Eureka! Eureka!

A long time ago, Archimedes was given a difficult task by his king. The king asked a goldsmith to manufacture a crown made out of gold. After the crown was finished, the king wondered if the goldsmith could have betrayed him by substituting some of the gold with silver. For this reason, the king asked Archimedes to find out if the crown consisted of pure gold - on condition that the crown should not be damaged.

Archimedes thought a lot about solving this problem and finally he had a brainwave by taking a bath. As he stepped into his bathtub which was filled up with water to the brim he observed, that water spilled out: exactly the same about of water as displaced by the volume of his body

Archimedes was so happy about this discovery that he ran out of the streets and shouted "Eureka! Eeureka!" (Eureka = I've found it!). Being full of joy it is told that he even forgot to put his clothes on.

But how is this discovery linked with the king's crown?