Difference between revisions of "International System of Electrical and Magnetic Units"
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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}}.</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>{{citation | contribution = Weber, Wilhelm Eduard | title = Encyclopædia Britannica | volume = 28 | year = 1911 | edition = 11th | page = 458}}.</ref><ref group="Note" name="Weber">Weber's original proposal was based on a millimetre–milligram–second system of units.</ref> | 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}}.</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>{{citation | contribution = Weber, Wilhelm Eduard | title = Encyclopædia Britannica | volume = 28 | year = 1911 | edition = 11th | 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 group="Note" name="Weber"/> however the resulting "absolute" units were both difficult to [[Realization|realize]] and 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. | + | 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 group="Note" name="Weber"/> however the resulting "absolute" units were both difficult to [[Realization|realize]] and 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">{{citation | contribution = Units, Physical | title = Encyclopædia Britannica | volume = 27 | year = 1911 | edition = 11th | pages = 738–45}}.</ref> |
==1893 system== | ==1893 system== | ||
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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 V<sub>int</sub> ≠ 1 A<sub>int</sub> × 1 Ω<sub>int</sub>. | 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 V<sub>int</sub> ≠ 1 A<sub>int</sub> × 1 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 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 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 °C (1.0184 V<sub>int</sub>), as this type of cell has a lower temperature coefficient than the Clark cell. | *the preferred realization of the international volt was in terms of the electromotive force of a [[Weston cell]] at 20 °C (1.0184 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"/> | *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; | + | ;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; | + | ;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 C.G.S. system, represented sufficiently well for practical use by the energy expended in one second by an international ampere in an international ohm; | ;[[Joule]]:10<sup>7</sup> units of [[work]] in the C.G.S. 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 C.G.S. system, represented sufficiently well for practical use by the work done at the rate of one joule per second; | ;[[Watt]]:10<sup>7</sup> units of [[power]] in the C.G.S. system, represented sufficiently well for practical use by the work done at the rate of one joule per second; | ||
Revision as of 10:17, 10 August 2010
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 Conference of Electricians (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.
Contents
Earlier systems
The link between electromagnetic units and the more familiar units of length, mass and time was first demonstrated by Gauss in 1832 with his measurement of the Earth's magnetic field,[1] and the principle was extended to electrical measurements by Neumann in 1845.[2] A complete system of metric electrical and magnetic units was proposed by Weber in 1851.[3][Note 1]
The development of the electric telegraph (an invention of Gauss and Weber) demonstrated the need for accurate electrical measurements. At the behest of 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:[Note 1] however the resulting "absolute" units were both difficult to realize and 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.[4]
1893 system
The International System was introduced in 1893 because of the practical difficulties in measuring electrical units in the cgs system. The 1893 system had three base units: the international ampere, the international ohm and the international volt.
| Unit | 1893 ("international") definition[Note 2] | cgs ("absolute") equivalent | Notes |
|---|---|---|---|
| Ampere | the unvarying current which, when passed through a solution of silver nitrate in water, deposits silver at the rate of 0.001 118 00 grams per second | the current produced in a conductor with a 1 ohm resistance when there is a potential difference of 1 volt between its ends | 0.1 cgs units of electric current |
| Ohm | the resistance offered to an unvarying electric current by a column of mercury at the temperature of melting ice 14.4521 grams in mass, of a constant cross-sectional area and of the length of 106.3 centimetres | 109 cgs units of electric resistance | |
| Volt | 1000⁄1434 of the electromotive force of a Clark cell at a temperature of 15 °C | the electromotive force produced in an electric circuit which cuts 108 magnetic lines of force per second | 108 cgs units of electromotive force |
Overdefinition and the 1908 modification
The 1893 system of units was overdefined, as can be seen from an examination of Ohm's law:
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 Vint ≠ 1 Aint × 1 Ωint.
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:[4]
- 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 realizations;
- the preferred realization of the international volt was in terms of the electromotive force of a Weston cell at 20 °C (1.0184 Vint), 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:[Note 2]
- International Coulomb
- the electric charge transferred by a current of one international ampere in one second;[Note 3]
- International Farad
- the capacitance of a capacitor charged to a potential of one international volt by one international coulomb of electricity;[Note 3]
- Joule
- 107 units of work in the C.G.S. system, represented sufficiently well for practical use by the energy expended in one second by an international ampere in an international ohm;
- Watt
- 107 units of power in the C.G.S. 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
Notes and references
Notes
- ↑ 1.0 1.1 Weber's original proposal was based on a millimetre–milligram–second system of units.
- ↑ 2.0 2.1 The terminology of some of the definitions has been updated to modern usage.
- ↑ 3.0 3.1 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".
References
- ↑ Gauss, C. F. Intensitas vis magneticae terrestris ad mensuram absolutam revocata. Commentationes Societatis Regiae Scientiarum Gottingensis Recentiores 1832–37, 8, 3–44.
- ↑ Neumann, F. E. Die mathematischen Gesetze der induciten elektrischen Ströme. Abhandlungen der Königlichen Preußischen Akademie der Wissenschaften zu Berlin 1845, 1–87, <http://bibliothek.bbaw.de/bbaw/bibliothek-digital/digitalequellen/schriften/anzeige/index_html?band=07-abh/1845&seite:int=24>; Franz Neumanns gesammelte Werke; B. G. Teubner: Leipzig, 1912; Vol. 3, pp 257–344, <http://quod.lib.umich.edu/cgi/t/text/text-idx?c=umhistmath;idno=AAN8146.0003.001;cc=umhistmath>. Neumann, F. Über ein allgemeines Princip der mathematischen Theorie inducirter elektrischer Ströme. Abhandlungen der Königlichen Preußischen Akademie der Wissenschaften zu Berlin 1847, 1–71, <http://bibliothek.bbaw.de/bbaw/bibliothek-digital/digitalequellen/schriften/anzeige/index_html?band=07-abh/1847&seite:int=27>; Franz Neumanns gesammelte Werke; B. G. Teubner: Leipzig, 1912; Vol. 3, pp 345–424, <http://quod.lib.umich.edu/cgi/t/text/text-idx?c=umhistmath;idno=AAN8146.0003.001;cc=umhistmath>.
- ↑ Weber, Wilhelm Eduard. In Encyclopædia Britannica, 11th ed., 1911; Vol. 28, p 458.
- ↑ 4.0 4.1 Units, Physical. In Encyclopædia Britannica, 11th ed., 1911; Vol. 27, pp 738–45.
External links
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