Cavendish Experiment (1798): Henry Cavendish Weighs the Earth

The Cavendish experiment, carried out by the English scientist Henry Cavendish in 1797–1798, was the first precise laboratory measurement of the gravitational pull between ordinary objects. Using a delicate torsion balance in an outbuilding of his house at Clapham, near London, he found the mean density of the Earth. His result effectively “weighed the Earth” and later allowed physicists to calculate the gravitational constant, G.

Background: Newton’s unknown number

In the Principia of 1687 Isaac Newton showed that every mass attracts every other mass. His law explained the motions of planets, but it could not reveal how massive the Earth was without knowing how strong gravity is between two known masses. That force is extremely weak between objects on human scale.

An earlier attempt came in 1774, when the Astronomer Royal Nevil Maskelyne measured how far the Scottish mountain Schiehallion deflected a plumb line. From his survey the mathematician Charles Hutton estimated the Earth’s mean density at about 4.5 times that of water. The figure depended on guesses about the mountain’s rock, so a direct laboratory test was desirable.

Henry Cavendish

Henry Cavendish (1731–1810) was a wealthy, intensely private member of the aristocratic Cavendish family and a fellow of the Royal Society. He made major contributions to chemistry, including identifying hydrogen as a distinct gas in 1766 and showing that water forms when hydrogen burns. He also did important unpublished work on electricity.

The apparatus he used had been designed by John Michell, a clergyman and natural philosopher who died in 1793 before he could carry out the experiment. It passed to Francis John Hyde Wollaston and then to Cavendish, who rebuilt much of it.

How the experiment worked

The core was a torsion balance: a wooden rod about 1.8 metres (6 feet) long, hung from its centre by a thin wire, with a small lead ball of about 5 centimetres (2 inches) diameter at each end. Two large lead balls, each about 30 centimetres (12 inches) across and weighing roughly 158 kilograms (348 pounds), could be swung close to the small ones.

The gravitational pull of the large balls twisted the rod by a very small angle, against the resistance of the wire. By measuring the angle and the rod’s slow oscillation period, Cavendish could calculate the force. Because temperature differences and air currents could swamp the effect, the apparatus stood in a sealed room. He observed it from outside through telescopes, with lamps shining on finely divided scales.

The result

Cavendish ran his series of measurements between August 1797 and May 1798 and reported them in “Experiments to Determine the Density of the Earth”, read to the Royal Society on 21 June 1798. He gave the Earth’s mean density as 5.48 times that of water. An arithmetic error in the paper means his own data average about 5.45, still close to the modern value of about 5.51.

Since the Earth’s mean density is roughly twice that of surface rocks, the result also showed that the planet’s interior must contain much denser material, consistent with an iron-rich core.

From density to G

Cavendish never wrote down the gravitational constant. Newton’s law was not commonly expressed with an explicit constant until the late nineteenth century. When later physicists derived G from Cavendish’s data, they obtained a value of about 6.74 × 10⁻¹¹ in modern units, within about 1 percent of today’s accepted 6.674 × 10⁻¹¹.

Myths and facts

The experiment is often said to have measured the gravitational constant, but Cavendish’s own aim and result were the density of the Earth; G was calculated from his figures much later. The popular phrase “weighing the Earth” is also loose: what his result really gave was the Earth’s mass, about 6 × 10²⁴ kilograms in modern terms, once the planet’s size was known.

Nor did Cavendish invent the torsion balance. John Michell conceived it for this purpose, and the French physicist Charles-Augustin de Coulomb independently used a torsion balance in 1785 to measure electrical forces. Cavendish’s achievement was to rebuild the instrument, identify the sources of error, such as temperature changes and magnetic effects, and carry the measurement through with exceptional care.

Legacy

Versions of the torsion balance are still used in laboratories and classrooms, and G remains one of the hardest fundamental constants to measure precisely. The Cavendish Laboratory at Cambridge, founded in 1874, is named after the family and honours Henry Cavendish among others. His experiment is often counted among the most elegant in the history of physics.

Timeline

• 1687: Newton publishes the law of universal gravitation.
• 1774: The Schiehallion experiment gives a first estimate of Earth’s density.
• 1793: John Michell dies, leaving his torsion balance unused.
• 1797, August: Cavendish begins measurements at Clapham.
• 1798, May: Cavendish completes the series.
• 1798, 21 June: His paper is read to the Royal Society.
• 1810, 24 February: Henry Cavendish dies in London.

Why it matters

The Cavendish experiment turned Newton’s law of gravitation into numbers that could be measured on Earth. It gave the first reliable figure for the planet’s density and mass and laid the basis for every later measurement of the gravitational constant.