In 1798 Henry Cavendish weighed the Earth from a shed on his estate. He hung a rod from a thin wire with a small lead ball at each end, set two large lead balls beside them, and measured how far their gravity twisted the wire, watching through telescopes from outside so that he would not disturb it. The pull was about one fifty-millionth of the small balls’ weight. From that twist he worked out the Earth’s density: 5.448 times that of water. Today’s value is 5.514. He was about 1% off, with lead, wire and patience.
A clergyman’s design
The idea was not Cavendish’s to begin with. John Michell, an English clergyman and natural philosopher who spent his later life as rector of Thornhill in Yorkshire, devised the experiment sometime before 1783 and built a torsion balance for it. He died in 1793 without completing the work. The apparatus passed to Francis John Hyde Wollaston and then to Cavendish, who rebuilt it, keeping close to Michell’s original plan, and carried out the measurements in 1797 and 1798.
Cavendish was perhaps the right man for a job that needed solitude. He was immensely rich and profoundly shy, uncomfortable in company and sparing with conversation. He kept most of his instruments at his house on Clapham Common, then south-west of London, and it was in an outbuilding in the garden there that the world was weighed.
A twist you could barely see
The balance was a wooden rod six feet long, hung level from a wire. At each end sat a small lead ball of 0.73 kilograms. Beside them, on a separate suspension, Cavendish placed two large lead balls of 158 kilograms each.
Every lump of matter pulls on every other. The big balls tugged the small ones towards them, and the rod turned until the twist in the wire balanced the pull. The force was tiny:
A draught or a warm hand would have swamped it. So Cavendish closed the apparatus in a box, closed the box in the shed, and stayed outside. He read the rod’s movement through telescopes set in holes in the shed walls, with fine scales at each end of the rod. The deflection was about 0.16 degrees. To learn how stiff the wire was, he timed the rod’s slow swing back and forth, minutes at a time.
From a twist to a planet
Here is the step that turns a twitching rod into the weight of a world. The small balls were pulled two ways: sideways by the big lead balls, a force measured by the twist, and downwards by the whole Earth, which is simply their weight. Gravity grows with mass, so the ratio of those two pulls compares the Earth with a lead ball. Put in the sizes and distances, and out comes the Earth’s average density.
Today’s value is 5.514 grams per cubic centimetre. Cavendish was about 1% off. No one beat his accuracy until C. V. Boys’s experiment of 1895. Cavendish himself called the work “weighing the world” in his letters, and the result said something about the inside of the planet. The Earth as a whole is far denser than the rock of its crust, evidence for a heavy core of metal beneath our feet.
What it means today
Cavendish never wrote down the number physicists now call G, the gravitational constant. In his day the density of the Earth was the prize, and the constant only became standard much later. But his density, converted to modern units, gives G to within about 1% of today’s value. Michell’s torsion balance became the standard tool for measuring it, and most modern measurements still use versions of it.
Cavendish measured gravity between objects you could fit in a shed. Its effects reach much further: high above the Earth, weaker gravity even changes the rate of clocks, as in why GPS needs Einstein.
A shed, a wire, a telescope, and the Earth on the scale. And that’s how we found out.
