THERE was once a king of Syracuse whose name was Hiero.
The country over which he ruled was quite small, but
for that very reason he wanted to wear the biggest
crown in the world. So he called in a famous goldsmith,
who was skillful in all kinds of fine work, and gave
him ten pounds of pure gold.
"Take this," he said, "and fashion it into a crown that
shall make every other king want it for his own. Be
sure that you put into it every grain of the gold I
give you, and do not mix any other metal with it."
"It shall be as you wish," said the goldsmith. "Here I
receive from you ten pounds of pure gold; within ninety
days I will return to you the finished crown which
shall be of exactly the same weight."
Ninety days later, true to his word, the goldsmith
brought the crown. It was a beautiful piece of work,
and all who saw it said that it had not its equal in
the world. When King Hiero put it on his head it felt
very uncomfortable, but he did not mind that—he was
sure that no other king had so fine a headpiece. After
he had admired it from this
 side and from that, he weighed it on his own scales. It
was exactly as heavy as he had ordered.
"You deserve great praise," he said to the goldsmith.
"You have wrought very skillfully and you have not lost
a grain of my gold."
There was in the king's court a very wise man whose
name was Archimedes. When he was called in to admire
the king's crown he turned it over many times and
examined it very closely.
"Well, what do you think of it?" asked Hiero.
" 'Well, what do you think of it?' asked Hiero."
"The workmanship is indeed very beautiful," answered
Archimedes, "but—but the gold—"
"The gold is all there," cried the king. "I weighed it
on my own scales."
"True," said Archimedes, "but it does not appear to
have the same rich red color that it had in the lump.
It is not red at all, but a brilliant yellow, as you
can plainly see."
"Most gold is yellow," said Hiero; "but now that you
speak of it I do remember that when this was in the
lump it had a much richer color."
"What if the goldsmith has kept out a pound or two of
the gold and made up the weight by adding brass or
silver?" asked Archimedes.
"Oh, he could not do that," said Hiero; "the gold has
merely changed its color in the working." But the more
he thought of the matter the less
 pleased he was with the crown. At last he said to
Archimedes, "Is there any way to find out whether that
goldsmith really cheated me, or whether he honestly
gave me back my gold?"
"I know of no way," was the answer.
But Archimedes was not the man to say that anything was
impossible. He took great delight in working out hard
problems, and when any question puzzled him he would
keep studying until he found some sort of answer to it.
And so, day after day, he thought about the gold and
tried to find some way by which it could be tested
without doing harm to the crown.
One morning he was thinking of this question while he
was getting ready for a bath. The great bowl or tub was
full to the very edge, and as he stepped into it a
quantity of water flowed out upon the stone floor. A
similar thing had happened a hundred times before, but
this was the first time that Archimedes had thought
"How much water did I displace by getting into the
tub?" he asked himself. "Anybody can see that I
displaced a bulk of water equal to the bulk of my body.
A man half my size would displace half as much.
"Now suppose, instead of putting myself into the tub, I
had put Hiero's crown into it, it would have
 displaced a bulk of water equal to its own bulk. All,
let me see! Gold is much heavier than silver. Ten
pounds of pure gold will not make so great a bulk as
say seven pounds of gold mixed with three pounds of
silver. If Hiero's crown is pure gold it will displace
the same bulk of water as any other ten pounds of pure
gold. But if it is part gold and part silver it will
displace a larger bulk. I have it at last! Eureka!
Forgetful of everything else he leaped from the bath.
Without stopping to dress himself, he ran through the
streets to the king's palace shouting, "Eureka! Eureka!
Eureka!" which in English means, "I have found it! I
have found it! I have found it!"
The crown was tested. It was found to displace much
more water than ten pounds of pure gold displaced. The
guilt of the goldsmith was proved beyond a doubt. But
whether he was punished or not, I do not know, neither
does it matter.
The simple discovery which Archimedes made in his bath
tub was worth far more to the world than Hiero's crown.
Can you tell why?