04. The Weight of the World — Cavendish in a Shed

Weighing a planet with two lead balls

In 1798 Henry Cavendish published "Experiments to Determine the Density of the Earth" in the Philosophical Transactions of the Royal Society. He suspended a light rod with two small lead balls from a thin wire, brought two large lead spheres close to them, and measured how far the rod twisted. The twist was produced by the gravitational attraction between the balls, a force so weak that a draught or a temperature gradient would swamp it. Cavendish sealed the apparatus in a case in an outbuilding and observed it from outside through a telescope, so his own body heat could not disturb the result. The instrument was not his idea: it was designed by John Michell, who died before using it, and passed to Cavendish through an intermediary. He reported the mean density of the Earth as about 5.48 times that of water, against a modern value of 5.514 grams per cubic centimetre.

The constant he did not measure

Cavendish is routinely credited with the first measurement of the gravitational constant, and he did not measure it or mention it. The constant G did not exist as a named quantity in his lifetime; his paper is about the density of the Earth, which is the question the Royal Society cared about. The value of G was extracted from his numbers much later, by others working in a formalism he never used. The modern figure is 6.67430(15) × 10⁻¹¹ m³ kg⁻¹ s⁻², carrying a relative uncertainty of about 22 parts per million in the 2022 CODATA adjustment. That makes G the worst-known of the fundamental constants by a wide margin, at a time when the second is known to a part in 10¹⁸. Gravity is the reason: it cannot be screened, it cannot be amplified, and every mass in the laboratory pulls on the experiment.

What two centuries of failure to improve means

Independent modern determinations of G disagree with each other by more than their stated uncertainties, which means at least some of them contain unrecognised systematic error. This is the ordinary condition of hard measurement rather than a scandal, and the discipline's response has been to publish the disagreement rather than average it away. Cavendish's real achievement was not a number but a technique: isolate the effect, remove the observer, and let a weak force accumulate into a visible displacement.

Example: Hearing a whisper in a quiet room is easy; the skill is building the quiet room.

Verdict. Cavendish measured the Earth's density to within about half a per cent of the modern value, and the constant credited to him is absent from his paper and still the least precisely known in physics.

Overturned if: a new determination of G brings the independent laboratory results into agreement within their stated uncertainties.

Sources. 1798 · Henry Cavendish, "Experiments to Determine the Density of the Earth," Philosophical Transactions 88:469–526 — Royal Society · 2022 · CODATA, "Recommended Values of the Fundamental Physical Constants" — NIST