Density Measurement (Archimedes)

Density measurement according to Archimedes' principle is one of the most reliable and, at the same time, most accessible methods for checking the authenticity of precious metal items. Every material has a characteristic specific density — a fixed ratio of mass to volume — that changes measurably as a result of alloys, counterfeit materials or cavities. The method is non-destructive, requires no chemicals and is reproducible with simple means.

Archimedes' principle

The Greek mathematician Archimedes of Syracuse (approx. 287–212 BC) recognised that a body immersed in a fluid experiences a buoyant force exactly equal to the weight of the fluid it displaces. For the density measurement of precious metals this means:

ρ_object = (m_air / (m_air − m_water)) × ρ_water

Key:

• ρ_object = density of the test object sought (g/cm³)
• m_air = weight of the object in air (g)
• m_water = weight of the object when immersed in water (g)
• ρ_water = density of water (≈ 0.9982 g/cm³ at 20 °C)

The difference m_air − m_water corresponds to the buoyancy and thus to the volume of the displaced water. Dividing the air weight by this volume gives the density of the object.

Step-by-step guide

1. Weigh the object dry – use a precision balance with a resolution of at least 0.01 g; note the value as m_air.
2. Prepare the water – distilled or filtered water at as constant a temperature as possible (20 °C is ideal). Read the water temperature and density ρ_water from a table, or assume ≈ 0.9982 g/cm³.
3. Set up the underwater fixture – suspend the object on a fine thread or wire below the balance pan into the water, without touching the bottom of the container. Many precision balances offer a hook for under-hook suspension.
4. Weigh under water – note the value as m_water.
5. Calculate the density – apply the formula; compare the result with the reference values in the table.

Reference densities of key precious metals and counterfeit materials

The table shows why tungsten is the most dangerous counterfeiting method: at 19.25 g/cm³ it lies so close to the fine-gold value of 19.32 g/cm³ that only high-precision measurements (±0.01 g/cm³) or complementary methods — such as X-ray fluorescence analysis or ultrasonic testing — allow a reliable distinction.

Strengths and limitations

Strengths:

• Non-destructive and chemical-free
• Reliably detects cavities, fillings and false alloys
• Low cost: a precision balance with an under-hook and a vessel of water are sufficient
• Equally suitable for bars, coins and jewellery

Limitations and sources of error:

• Air bubbles on the object distort the buoyancy (degrease the object before measuring)
• Very small objects (under 1 g) require microbalances for reliable results
• A tungsten core in gold-clad bars can bring the overall density close to the reference value if the ratio is right — here an additional ultrasonic test or drill sample is advisable
• Alloys of unknown composition yield only a suspicion value, not a definitive fineness
• Uneven surfaces (reliefs, milling) and trapped air require careful preparation

Combining with other test methods

For a reliable assessment, density measurement is recommended as the first stage in a multi-step testing protocol:

1. Density measurement – quick rough classification (counterfeit or plausible)
2. Magnet test – rules out ferromagnetic counterfeit materials
3. Ping test – gives indications of cavities
4. X-ray fluorescence analysis (XRF) – exact elemental composition at the surface
5. Acid test – chemical proof where gold-plated counterfeits are suspected

For coins and bars to be valued against the current gold price, density measurement offers a solid first orientation before a dealer or refinery formally assesses the piece.

Practical tip: temperature correction

Water has its greatest density at 4 °C (1.0000 g/cm³). At a room temperature of 20 °C it is 0.9982 g/cm³. Anyone wanting to measure to within ±0.05 g/cm³ should measure the actual water temperature and use the corresponding density value from a reference table. For most home tests the approximate value of 0.998 g/cm³ is sufficient.

In brief

Archimedean density measurement is a simple, reliable and inexpensive tool for the initial authenticity testing of precious metals. It detects most counterfeits immediately — only high-quality tungsten counterfeits require complementary methods. Combined with weight and dimension checks via the coin weight checker, it covers the broad range of everyday testing situations.