Archimedes and the Golden Crown

Archimedes is credited with many inventions and discoveries, but a story about how he checked a golden crown to show if it had the proper amount of gold used in its making provides an interesting historical tale. The king at the time (Hero) had a golden crown that was supposed to be made of pure gold. If the crown was made with other cheaper metals like silver then the king would have felt cheated. The problem that faced Archimedes was that he could not cut into or damage the crown in any way. As he pondered the problem at his home his servants prepared a bath for him. The servants wanting to please him filled the bath to the very brim and Archimedes being a hefty person (rotund) stepped into the bath. As he sat down fully into the bath water went over the edge of the tub. He supposedly suddenly knew how to solve the problem of the crown and jumped out of the tub running naked into the street yelling “Eureka I’ve found it!” meaning that he had found the method to solve the crown problem. Students sometimes ask if he would have grabbed a towel and it gives the teacher a chance to talk about how they looked at the human body, male and female, as a part of nature with a beauty that would often be fully displayed in their art.

He realized that the crown like his body occupied space and that space could be measured by the displacement of water. If the overflow of water was captured and accurately measured then the overflow would equal the volume of water displaced. This meant that something with a very irregular shape like the crown could displace a volume of water exactly equal to the amount of volume of the crown. Once the volume of water was captured it then only had to be compared to an equal volume of gold dust. If the volume of gold dust equal in volume to the displaced crown water was able to balance the scale, then the crown was made of the proper amount of gold. If the crown was lighter than the gold dust that represented the volume, then the crown might be made of some lighter metals or could have empty space inside it at various points.

This whole process is a method of measuring “density” of materials and how displacement can be used to measure volume of irregular objects. When a miner pans for gold the pan is swirled so that the heavier gold particles will be thrown to the outer regions of the swirling water in the pan. Again the density of gold being so much greater than most other substances creates the situation where panning for gold actually works. There are other theories about how Archimedes may have tested the crown, but this story is pretty good overall. Students at the junior high and high school level enjoy hearing a story about this “old dude” running into the streets naked. If nothing else it keeps them interested in science.