Editing Boyle's law (section)

==History==
{{main article|History of thermodynamics}}
[[File:Boyles Law.svg|thumb|Graph of Boyle's original data<ref>{{cite book | page=60 | url=https://bvpb.mcu.es/en/catalogo_imagenes/grupo.do?path=11143411 | title=A Defence Of the Doctrine touching the Spring and Weight Of the Air | author=Robert Boyle | year=1662}}</ref> showing the [[Hyperbola#Hyperbola with equation y = A/x|hyperbolic curve]] of the relationship between pressure ({{mvar|P}}) and volume ({{mvar|V}}) of the form {{mvar|1=P = k/V}}. ]] 
The relationship between pressure and volume was first noted by [[Richard Towneley]] and [[Henry Power]] in the 17th century.<ref>See:
*  Henry Power, ''Experimental Philosophy, in Three Books'' (London:  Printed by T. Roycroft for John Martin and James Allestry, 1663), pp. 126–130.  Available online at  [https://quod.lib.umich.edu/e/eebo/a55584.0001.001/155?page=root;size=125;view=text Early English Books Online]. On page 130, Power presents (not very clearly) the relation between the pressure and the volume of a given quantity of air: "That the measure of the Mercurial Standard, and Mercurial Complement, are measured onely by their perpendicular heights, over the Surface of the restagnant Quicksilver in the Vessel: But Ayr, the Ayr's Dilatation, and Ayr Dilated, by the Spaces they fill. So that here is now four Proportionals, and by any three given, you may strike out the fourth, by Conversion, Transposition, and Division of them. So that by these Analogies you may prognosticate the effects, which follow in all Mercurial Experiments, and predemonstrate them, by calculation, before the senses give an Experimental [eviction] thereof." In other words, if one knows the volume V<sub>1</sub> ("Ayr") of a given quantity of air at the pressure p<sub>1</sub> ("Mercurial standard", i.e., atmospheric pressure at a low altitude), then one can predict the volume V<sub>2</sub> ("Ayr dilated") of the same quantity of air at the pressure p<sub>2</sub> ("Mercurial complement", i.e., atmospheric pressure at a higher altitude) by means of a proportion (because p<sub>1</sub> V<sub>1</sub> = p<sub>2</sub> V<sub>2</sub>).
* Charles Webster (1965). "The discovery of Boyle's law, and the concept of the elasticity of air in seventeenth century", ''Archive for the History of Exact Sciences'', '''2''' (6): 441–502; see especially pp. 473–477.
*  Charles Webster (1963). "Richard Towneley and Boyle's Law", ''Nature'', '''197''' (4864):  226–228.
*  Robert Boyle acknowledged his debts to Towneley and Power in: R. Boyle, ''A Defence of the Doctrine Touching the Spring and Weight of the Air'' (London, England:  Thomas Robinson, 1662).  Available online at [http://bvpb.mcu.es/en/consulta/registro.cmd?id=406806 {{lang|es|italic=no|La Biblioteca Virtual de Patrimonio Bibliográfico}}]. On pages 50, 55–56, and 64, Boyle cites experiments by Towneley and Power showing that air expands as the ambient pressure decreases. On p. 63, Boyle acknowledges Towneley's help in interpreting Boyle's data from experiments relating the pressure to the volume of a quantity of air. (Also, on p. 64, Boyle acknowledges that [[William Brouncker, 2nd Viscount Brouncker|Lord Brouncker]] had also investigated the same subject.)</ref><ref name="Holton2001">{{cite book|author=Gerald James Holton|title=Physics, the Human Adventure: From Copernicus to Einstein and Beyond|url=https://books.google.com/books?id=czaGZzR0XOUC&pg=PA270|year=2001|publisher=Rutgers University Press|isbn=978-0-8135-2908-0|pages=270–}}</ref> [[Robert Boyle]] confirmed their discovery through experiments and published the results.<ref>R. Boyle, ''A Defence of the Doctrine Touching the Spring and Weight of the Air'' (London: Thomas Robinson, 1662).  Available online at [http://bvpb.mcu.es/en/consulta/registro.cmd?id=406806 {{lang|es|italic=no|Spain's La Biblioteca Virtual de Patrimonio Bibliográfico}}]. Boyle presents his law in "Chap. V. Two new experiments touching the measure of the force of the spring of air compress'd and dilated", pp. 57–68. On p. 59, Boyle concludes that "the same air being brought to a degree of density about twice as that it had before, obtains a spring twice as strong as formerly". That is, doubling the density of a quantity of air doubles its pressure. Since air's density is proportional to its pressure, then for a fixed quantity of air, the product of its pressure and its volume is constant.  On page 60, he presents his data on the compression of air: "A Table of the Condensation of the Air." The legend (p. 60) accompanying the table states: "E. What the pressure should be according to the ''Hypothesis'', that supposes the pressures and expansions to be in reciprocal relation." On p. 64, Boyle presents his data on the expansion of air: "A Table of the Rarefaction of the Air."</ref> According to [[Robert Gunther]] and other authorities, it was Boyle's assistant, [[Robert Hooke]], who built the experimental apparatus.  Boyle's law is based on experiments with [[air]], which he considered to be a fluid of particles at rest in between small invisible springs. Boyle may have begun experimenting with gases due to an interest in air as an essential element of life;<ref>''The Boyle Papers'' [http://www.bbk.ac.uk/boyle/boyle_papers/bp09_docs/bp9_075v-076r.htm BP 9, fol. 75v–76r]. {{webarchive|url=https://web.archive.org/web/20091122203756/http://www.bbk.ac.uk/boyle/boyle_papers/bp09_docs/bp9_075v-076r.htm |date=2009-11-22 }}</ref> for example, he published works on the growth of plants without air.<ref>''The Boyle Papers'', [http://www.bbk.ac.uk/boyle/boyle_papers/bp10_docs/bp10_138v-139r.htm BP 10, fol. 138v–139r]. {{webarchive|url=https://web.archive.org/web/20091122203809/http://www.bbk.ac.uk/boyle/boyle_papers/bp10_docs/bp10_138v-139r.htm |date=2009-11-22 }}</ref> Boyle used a closed J-shaped tube and after pouring [[Mercury (element)|mercury]] from one side he forced the air on the other side to contract under the pressure of mercury. After repeating the [[experiment]] several times and using different amounts of mercury he found that under controlled conditions, the pressure of a gas is inversely proportional to the volume occupied by it.<ref name="scientists">{{cite book |title=Scientists and Inventors of the Renaissance |date=2012 |publisher=Britannica Educational Publishing |pages=94–96 |url=https://books.google.com/books?id=ndubAAAAQBAJ&pg=PA94|isbn=978-1615308842 }}</ref> 

The French [[physicist]] [[Edme Mariotte]] (1620–1684) discovered the same law independently of Boyle in 1679,<ref>See:
*  Mariotte, ''Essais de Physique, ou mémoires pour servir à la science des choses naturelles'' (Paris, France: E. Michallet, 1679); {{lang|fr|italic=no|"Second essai. De la nature de l'air"}}.
* Mariotte, Edmé, {{lang|fr|Oeuvres de Mr. Mariotte, de l'Académie royale  des sciences}}, vol. 1 (Leiden, Netherlands: P. Vander Aa, 1717); see especially [http://babel.hathitrust.org/cgi/pt?id=nyp.33433084031396;view=1up;seq=181 pp. 151–153].
* Mariotte's essay {{lang|fr|italic=no|"De la nature de l'air"}} was reviewed by the French Royal Academy of Sciences in 1679.  See: Anon. (1733), [https://archive.org/stream/histoiredelacad00acad#page/270/mode/2up {{lang|fr|italic=no|"Sur la nature de l'air"}}], {{lang|fr|Histoire de l'Académie Royale des Sciences}}, '''1''':  270–278.
* Mariotte's essay {{lang|fr|italic=no|"De la nature de l'air"}} was also reviewed in the {{lang|fr|Journal des Sçavans}} (later:  {{lang|fr|Journal des Savants}}) on 20 November 1679. See: Anon. (20 November 1679), [https://books.google.com/books?id=Wsrc_p4pHK8C&pg=PA269 {{lang|fr|italic=no|"Essais de physique"}}], {{lang|fr|Journal des Sçavans}}, pp. 265–269.</ref> after Boyle had published it in 1662.<ref name="scientists"/> Mariotte did, however, discover that air volume changes with temperature.<ref name="ley196606">{{Cite magazine
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}}</ref> Thus this law is sometimes referred to as Mariotte's law or the Boyle–Mariotte law. Later, in 1687 in the {{lang|la|[[Philosophiæ Naturalis Principia Mathematica]]}}, [[Isaac Newton|Newton]] showed mathematically that in an [[Elasticity (physics)|elastic]] fluid consisting of particles at rest, between which are repulsive forces inversely proportional to their distance, the density would be directly proportional to the pressure,<ref>{{lang|la|Principia}}, Sec. V, prop. XXI, Theorem XVI</ref> but this mathematical treatise does not involve any Mariott temperature dependance and is not the proper physical explanation for the observed relationship. Instead of a static theory, a [[Kinetic theory of gases|kinetic theory]] is needed, which was developed over the next two centuries by [[Daniel Bernoulli]] (1738) and more fully by [[Rudolf Clausius]] (1857), [[James Clerk Maxwell|Maxwell]] and [[Ludwig Boltzmann|Boltzmann]].

This law was the first physical law to be expressed in the form of an equation describing the dependence of two variable quantities.<ref name="scientists"/>