Editing Volume (section)

== History ==
=== Ancient history ===
[[File:Pompeji_6_Hohlmaße_aus_Glas.jpg|thumb|6&nbsp;volumetric measures from the ''mens ponderia'' in [[Pompeii]], an ancient municipal institution for the control of weights and measures]]

The precision of volume measurements in the ancient period usually ranges between {{Cvt|10–50|mL|USoz impoz|sigfig=1}}.<ref name="Imhausen-2016" />{{Rp|page=8}} The earliest evidence of volume calculation came from [[ancient Egypt]] and [[Mesopotamia]] as mathematical problems, approximating volume of simple shapes such as [[cuboid]]s, [[cylinder]]s, [[frustum]] and [[cone]]s. These math problems have been written in the [[Moscow Mathematical Papyrus]] (c. 1820 BCE).<ref name="Treese-2018" />{{Rp|page=403}} In the [[Reisner Papyrus]], ancient Egyptians have written concrete units of volume for grain and liquids, as well as a table of length, width, depth, and volume for blocks of material.<ref name="Imhausen-2016">{{Cite book |last=Imhausen |first=Annette |url= |title=Mathematics in Ancient Egypt: A Contextual History |date=2016 |publisher=[[Princeton University Press]] |isbn=978-1-4008-7430-9 |location= |oclc=934433864}}</ref>{{Rp|page=116}} The Egyptians use their units of length (the [[cubit]], [[Palm (unit)|palm]], [[Digit (unit)|digit]]) to devise their units of volume, such as the volume cubit<ref name="Imhausen-2016" />{{Rp|page=117}} or deny<ref name="Treese-2018" />{{Rp|page=396}} (1 cubit × 1 cubit × 1 cubit), volume palm (1 cubit × 1 cubit × 1 palm), and volume digit (1 cubit × 1 cubit × 1 digit).<ref name="Imhausen-2016" />{{Rp|page=117}}

The last three books of [[Euclid's Elements|Euclid's ''Elements'']], written in around 300 BCE, detailed the exact formulas for calculating the volume of [[parallelepiped]]s, cones, [[pyramid]]s, cylinders, and [[sphere]]s. The formula were determined by prior mathematicians by using a primitive form of [[Integral|integration]], by breaking the shapes into smaller and simpler pieces.<ref name="Treese-2018">{{Cite book |last=Treese |first=Steven A. |title=History and Measurement of the Base and Derived Units |date=2018 |publisher=[[Springer Science+Business Media]] |isbn=978-3-319-77577-7 |location=Cham, Switzerland |lccn=2018940415 |oclc=1036766223}}</ref>{{Rp|page=403}} A century later, [[Archimedes]] ({{Circa|287 – 212 BCE}}) devised approximate volume formula of several shapes using the [[method of exhaustion]] approach, meaning to derive solutions from previous known formulas from similar shapes. Primitive integration of shapes was also discovered independently by [[Liu Hui]] in the 3rd century CE, [[Zu Chongzhi]] in the 5th century CE, the [[Middle East]] and [[India]].<ref name="Treese-2018" />{{Rp|page=404}}

Archimedes also devised a way to calculate the volume of an irregular object, by submerging it underwater and measure the difference between the initial and final water volume. The water volume difference is the volume of the object.<ref name="Treese-2018" />{{Rp|page=404}} Though highly popularized, Archimedes probably does not submerge the golden crown to find its volume, and thus its density and purity, due to the extreme precision involved.<ref>{{cite web |last=Rorres |first=Chris |title=The Golden Crown |url=http://www.math.nyu.edu/~crorres/Archimedes/Crown/CrownIntro.html |url-status=live |archive-url=https://web.archive.org/web/20090311051318/http://www.math.nyu.edu/~crorres/Archimedes/Crown/CrownIntro.html |archive-date=11 March 2009 |access-date=24 March 2009 |publisher=[[Drexel University]]}}</ref> Instead, he likely have devised a primitive form of a [[Hydrostatic Balance|hydrostatic balance]]. Here, the crown and a chunk of pure gold with a similar weight are put on both ends of a [[weighing scale]] submerged underwater, which will tip accordingly due to the [[Archimedes' principle]].<ref>{{Cite journal |last=Graf |first=E. H. |date=2004 |title=Just what did Archimedes say about buoyancy? |url=https://aapt.scitation.org/doi/10.1119/1.1737965 |journal=The Physics Teacher |volume=42 |issue=5 |pages=296–299 |bibcode=2004PhTea..42..296G |doi=10.1119/1.1737965 |access-date=2022-08-07 |archive-date=2021-04-14 |archive-url=https://web.archive.org/web/20210414102422/https://aapt.scitation.org/doi/10.1119/1.1737965 |url-status=live }}</ref>

=== Calculus and standardization of units ===
{{Further|History of calculus|Apothecaries' system}}
[[File:"How to Measure" diagram, with graduated cylinder measuring fluid drams, 1926.jpg|alt=Pouring liquid to a marked flask|left|thumb|Diagram showing how to measure volume using a graduated cylinder with [[fluid dram]] markings, 1926]]
In the [[Middle Ages]], many units for measuring volume were made, such as the [[sester]], [[Amber (unit)|amber]], [[Coomb (unit)|coomb]], and [[Seam (unit)|seam]]. The sheer quantity of such units motivated British kings to standardize them, culminated in the [[Assize of Bread and Ale]] statute in 1258 by [[Henry III of England]]. The statute standardized weight, length and volume as well as introduced the peny, ounce, pound, gallon and bushel.<ref name="Imhausen-2016" />{{Rp|page=|pages=73–74}} In 1618, the ''[[London Pharmacopoeia]]'' (medicine compound catalog) adopted the Roman gallon<ref name="RPS-2020">{{Cite web |date=4 Feb 2020 |title=Balances, Weights and Measures |url=https://www.rpharms.com/Portals/0/MuseumLearningResources/11%20Balances%20Weights%20and%20Measures.pdf |access-date=13 August 2022 |website=[[Royal Pharmaceutical Society]] |page=1 |archive-date=20 May 2022 |archive-url=https://web.archive.org/web/20220520094140/https://www.rpharms.com/Portals/0/MuseumLearningResources/11%20Balances%20Weights%20and%20Measures.pdf |url-status=live }}</ref> or ''[[congius]]''<ref>{{Cite book |last=Cardarelli |first=François |title=Scientific Unit Conversion: A Practical Guide to Metrication |date=6 Dec 2012 |publisher=[[Springer Science+Business Media]] |isbn=978-1-4471-0805-4 |edition=2nd |location=London |pages=151 |oclc=828776235}}</ref> as a basic unit of volume and gave a conversion table to the apothecaries' units of weight.<ref name="RPS-2020" /> Around this time, volume measurements are becoming more precise and the uncertainty is narrowed to between {{Cvt|1–5|mL|USoz impoz|sigfig=1}}.<ref name="Imhausen-2016" />{{Rp|page=8}}

Around the early 17th century, [[Bonaventura Cavalieri]] applied the philosophy of modern integral calculus to calculate the volume of any object. He devised [[Cavalieri's principle]], which said that using thinner and thinner slices of the shape would make the resulting volume more and more accurate. This idea would then be later expanded by [[Pierre de Fermat]], [[John Wallis]], [[Isaac Barrow]], [[James Gregory (mathematician)|James Gregory]], [[Isaac Newton]], [[Gottfried Wilhelm Leibniz]] and [[Maria Gaetana Agnesi]] in the 17th and 18th centuries to form the modern integral calculus, which remains in use in the 21st century.<ref name="Treese-2018" />{{Rp|page=404}}

=== Metrication and redefinitions ===
{{Further|History of the metric system}}

On 7 April 1795, the metric system was formally defined in French law using six units. Three of these are related to volume: the ''[[stère]]''&nbsp;(1&nbsp;m<sup>3</sup>) for volume of firewood; the ''[[litre]]''&nbsp;(1&nbsp;dm<sup>3</sup>) for volumes of liquid; and the ''[[gram]]me'', for mass—defined as the mass of one cubic centimetre of water at the temperature of melting ice.<ref>
{{cite thesis
 | last = Cox | first = Edward Franklin
 | id = {{ProQuest|301905667}}
 | pages = 99–100
 | publisher = Indiana University
 | title = A History of the Metric System of Weights and Measures, with Emphasis on Campaigns for its Adoption in Great Britain, and in The United States Prior to 1914
 | type = PhD thesis
 | year = 1958
}}</ref> Thirty years later in 1824, the [[imperial gallon]] was defined to be the volume occupied by ten [[Pound (mass)|pounds]] of water at {{Cvt|62|F|C|order=flip}}.<ref name="Treese-2018" />{{Rp|page=394}} This definition was further refined until the United Kingdom's [[Weights and Measures Act 1985]], which makes 1 imperial gallon precisely equal to 4.54609&nbsp;litres with no use of water.<ref>{{Cite book |last=Cook |first=James L. |url= |title=Conversion Factors |date=1991 |publisher=[[Oxford University Press]] |isbn=0-19-856349-3 |location=Oxford [England] |pages=xvi |oclc=22861139}}</ref>

The 1960 redefinition of the metre from the [[International Prototype Metre]] to the orange-red [[Spectral line|emission line]] of [[krypton-86]] atoms unbounded the metre, cubic metre, and litre from physical objects. This also make the metre and metre-derived units of volume resilient to changes to the International Prototype Metre.<ref>{{cite book |last=Marion |first=Jerry B. |title=Physics For Science and Engineering |publisher=CBS College Publishing |year=1982 |isbn=978-4-8337-0098-6 |page=3}}</ref> The definition of the metre was redefined again in 1983 to use the [[speed of light]] and [[second]] (which is derived from the [[caesium standard]]) and [[2019 revision of the SI|reworded for clarity in 2019]].<ref>{{Cite web |date=20 May 2019 |title=''Mise en pratique'' for the definition of the metre in the SI |url=https://www.bipm.org/documents/20126/41489670/SI-App2-metre.pdf |website=[[International Bureau of Weights and Measures]] |publisher=Consultative Committee for Length |pages=1 |access-date=13 August 2022 |archive-date=13 August 2022 |archive-url=https://web.archive.org/web/20220813164032/https://www.bipm.org/documents/20126/41489670/SI-App2-metre.pdf |url-status=live }}</ref>