Editing Dimensional analysis (section)

== History ==
The origins of dimensional analysis have been disputed by historians.<ref>{{Cite journal |last=Macagno |first=Enzo O. |year=1971 |title=Historico-critical review of dimensional analysis |journal=Journal of the Franklin Institute |volume=292 |issue=6 |pages=391–340 |doi=10.1016/0016-0032(71)90160-8}}</ref><ref name="Martins 1981">{{Cite journal |last=Martins |first=Roberto De A. |year=1981 |title=The origin of dimensional analysis |journal=Journal of the Franklin Institute |volume=311 |issue=5 |pages=331–337 |doi=10.1016/0016-0032(81)90475-0}}</ref> The first written application of dimensional analysis has been credited to [[François Daviet de Foncenex|François Daviet]], a student of [[Joseph-Louis Lagrange]], in a 1799 article at the [[Turin]] Academy of Science.<ref name="Martins 1981" />

This led to the conclusion that meaningful laws must be homogeneous equations in their various units of measurement, a result which was eventually later formalized in the [[Buckingham π theorem]].
[[Simeon Poisson]] also treated the same problem of the [[parallelogram law]] by Daviet, in his treatise of 1811 and 1833 (vol&nbsp;I, p.&nbsp;39).<ref>Martins, p.&nbsp;403 in the Proceedings book containing his article</ref> In the second edition of 1833, Poisson explicitly introduces the term ''dimension'' instead of the Daviet ''homogeneity''.

In 1822, the important Napoleonic scientist [[Joseph Fourier]] made the first credited important contributions<ref>{{Citation |last=Mason |first=Stephen Finney |title=A history of the sciences |page=169 |year=1962 |place=New York |publisher=Collier Books |isbn=978-0-02-093400-4}}</ref> based on the idea that physical laws like [[Newton's second law|{{nowrap|1=''F'' = ''ma''}}]] should be independent of the units employed to measure the physical variables.

[[James Clerk Maxwell]] and [[Fleeming Jenkin]] played a major role in establishing modern use of dimensional analysis by distinguishing mass, length, and time as fundamental units, while referring to other units as derived.<ref name="maxwell">{{Citation |last=Roche |first=John J |title=The Mathematics of Measurement: A Critical History |page=203 |year=1998 |publisher=Springer |isbn=978-0-387-91581-4 |url= https://books.google.com/books?id=eiQOqS-Q6EkC&pg=PA203|quote = Beginning apparently with Maxwell, mass, length and time began to be interpreted as having a privileged fundamental character and all other quantities as derivative, not merely with respect to measurement, but with respect to their physical status as well.}}</ref> <ref>{{ cite journal  | title=Making sense of absolute measurement: James Clerk Maxwell, William Thomson, Fleeming Jenkin, and the invention of the dimensional formula | year=2017 | pages=63-79 | journal=Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics | doi=10.1016/j.shpsb.2016.08.004 | volume=58 | url=http://dx.doi.org/10.1016/j.shpsb.2016.08.004 | last1=Mitchell | first1= Daniel Jon }}
</ref> Although Maxwell defined length, time and mass to be "the three fundamental units", he also noted that gravitational mass can be derived from length and time by assuming a form of [[Newton's law of universal gravitation]] in which the [[gravitational constant]] {{math|''G''}} is taken as [[1|unity]], thereby defining {{nowrap|1=M = T<sup>−2</sup>L<sup>3</sup>}}.<ref name="maxwell2">{{Citation |last=Maxwell |first=James Clerk |title=A Treatise on Electricity and Magnetism |page=4 |year=1873}}</ref> By assuming a form of [[Coulomb's law]] in which the [[Coulomb constant]] ''k''<sub>e</sub> is taken as unity, Maxwell then determined that the dimensions of an electrostatic unit of charge were {{nowrap|1=Q = T<sup>−1</sup>L<sup>3/2</sup>M<sup>1/2</sup>}},<ref name="maxwell3">{{Citation |last= Maxwell |first=James Clerk |title=A Treatise on Electricity and Magnetism |series=Clarendon Press series |page=45 |year=1873 |publisher=Oxford |hdl=2027/uc1.l0065867749 |hdl-access=free}}</ref> which, after substituting his {{nowrap|1=M = T<sup>−2</sup>L<sup>3</sup>}} equation for mass, results in charge having the same dimensions as mass, viz. {{nowrap|1=Q = T<sup>−2</sup>L<sup>3</sup>}}.

Dimensional analysis is also used to derive relationships between the physical quantities that are involved in a particular phenomenon that one wishes to understand and characterize.  It was used for the first time in this way in 1872 by [[Lord Rayleigh]], who was trying to understand why the sky is blue.<ref>{{harv|Pesic|2005}}</ref>  Rayleigh first published the technique in his 1877 book ''The Theory of Sound''.<ref>{{Citation |last=Rayleigh |first=Baron John William Strutt |title=The Theory of Sound |url=https://books.google.com/books?id=kvxYAAAAYAAJ |year=1877 |publisher=Macmillan}}</ref>

The original meaning of the word ''dimension'', in Fourier's ''Theorie de la Chaleur'', was the numerical value of the exponents of the base units. For example, acceleration was considered to have the dimension 1 with respect to the unit of length, and the dimension −2 with respect to the unit of time.{{sfnp|Fourier |1822 |page=[https://books.google.com/books?id=TDQJAAAAIAAJ&pg=PA156 156]}} This was slightly changed by Maxwell, who said the dimensions of acceleration are T<sup>−2</sup>L, instead of just the exponents.<ref name="maxwell4">{{Citation |last=Maxwell |first=James Clerk |title=A Treatise on Electricity and Magnetism, volume 1 |url=https://archive.org/stream/electricandmagne01maxwrich#page/n41/mode/2up |page=5 |year=1873}}</ref>