realized that the leg in the water seemed considerably lighter than the one on the ground. He put his other leg in and moved it up and down. He knew that the water was buoying his leg, but he didn't know how. Getting out of the cold water, he sat back down in his chair. After a very brief moment of contemplating what happens in water, he almost forgot about the crown, until it hit him.
Gold is heavier per pound than the other precious metals.
An experiment for solving the king's problem was formulating in Archimedes' mind. All he needed was a balance, the crown, some water and Archimedes' brilliantly eccentric mind raced. He knew how he could find out if the crown was real. Forgetting his lack of appropriate, or any, attire, he ran out of his house. He passed an encumbered merchant, nearly knocking him off his feet.