19/07/2025
The more you read biographies and stories of people in the past, the more in awe you are of their wisdom and intellect. I am reminded of one this morning; a story told to us in secondary school physics.
It is a story that has the great Greek genius called Archimedes in it.
Over 2,000 years ago in ancient Syracuse, King Hiero II had commissioned a beautiful golden crown for his royal court. But he was suspicious as rumors swirled that the goldsmith had cheated him, mixing in cheaper metals like silver. The king wanted the truth, but he didn’t want his crown destroyed in the process.
Destroy because in ancient times, the standard method for testing if a gold item was truly pure was to melt it down and compare its mass to the volume of pure gold or to re-cast it and weigh it against the original gold given to the goldsmith.
Another method was to scrape or cut off pieces of the metal to test its hardness and purity using acids, but that would damage the crown too.
And why destroy a beautiful crown that could turn out to be pure gold?
So, the king called Archimedes. Archmedes was already famous as a mathematician, and the king wanted him to find him the answer without destroying his crown.
It was a difficult, and, to many people, impossible riddle. Even Archimedes was stunned.
For many days, Archimedes mulled it over without getting anywhere. Then one day, according to the ancient story, not thinking of the problem at all, Archimedes went to take his bath, a public bath. As he lowered himself into the warm water, he noticed something so simple yet so profound: his body pushed the water up and out of the tub. The water level rose, exactly equal to the volume of his submerged body.
In that instant, it hit him — if he could find out how much water the crown displaced, he could know its true volume. Gold has a unique density, heavier than silver or bronze. By comparing the crown’s weight to its displaced water, he could calculate whether it was pure or diluted with lesser metals.
Legend says Archimedes was so overwhelmed with excitement that he leapt out of the bath, running naked through the streets shouting “Eureka!” — Greek for “I have found it!”
Using this method, it was discovered that the goldsmith had indeed cheated the king.
The bathhouse “Eureka!” moment is the legendary origin of what we now call Archimedes’ Principle, which states:
“Any object, wholly or partially immersed in a fluid, is buoyed up by a force equal to the weight of the fluid it displaces.”
In simple terms:
An object displaces its own volume of fluid. and the upward buoyant force equals the weight of the fluid displaced.
This principle has done a lot for the world. It is one of the cornerstones of fluid mechanics. It explains why ships float, how submarines dive, how hot air balloons rise, and even how fish use swim bladders. And in practical engineering, it has helped in the designing of floating structures, ships, submarines, and later airships. And of course, as people in quality control know, it is one of the first famous examples of non-destructive testing, as used in engineering and manufacturing.
Eureka! "I have found it."