I am very sceptical about that myth involving the measuring the volume of displaced water, which then, and even now, would be a very inaccurate method. I suggest that Archimedes’ eureka moment involved the balancing a piece of gold and the crown on a beam balance in air, then, without moving the gold or crown, immersing each in water. If the crown was an alloy less dense than the gold, the gold would sink revealing the fraud. If the density of the crown was needed then move the gold to a position where the gold and crown are balanced in water, then do the maths.
