Experiment #153 · Scientific experiment

Archimedes' Eureka — The Displacement Principle

Volume by immersion

Archimedes of Syracuse · c. 250 BC · Hydrostatics, metrology

First published: Vitruvius, *De Architectura*, Book IX, preface (c. 15 BC).

A body immersed in fluid displaces a volume of fluid equal to the volume of the body. The king's crown can be tested without destruction: immerse it and compare the overflow with that of an equal weight of pure gold.

According to Vitruvius, King Hiero II of Syracuse commissioned a gold crown and suspected the goldsmith had adulterated it with silver. Archimedes was tasked with determining the crown's composition without damaging it. While stepping into a bath he noticed the water level rise and realised that a submerged object displaces a volume of fluid equal to its own volume. Since gold is denser than silver, a crown of pure gold would displace less water than one adulterated with silver (for the same weight). Archimedes reportedly ran through the streets crying "Eureka!" The deeper principle — that a body submerged in fluid experiences an upward buoyant force equal to the weight of the displaced fluid — was formalised in *On Floating Bodies*, the founding text of hydrostatics.

Formulation

Immerse the crown in a vessel filled to the brim; collect the overflow. Repeat with an equal weight of pure gold. If the crown displaces more water, it contains a less-dense adulterant. Generalisation: buoyant force = weight of displaced fluid (Archimedes' Principle).

Compare this experiment

Dimensions Engaged

◉

Matter

Reveals that matter has an intrinsic volumetric property (density) that is independent of shape or surface appearance — a foundational move for quantitative physical science.

Responses — How Schools Engage

Affirms / takes the bait 6

Empiricism

A paradigmatic empirical discovery: a sensory observation (water rising) yields a quantitative law. The method generalises immediately to all density measurements.

Naturalism

Density is a mind-independent property of matter; Archimedes' test exploits it. Nature furnishes the regularity; the experimenter merely reads it off.

Realism

The crown's composition is a fact of the matter — gold or adulterated — and the displacement test reveals it. Realism about material properties is vindicated at the most practical level.

Pragmatism

A working test that answers a real question (is the crown pure?) without destroying the object. Knowledge is instrumental; Archimedes' method is pragmatism avant la lettre.

Rationalism

The mathematical law (buoyant force = weight of displaced fluid) is a necessary truth about fluids in equilibrium; the bath episode merely occasions the intellectual grasp of it.

Hylomorphism

The density distinction between gold and silver reflects their different material natures. Hylomorphism provides a framework: same form (crown) but different matter yields different displacement.