Editing Cavendish experiment (section)

==The experiment==
The apparatus consisted of a [[torsion balance]] made of a {{convert|6|ft|spell=in|adj=on}} wooden rod horizontally suspended from a wire, with two {{convert|2|in|0|adj=mid|-diameter}}, {{convert|1.61|lb|adj=on}} [[lead]] spheres, one attached to each end. Two massive {{convert|12|in|adj=on}}, {{convert|348|lb|adj=on}} lead balls, suspended separately, could be positioned away from or to either side of the smaller balls, {{convert|8.85|in}} away.<ref>[https://books.google.com/books?id=O58mAAAAMAAJ&pg=PA59 Cavendish 1798], p. 59</ref> 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).
[[File:Cavendish Experiment.png|thumb|left|250px|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 by a pulley from outside. Figure 1 of Cavendish's paper]]
[[File:CavendishSchematic111.jpg|thumb|left|250px|Detail showing torsion balance arm (''m''), large ball (''W''), small ball (''x''), and isolating box (''ABCDE'').]]

The two large balls could be positioned either away from or to either side of the torsion balance rod. Their mutual attraction to the small balls caused the arm to rotate, twisting the suspension wire. 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. 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 [[relative density]] of the Earth to be calculated, using [[Newton's law of universal gravitation|Newton's law of gravitation]].

Cavendish found that the Earth's density was {{val|5.448|0.033}} times that of water (although due to a simple [[arithmetic]] error, found in 1821 by [[Francis Baily]], the erroneous value {{val|5.480|0.038}} appears in his paper).<ref name="Poynting 1894">[https://books.google.com/books?id=dg0RAAAAIAAJ&pg=PA45 Poynting 1894], p. 45</ref><ref>{{Cite EB1911 |wstitle=Cavendish, Henry |volume=5 |pages=580–581}}</ref> The current accepted value is 5.514 g/cm<sup>3</sup>.

To find the wire's [[Torsion spring#Torsion coefficient|torsion coefficient]], the torque exerted by the wire for a given angle of twist, Cavendish timed the natural [[Torsion spring#Torsional harmonic oscillators|oscillation period]] of the balance rod as it rotated slowly clockwise and counterclockwise against the twisting of the 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. The period changed because after the third experiment Cavendish put in a stiffer wire. 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.<ref>[https://books.google.com/books?id=O58mAAAAMAAJ&pg=PA64 Cavendish 1798], p. 64</ref>

Cavendish's equipment was remarkably sensitive for its time.<ref name="Poynting 1894"/> The force involved in twisting the torsion balance was very small, {{val|1.74e-7|u=N}},<ref>[https://books.google.com/books?id=ZrloHemOmUEC&pg=PA357 Boys 1894] p. 357</ref> (the weight of only 0.0177 milligrams) or about {{frac|50,000,000}} of the weight of the small balls.<ref>[https://books.google.com/books?id=O58mAAAAMAAJ&pg=PA60 Cavendish 1798] p. 60</ref> 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&nbsp;cm thick,[http://cavendish-deneyi.com/pdf/Cavendish-c%CC%A7izim-03.pdf] 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 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).<ref>[https://books.google.com/books?id=O58mAAAAMAAJ&pg=PA99 Cavendish 1798], p. 99, Result table, (scale graduations = {{frac|20}}&nbsp;in ≈ 1.3&nbsp;mm) The total deflection shown in most trials was twice this since he compared the deflection with large balls on opposite sides of the balance beam.</ref> Cavendish was able to measure this small deflection to an accuracy of better than {{convert|0.01|in}} using [[vernier scale]]s on the ends of the rod.<ref>[https://books.google.com/books?id=O58mAAAAMAAJ&pg=PA63 Cavendish 1798], p. 63</ref>
The accuracy of Cavendish's result was not exceeded until [[C. V. Boys]]' 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.<ref>[https://books.google.com/books?id=EUoLAAAAIAAJ&pg=PA341 Jungnickel & McCormmach 1996], p. 341</ref>

Cavendish's result provided additional evidence for a [[outer core|planetary core]] made of metal, an idea first proposed by [[Charles Hutton]] based on his analysis of the 1774 [[Schiehallion experiment]].<ref name="Danson_p153-154">{{Cite book|last=Danson|first=Edwin |title=Weighing the World |publisher=Oxford University Press|date=2006|pages=153–154|isbn=978-0-19-518169-2|url=https://books.google.com/books?id=UNH_Y7ERFeoC&pg=PA153}}</ref> Cavendish's result of 5.4 g·cm<sup>&minus;3</sup>, 23% bigger than Hutton's, is close to 80% of the density of liquid [[iron]], and 80% higher than the density of the Earth's outer [[Crust (geology)|crust]], suggesting the existence of a dense iron core.<ref>see e.g. Hrvoje Tkalčić, ''The Earth's Inner Core'', Cambridge University Press (2017), [https://books.google.com/books?id=wa7DDQAAQBAJ&pg=PA2 p. 2].</ref>