Eureka in Greek is, "I have found it".

These are the words excitedly cried out by Archimedes, an ancient Greek scientist and mathematician, as he left his bathtub and ran down the street having discovered the riddle of the crown.

Archimedes had been summoned by King Hiero of Syracuse, Sicily to examine a crown made for the king by a goldsmith. The King was suspicious that the goldsmith had deceived him in some way. The King felt that the goldsmith may not have made the crown totally out of the pure gold originally provided. Archimedes tried without success to find a solution to the King's concerns.

But, one day, as he sat in his bathtub, he noticed how the water level rose as more of his body was submerged. This is when he realized he had discovered a method of providing an answer to the King. Was the crown made of pure gold, or was some other metal substituted?

The ancient scientist decided to conduct an experiment comparing the volume of the crown and a piece of pure gold having the same weight as the crown.
He knew that silver weighed less than gold.
He also reasoned that an ounce of gold would take up less volume than an ounce of silver since more silver would be needed to equal the ounce of gold.
He lowered bars of gold equal to the weight of the crown into the water marking the water level as it rose.
He then did the same with the crown.
He observed the water level had risen higher when the crown had been submerged. Had the crown been made of pure gold, both water levels would have been comparable.

Since more water was displaced when the crown was submerged, this indicated that the goldsmith had indeed been deceitful. He had substituted some silver for the gold when making the crown. Archimedes had discovered the solution. EUREKA!

RIBERA, Jusepe de
(b. 1591, Játiva, d. 1652, Napoli)

1630 Oil on canvas, 125 x 81 cm Museo del Prado, Madrid