The story

Archimedes's tale takes place some 2,200

years ago when King Hieron II of Syracuse in

Sicily gave a jeweller a bar of gold and

ordered him to make it into a crown. The

king, however, suspected that the jeweller

had substituted some of the gold for cheaper

metal like silver, while pocketing the leftover

gold.

At the time, Archimedes had known that gold

was denser than silver, so if a certain weight

of silver had been substituted for the same

weight of gold, the crown would occupy a

larger space than an identical one of pure

gold.

So to find the crown’s volume, all Archimedes

had to do was essentially immerse the crown

and exact measurement of pure gold in a tub

filled with water to the brim, measure the

spillage, and compare the volume of spillages

– if the jeweller had indeed made a crown of

pure gold the volume should be the same.

Archimedes's principle states that the same

weight of the same substance must occupy

the same volume, whatever the shape.

If the crown was impure, it would have a

slightly larger volume than one of pure gold –

remember, silver takes up more space than

the equivalent weight of gold. Immersed in

water, a larger-volume crown would be

buoyed more strongly than the matching gold

bar; this would cause the balance to tip, with

the crown side higher than the side

containing the pure gold bar.

What Archimedes's discovery meant

Archimedes' soak in the tub gave rise to

Archimedes Principle, which states that

when a body is immersed in water, it

experiences a kind of force we call buoyancy.

This force is equal to the weight of the water

displaced by the body.

Buoyancy explains why some things float,

and others don't. A ball of steel, for instance,

will sink because it's unable to displace

water that equals its weight. But steel of the

same weight but shaped as a bowl will float

because the weight gets distributed over a

larger area and the steel displaces water

equal to its weight.

Different metals of the same weight have

different volumes. Objects, put in water, will

displace water. The displaced water will be

equal to their volume.

For example, an iron cube weighing a kilogram

will disperse some water. But an aluminums

cube of the same weight will displace more

water than the iron cube.

Archimedes knew all these theories. Using

this as the basic knowledge, Archimedes

worked out a plan to find out the purity of

the crown.

Archimedes took two bowls. He filled them

with water to the brim. Then he placed each

bowl separately in the middle of the large

vessels. He placed the crown in one bowl.

Water overflowed. It collected at the bottom

of the outer vessel. Then he took a cube of

pure gold. This cube of gold was equal in

weight to the crown. He kept this gold cube in

the middle of the second bowl. Here also

water overflowed. Water got collected at the

bottom of the outer bowl.

Archimedes then measured the quantity of

water in the two vessels. He found out the

difference in the water overflow.

The crown had sent out more water. The cube

of gold had sent out less water. But both

the crown and the gold cube were of the same

weight. So, they should have sent out the

same quantity of water. Therefore,

the crown had some other metals mixed in it.

These metals took up more space in the

water than pure gold.

Archimedes reported this finding to the King.

The King demanded the truth from the

goldsmith. The goldsmith then confessed. He

had stolen some gold. He had added

some other metals.