Everything about The Cavendish Experiment totally explained
The
Cavendish experiment, done in 1797 – 1798 by
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 and the mass of the
Earth. However, these were derived by others from Cavendish's result, which was a value for the Earth's density. The experiment was devised sometime before 1783 by
John Michell, who constructed a
torsion balance apparatus for it. However, Michell died in 1793 without completing the work, and after his death the apparatus passed to Francis John Hyde Wollaston and then to Henry 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.
The experiment
The apparatus constructed by Cavendish was a
torsion balance made of a six-foot wooden rod suspended from a wire, with a 2 inch diameter 1.61 pound
lead sphere attached to each end. Two 12 inch 348 pound lead balls were located near the smaller balls, about 9 inches 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 7 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, 1.47 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 thick, 10 feet tall, and 10 feet 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 inch. 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 wasn't 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.
Did Cavendish determine G?
It isn't unusual to find books that state erroneously that Cavendish's purpose was determining the
gravitational constant (G), and this mistake has been pointed out by several authors. In actuality, Cavendish's only goal was to measure the density of the Earth; he called it 'weighing the world'. The method Cavendish used to calculate the Earth's density consists in measuring the force on a small ball caused by a large ball of known mass, and comparing it with the force on the small ball caused by the Earth, so the Earth can be calculated to be
N times more massive than the large ball without the need to obtain a numeric value for
G. The gravitational constant doesn't appear in Cavendish's paper, and there's no indication that he regarded it as a goal of his experiment. One of the first references to
G is in 1873, 75 years after Cavendish's work.
In Cavendish's time,
G didn't have the importance among scientists that it has today; it was simply a proportionality constant in
Newton's law. The purpose of measuring the force of gravity was instead to determine the Earth's density. This was a much-desired quantity in 18th-century
astronomy, since once the Earth's density was known, the densities of the Moon, Sun, and the other planets could be found from it.
A further complication is that up through the mid-nineteenth century, scientists didn't use a specific unit of measurement for
force. This unnecessarily tied
G to the mass of the Earth, as opposed to
G being recognized as a universal constant. However, even though Cavendish didn't report a value for
G, the results of his experiment allowed it to be determined. During the late 1800s, as scientists began to recognize
G as a
fundamental constant of nature, they calculated it from Cavendish's accurate results, thus:
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