Archimedes and the Crown
Or
Rub a dub dub the kings crown in a tub
© Eric Hoeppner 2006
It was the year 260 BC,or
240 or thereabout, (they counted backwards in the BC years) that was a long time ago, I was only 14 and a servant in the court
of the tyrant king, Hiero of Syracuse, I don’t mean New York, I’m talking the Greek independent state in Sicily.
Hiero was not that bad a guy back then and only used the tyrant thing when he meant business.
I had been given the
job of working with the now famous, but this was before he got famous, the now famous Greek mathematician, Archimedes.
I never did find out if that was his first name or last name, we all just called him Archimedes.
On this one particular
day the new crown came back from the crown maker guy and Hiero wanted to know if the crown maker guy had really used all the
gold to make the crown or had he mixed in some silver or some other cheap stuff. We put it on the official scale with that
smooth stone on the other end and it balanced the same as the lump of gold Hiero had sent away for the crown making.
He still did not trust
the crown maker guy and told Archimedes, “As your Tyrant king, Hiero of Syracuse, you need to prove to me this crown
is pure gold and no filler, be off with you, and take the boy with you.”
We are back at the lab, well, Archimedes’
place, and he sits there staring at that crown for almost a day. He claimed he was pondering. Me? I was bringing in food and
cleaning up the dishes and watching him stare. I kept trying to figure what that strange smell was and from where it was coming.
I finally figured it out after I had carefully cleaned the entire place. It was him, he and his pondering. I don’t
think he had bathed in years. If he was going back to see the king I thought it a good Idea to clean him up a little.
I hauled buckets of water
to fill a tub, got all his bath stuff set out, and then stuck my hand in to see how cold the water was… cold!
I put a pot of water over the fire and heated it until it boiled, then I added the hot water to the tub. It took the
chill off, but now the tub was full to the very top.
Now what happened next was a little strange. When Archimedes
got in the tub he noticed that as he immersed himself in the tub, not only did the water level rise, and over flow onto the
floor, but his apparent weight seemed to decrease, he felt lighter.
I stood there ready to take a good verbal
lashing for my foolishness; I should have realized that an object displaces water equal to its volume. Instead he looked at
me as he realized that two objects of equal weight will displace different volumes of water when immersed unless their densities
are equal.
He leapt out of the tub, grabbed the crown and ran down the street yelling, "Eureka! Eureka!".
I took of after him, tripping over his clothes. I grabbed the clothes, thinking he would realize he forgot them by the time
he got to Hiero’s place.
I wanted to find out why he was running naked through the streets of Syracuse yelling, “I
have found it, I have found it.”
He explained to the king that silver or almost any metal is
less dense then gold. If we filled some pails with water and got some lumps of silver of the same weight, bla bla bla, well
any way this went on for hours. What was I doing? I was bringing in more and more pails of water and running all over
getting chunks of metal of different types from the metal smith. Just after sunrise I heard Hiero call for a messenger
to bring him the crown-making guy, he said, “Tell him the Tyrant King, Hiero wants to see him.”
It got pretty ugly. After
that, it seemed that the crown-making guy had taken out a good chunk of gold and replaced it with some cheap filler.
Archimedes proved this.
He put a chunk of gold on the balance and a stone on the other end; it balanced. Then he put the solid lump of gold in a pail
full to the top with water. It overflowed in to the bowl it was in. Next he put the crown in another full pail and collected
the water as it overflowed. There was more water displaced, proving that the crown was not pure gold.
They took the crown maker
guy away and I don’t think I want to know where.
I got to clean up the mess while Hiero and Archimedes
had several vessels of wine and slapped each other on the back and talked of what a team they were. As we left, Hiero
hollered to him, “Hey, Archimedes write it all down, I will call it Archimedes Principle and present it when I meet
with the other rulers at the rulers convention at the end of next month.”
Archimedes went on to do a bunch of boring
math stuff. It kept me busy with getting papyrus and making ink from berries and such and cleaning up all his stuff
from failed inventions. Later on he would be known as one of the three greatest mathematicians of all time together with the
English guy, Isic Newton (1643-1727) and the German Caral Gauss (1777-1855). But Archimedes was almost 2 thousand
years ahead of them with his math stuff.
Occasionally I would get out in the field with him to
build some of his crazy inventions. He made some great war machines that were used to defend Syracuse. Some really
strange contraptions with compound pulley systems. He made some non war stuff too, like that irrigation screw pump thing that
real helped with the food production. This created more leisure time and more people moving in and more land being converted
to agriculture and, well… civilization and life. So, if you can, get a part time job with someone
that may become famous some day. That’s probably what moved me to become a science teacher and why I am standing here
today.