The Cavendish Experiment: Weighing the Earth with a Wire and Two Lead Balls

In 1797, Henry Cavendish was 65 years old, reclusive to the point of pathology, and possessed of one of the sharpest experimental minds of the Enlightenment. He spent two years in the outbuilding of his Clapham home in London, hunched over a delicate apparatus designed by a dead colleague, watching a wire twist by fractions of a degree, and measuring those twists through a telescope from outside the room to avoid disturbing the air inside. What he produced was the first accurate measurement of the gravitational force between two objects in a laboratory, and from it he calculated the density of the Earth to within 1% of the value accepted today. What he did not know — what no one knew for another century — was that his result also contained the gravitational constant G, the most poorly determined fundamental constant in all of physics.

The Man Who Weighed the Earth Without Knowing His Own Net Worth

Henry Cavendish was one of the wealthiest people in Britain and one of its most isolated. He communicated with his female servants entirely through written notes to avoid speaking with women. He ate alone. He added his laboratory to his house specifically so that he could enter it without passing through any room where he might encounter a visitor.

Source: Jungnickel, C. & McCormmach, R. (1999), Cavendish: The Experimental Life (Bucknell University Press) — the definitive biography, detailing Cavendish's personal habits and laboratory methods.

His scientific output was extraordinary — he discovered hydrogen (which he called "inflammable air"), determined the composition of water, and calculated the specific heat of numerous substances — but much of it was not published during his lifetime. When James Clerk Maxwell edited Cavendish's papers decades after his death, he found results that anticipated major discoveries others had received credit for.

The torsion balance experiment was different: Cavendish did publish it, and in detail.

Source: Cavendish, H. (1798), "Experiments to determine the density of the earth," Philosophical Transactions of the Royal Society, 88, 469–526 — the original paper, read to the Royal Society on June 21, 1798.

The Backstory — John Michell's Apparatus

Cavendish did not design the apparatus he used. It was designed by John Michell, a geologist and natural philosopher who is now better known for predicting the existence of black holes in 1783 (which he called "dark stars") than for his experimental work.

Michell conceived the torsion balance experiment before 1783 and began constructing the apparatus. He died in 1793 before completing it. The apparatus passed to Francis Wollaston, who found it too complex to use. Wollaston gave it to Cavendish.

Source: Cavendish (1798), Philosophical Transactions — Cavendish explicitly credits Michell in the paper's opening: "The apparatus for determining the density of the earth... was contrived by the late Reverend John Michell."

Cavendish rebuilt the apparatus substantially, keeping Michell's general design but improving the sensitivity and the method of measurement.

This attribution matters for a reason beyond historical fairness. The "Cavendish experiment" is sometimes called "Michell's experiment performed by Cavendish" by historians of science. The experiment represents a collaboration across death — one person's design, another person's execution, separated by years.

The Setup — Torsion Balance and Extreme Isolation

The torsion balance is a beautiful example of physics leveraging sensitivity rather than brute force. Gravity is the weakest of the four fundamental forces — so weak that the gravitational attraction between two human-scale objects is smaller than the weight of a grain of sand. To measure it, you need to trade force for rotation, and rotation for very small angles.

The apparatus Cavendish used consisted of:

A wooden rod, approximately 6 feet (1.83 m) long, suspended horizontally from a thin wire at its center. At each end of the rod, a small lead sphere 2 inches (5.1 cm) in diameter and weighing approximately 1.61 pounds (0.73 kg) was attached.

Two large lead spheres, each 12 inches (30.5 cm) in diameter, weighing approximately 348 pounds (158 kg) each. These were mounted on a separate arm that could be swung to bring each large sphere close to one of the small spheres on the rod.

The wire from which the rod was suspended was the key element. When the large spheres were brought close to the small ones, their gravitational attraction pulled the small spheres toward them, causing the rod to rotate. The wire resisted this rotation, providing a restoring torque proportional to the angle of twist. By measuring the twist angle, Cavendish could calculate the gravitational force between the spheres.

Source: Cavendish (1798), Philosophical Transactions 88, 469–526 — detailed description of apparatus dimensions, sphere masses, and measurement method.

The measurement was made by telescope from outside the room. A small paper scale was attached to the rod. Cavendish read the scale position through a telescope peering through a small hole in the wall of the building. This was essential: even a person's body heat, or a gentle breath, could disturb the air enough to move the suspended rod and corrupt the measurement.

Component	Dimensions / Properties
Suspension rod	6 ft (1.83 m) wooden, suspended by wire
Small lead spheres	2 in (5.1 cm) diameter, ~0.73 kg each
Large lead spheres	12 in (30.5 cm) diameter, ~158 kg each
Separation (small to large)	~8.85 in (22.5 cm) center-to-center
Measurement method	Telescope through hole in wall
Duration	1797–1798, multiple runs
Result	Earth density 5.448 g/cm³ (modern: 5.515 g/cm³)

The Protocol — How Cavendish Made the Measurement

The procedure required patience measured in hours per data point.

Cavendish would position the large spheres on one side of the small spheres and wait for the system to reach equilibrium — the rod twisting toward the large spheres until the gravitational pull and the wire's restoring torque balanced. He read the equilibrium position through the telescope, then swung the large spheres to the opposite side and waited again for a new equilibrium. The difference in the rod's angular position between the two equilibrium states gave him the twist angle due to gravitational attraction.

He also measured the wire's restoring constant by timing the period of oscillation of the rod when the large spheres were removed. A stiff wire has a short oscillation period; a more compliant wire has a longer one. This let him convert the angular twist into a force using the wire's known restoring constant.

Source: Cavendish (1798), Philosophical Transactions 88 — the paper reports 29 separate experimental runs, with Cavendish calculating the Earth's density from each one.

The 29 runs gave a distribution of results. Cavendish averaged them to get his final value: the Earth's density is 5.448 times that of water, with an uncertainty of about 1%.

The modern accepted value is 5.515 g/cm³ (5.515 times the density of water). Cavendish was off by 1.2% — an extraordinary result given that the instrument was measuring forces equivalent to a few ten-thousandths of a newton, using a telescope through a hole in a wall, over the course of two years.

The G He Did Not Calculate

Here is the subtle historical point that is almost always missed: Cavendish did not calculate G, the gravitational constant in Newton's law F = Gm₁m₂/r².

His paper makes no mention of G. He calculated the density of the Earth. Newton's law of universal gravitation had been known for a century, but expressing it in terms of a universal constant was not standard practice at the time. Cavendish's result implied a value of G, but he did not extract it. The concept of G as a fundamental constant requiring its own measurement was not fully articulated until the late nineteenth century.

Source: Lally, S. P. (1999), "Henry Cavendish and the density of the Earth," The Physics Teacher, 37, 34–37 — history of how Cavendish's result relates to G.

Using his published data and modern notation:

G = (3 × density_Earth × g × r_Earth²) / (4π × density_Earth²)

Working backward from Cavendish's density gives G ≈ 6.74 × 10⁻¹¹ N m² kg⁻². The modern CODATA value is G = 6.674 × 10⁻¹¹ N m² kg⁻².

The agreement is within 1%.

The Controversy — Why G Is Still the Worst-Known Fundamental Constant

For most fundamental constants in physics, modern measurement precision is stunning. The electron's charge is known to better than one part per billion. The speed of light is defined exactly. The fine structure constant is known to one part in 10¹⁰.

G is different. In a field where constants are known to parts per billion, G is known only to about 22 parts per million (ppm) — roughly 45,000 times less precisely than the electron charge.

Source: CODATA 2018 recommended value of G: 6.67430 × 10⁻¹¹ m³ kg⁻¹ s⁻², relative standard uncertainty 2.2 × 10⁻⁵ (22 ppm), published by NIST.

But the 22 ppm CODATA uncertainty is itself contested. The deeper problem is not that individual measurements are imprecise — several measurements have achieved precisions of 10–15 ppm. The problem is that the best measurements from different groups disagree with each other by much more than their stated uncertainties.

Source: The curious case of the gravitational constant, PNAS (2016) — review of the G measurement discrepancy problem.

Two groups using similar torsion balance methods get values that differ by 40–50 ppm. Their quoted uncertainties are each around 10–15 ppm. The discrepancy is four to five times larger than either error bar, which means at least one group is systematically wrong — but no one can identify the source of the systematic error.

This is the gravest measurement discrepancy in modern physics. No other fundamental constant has this problem.

Source: Schlamminger, S. & Gundlach, J. H. (2019), "On the inconsistency in experimental results of the gravitational constant," Measurement, 136, 630–634.

Why G Is So Hard to Measure

Gravity is extraordinarily weak. The gravitational force between two 1-kilogram masses separated by 1 meter is about 6.67 × 10⁻¹¹ newtons — roughly 10 billion times weaker than the electromagnetic force between two protons at the same distance.

This extreme weakness means that any extraneous force — seismic vibrations, air currents, thermal gradients, the gravitational pull of a person walking past the laboratory — can be comparable in magnitude to the signal being measured. Experiments measuring G must be housed in seismically quiet locations, thermally stabilized buildings, vacuum enclosures, and must correct for the gravitational influence of every nearby mass — including the laboratory walls.

Torsion balance methods (descended from Cavendish's original design) achieve the best precision but face correlated systematic errors: the gravitational pull of the large attracting masses depends on their exact geometry and density distribution, both of which are hard to characterize perfectly.

Atom interferometry offers a completely different approach: laser-cooled rubidium atoms fall in a precisely controlled way, and their quantum wave-mechanical interference pattern is sensitive to the local gravitational acceleration. By placing a known mass near the falling atoms and measuring how it changes the interference pattern, researchers can extract G.

Source: Fixler, J. B. et al. (2007), "Atom interferometer measurement of the Newtonian constant of gravity," Science, 315(5808), 74–77 — first atom-interferometry G measurement, achieving 150 ppm relative uncertainty.

Atom interferometry measurements and torsion balance measurements have not yet converged to a consistent value. The discrepancy remains unresolved.

The Timeline

Year	Event
Before 1783	John Michell conceives the torsion balance experiment
1793	Michell dies; apparatus passes eventually to Cavendish
1797	Cavendish rebuilds the apparatus and begins measurements
1798	29 experimental runs completed; result: Earth density 5.448 g/cm³
June 21, 1798	Paper read to the Royal Society
1810	Cavendish dies, age 78
1873	James Clerk Maxwell edits and publishes Cavendish's unpublished scientific papers
1894	Charles Boys uses a much smaller torsion balance to measure G directly — first explicit G determination
1969–2000	Multiple precision G measurements; growing awareness of systematic discrepancies between groups
2007	Atom interferometry first used to measure G (Fixler et al.)
2016	PNAS review article documents G measurement discrepancy as unresolved crisis
2018	CODATA recommends G = 6.67430 × 10⁻¹¹ m³ kg⁻¹ s⁻², 22 ppm uncertainty

Replication and the Modern Measurement Landscape

In a sense, the Cavendish experiment has been replicated continuously for 230 years. Every modern G measurement uses the same basic physical principle — gravitational attraction between known masses, detected by a highly sensitive mechanical system. The challenge has been moving from Cavendish's ~1% precision to the <100 ppm precision that modern physics demands.

The BIPM (Bureau International des Poids et Mesures) has conducted its own torsion balance measurements, published in 2001 and 2014. Both BIPM values are systematically higher than the CODATA recommended value by about 200–220 ppm — far outside the stated experimental uncertainties.

Source: Quinn, T. J. et al. (2001), "A new determination of G using two methods," Physical Review Letters, 87, 111101 — BIPM torsion balance measurement, higher than CODATA value.

A replication of the BIPM measurement at NIST, published in 2025, found a value lower than BIPM's by a relative amount that exceeds both experiments' stated uncertainties.

Source: Redetermination of the gravitational constant with the BIPM torsion balance at NIST, Metrologia (2025), IOPscience doi:10.1088/1681-7575/ae570f — most recent G measurement resolving BIPM-NIST comparison.

This situation has no analog in fundamental physics. The electron charge, Planck's constant, and the speed of light are known to such precision that they are now used to define the SI unit system itself. G is not, and may not be for decades.

Some physicists have speculated that the discrepancies might indicate that G is not, in fact, a universal constant — that it might vary slightly with position, orientation, or time. This idea is not supported by any established theory, but the measurement situation is peculiar enough to keep the hypothesis alive in fringe discussions.

Source: Anderson, J. D. et al. (2015), "Measurements of Newton's gravitational constant and the length of day," Europhysics Letters, 110, 10002 — controversial claim of a periodic variation in G correlated with Earth's rotation rate, not widely accepted.

Where It Stands Today — G and Fundamental Physics

The failure to pin down G precisely has concrete consequences for fundamental physics.

Planetary science. The mass of the Earth, Moon, Sun, and all planets is calculated from G combined with orbital mechanics. Because G is known only to ~22 ppm, planetary masses carry that same uncertainty. For most practical purposes this is irrelevant — spacecraft navigation uses relative measurements that are independent of G's absolute value — but for fundamental science linking gravity to other forces, it matters.

Tests of equivalence. Einstein's general relativity rests on the equivalence principle: gravitational mass equals inertial mass. Precision tests of equivalence use G measurements. The quality of those tests is limited by G's uncertainty.

Quantum gravity. The unification of quantum mechanics and general relativity — the central unsolved problem of fundamental physics — requires a theory that correctly predicts G from more fundamental principles. Until G is known precisely, any candidate quantum gravity theory faces a loose target.

The irony is plain: Cavendish, working alone in an outbuilding with a borrowed apparatus and a telescope through a hole in the wall, achieved 1% accuracy in 1798. Twenty-three decades of technological progress have improved that by a factor of roughly 450 — to 22 ppm. But the different modern measurements, each claiming 10–20 ppm precision, do not agree with each other. The absolute value of the force that governs galaxies, holds planets in orbit, and keeps every person on the ground is known less accurately than almost any other physical constant.

What People Get Wrong About the Cavendish Experiment

"Cavendish measured G." He did not. He measured the density of the Earth. G can be extracted from his data retroactively, but Cavendish's paper discusses his goal as determining the Earth's mean density — a different framing that does not require conceiving of a universal gravitational constant.

"The apparatus was Cavendish's design." It was John Michell's design, built before Michell's death in 1793. Cavendish rebuilt it, made improvements, and performed the experiment, but gave explicit credit to Michell in his paper.

"G has been nailed down since Cavendish." The best modern G measurements disagree with each other by far more than their stated uncertainties. G remains, by a large margin, the least precisely known of all fundamental constants.

"Measuring gravity in the lab is routine." Gravity's extreme weakness makes it the hardest force to measure precisely. Electromagnetic forces between equivalent-sized objects are roughly 10³⁶ times stronger than gravitational forces — 36 orders of magnitude. Every G measurement experiment is fighting an inherently unfavorable signal-to-noise ratio.

FAQs

Q: What did the Cavendish experiment actually measure? A: Cavendish measured the mean density of the Earth, which he found to be 5.448 times that of water. The experiment also implicitly determined the gravitational constant G, though Cavendish did not frame his result that way. The modern value for Earth's density is 5.515 g/cm³, making Cavendish's result accurate to within 1.2%.

Q: Who designed the torsion balance that Cavendish used? A: John Michell, a geologist and natural philosopher who is also credited with predicting the existence of black holes in 1783. Michell died in 1793 before completing the experiment, and the apparatus eventually came to Cavendish, who rebuilt and improved it.

Q: Why is the gravitational constant G so difficult to measure? A: Gravity is the weakest of the four fundamental forces by an enormous margin. The gravitational force between two 1-kilogram masses 1 meter apart is about 6.67 × 10⁻¹¹ newtons — comparable to the weight of a bacterium. Any environmental perturbation (seismic vibrations, air currents, thermal gradients) can be larger than the signal.

Q: How precise is our current measurement of G? A: CODATA 2018 recommends G = 6.67430 × 10⁻¹¹ m³ kg⁻¹ s⁻², with a relative uncertainty of about 22 parts per million (22 ppm). This makes G the least precisely known of all fundamental constants — roughly 45,000 times less precisely known than the electron charge.

Q: Why do modern G measurements disagree with each other? A: Different groups using different methods achieve precisions of 10–15 ppm individually, but their central values differ by 40–50 ppm. The source of this systematic discrepancy is unknown. It is the most unresolved precision measurement problem in fundamental physics.

Q: Why did Cavendish measure through a telescope from outside the room? A: The torsion balance rod, suspended from a fine wire, was so sensitive that even the air currents from a person's body heat could displace it, corrupting the measurement. By reading scales through a telescope from outside the isolated room, Cavendish eliminated this source of systematic error.

The Takeaway

Cavendish sat alone in an outbuilding, reading a scale through a telescope, and determined the density of the Earth to within 1.2%. The gravitational constant G, which his data implied, is still being measured today — and the measurements still disagree. The experiment's legacy is twofold: it proved that laboratory physics can weigh a planet, and it revealed that gravity, the force most obviously present in everyday experience, is also the most resistant to precise quantification.

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