Cavendish Experiment - The Experiment

The Experiment

The apparatus constructed by Cavendish was a torsion balance made of a six-foot (1.8 m) wooden rod suspended from a wire, with a 2-inch (51 mm) diameter 1.61-pound (0.73 kg) lead sphere attached to each end. Two 12-inch (300 mm) 348-pound (158 kg) lead balls were located near the smaller balls, about 9 inches (230 mm) away, and held in place with a separate suspension system. The experiment measured the faint gravitational attraction between the small balls and the larger ones.

The two large balls were positioned on alternate sides of the horizontal wooden arm of the balance. Their mutual attraction to the small balls caused the arm to rotate, twisting the wire supporting the arm. The arm stopped rotating when it reached an angle where the twisting force of the wire balanced the combined gravitational force of attraction between the large and small lead spheres. By measuring the angle of the rod, and knowing the twisting force (torque) of the wire for a given angle, Cavendish was able to determine the force between the pairs of masses. Since the gravitational force of the Earth on the small ball could be measured directly by weighing it, the ratio of the two forces allowed the density of the earth to be calculated, using Newton's law of gravitation.

Cavendish found that the Earth's density was 5.448 ± 0.033 times that of water (due to a simple arithmetic error, found in 1821 by F. Baily, the erroneous value 5.48 ± 0.038 appears in his paper).

To find the wire's torsion coefficient, the torque exerted by the wire for a given angle of twist, Cavendish timed the natural oscillation period of the balance rod as it rotated slowly clockwise and counterclockwise against the twisting of the wire. The period was about 20 minutes. The torsion coefficient could be calculated from this and the mass and dimensions of the balance. Actually, the rod was never at rest; Cavendish had to measure the deflection angle of the rod while it was oscillating.

Cavendish's equipment was remarkably sensitive for its time. The force involved in twisting the torsion balance was very small, 1.74 x 10–7 N, about 1/50,000,000 of the weight of the small balls or roughly the weight of a large grain of sand. To prevent air currents and temperature changes from interfering with the measurements, Cavendish placed the entire apparatus in a wooden box about 2 feet (0.61 m) thick, 10 feet (3.0 m) tall, and 10 feet (3.0 m) wide, all in a closed shed on his estate. Through two holes in the walls of the shed, Cavendish used telescopes to observe the movement of the torsion balance's horizontal rod. The motion of the rod was only about 0.16 inches (4.1 mm). Cavendish was able to measure this small deflection to an accuracy of better than one hundredth of an inch using vernier scales on the ends of the rod.

Cavendish's experiment was repeated by Reich (1838), Baily (1843), Cornu & Baille (1878), and many others. Its accuracy was not exceeded for 97 years, until C. V. Boys' 1895 experiment. In time, Michell's torsion balance became the dominant technique for measuring the gravitational constant (G), and most contemporary measurements still use variations of it. This is why Cavendish's experiment became the Cavendish experiment.