The Science Book

25

See also: Nicolaus Copernicus 34–39 ■ Isaac Newton 62–69

THE BEGINNING OF SCIENCE

in any way. He went to the public
baths in Syracuse to ponder the
problem. The bath was full to the
brim, and when he climbed in, he
noticed two things: the water level
rose, making some water slop over
the side, and he felt weightless. He
shouted “Eureka!” (I have found the
answer!) and ran home stark naked.

Measuring volume
Archimedes had realized that
if he lowered the crown into a
bucket filled to the brim with water,
it would displace some water—
exactly the same amount as its own
volume—and he could measure
how much water spilled out. This
would tell him the volume of the
crown. Silver is less dense than
gold, so a silver crown of the same
weight would be bigger than a gold
crown, and would displace more
water. Therefore, an adulterated
crown would displace more water
than a pure gold crown—and more
than a lump of gold of the same
weight. In practice, the effect would
have been small and difficult to
measure. But Archimedes had also

realized that any object immersed

in a liquid experiences an upthrust

(upward force) equal to the weight

of the liquid it has displaced.

Archimedes probably solved the

puzzle by hanging the crown and

an equal weight of pure gold on

opposite ends of a stick, which he

then suspended by its center so

that the two weights balanced.

Then he lowered the whole thing

into a bath of water. If the crown

was pure gold, it and the lump of

gold would experience an equal

upthrust, and the stick would stay

horizontal. If the crown contained

some silver, however, the volume

of the crown would be greater than

the volume of the lump of gold—the

crown would displace more water,

and the stick would tilt sharply.

Archimedes’ idea became

known as Archimedes’ principle,

which states that the upthrust on

an object in a fluid is equal to the

weight of the fluid the object

displaces. This principle explains

how objects made of dense material

can still float on water. A steel ship

that weighs one ton will sink until

A solid heavier than a fluid

will, if placed in it, descend to

the bottom of the fluid, and the

solid will, when weighed in

the fluid, be lighter than its

true weight by the weight of

the fluid displaced.

Archimedes

it has displaced one ton of water,

but then will sink no further. Its

deep, hollow hull has a greater

volume and displaces more water

than a lump of steel of the same

weight, and is therefore buoyed up

by a greater upthrust.

Vitruvius tells us that Hieron’s

crown was indeed found to contain

some silver, and that the crown

maker was duly punished. ■

Archimedes Archimedes was possibly the

greatest mathematician in

the ancient world. Born around

287 BCE, he was killed by a soldier

when his home town Syracuse

was taken by the Romans in

212 BCE. He had devised several

fearsome weapons to keep at bay

the Roman warships that attacked

Syracuse—a catapult, a crane to

lift the bows of a ship out of the

water, and a death array of mirrors

to focus the Sun’s rays and set

fire to a ship. He probably

invented the Archimedes screw,

still used today for irrigation,

during a stay in Egypt.

Archimedes also calculated an

approximation for pi (the ratio

of a circle’s circumference to

its diameter), and wrote down

the laws of levers and pulleys.

The achievement Archimedes

was most proud of was a

mathematical proof that the

smallest cylinder that any given

sphere can fit into has exactly

1.5 times the sphere’s volume. A

sphere and a cylinder are carved

into Archimedes’ tombstone.

Key work

c.250 BCE On Floating Bodies