Editing Gravitational constant (section)

=== 19th century ===
The accuracy of the measured value of {{math|''G''}} has increased only modestly since the original Cavendish experiment.<ref>
{{cite book|last1=Brush |first1=Stephen G. |last2=Holton |first2=Gerald James |title=Physics, the human adventure: from Copernicus to Einstein and beyond |url=https://archive.org/details/physicshumanadve00ghol |url-access=limited |publisher=Rutgers University Press |location=New Brunswick, NJ |date=2001 |pages= [https://archive.org/details/physicshumanadve00ghol/page/n151 137] |isbn=978-0-8135-2908-0 }}
{{cite journal |first=Jennifer Lauren |last=Lee |title=Big G Redux: Solving the Mystery of a Perplexing Result |date=16 November 2016 |journal=NIST |url=https://www.nist.gov/news-events/news/2016/11/big-g-redux-solving-mystery-perplexing-result}}</ref> {{math|''G''}} is quite difficult to measure because gravity is much weaker than other fundamental forces, and an experimental apparatus cannot be separated from the gravitational influence of other bodies.

Measurements with pendulums were made by [[Francesco Carlini]] (1821, {{val|4.39|u=g/cm3}}), [[Edward Sabine]] (1827, {{val|4.77|u=g/cm3}}), Carlo Ignazio Giulio (1841, {{val|4.95|u=g/cm3}}) and [[George Biddell Airy]] (1854, {{val|6.6|u=g/cm3}}).<ref>{{cite book | last = Poynting | first = John Henry | title = The Mean Density of the Earth | publisher = Charles Griffin | date = 1894 | location = London | pages = [https://archive.org/details/meandensityeart00poyngoog/page/n44 22]–24 | url = https://archive.org/details/meandensityeart00poyngoog }}</ref>

Cavendish's experiment was first repeated by [[Ferdinand Reich]] (1838, 1842, 1853), who found a value of {{val|5.5832|(149)|u=g.cm-3}},<ref>F. Reich, "On the Repetition of the Cavendish Experiments for Determining the mean density of the Earth, ''Philosophical Magazine''  12: 283–284.</ref> which is actually worse than Cavendish's result, differing from the modern value by 1.5%. Cornu and Baille (1873), found {{val|5.56|u=g.cm-3}}.<ref>Mackenzie (1899), p. 125.</ref>

Cavendish's experiment proved to result in more reliable measurements than pendulum experiments of the "Schiehallion" (deflection) type or "Peruvian" (period as a function of altitude) type. Pendulum experiments still continued to be performed, by [[Robert von Sterneck]] (1883, results between {{val|5.0|and|6.3|u=g/cm3}}) and [[Thomas Corwin Mendenhall]] (1880, {{val|5.77|u=g/cm3}}).<ref>A.S. Mackenzie, ''The Laws of Gravitation'' (1899), [https://archive.org/stream/lawsgravitation01newtgoog#page/n140/mode/2up 127f.]</ref>

Cavendish's result was first improved upon by [[John Henry Poynting]] (1891),<ref>{{cite book |url=https://archive.org/details/meandensityofear00poynuoft |title=The mean density of the earth |last=Poynting |first=John Henry |date=1894 |publisher=London |others=Gerstein - University of Toronto }}</ref> who published a value of {{val|5.49|(3)|u=g.cm-3}}, differing from the modern value by 0.2%, but compatible with the modern value within the cited relative standard uncertainty of 0.55%. In addition to Poynting, measurements were made by [[C. V. Boys]] (1895)<ref>{{cite journal | last=Boys | first=C. V. | title=On the Newtonian Constant of Gravitation | journal=Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences | publisher=The Royal Society | volume=186 | date=1895-01-01 | issn=1364-503X | doi=10.1098/rsta.1895.0001 | bibcode=1895RSPTA.186....1B | pages=1–72| doi-access=free }}</ref> and [[Carl Braun (astronomer)|Carl Braun]]<!--[[:de:Carl Braun (Astronom)]]--> (1897),<ref>Carl Braun, ''Denkschriften der k. Akad. d. Wiss. (Wien), math. u. naturwiss. Classe'', 64 (1897).
Braun (1897) quoted an optimistic relative standard uncertainty of 0.03%, {{val|6.649|(2)|e=−11|u=m<sup>3</sup>⋅kg<sup>−1</sup>⋅s<sup>−2</sup>}} but his result was significantly worse than the 0.2% feasible at the time.</ref> with compatible results suggesting {{math|''G''}} = {{val|6.66|(1)|e=−11|u=m<sup>3</sup>⋅kg<sup>−1</sup>⋅s<sup>−2</sup>}}. The modern notation involving the constant {{math|''G''}} was introduced by Boys in 1894<ref name=BoysG/> and becomes standard by the end of the 1890s, with values usually cited in the [[cgs]] system. Richarz and Krigar-Menzel (1898) attempted a repetition of the Cavendish experiment using 100,000&nbsp;kg of lead for the attracting mass. The precision of their result of {{val|6.683|(11)|e=-11|u=m<sup>3</sup>⋅kg<sup>−1</sup>⋅s<sup>−2</sup>}} was, however, of the same order of magnitude as the other results at the time.<ref name=Sagitov>Sagitov, M. U., "Current Status of Determinations of the Gravitational Constant and the Mass of the Earth", Soviet Astronomy, Vol. 13 (1970), 712–718, translated from ''Astronomicheskii Zhurnal'' Vol. 46, No. 4 (July–August 1969), 907–915 (table of historical experiments p. 715).</ref>

[[Arthur Stanley Mackenzie]] in ''The Laws of Gravitation'' (1899) reviews the work done in the 19th century.<ref>Mackenzie, A. Stanley, ''[https://archive.org/stream/lawsgravitation01newtgoog#page/n6/mode/2up The laws of gravitation; memoirs by Newton, Bouguer and Cavendish, together with abstracts of other important memoirs]'', American Book Company (1900 [1899]).</ref> Poynting is the author of the article "Gravitation" in the [[Encyclopædia Britannica Eleventh Edition|''Encyclopædia Britannica'' Eleventh Edition]] (1911). Here, he cites a value of {{math|''G''}} = {{val|6.66|e=−11|u=m<sup>3</sup>⋅kg<sup>−1</sup>⋅s<sup>−2</sup>}} with a relative uncertainty of 0.2%.