View source for International System of Electrical and Magnetic Units

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The '''International System of Electrical and Magnetic Units''' is an obsolete system of units used solely for measuring electrical and magnetic quantities. It was introduced by the Fourth International Electrical Congress (Chicago, 1893) and modified in 1908. It was rendered obsolete by the inclusion of electromagnetic units in the [[International System of Units]] (SI) in 1948.

==Earlier systems==
The link between electromagnetic units and the more familiar units of [[length]], [[mass]] and [[time]] was first demonstrated by [[Carl Friedrich Gauss|Gauss]] in 1832 with his measurement of the Earth's magnetic field,<ref>{{citation | first = C. F. | last = Gauss | authorlink = Carl Friedrich Gauss | title = Intensitas vis magneticae terrestris ad mensuram absolutam revocata | journal = Commentationes Societatis Regiae Scientiarum Gottingensis Recentiores | volume = 8 | year = 1832–37 | pages = 3–44}}. [http://www.21stcenturysciencetech.com/Translations/gaussMagnetic.pdf English translation].</ref> and the principle was extended to electrical measurements by [[Franz Neumann|Neumann]] in 1845.<ref>{{citation | first = F. E. | last = Neumann | authorlink = Franz Neumann | contribution = Die mathematischen Gesetze der induciten elektrischen Ströme | year = 1845 | journal = Abhandlungen der Königlichen Preußischen Akademie der Wissenschaften zu Berlin | pages = 1–87 | url = http://bibliothek.bbaw.de/bbaw/bibliothek-digital/digitalequellen/schriften/anzeige/index_html?band=07-abh/1845&seite:int=24}}; {{citation | title = Franz Neumanns gesammelte Werke | publisher = B. G. Teubner | location = Leipzig | year = 1912 | volume = 3 | pages = 257–344 | url = http://quod.lib.umich.edu/cgi/t/text/text-idx?c=umhistmath;idno=AAN8146.0003.001;cc=umhistmath}}. {{citation | first = F. | last = Neumann | authorlink = Franz Neumann | title = Über ein allgemeines Princip der mathematischen Theorie inducirter elektrischer Ströme | year = 1847 | journal = Abhandlungen der Königlichen Preußischen Akademie der Wissenschaften zu Berlin | pages = 1–71 | url = http://bibliothek.bbaw.de/bbaw/bibliothek-digital/digitalequellen/schriften/anzeige/index_html?band=07-abh/1847&seite:int=27}}; {{citation | title = Franz Neumanns gesammelte Werke | publisher = B. G. Teubner | location = Leipzig | year = 1912 | volume = 3 | pages = 345–424 | url = http://quod.lib.umich.edu/cgi/t/text/text-idx?c=umhistmath;idno=AAN8146.0003.001;cc=umhistmath}}.</ref> A complete system of metric electrical and magnetic units was proposed by [[Wilhelm Weber|Weber]] in 1851.<ref>{{EB11 | contribution = Weber, Wilhelm Eduard | volume = 28 | page = 458}}.</ref><ref group="Note" name="Weber">Weber's original proposal was based on a millimetre–milligram–second system of units.</ref>

The development of the electric telegraph (an invention of Gauss and Weber) demonstrated the need for accurate electrical measurements. At the behest of [[William Thomson|Thomson]], the [[British Association for the Advancement of Science]] (B.A.) set up a committee in 1862 to examine the options for standardizing electrical and magnetic units. After much discussion, the committee decided to adapt Weber's proposals to the [[CGS system]] of units:<ref>{{citation | first = Fleeming | last = Jenkin | authorlink = Fleeming Jenkin | title = Reports of the Committee on Electrical Standards | location = London | year = 1873}}.</ref><ref group="Note" name="Weber"/> however the resulting "absolute" units were both difficult to [[Realization|realize]] and (often) impractically small. To overcome these handicaps, the B.A. also proposed a set of "practical" or "reproduceable" units, which were not directly linked to the CGS system but which were, as near as experimental accuracy allowed, equal to multiples of the corresponding CGS units.<ref name="EB11">{{EB11 | contribution = Units, Physical | volume = 27 | pages = 738–45}}.</ref><ref group="Note">It soon became apparent that the B.A. had developed ''two'' sets of CGS units. The practical units were based on the [[CGS electromagnetic units|electromagnetic set of units]] rather than on the [[CGS electrostatic units|electrostatic set]].</ref>

==1893 system==
The B.A. system of practical units gained considerable international support, and was adopted – with one important modification – by the First International Conference of Electricians (Paris, 1881). The British Association had constructed an artefact representation of the ohm (a standard length of resistance wire which had a resistance of 10<sup>9</sup>&nbsp;CGS&nbsp;units of electric resistance, that is one ohm) whereas the international conference preferred a method of [[realization]] that could be repeated in different laboratories in different countries. The chosen method was based on the [[resistivity]] of [[mercury]], by measuring the resistance of a column of mercury of specified dimensions (106&nbsp;cm&nbsp;×&nbsp;1&nbsp;mm<sup>2</sup>): however, the chosen length of column was almost 3&nbsp;millimetres too short, leading to a difference of 0.28% between the new practical units and the CGS units which were supposedly their basis.<ref>{{citation | title = ohm | url = http://www.sizes.com/units/ohm.htm | publisher = sizes.com | accessdate = 2010-08-11}}.</ref>

The anomaly was resolved at another international conference, in Chicago in 1893, by a correction in the definition of the ohm. The units agreed at this conference were termed "international" units, to distinguish them from their predecessors.

The 1893 system had three base units: the international [[ampere]], the international [[ohm]] and the international [[volt]].

{| class="wikitable"
|-
! Unit
! 1893 ("international") definition<ref group="Note" name="update">The terminology of some of the definitions has been updated to modern usage.</ref>
! CGS ("absolute") equivalent
! Notes
|-
| [[Ampere]]
| the unvarying [[electric current|current]] which, when passed through a solution of [[silver nitrate]] in water, deposits [[silver]] at the rate of {{nowrap|0.001 118 00&nbsp;grams}} per second
| the current produced in a conductor with a 1&nbsp;ohm resistance when there is a potential difference of 1&nbsp;volt between its ends
| 0.1 cgs units of electric current
|-
| [[Ohm]]
| the [[electric resistance|resistance]] offered to an unvarying [[electric current]] by a column of [[mercury]] at the temperature of melting ice 14.4521&nbsp;grams in mass, of a constant cross-sectional area and of the length of 106.3&nbsp;centimetres
| 
| 10<sup>9</sup> cgs units of electric resistance
|-
| [[Volt]]
| {{frac|1000|1434}} of the [[electromotive force]] of a [[Clark cell]] at a temperature of 15&nbsp;°C
| the electromotive force produced in an [[electric circuit]] which cuts 10<sup>8</sup> magnetic lines of force per second
| 10<sup>8</sup> cgs units of electromotive force
|-
|}

The international units did not have the same formal legal status as the [[metre]] and the [[kilogram]] through the [[Metre Convention]] (1875), although several countries adopted the definition within their national laws (e.g., the United States, through Public Law&nbsp;105 of July&nbsp;12, 1894).

==Overdefinition and the 1908 modification==
The 1893 system of units was overdefined, as can be seen from an examination of [[Ohm's law]]:
:[[Electric potential difference|''V'']] = [[Electric current|''I'']][[Electric resistance|''R'']]
By Ohm's law, knowing any two of the physical quantities ''V'', ''I'' or ''R'' (potential difference, current or resistance) will define the third, and yet the 1893 system defines the units for all three quantities. With improvements in measurement techniques, it was soon realized that 1&nbsp;V<sub>int</sub>&nbsp;≠ 1&nbsp;A<sub>int</sub>&nbsp;×&nbsp;1&nbsp;Ω<sub>int</sub>.

The solution came at an international conference in London in 1908. The essential point was to reduce the number of base units from three to two by redefining the international volt as a derived unit. There were several other modifications of less practical importance:<ref name="EB11"/>
*the international ampere and the international ohm were formally defined in terms of the corresponding [[CGS electromagnetic units]], with the 1893 definitions retained as preferred [[realization]]s;
*the preferred realization of the international volt was in terms of the electromotive force of a [[Weston cell]] at 20&nbsp;°C (1.0184&nbsp;V<sub>int</sub>), as this type of cell has a lower temperature coefficient than the Clark cell;
*several other derived units for use in electrical and magnetic measurements were formally defined:<ref group="Note" name="update"/>
;International [[Coulomb]]:the [[electric charge]] transferred by a current of one international ampere in one second;<ref group="Note" name="CF">The [[coulomb]] and the [[farad]] had been used in earlier B.A. systems of electrical units with slightly different definitions, hence the need to add the qualifier "international".</ref>
;International [[Farad]]:the [[capacitance]] of a [[capacitor]] charged to a potential of one international volt by one international coulomb of electricity;<ref group="Note" name="CF"/>
;[[Joule]]:10<sup>7</sup> units of [[work]] in the CGS system, represented sufficiently well for practical use by the energy expended in one second by an international ampere in an international ohm;
;[[Watt]]:10<sup>7</sup> units of [[power]] in the CGS system, represented sufficiently well for practical use by the work done at the rate of one joule per second;
;[[Henry]]:the [[inductance]] in a circuit when an electromotive force induced in this circuit is one international volt, while the inducing current varies at the rate of one ampere per second.

==SI units==
With advances in the theory of [[electromagnetism]] and in [[quantity calculus]], it became apparent that a coherent absolute system of units could only include one electromagnetic [[base unit]]. The first such system was proposed by [[Giovanni Giorgi|Giorgi]] in 1901:<ref name="EB11"/><ref name="IEC">{{citation | title = Giovanni Giorgi | url = http://www.iec.ch/about/history/articles/giovanni_giorgi.htm | publisher = International Electrotechnical Commission | accessdate = 2010-08-11}}.</ref><ref>{{citation | last = Giorgi | first = G. | authorlink = Giovanni Giorgi | title = Rational Units of Electromagnetism}}. [http://www.iec.ch/about/history/pdf_history/giorgi/Giorgi2.pdf Original manuscript with handwritten notes by Oliver Heaviside].</ref> it used the [[ohm]] as the additional base unit in the [[MKS system]], and so is often referred to as the MKSΩ system or the Giorgi system. 

An additional problem with the CGS system of electrical units, pointed out as early as 1882 by [[Oliver Heaviside|Heaviside]],<ref>{{citation | last = Heaviside | first = O. | authorlink = Oliver Heaviside | title = The Relations between Magnetic Force and Electric Current | journal = The Electrician | issue = 18 November | year = 1882}}.</ref> was that they were not "rationalized", that is they failed to properly take account of [[permittivity]] and [[permeability]] as properties of a medium. Georgi was also a great proponent of rationalization of the electrical units.<ref name="IEC"/>

The choice of electrical unit for the base unit in a rationalized system depends only on practical considerations, particularly the ability to [[Realization|realize]] the unit accurately and reproducibly. The [[ampere]] rapidly gained support over the ohm, as many national standards laboratories were already realizing the ampere in absolute terms using [[ampere balance]]s.<ref name="EB11"/><ref>{{citation | first = R. T. | last = Glazebrook | authorlink = Richard Glazebrook | title = The fourth unit of the Giorgi system of electrical units | year = 1936 | journal = Proc. Phys. Soc. | volume = 48 | pages = 452 | doi = 10.1088/0959-5309/48/3/312}}.</ref> The [[International Electrotechnical Commission]] (IEC) adopted the Giorgi system with the ampere replacing the ohm in 1935, and this choice of base units is often called the MKSA system.<ref name="IEC"/>

The [[International Committee for Weights and Measures]] (CIPM) approved a new set of definitions for electrical units, based on the rationalized MKSA system, in 1946, and these were internationally adopted under the [[Metre Convention]] by the 9th&nbsp;[[General Conference on Weights and Measures]] in 1948.<ref>{{SIbrochure8th|page=144}}.</ref> Under this system, which would become the [[International System of Units]] (SI), the ohm is a derived unit.<ref group="Note">The ohm is the electric resistance between two points of a conductor when a constant potential difference of 1&nbsp;volt, applied to these points, produces in the conductor a current of 1&nbsp;ampere, the conductor not being the seat of any electromotive force.</ref>

The SI definitions of the electrical units are formally equivalent to the 1908 international definitions, and so there should not have been any change in the size of the units. Nevertheless, the international ohm and the international volt were not usually realized in absolute terms but by reference to a standard resistance and a standard electromotive force respectively. The realizations recommended in 1908 are not exactly equivalent to the absolute definitions: recommended conversion factors<ref>{{GreenBook2nd|page=114}}.</ref> are
:1 Ω<sub>int</sub> ≈ 1.000 49 Ω
:1 V<sub>int</sub> ≈ 1.000 34 V
although slightly different factors may apply for individual standards in national measurement laboratories.<ref group="Note">Conversion factors for the U.S. national standards (NIST) are 1&nbsp;Ω<sub>int</sub>&nbsp;= {{nowrap|1.000 495&nbsp;Ω}} and 1&nbsp;V<sub>int</sub>&nbsp;= {{nowrap|1.000 330&nbsp;V}}.</ref> As the international ampere was usually realized by means of an ampere balance rather than electrolytically,<ref name="EB11"/> 1&nbsp;A<sub>int</sub>&nbsp;= 1&nbsp;A. The conversion factor for the "electrolytic" ampere (A<sub>elec</sub>) can be calculated from modern values of the [[atomic weight]] of [[silver]] and the [[Faraday constant]]:
:1 A<sub>elec</sub> = 1.000 022(2) A

==See also==
*[[Conventional electrical units]]

==Notes and references==
===Notes===
{{reflist|group=Note}}

===References===
{{reflist|2}}

==External links==
*[http://www.sizes.com/units/int_ENMsys.htm Sizes.com]

[[Category:Electrical units|*]]

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