The Cavendish experiment, performed in 1797–98 by British scientist Henry Cavendish, was the first experiment to measure the force of gravity between masses in the laboratory,^[1] and the first to yield accurate values for the gravitational constant.^[2][3] 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,^[4] or equivalently the mass of the Earth; and were the first accurate values for these geophysical constants. The experiment was devised sometime before 1783^[5] by geologist John Michell,^[6] 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.^[7]

The experiment[link]

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.^[8] The experiment measured the faint gravitational attraction between the small balls and the larger ones.

Vertical section drawing of Cavendish's torsion balance instrument including the building in which it was housed. The large balls were hung from a frame so they could be rotated into position next to the small balls by a pulley from outside. Figure 1 of Cavendish's paper.

Detail showing torsion balance arm (m), large ball (W), small ball (x), and isolating box (ABCDE).

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).^[9]

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.^[10]

Cavendish's equipment was remarkably sensitive for its time.^[9] The force involved in twisting the torsion balance was very small, 1.74 x 10^–7 N,^[11] about 1/50,000,000 of the weight of the small balls^[12] or roughly the weight of a large grain of sand.^[13] 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).^[14] 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.^[15]

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.^[16]

[edit] Did Cavendish determine G?

The formulation of Newtonian gravity in terms of a gravitational constant did not become standard until long after Cavendish's time. Indeed, one of the first references to G is in 1873, 75 years after Cavendish's work.^[17] Cavendish expressed his result in terms of the density of the Earth, and he referred to his experiment in correspondence as 'weighing the world'. Later authors reformulated his results in modern terms.^[18][19][20] thus:

Failed to parse (Missing texvc executable; please see math/README to configure.): G = g\frac{R_\text{earth}^2}{M_\text{earth}} = \frac{3g}{4\pi R_\text{earth}\rho_\text{earth}}\,

After converting to SI units, Cavendish's value for the Earth's density, 5.448 g cm⁻³, gives

G = 6.74 × 10⁻¹¹ m³ kg⁻¹ s⁻²,

which differs by only 1% from the currently accepted value: 6.67428 × 10⁻¹¹ m³ kg⁻¹ s⁻².

For this reason, historians of science have argued that Cavendish did not measure the gravitational constant.^{[21][22][23][24]}

Physicists, however, often use units where the gravitational constant takes a different form. The Gaussian gravitational constant used in space dynamics is a defined constant, and the Cavendish experiment can be considered as a measurement of the astronomical unit. In Cavendish's time, physicists used the same units for mass and weight, in effect taking Failed to parse (Missing texvc executable; please see math/README to configure.): g

as a standard acceleration.   Then, since Failed to parse (Missing texvc executable; please see math/README to configure.): R_\text{earth}
was known, Failed to parse (Missing texvc executable; please see math/README to configure.): \rho_\text{earth}
played the role of an inverse gravitational constant.  The density of the Earth was hence a much sought-after quantity at the time, and there had been earlier attempts to measure it, such as the Schiehallion experiment in 1774.

For these reasons, physicists generally do credit Cavendish with the first measurement of the gravitational constant.^{[25][26][27][28][29]}

Derivation of G and the Earth's mass[link]

For the definitions of terms, see the drawing below and the table at the end of this section.

The following is not the method Cavendish used, but shows how modern physicists would use his results.^[30][31][32] From Hooke's law, the torque on the torsion wire is proportional to the deflection angle Failed to parse (Missing texvc executable; please see math/README to configure.): \theta of the balance. The torque is Failed to parse (Missing texvc executable; please see math/README to configure.): \kappa\theta where Failed to parse (Missing texvc executable; please see math/README to configure.): \kappa is the torsion coefficient of the wire. However, the torque can also be written as a product of the attractive forces between the balls and the distance to the suspension wire. Since there are two pairs of balls, each experiencing force F at a distance L / 2 from the axis of the balance, the torque is LF. Equating the two formulas for torque gives the following:

Failed to parse (Missing texvc executable; please see math/README to configure.): \kappa\theta\ = LF \,

For F, Newton's law of universal gravitation is used to express the attractive force between the large and small balls:

Diagram of torsion balance

Failed to parse (Missing texvc executable; please see math/README to configure.): F = \frac{G m M}{r^2}\,

Substituting F into the first equation above gives

Failed to parse (Missing texvc executable; please see math/README to configure.): \kappa\theta\ = L\frac{GmM}{r^2} \qquad\qquad\qquad(1)\,

To find the torsion coefficient (Failed to parse (Missing texvc executable; please see math/README to configure.): \kappa\, ) of the wire, Cavendish measured the natural resonant oscillation period T of the torsion balance:

Failed to parse (Missing texvc executable; please see math/README to configure.): T = 2\pi\sqrt{I/\kappa}

Assuming the mass of the torsion beam itself is negligible, the moment of inertia of the balance is just due to the small balls:

Failed to parse (Missing texvc executable; please see math/README to configure.): I = m(L/2)^2 + m(L/2)^2 = 2m(L/2)^2 = mL^2/2\,

,

and so:

Failed to parse (Missing texvc executable; please see math/README to configure.): T = 2\pi\sqrt{\frac{mL^2}{2\kappa}}\,

Solving this for Failed to parse (Missing texvc executable; please see math/README to configure.): \kappa , substituting into (1), and rearranging for G, the result is:

Failed to parse (Missing texvc executable; please see math/README to configure.): G = \frac{2 \pi^2 L r^2}{M T^2} \theta\,

Once G has been found, the attraction of an object at the Earth's surface to the Earth itself can be used to calculate the Earth's mass and density:

Failed to parse (Missing texvc executable; please see math/README to configure.): mg = \frac{GmM_{earth}}{R_{earth}^2}\,

Failed to parse (Missing texvc executable; please see math/README to configure.): M_{earth} = \frac{gR_{earth}^2}{G}\,

Failed to parse (Missing texvc executable; please see math/README to configure.): \rho_{earth} = \frac{M_{earth}}{4 \pi R_{earth}^3/3} = \frac{3g}{4 \pi R_{earth} G}\,

See also[link]

Physics portal

• Schiehallion experiment

References[link]

• Boys, C. Vernon (1894). "On the Newtonian constant of gravitation". Nature 50 (1292): 330–4. Bibcode 1894Natur..50..330.. DOI:10.1038/050330a0. http://books.google.com/?id=ZrloHemOmUEC&pg=PA353. 
• Cavendish, Henry (1798). "Experiments to Determine the Density of the Earth". In MacKenzie, A. S.. Scientific Memoirs Vol.9: The Laws of Gravitation. American Book Co.. 1900. pp. 59–105. http://books.google.com/?id=O58mAAAAMAAJ&pg=PA59  Online copy of Cavendish's 1798 paper, and other early measurements of gravitational constant.
• Clotfelter, B. E. (1987). "The Cavendish experiment as Cavendish knew it". American Journal of Physics 55 (3): 210–213. Bibcode 1987AmJPh..55..210C. DOI:10.1119/1.15214.  Establishes that Cavendish didn't determine G.
• Falconer, Isobel (1999). "Henry Cavendish: the man and the measurement". Measurement Science and Technology 10 (6): 470–477. Bibcode 1999MeScT..10..470F. DOI:10.1088/0957-0233/10/6/310. 
• "Gravitation Constant and Mean Density of the Earth". Encyclopædia Britannica, 11th Ed.. 12. The Encyclopædia Britannica Co.. 1910. pp. 385–389. http://books.google.com/books?id=DgTALFa3sa4C&pg=PA385. 
• Hodges, Laurent (1999). "The Michell-Cavendish Experiment, faculty website, Iowa State Univ.". http://www.public.iastate.edu/~lhodges/Michell.htm. Retrieved 2007-08-28.  Discusses Michell's contributions, and whether Cavendish determined G.
• Lally, Sean P. (1999). "Henry Cavendish and the Density of the Earth". The Physics Teacher 37 (1): 34–37. Bibcode 1999PhTea..37...34L. DOI:10.1119/1.880145. 
• McCormmach, Russell; Jungnickel, Christa (1996). Cavendish. Philadelphia, Pennsylvania: American Philosophical Society. ISBN 0-87169-220-1. http://books.google.com/?id=EUoLAAAAIAAJ. 
• Poynting, John H. (1894). The Mean Density of the Earth: An essay to which the Adams prize was adjudged in 1893. London: C. Griffin & Co.. http://books.google.com/?id=dg0RAAAAIAAJ.  Review of gravity measurements since 1740.
•  This article incorporates text from a publication now in the public domain: Chisholm, Hugh, ed. (1911). Encyclopædia Britannica (11th ed.). Cambridge University Press. 

Notes[link]

External links[link]

• Sideways Gravity in the Basement, The Citizen Scientist, July 1, 2005, retrieved Aug. 9, 2007. Homebrew Cavendish experiment, showing calculation of results and precautions necessary to eliminate wind and electrostatic errors.
• Measuring Big G, Physics Central, retrieved Aug. 9, 2007. Recent experiment at Univ. of Washington to measure the gravitational constant using variation of Cavendish method.
• The Controversy over Newton's Gravitational Constant, Eöt-Wash Group, Univ. of Washington, retrieved Aug. 9, 2007. Discusses current state of measurements of G.
• Model of Cavendish's torsion balance, retrieved Aug. 28, 2007, at Science Museum, London.
• Weighing the Earth - background and experiment

Henry Cavendish
Henry Cavendish
Born	(1731-10-10)10 October 1731 Nice, France
Died	24 February 1810(1810-02-24) (aged 78) London, England
Nationality	United Kingdom
Fields	Chemistry, physics
Alma mater	University of Cambridge
Known for	Discovery of hydrogen Measured the Earth's density

Henry Cavendish FRS (10 October 1731 – 24 February 1810) was a British scientist noted for his discovery of hydrogen or what he called "inflammable air".^[1] He described the density of inflammable air, which formed water on combustion, in a 1766 paper "On Factitious Airs". Antoine Lavoisier later reproduced Cavendish's experiment and gave the element its name. Cavendish is also known for the Cavendish experiment, his measurement of the Earth's density, and early research into electricity.

Biography[link]

Henry Cavendish was born on 10 October 1731 in Nice, France, where his family was living at the time. His mother was Lady Anne Grey, daughter of Henry Grey, 1st Duke of Kent and his father was Lord Charles Cavendish, son of William Cavendish, 2nd Duke of Devonshire. The family traces its lineage across eight centuries to Norman times and was closely connected to many aristocratic families of Great Britain.

At age 11, Cavendish was a pupil at Peter Newcome's School in Hackney. At age 18 (on 24 November 1749) he entered the University of Cambridge in St Peter's College, now known as Peterhouse, but left four years later on 23 February 1753 without graduating.^[2][3] His first paper, "Factitious Airs", appeared thirteen years later, in 1766.

Cavendish was silent and solitary, and was viewed as somewhat eccentric by many. He only communicated with his female servants by notes and formed no close personal relationships outside his family. By one account, Cavendish had a back staircase added to his house in order to avoid encountering his housekeeper because he was especially shy of women. The contemporary accounts of his personality have led some modern commentators, such as Oliver Sacks, to speculate that he had Asperger syndrome, though he may merely have been painfully shy. His only social outlet was the Royal Society Club, whose members dined together before weekly meetings. Cavendish seldom missed these meetings, and was profoundly respected by his contemporaries. However his shyness made those who "sought his views... speak as if into vacancy. If their remarks were...worthy, they might receive a mumbled reply, but more often than not they would hear a peeved squeak (his voice appears to have been high-pitched) and turn to find an actual vacancy and the sight of Cavendish fleeing to find a more peaceful corner"^[4] He also enjoyed collecting fine furniture exemplified by his purchase of a set of "ten inlaid satinwood chairs with matching cabriole legged sofa".^[5]

Because of his asocial and secretive behaviour, Cavendish often avoided publishing his work, and much of his findings were not even told to his fellow scientists. In the late nineteenth century, long after his death, James Clerk Maxwell looked through Cavendish's papers and found things for which others had been given credit. Examples of what was included in Cavendish's discoveries or anticipations were Richter's Law of Reciprocal Proportions, Ohm's Law, Dalton's Law of Partial Pressures, principles of electrical conductivity (including Coulomb's Law), and Charles's Law of Gases.

A manuscript "Heat", tentatively dated between 1783 and 1790, describes a "mechanical theory of heat". Hitherto unknown, the manuscript was analyzed in the early 21st century. Historian of science Russell McCormmach proposed that "Heat" is the only 18th century work prefiguring thermodynamics. Theoretical physicist Dietrich Belitz concluded that in this work Cavendish "got the nature of heat essentially right."^[6]

Cavendish died in 1810 (as one of the wealthiest men in Britain) and was buried, along with many of his ancestors, in the church that is now Derby Cathedral and the road he used to live on in Derby has been named after him. The University of Cambridge's Cavendish Laboratory was endowed by one of Cavendish's later relatives, William Cavendish, 7th Duke of Devonshire (Chancellor of the University from 1861 to 1891).

Gases and the atmosphere[link]

Cavendish's apparatus for making and collecting hydrogen^[1]

Cavendish is considered to be one of the so-called pneumatic chemists of the eighteenth and nineteenth centuries, along with, for example, Joseph Priestley, Joseph Black, and Daniel Rutherford. By combining metals with strong acids, Cavendish made hydrogen (H₂) gas, which he isolated and studied. Although others, such as Robert Boyle, had prepared hydrogen gas earlier, Cavendish is usually given the credit for recognizing its elemental nature.

Cavendish observed that hydrogen, which he called "inflammable air", reacts with oxygen, then known as "dephlogisticated air", to form water. James Watt and Antoine Lavoisier made a similar observation, resulting in a controversy as to who should receive credit for it. Cavendish however resisted Lavoisier's theory of chemical compounds, and attempted to explain his experiment in terms of phlogiston.^[7][8]

Cavendish also accurately determined the composition of Earth's atmosphere. In a 1785 paper, he described experiments in which hydrogen and ordinary air were combined in known ratios, and then exploded with a spark of electricity. In each case, Cavendish observed both the formation of water and that the gas volume after the explosion was always less than it was before it. By careful measurements he was led to conclude that, "common air consists of one part of dephlogisticated air [oxygen], mixed with four of phlogisticated [nitrogen]".^[9][10]

The same paper described an experiment in which Cavendish was able to remove, in modern terminology, both the oxygen and nitrogen gases from a sample of atmospheric air until only a small bubble of unreacted gas was left in the original sample. From this experiment Cavendish concluded that not more than 1/120 of the Earth's atmosphere was other than oxygen and nitrogen.^[11] Although a seemingly small fraction, about 100 years later William Ramsay and Lord Rayleigh showed that this residual gas contained argon, an element that was unknown at the time.

Density of the Earth[link]

In addition to his achievements in chemistry, Cavendish is also known for the Cavendish experiment, the first to measure the force of gravity between masses in a laboratory and to produce an accurate value for Earth's density. His work led others to accurate values for the gravitational constant (G) and Earth's mass. Based on his results, one can calculate a value for G of 6.754 × 10⁻¹¹N-m²/kg²,^[12] which compares favourably with the modern value of 6.67428 × 10⁻¹¹N-m²/kg².^[13]

The equipment Cavendish used was designed and built by geologist John Michell, who died before he could begin the experiment. The apparatus was sent in crates to Cavendish, who completed the experiment in 1797 – 1798,^[4] and published the results.^[14] Cavendish noticed that Michell's apparatus would be sensitive to temperature differences and induced air currents so he made modifications by isolating the apparatus in a separate room with external controls and telescopes for making observations.^[15]

The experimental apparatus consisted of a torsion balance to measure the gravitational attraction between two 350-pound lead spheres and a pair of 2-inch 1.61-pound lead spheres.^[4] Using this equipment, Cavendish found that the Earth's average density is 5.48 times greater than that of water. John Henry Poynting later noted that the data should have led to a value of 5.448,^[16] and indeed that is the average value of the twenty-nine determinations Cavendish included in his paper.^[17]

Books often describe Cavendish's work as a measurement either of the gravitational constant (G), or of the Earth's mass. Since these are related to the Earth's density by a trivial web of algebraic relations, none of these sources are wrong, but they do not match the exact word choice of Cavendish,^[18][19] and this mistake has been pointed out by several authors.^[20][21] Cavendish's stated goal was to measure the Earth's density, although his result obviously calculates G in order to do so.

The first time that the constant got this name was in 1873, almost 100 years after the Cavendish experiment, but the constant was in use since the time of Newton.^[22] Cavendish's results obviously also give the Earth’s mass.

Cavendish performed his experiment in an outbuilding in the garden of his Clapham Common estate. For years afterward, his neighbours would point out the building and tell their children that it was where the world was weighed.^[5]

Electrical research[link]

Cavendish wrote papers on electrical topics for the Royal Society^[23][24] but the bulk of his electrical experiments did not become known until they were collected and published by James Clerk Maxwell a century later, in 1879, long after other scientists had been credited with the same results. According to the 1911 edition of Encyclopædia Britannica, among Cavendish's discoveries were the following:^[25]

• The concept of electric potential, which he called the "degree of electrification"
• An early unit of capacitance, that of a sphere one inch in diameter
• The formula for the capacitance of a plate capacitor
• The concept of the dielectric constant of a material
• The relationship between electric potential and current, now called Ohm's Law. (1781)
• Laws for the division of current in parallel circuits, now attributed to Charles Wheatstone
• Inverse square law of variation of electric force with distance, now called Coulomb's Law^[26]

Selected writings[link]

• Cavendish, Henry (1921). Scientific Papers. 1. Cambridge: Cambridge University Press. http://www.archive.org/details/scientificpapers01caveuoft.  - edited by James Clerk Maxwell and revised by Joseph Larmor
• Cavendish, Henry (1921). Scientific Papers. 2. Cambridge: Cambridge University Press. http://www.archive.org/details/scientificpaper00cavegoog.  - edited by James Clerk Maxwell and revised by Joseph Larmor
• Cavendish, Henry (1879). The Electrical Researches of the Honourable Henry Cavendish. Cambridge: Cambridge University Press. http://books.google.com/?id=3gYJAAAAIAAJ&pg=PR24&dq=cavendish+henry#PPR3,M1.  - edited by James Clerk Maxwell

See also[link]

• Timeline of hydrogen technologies

Notes and references[link]

Further reading[link]

• Cavendish, Christa Jungnickel and Russell McCormmach, American Philosophical Society, 1996, ISBN 0-87169-220-1, 414 pp.
• Cavendish: The Experimental Life, Christa Jungnickel and Russell McCormmach, Bucknell University Press, 1999, ISBN 0-8387-5445-7, 814 pp.

External links[link]

Wikiquote has a collection of quotations related to: Henry Cavendish

• The Life of the Honourable Henry Cavendish by George Wilson, London, 1851.
• Experiments on Air by Henry Cavendish, Edinburgh: William F. Clay (1893) - Alembic Club reprint number 3.
• "The Mean Density of the Earth" by J. H. Poynting, London: Charles Griffin and Company (1894).
• The Laws of Gravitation: Memoirs by Newton, Bouguer and Cavendish, edited and translated by A. Stanley MacKenzie, New York: American Book Company (1900).
•  Chisholm, Hugh, ed. (1911). "Cavendish, Henry". Encyclopædia Britannica (11th ed.). Cambridge University Press.