How did Henry Cavendish weigh the Earth in 1798?

Henry Cavendish measured the gravitational attraction between lead spheres using a torsion balance, a rod hanging from a thin wire. He compared that tiny pull with the Earth's pull on the same spheres, which is simply their weight. The ratio gave the Earth's average density, reported in June 1798 as 5.48 times the density of water. The accepted value is about 5.52. Density combined with the Earth's volume gives its mass, which is why the experiment is described as weighing the world. [1] [2]

Newton published his law of gravitation in 1687 but made no attempt to determine the gravitational constant G or the mass of the Earth. By the 1700s astronomers wanted the Earth's density, since it would allow the densities of other planets to be worked out. In 1772 the Royal Society set up a Committee of Attraction, which included Cavendish. It tried measuring how far a large Scottish mountain deflected a plumb bob and obtained about 4.5 times the density of water, but Cavendish thought its assumptions unfounded. [1]

The apparatus came from the geologist John Michell, who died before he could carry out the experiment. Cavendish found Michell's equipment inadequate and rebuilt it, beginning his own work in 1797 at age 67. He hung a six-foot wooden rod from a wire, with a two-inch lead sphere at each end. Two much larger lead spheres, 12 inches across and about 350 pounds each, were brought near the small ones. Their attraction twisted the wire slightly, and the rod stopped moving when the wire's twisting force balanced the gravitational pull. [1] [2]

Comparing that measured pull with the weight of the small spheres, which is the Earth's pull on them, shows how many times more massive the Earth is than the large spheres. Because of this, the method did not require a numerical value for G, and the constant does not appear in his paper. [3] [2]

The force involved is so weak that a small air current could ruin the result. Cavendish enclosed the apparatus in a closed room, watched it through a telescope, and moved the weights from outside with pulleys. The room was kept dark so temperature differences would not disturb it. He also checked for magnetization by rotating the spheres, observed the rods without spheres, and tried different wires. The rod's movement was no more than about two-tenths of an inch. [1] [2]

Cavendish published a 57-page paper, "Experiments to Determine the Density of the Earth," which gave 5.48 times the density of water. This is within about one percent of the modern figure, and for almost a century no one improved on it. Multiplying density by volume gives a mass of roughly six trillion trillion kilograms. Today the experiment is mostly seen as a way to measure G, though one lab manual notes that this use began only with C. V. Boys in 1892. One source gives the publication year as 1789, but the other sources say 1798. [1] [2] [4] [5]