Search the Properties of Matter site Properties of Matter glossary Photos, illustrations and streaming media on the Properties of Matter site Properties of Matter table of contents Properties of Matter home page Link to NSRC home page

Reading Selection, Lesson 2

Archimedes' Crowning Moment

Click here for audio and Spanish translation
Archimedes was an expert on mass, volume, and density.

Archimedes was an expert on mass, volume, and density.

Archimedes, one of the most famous mathematicians and scientists of ancient Greece, had a problem. The king had a new crown. It looked like pure gold. But the king was suspicious. How could he be sure that the jeweler hadn’t cheated him by adding another, less valuable metal to the molten gold? The king asked Archimedes to find out whether the crown was made from pure gold.

Archimedes knew his reputation was on the line. He could have taken the problem down to the public marketplace, where he often went to discuss scientific questions with other scholars. But instead, he decided to relax in a bath. The tub was filled to the brim. Still concentrating on his problem, Archimedes immersed himself in the water.

Splash! Water spilled over the sides of the tub and onto the floor. He had made a real mess. But that mess triggered an idea—an idea that would help solve the king’s dilemma.

“When I got into the tub,” Archimedes reasoned, “my body displaced a lot of water. Now, there must be a relationship between my volume and the volume of water that my body displaced—because if I weren’t so big, less water would have spilled on my floor.”

Archimedes in the bath examining water spilled on the floor.

“Hmmm . . . the volume of my body equals the volume of water on the bathroom floor.”

This observation brought Archimedes back to the problem of the gold crown. What if he put it in water? How much water would it displace? And could he apply this observation to prove that the crown was made of pure gold?

Archimedes knew about the importance of controls, so he began by finding a piece of gold and a piece of silver with exactly the same mass. He dropped the gold into a bowl filled to the brim with water and measured the volume of water that spilled out. Then he did the same thing with the piece of silver.

Although both metals had the same mass, the silver had a larger volume; therefore, it displaced more water than did the gold. That’s because the silver was less dense than gold.

Now it was time to check out the crown. Archimedes found a piece of pure gold that had the same mass as the crown. He placed the pure gold chunk and the crown in water, one at a time.

The crown displaced more water than the piece of gold. Therefore, its density was less than pure gold. The king had been cheated! Although this was just one of Archimedes’ many contributions to science, there’s no doubt that it was his “crowning moment”!

QUESTION

Pretend you are Archimedes. What instructions would you give for comparing the density of a crown with the density of gold?

 
Information about the STC/MS curriculum Link to NSRC home page NSRC contact information NSRC copyright and permissions information Smithsonian Institution privacy policy Properties of Matter site map