Archimedes’ Buoyancy Principle

Archimedes, a Greek engineer and inventor, stands out as one of history’s greatest scientists, often hailed as the father of mathematics. Among his most celebrated discoveries is the principle of buoyancy, famously associated with his “Eureka” moment.

Living in Syracuse, a prominent Greek colony on Sicily during the third century BCE, Archimedes was at the heart of a bustling hub where trading vessels from Egypt, Greece, and Phoenicia converged. His education unfolded in Alexandria, Egypt, where he forged friendships with notable figures such as the polymath Eratosthenes and the astronomer Conon of Samos.

After returning to Syracuse, Archimedes served King Hiero II, who commissioned him to design an unprecedentedly massive ship, the Syracusia. This ship was intended to surpass all others in size and function, serving as a cargo ship, a luxury vessel, and a warship. The Syracusia became the largest ship ever built, featuring an intricate temple dedicated to Aphrodite, gardens, a gym, and accommodations for over 1,900 passengers, crew, and soldiers. It was also equipped with war towers and a full-sized catapult.

However, the ship’s immense size and weight led to significant leaking through its hull. To address this issue, Archimedes invented the Archimedes screw, a device capable of elevating water from lower to higher levels. This invention, consisting of a cylinder with a helical blade inside, could draw water up and out of the ship when its crank was turned. The Archimedes screw, still in use globally for various applications, illustrates his innovative problem-solving skills.

The Syracusia embarked on a single voyage from Syracuse to Alexandria, where it was gifted to Ptolemy III Euergetes. The ship’s fate thereafter remains a mystery.

Archimedes dedicated considerable effort to understanding how a massive ship like the Syracusia could float. His breakthrough came unexpectedly while addressing a different challenge: verifying the purity of a new crown made for Hieron II, which led to his famous “Eureka” moment.

The Roman architect Vitruvius recounts that Hieron II had provided a goldsmith with pure gold for a crown, but upon receiving the finished piece, he suspected it was adulterated with a cheaper metal and had merely been gold-plated.

Tasked with determining the truth without harming the crown, Archimedes pondered the problem until a moment of insight struck him during a bath. Observing how the water level rose as he entered, he realized this phenomenon could help determine the crown’s density. Overwhelmed with excitement, Archimedes famously sprinted through the streets naked, exclaiming “Eureka!”—meaning, “I have found it!”

This principle, now known as Archimedes’ principle, posits that the buoyant force on a submerged object equals the weight of the fluid displaced by it. For instance, adding a stone to a full glass of water causes it to overflow; the weight of the spilled water is equivalent to the buoyant force exerted on the stone. This principle allowed Archimedes to calculate an object’s volume or average density based on buoyancy.

By applying this principle to the crown, Archimedes demonstrated that it was not made of pure gold. Despite having the same weight as the provided gold, the crown’s larger volume, due to the inclusion of less dense metals, revealed the goldsmith’s deception.

During the Second Punic War, Syracuse initially allied with Rome but later sided with Carthage. In response, Rome dispatched General Claudius Marcellus to Syracuse in 214 BCE to reclaim control. The Romans anticipated an easy victory, but they underestimated the ingenuity of Archimedes and his defensive war machines, including advanced catapults, the Archimedes’ Claw, and a purported heat ray.

For two years, Archimedes’ inventions repelled the Roman forces until they finally breached Syracuse’s outer defenses during a festival dedicated to Artemis, exploiting the distraction of the defenders. Marcellus, recognizing Archimedes’ pivotal role in Syracuse’s resistance, ordered that he be captured alive, valuing him as a strategic asset.

Plutarch recounts that Archimedes was absorbed in mathematical calculations on the beach, drawing diagrams in the sand, when a Roman soldier approached him with orders to come along. Immersed in his work, Archimedes pleaded, “Do not disturb my circles.” These words became his last as the soldier, failing to recognize him, fatally struck him.

Archimedes was laid to rest in Syracuse, with his tomb adorned by a sculpture representing a sphere and a cylinder. This tribute celebrated his significant contributions to geometry and honored his legacy as one of antiquity’s most brilliant minds.