page_title: Cavendish experiment
section_title: The experiment
hierarchical_section_title: Cavendish experiment / The experiment
caption_attribution_description: English: This is a detail of a cross section drawing from Henry Cavendish's 1798 paper published in Philosophical Magazine. This is a scientific paper with no copyright restrictions.
context_page_description: The Cavendish experiment, performed in 1797–1798 by English scientist Henry Cavendish, was the first experiment to measure the force of gravity between masses in the laboratory and the first to yield accurate values for the gravitational constant. Because of the unit conventions then in use, the gravitational constant does not appear explicitly in Cavendish's work. Instead, the result was originally expressed as the specific gravity of the Earth, or equivalently the mass of the Earth. His experiment gave the first accurate values for these geophysical constants.
  The experiment was devised sometime before 1783 by geologist John Michell, who constructed a torsion balance apparatus for it. However, Michell died in 1793 without completing the work. After his death the apparatus passed to Francis John Hyde Wollaston and then to Cavendish, who rebuilt the apparatus but kept close to Michell's original plan. Cavendish then carried out a series of measurements with the equipment and reported his results in the Philosophical Transactions of the Royal Society in 1798.
context_section_description: The apparatus constructed by Cavendish was a torsion balance made of a six-foot (1.8 m) wooden rod horizontally suspended from a wire, with two 2-inch (51 mm) diameter 1.61-pound (0.73 kg) lead spheres, one 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 Specific gravity 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 Francis Baily, the erroneous value 5.480±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, 1.74×10⁻⁷ N, about ​¹⁄₅₀ ₀₀₀ ₀₀₀ of the weight of the small balls. 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 0.01 inches (0.25 mm) using vernier scales on the ends of the rod.
  The accuracy of Cavendish's result was not exceeded until C. V. Boys's experiment in 1895. 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.
  Cavendish's result was also the first evidence for a planetary core made of metal. The result of 5.4 g·cm⁻³ is close to 80% of the density of liquid iron, and 80% higher than the density of the Earth's outer crust, suggesting the existence of a dense iron core.
caption: Detail showing torsion balance arm (m), large ball (W), small ball (x), and isolating box (ABCDE).
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