Density of the Earth
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Henry Cavendish was born on 10 October 1731. In 2026 that birthday falls on a Saturday, inside a week otherwise owned by prize announcements. The experiment people mean when they say his name was not done on his birthday. It was written up in 1798, in the Philosophical Transactions of the Royal Society, under a title with no poetry in it: Experiments to Determine the Density of the Earth.
The idea was John Michell's. Michell, a clergyman and geologist, designed a torsion balance that could feel the attraction of masses you could put in a room. He built the apparatus and did not live to use it. He died in 1793. The instrument passed to Francis John Hyde Wollaston at Cambridge, who did not have a convenient place to run it, and Wollaston gave it to Cavendish. Cavendish kept Michell's plan and rebuilt most of the hardware. A wooden arm about six feet long hung level from a wire roughly forty inches long. At each end of the arm was a lead ball about two inches across. The whole arm sat inside a narrow wooden case, to keep the wind off it. Bring a much larger lead weight near one of the small balls and the wire twists. The twist is the measurement.
It is a miserable measurement to make if anyone is in the room. Body heat stirs the air. A draft moves the arm by more than the attraction of the lead. Cavendish's fix is the part worth picturing. He put the apparatus in a room that stayed shut. He watched the arm from outside, through telescopes. He arranged the large weights so he could move them without going in. The paper is explicit about this. He was not performing solitude. He was refusing to become a source of error.
What he published was a density. The Earth, on average, came out 5.48 times as dense as water. In 1821 Francis Baily went back through the arithmetic and found a slip. The experiments themselves sit nearer 5.45 times water. The modern value is about 5.51. Cavendish was not "off" in the way a failed experiment is off. He was close, and the printed headline number was a calculation error on top of a real result. He did not report a constant called G. That name, and the habit of treating the experiment as a measurement of the gravitational constant, came later. The attraction of the lead and the attraction of the Earth are the same kind of fact. Once you trust one, you can scale to the other. He scaled it to a density, because a density is what he had set out to weigh.
The popular sentence is that he weighed the Earth. It is fair, as long as you remember the apparatus: not a planet on a scale, a closed case, a wire, two small lead balls, and a man outside with a telescope, moving the large weights by a mechanism so his own warmth would not invent a breeze.
There is no tee for that case in the shop. A shirt that says gravity, in the abstract, is a different joke, and it has already been printed. This note is the room, the wire, and a number that was almost right twice — once in the lead, and once after someone re-added the column.