![]() 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. The accuracy of Cavendish's result was not exceeded until C. 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 key observable was of course the deflection of the torsion balance rod, which Cavendish measured to be about 0.16" (or only 0.03" for the stiffer wire used mostly). Through two holes in the walls of the shed, Cavendish used telescopes to observe the movement of the torsion balance's horizontal rod. To prevent air currents and temperature changes from interfering with the measurements, Cavendish placed the entire apparatus in a mahogany box about 1.98 meters wide, 1.27 meters tall, and 14 cm thick, all in a closed shed on his estate. The force involved in twisting the torsion balance was very small, 1.74 ×10 −7 N, (the weight of only 0.0177 milligrams) or about 1⁄ 50,000,000 of the weight of the small balls. Ĭavendish's equipment was remarkably sensitive for its time. ![]() Actually, the rod was never at rest Cavendish had to measure the deflection angle of the rod while it was oscillating. The torsion coefficient could be calculated from this and the mass and dimensions of the balance. The period changed because after the third experiment Cavendish put a stiffer wire. For the first 3 experiments the period was about 15 minutes and for the next 14 experiments the period was half of that, about 7.5 minutes. 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 current accepted value is 5.514 g/cm3. 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.Ĭavendish found that the Earth's density was 5.448 ☐.033 times that of water (due to a simple arithmetic error, found in 1821 by Francis Baily, the erroneous value 5.480 ☐.038 appears in his paper). 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. The arm rotated until 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. Their mutual attraction to the small balls caused the arm to rotate, twisting the suspension wire. The two large balls could be positioned either away from or to either side of the torsion balance rod. The experiment measured the faint gravitational attraction between the small and large balls, which deflected the torsion balance rod by about 0.16" (or only 0.03" with a stiffer suspending wire).ĭetail showing torsion balance arm ( m), large ball ( W), small ball ( x), and isolating box ( ABCDE). Two massive 12-inch (300 mm), 348-pound (158 kg) lead balls, suspended separately, could be positioned away from or to either side of the smaller balls, 8.85 inches (225 mm) away. ![]() The apparatus consisted of a torsion balance made of a six-foot (1.8 m) wooden rod horizontally suspended from a wire, with two 2-inch-diameter (51 mm), 1.61-pound (0.73 kg) lead spheres, one attached to each end. 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. 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. However, Michell died in 1793 without completing the work. The experiment was devised sometime before 1783 by geologist John Michell, who constructed a torsion balance apparatus for it. His experiment gave the first accurate values for these geophysical constants. Instead, the result was originally expressed as the specific gravity of Earth, or equivalently the mass of Earth. Because of the unit conventions then in use, the gravitational constant does not appear explicitly in Cavendish's work. 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.
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