Mercy! Mercy! That Dang Nabed PERCY!

Episode 8: Archimedes and the Metal Cubes

“Tell us what happened when Archimedes returned to the bathhouse,” the King wanted to know.

“Did he pinch the bath maiden’s nipple?” Inquired Dunazad.

Scheherazade rolled her eyes and continued.

When Archimedes returned to the bathhouse the tub was filled to the brim and the matron smiled as she unbuttoned her blouse. He undressed and she took his garments hanging them on the wall pegs. When he was naked, Archimedes smiled back and stepped into the tub. As he did, water began sloshing over the side and as he sat down still more poured over the edges.

“ Hmmm” he thought to himself.

He sat back cogitating and propped his ankles over the edge. The maid began to lather his feet working the oil between his toes and along his sole and instep.

“Ahhhh, he sighed as she began the massage of first one and then the other. The more she rubbed the more delicious came the delight, growing more and more intense. At length it became all but unbearable. Arching his back the pleasure peaked and once more he slid down deeply in the tub. Water spilled out like a great tsunami rolling onto the beach of paradise. At that instant, as the wise man wiggled on the cusp, his mind made the leap from ignorance to understanding. It was the connection he was searching for." Eureka! Eureka!" he cried out, which in Greek means, "I have the answer!”

The next day Archimedes returned to the King. He had a glass beaker, four cubes of metal and a scale. He put these on a table before the Sultan and asked him to weigh each one.

The first was one of gold and it weighed one ounce. The second was lead and it weighted one ounce. The third was silver and it weighed one ounce and finally the last was copper and it too weighted one ounce.

When he finished the king looked up and said, “So what?”

"Look closely at the cubes and tell me what you see."

The king looked closer and as they sat arrayed, one next to the other, he suddenly noted the difference. They were different sizes. The gold one was smallest, then the lead, then the silver and last the copper.

Archimedes put the beaker on the table and filled it brimming with water and underneath placed a saucer. When he immersed the gold cube a little water spilled over, the lead a bit more, the silver still more and finally the copper most of all.

“Hmmmm,” said the King then, "Oh my goodness!” as the light of understanding spilled into his mind.

“I don’t get it,” said Dunazad scratching her head.

“Think! replied the King. A larger cube displaces more water than a smaller cube.”

“So?”

“If the crown is pure gold it will displace the same amount of water as a pound of pure gold.”

“So?”

“If the crown is mixed with the copper or silver it will displace more water since these are larger than a like amount of gold.”

“Oh! I get it. “

"Duh..!" said Scheherazade and continued.

He summoned the Excelsior.

"Make me a perfect pound cube of lead, gold, silver and copper."

The next morning Archimedes returned with a larger beaker and immersed the cube containing the pound of gold. Doing thus, he watched the water spill over the lip. Then he did the same with the Crown and a small additional amount dribbled over the edge.

“Summon the Royal Goldsmith!” demanded the King.