What happened when Archimedes took a bath?

There is such an interesting story about Archimedes. According to legend, King Guhennon of Silas asked craftsmen to make him a pure gold crown. When it was finished, the king suspected that the craftsman had mixed a fake gold crown, but the gold crown was as heavy as the pure gold originally given to the goldsmith. Did the craftsman play tricks? The problem of trying to test the authenticity without destroying the crown not only stumped the king, but also made the ministers look at each other.

Later, the king asked Archimedes to test it. At first Archimedes was also thinking hard, to the point. One day, he went to the bathhouse to take a bath. When he was sitting in the bathtub, he saw the water overflowing and felt his body being gently lifted. He suddenly realized that the proportion of gold crowns can be determined by measuring the displacement of solids in water.

He jumped out of the bathtub excitedly and ran out without even considering his clothes, shouting "found it!" Eureka! " . Fureka means "I know". After further experiments, he came to the palace. He put the crown and pure gold with the same weight in two jars filled with water, and compared the water overflowing from the two jars, and found that the jar with the crown overflowed more water than the other jar. This shows that the volume of the crown is larger than that of pure gold with the same weight, so it proves that other metals are mixed in the crown.

The significance of this experiment is far greater than finding out that the goldsmith cheated the king. Archimedes discovered the law of buoyancy: the buoyancy gained by an object in a liquid is equal to the weight of the liquid it discharges. Until modern times, people are still using this principle to calculate the specific gravity of objects and determine the load capacity of ships.

Extended data:

According to the principle that the specific gravity (density) determines the ups and downs, we can know that the displacement of the same gold nugget submerged in the water is less than the maximum displacement when the gold nugget is made into a box floating on the water 18.3 times. Therefore, regardless of whether there are hollowed-out ornaments on the crown, it is inevitable that there will be unintentional bubbles in the castings only by the casting process at that time.

Therefore, it is entirely possible that Archimedes' above calculation method has caused unjust, false and wrong cases in history. So what? Obviously, it is not the old woman who made mistakes here, but Archimedes. It can be seen that what scientists say is not necessarily correct, and the truth is sometimes in the hands of ordinary people.