Editing Henry Cavendish (section)

==Density of the Earth==
{{Main|Cavendish experiment}}

Following his father's death, Henry bought another house in town and also a house in [[Clapham Common]] (built by [[Thomas Cubitt]]), at that time to the south-west of London.<ref>{{cite web |url=https://www.europeana.eu/portal/en/record/2022321/DA848BBA9165D8B05B218432F43A8BE2F78E15B8.html |title=Cavendish House, Clapham Common South Side |author=Lambeth Libraries |access-date=11 April 2019 |work=[[Europeana Collections 1914-1918]] |publisher=[[Connecting Europe Facility]] |agency=[[European Union]]}}</ref> The London house contained the bulk of his library, while he kept most of his instruments at Clapham Common, where he carried out most of his experiments. The most famous of those experiments, published in 1798, was to determine the density of the Earth and became known as the [[Cavendish experiment]]. The apparatus Cavendish used for weighing the Earth was a modification of the [[Torsion spring#Torsion balance|torsion balance]] 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<ref name="Bryson" /> and published the results.<ref>{{cite journal |last=Cavendish |first=Henry |year=1798 |title=Experiments to Determine the Density of Earth |journal=Philosophical Transactions of the Royal Society |volume=88 |pages=469–526 |doi=10.1098/rstl.1798.0022 |jstor=106988|doi-access=free }}</ref>

The experimental apparatus consisted of a torsion balance with a pair of 2-inch 1.61-pound lead spheres suspended from the arm of a torsion balance and two much larger stationary lead balls (350 pounds). Cavendish intended to measure the force of [[gravitation]]al attraction between the two.<ref name="Bryson" /> He 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.<ref>{{cite book |last=Magie |first=William Francis |title=A Source Book in Physics |date=1 January 1935 |url=https://archive.org/details/sourcebookphysic00magi |url-access=limited |publisher=[[Harvard University Press]] |location=Cambridge, MA |page=[https://archive.org/details/sourcebookphysic00magi/page/n120 107]|isbn=9780674823655 }}</ref>

Using this equipment, Cavendish calculated the attraction between the balls from the period of oscillation of the torsion balance, and then he used this value to calculate the density of the Earth. 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,<ref>Poynting, J. H. (1894), "The Mean Density of the Earth" London: Charles Griffin and Company, page 45.</ref> and indeed that is the average value of the twenty-nine determinations Cavendish included in his paper.<ref>Cavendish, Henry, "Experiments to Determine the Density of the Earth", reprinted in ''A Source Book in Geology'', K. F. Mather and S. L. Mason, editors, New York: McGraw-Hill (1939), pp. 103–107.</ref> The error in the published number was due to a simple [[arithmetic|arithmetical]] mistake on his part.<ref>{{Cite EB1911|wstitle= Cavendish, Henry |volume= 05 | pages = 580&ndash;581; see page 581, five lines from end |quote= The figure he gives for the specific gravity of the earth is 5.48, water being 1, but in fact the mean of the 29 results he records works out at 5.448}}</ref> What was extraordinary about Cavendish's experiment was its elimination of every source of error and every factor that could disturb the experiment, and its precision in measuring an astonishingly small attraction, a mere 1/50,000,000 of the weight of the lead balls. The result that Cavendish obtained for the density of the Earth is within 1 per cent of the currently accepted figure.

Cavendish's 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<sup>−11</sup>N-m<sup>2</sup>/kg<sup>2</sup>,<ref>{{cite book |author1=Brush, Stephen G. |author2=Holton, Gerald James |title=Physics, the human adventure: from Copernicus to Einstein and beyond |url=https://archive.org/details/physicshumanadve00holt |url-access=limited |publisher=[[Rutgers University Press]] |location=New Brunswick, NJ |year=2001 |pages=[https://archive.org/details/physicshumanadve00holt/page/n151 137] |isbn=0-8135-2908-5 }}</ref> which compares favourably with the modern value of 6.67428 × 10<sup>−11</sup>N-m<sup>2</sup>/kg<sup>2</sup>.<ref>[http://www.physics.nist.gov/cgi-bin/cuu/Value?bg CODATA Value: Newtonian constant of gravitation<!-- Bot generated title -->]</ref>

Books often describe Cavendish's work as a measurement of either ''G'' or 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,<ref>Tipler, P. A. and Mosca, G. (2003), ''Physics for Scientists and Engineers: Extended Version'', W. H. Freeman {{ISBN|0-7167-4389-2}}.</ref><ref>Feynman, R. P. (1970), ''Feynman Lectures on Physics'', Addison Wesley Longman, {{ISBN|0-201-02115-3}}</ref> and this mistake has been pointed out by several authors.<ref>{{cite journal |last1=Clotfelter |first1=B.E. |year = 1987 |title=The Cavendish Experiment as Cavendish Knew It |journal=American Journal of Physics |volume=55 |issue = 3 |pages=210–213 |doi=10.1119/1.15214 |bibcode=1987AmJPh..55..210C}}</ref><ref>{{cite journal |last1=Falconer |first1=I. |year=1999 |title=Henry Cavendish: the man and the measurement |journal=Measurement Science and Technology |volume=10 |issue=6 |pages=470–477 |doi=10.1088/0957-0233/10/6/310 |bibcode = 1999MeScT..10..470F|s2cid=250862938 }}</ref> Cavendish's stated goal was to measure the Earth's density.

The first time that the constant got this name was in 1873, almost 100 years after the Cavendish experiment.<ref>Cornu, A. and Baille, J. B. (1873), Mutual determination of the constant of attraction and the mean density of the earth, ''C. R. Acad. Sci.'', Paris Vol. 76, 954–958.</ref> Cavendish's results also give [[Cavendish experiment|the Earth's mass]].