Editing Metric system (section)

=== Coherence ===
{{Main|Coherence (units of measurement)}}
[[File:James Clerk Maxwell.jpg|thumb|upright|[[James Clerk Maxwell]] played a major role in developing the concept of a coherent CGS system and in extending the metric system to include electrical units.]]
Each variant of the metric system has a degree of coherence—the derived units are directly related to the base units without the need for intermediate conversion factors.<ref>{{citation
| author = Working Group 2 of the Joint Committee for Guides in Metrology (JCGM/WG 2).
| publisher = [[International Bureau of Weights and Measures]] (BIPM) on behalf of the Joint Committee for Guides in Metrology
| year = 2008
| url = http://www.bipm.org/utils/common/documents/jcgm/JCGM_200_2008.pdf
| title = International vocabulary of metrology – Basic and general concepts and associated terms (VIM)
| edition = 3rd
| at = 1.12
|access-date = 12 April 2012}}</ref> For example, in a coherent system the units of [[force]], [[energy]], and [[Power (physics)|power]] are chosen so that the equations
{| style="margin-left:3em !important"
|-
| ''force''  || = || ''mass''  || × || ''acceleration''
|-
| ''energy'' || = || ''force'' || × || ''distance''
|-
| ''energy'' || = || ''power'' || × || ''time''
|}
hold without the introduction of unit conversion factors. Once a set of coherent units has been defined, other relationships in physics that use this set of units will automatically be true. Therefore, [[Albert Einstein|Einstein]]'s [[Mass–energy equivalence|mass–energy equation]], {{nowrap|1=''E'' = ''mc''{{i sup|2}}}}, does not require extraneous constants when expressed in coherent units.<ref>{{cite web
 |url=http://www.unc.edu/~mgood/research/RestEnergy.pdf
 |title=Some Derivations of ''E'' = ''mc''<sup>2</sup>
 |first1=Michael
 |last1=Good
 |access-date=18 March 2011
 |url-status=dead
 |archive-url=https://web.archive.org/web/20111107023429/https://www.unc.edu/~mgood/research/RestEnergy.pdf
 |archive-date=7 November 2011
}}</ref>

The [[centimetre–gram–second system of units|CGS system]] had two units of energy, the [[erg]] that was related to [[mechanics]] and the [[calorie]] that was related to [[thermal energy]]; so only one of them (the erg) could bear a coherent relationship to the base units. Coherence was a design aim of SI, which resulted in only one unit of energy being defined – the [[joule]].<ref name=SI_units>{{SIbrochure8th|pages = 111–120}}</ref>