Editing Virial theorem (section)

== History ==
In 1870, [[Rudolf Clausius]] delivered the lecture "On a Mechanical Theorem Applicable to Heat" to the Association for Natural and Medical Sciences of the Lower Rhine, following a 20-year study of thermodynamics. The lecture stated that the mean [[vis viva]] of the system is equal to its virial, or that the average kinetic energy is one half of the average potential energy. The virial theorem can be obtained directly from [[Lagrange's identity]]{{Moved resource|date=December 2023}} as applied in classical gravitational dynamics, the original form of which was included in Lagrange's "Essay on the Problem of Three Bodies" published in 1772. [[Carl Gustav Jacob Jacobi|Carl Jacobi's]] generalization of the identity to ''N''&nbsp;bodies and to the present form of Laplace's identity closely resembles the classical virial theorem. However, the interpretations leading to the development of the equations were very different, since at the time of development, statistical dynamics had not yet unified the separate studies of thermodynamics and classical dynamics.<ref>{{Cite book |last=Collins |first=G. W. |year=1978 |title=The Virial Theorem in Stellar Astrophysics |publisher=Pachart Press |url=http://ads.harvard.edu/books/1978vtsa.book/ |bibcode=1978vtsa.book.....C |isbn=978-0-912918-13-6 |chapter=Introduction}}</ref> The theorem was later utilized, popularized, generalized and further developed by [[James Clerk Maxwell]], [[John Strutt, 3rd Baron Rayleigh|Lord Rayleigh]], [[Henri Poincaré]], [[Subrahmanyan Chandrasekhar]], [[Enrico Fermi]], [[Paul Ledoux]], [[Richard Bader]] and [[Eugene Parker]]. [[Fritz Zwicky]] was the first to use the virial theorem to deduce the existence of unseen matter, which is now called [[dark matter]]. [[Richard Bader]] showed that the charge distribution of a total system can be partitioned into its kinetic and potential energies that obey the virial theorem.<ref name=rfwbpmb1972>{{cite journal |author1-last=Bader |author1-first=R. F. W. |author1-link=Richard Bader |author2-last=Beddall |author2-first=P. M. |title=Virial Field Relationship for Molecular Charge Distributions and the Spatial Partitioning of Molecular Properties | journal=The Journal of Chemical Physics |volume=56 |issue=7 |url=https://aip.scitation.org/doi/pdf/10.1063/1.1677699 |year=1972 |pages=3320–3329 |doi=10.1063/1.1677699 |bibcode=1972JChPh..56.3320B}}</ref> As another example of its many applications, the virial theorem has been used to derive the [[Chandrasekhar limit]] for the stability of [[white dwarf]] [[star]]s.