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Is this system still in use. To my knowledge nowadays international standards recommend people to use SI which is done in Europe.
It's used primarily in physics E&M textbooks because the coulomb and tesla are rediculously large, and in SI they are different units. In CGS, the Gauss is the same as a statvolt/meter. I suppose that it is primarily an informational peice, mainly for completeness.--BlackGriffen
The equations for the force due to magnetic field and other magnetic equations are slightly different in CGS units than SI becuase it includes the speed of light rahter than a constant. CGS units are used in E&M textbooks becuase when using CGS units it is more obvious that magnetic forces are simply a consequence of relativity rather than a phenomena on their own.
They were used not so long ago in physics papers (20-30 years) and they are still used by people which works with magnetic fields. Braice ( talk) 11:37, 4 December 2008 (UTC)
It should be mentioned that chemists only recently converted from cgs to SI units. I suspect that it will be a long time before people who work in the lab use kilograms instead of grams.
Even today the lack of mks units for such quantities as magnetic flux density and viscosity leads people to continue using the gauss and the centipoise. —The preceding unsigned comment was added by 71.250.142.249 ( talk • contribs) .
So, much as I hate to throw anything new in here after a few months, I thought it was prudent to note that astronomers still use CGS units. I'm taking classes and trying to deal with the electromagnetic units are more of a headache than anything else, but every astronomy class that I've had has only grudgingly accepted MKS units instead of CGS. And sometimes its more of a headache trying to figure out how to modify equations written for CGS into MKS anyway. But yeah, astronomers haven't switched yet. Adrieth ( talk) 07:55, 26 March 2009 (UTC)
A centimeter is the capacitance between a 1-cm sphere in vacuum and infinity. Is this true in the CGS system? It doesn't make sense to someone raised on SI units. Could this sentence be better worded to explain why a unit normally used for distance is also a unit of capacitance, please? -- Heron
Yes, it is true, although it is a 1 cm radius sphere I think. The concept of capacitance being used in this case is this: if you start out with this sphere and some charge Q at a distance of infinity from the sphere, then you force that charge to come from infinity to the sphere, little by little, then the energy required to do this is E, where E=0.5*Q^2/C. In other words, the energy required to compress a charge Q from infinitely spread-out down into a sphere of radius 1 cm.
72.70.42.173 (
talk) 19:00, 6 January 2012 (UTC)
Would anyone object to my removing the 'not used' from Gauss? I, and many others astronomers, use them every day.
He's far better known for his contributions to mathematics IMO he should be referred to as a mathematian rather than an astronomer (readers can read about his many other talents on the Gauss page).
In his recent edit summary, Crissov stated "clearer distinction between mechanical and electromechanic CGS is needed".
Even allowing for the fact that edit summaries are often cryptic, that is not what is needed. These aren't what need to be "distinguished". The likely reason that the mechanical units are listed separately is not because they need to be distiguished, but rather that they are pretty much common to all the various cgs systems. It is the electrical and magnetic units, and the electromagnetic system, the electromagnetic system, and the hybrid Gaussian system which need to be better distinguished (all sharing the same mechanical units). Another distinction can be made between three-base-unit (with, for example, electrical charge measured in units of erg1/2·cm1/2) and four-base-unit systems using a franklin or a biot as a base unit, and between rationalized and non-rationalized systems. It hurts my head to even try to figure them all out; thank God for the International System of Units. Gene Nygaard 21:30, 24 September 2005 (UTC)
What's wrong: k_1/k_2=c^2 or k_2 in the electrostatic cgs system?
I propose a separate spin-off article, Gaussian units (or cgs-Gaussian units or Gaussian-cgs units). My reasoning:
The article would list out the units and their conversions, Maxwell's equations and the Lorentz force law in Gaussian units, physical constants in Gaussian, something like the SI-Gaussian translation guide from the appendix of Jackson's E&M textbook, and where it's used in the world. Obviously it would link to this article as the place to learn about cgs in general, and also for more general notes on unit systems.
Thoughts? :-) -- Steve ( talk) 23:11, 23 December 2008 (UTC)
This article repeatedly praises CGS/Gaussian units for reducing pre-factors in Maxwell's Equations and giving and fields the same units. So, those things may make the equations easier to read and write, but they generally make it an absolute NIGHTMARE to figure out what those equations actually mean, and to do unit analysis.
For example, electrostatic units posit that the basic unit of charge is the statcoulomb, which is = √(g·cm3/s2). Likewise the unit of resistance is s/cm and that of capacitance, cm. These are quite unintuitive and disagree with the intuitive notion of electric charge as a unit distinct from other physical quantities like mass, time, and distance. And a the article itself explains, there are multiple choices for the basic units, further complicating things.
In my experience, only theoretical physicists prefer CGS units (and not all of them). Experimentalists who have to compare values from equations to actual measurable quantities typically hate them with a passion, since they make it so hard to relate E&M and mechanical quantities in an intuitive, consistent way. So I'd like to rewrite the article to reflect these issues. Can anyone suggest a good approach, or any good sources?? Moxfyre ( ÇɹʎℲxoɯ | contrib) 16:54, 29 April 2009 (UTC)
Woohoo, found one! Here is a very good explanation by a German professor of why CGS units are horribly ambiguous and yield the temptation to compare to mechanical units in nonsensical ways. Moxfyre ( ÇɹʎℲxoɯ | contrib) 23:07, 29 April 2009 (UTC)
As I proposed above, I just made a dedicated article for Gaussian units. -- Steve ( talk) 07:25, 4 August 2009 (UTC)
I added a note to clarify the meaning of impedance of free space. It would appear to be correct (i.e. E/H by definition) for ESU, EMU and Gaussian, but should the value not then be 4π instead of 1 for Heaviside-Lorentz units? —Preceding unsigned comment added by 194.81.223.66 ( talk) 15:41, 12 August 2009 (UTC)
The units gram and centimetre remain useful as prefixed units within the SI system, What's the prefix on "gram"Â ? Very logical system, this SI system. Base units don't have prefixes, except for the kilogram. -- Wtshymanski ( talk) 16:32, 16 July 2010 (UTC)
We presently have " c = 29,979,245,800 ≈ 3·1010 " used as if it were a dimensionless number rather than a speed in cm/s. This is at best confusing. LeadSongDog come howl! 18:41, 11 August 2010 (UTC)
A thread in Physics Forums discusses how this wikipedia article explains the replacement of the cgs- by the mks-system: "The values (by order of magnitude) of many cgs units turned out to be inconvenient for practical purposes. For example, many everyday length measurements yield hundreds or thousands of centimetres, such as those of human height and sizes of rooms and buildings" and "The units gram and centimetre remain useful .., especially for instructional physics and chemistry experiments, where they match the small scale of table-top setups". That does not make sense, does it? Lengths and masses are expressed identically in cgs and mks, when using the prefixes properly: 5 meters is 5 meters and 7 kilograms is 7 kilograms.
An alternative explanation is given elsewhere in the thread: Cgs was replaced by mks because mks turned out to be the only system of units in which volt, ohm, and ampere are coherent with our units of length, mass, and time. The cgs, which was adopted by the 1881 International Electrical Congress (IEC), contained three electrical quantities with a prototype: voltage, resistance and current. The coherent cgs-units were abvolt, abohm and abampere. The prototypes were called volt (a specification using a chemical cell), ohm (a thin, long column of mercury), and ampere (current which deposits silver by electrolysis at a certain rate). The cgs-units abvolt and abohm were unpractically small, 1 abvolt = 10-8 volt and 1 abohm = 10-9 ohm. Because of the large difference between these electrical base units and their prototypes, the cgs was unsatisfactory. Giorgi discovered that the prototype units were coherent in another unit system, mksA. Ampere's Force Law, which relates current to force, got a new coefficient in the mksA system (2·10-7 instead of 2). The mksA system was adopted some time later by the IEC. Fortuitously, in the new unit system, the base units for mass and length coincided with the prototypes from 1799 (kilogram and meter). Just lucky, not on purpose.
In my opinion the alternative explanation is better. Ceinturion ( talk) 16:56, 1 September 2011 (UTC)
It seems strange to me that this section does not even mention the units of the
gauss,
maxwell (unit), and
oersted. Those contain statemts like "two charges one centimeter apart". That sounds like CGS to me.
`=
98.67.108.12 (
talk) 23:06, 31 August 2012 (UTC)
In the sections "Electrostatic units (ESU)" and "Electromagnetic units (EMU)", we have the definitions
and
It would seem that
where . It is true by definition that
and it can be readily checked that
and
A direct comparison of the three equations would argue that
This also illustrates that should always be considered as an inseparable whole when dealing with unit transformations.
Machina Lucis ( talk) 03:07, 19 June 2013 (UTC)
One might first note that the great confusions with the CGS comes from the use of the incorrect theories applied to SI, and that there really is only one CGS system. The fault is not in these systems, but incorrect terminology applied in dimensional analysis.
Quantities have 'scales', and it is the scales that have 'dimensions', when these numbers are set in a body of equations. The number, choice and use of the base quantities is purely arbitary.
CGS was accepted at the 1873 meeting of the British Association for the Advancement of Science, (ie BA). The system was accepted on the assumption of 'length, density of water, second'. Maxwell insisted the density of water ought be one. The system we have is not the Gauss-weber (mm, mg, s) or Thompson (lord Kelvin's) dm, kg, s, but the cm,g,s. With this system, one moves away from calling systems 'metric' vs 'imperial', to base units in line with Gauss's paper "mass, length, time", which provided the 'body of equations' necessary for dimensional analysis.
Concurrent with this, two units that Prof Preece had suggested in 1861 for the foot,pound,second were used to represent the CGS units of the same scale, ie dyne, erg. The sub-multiples are prepended by an ordinal, the super-multiples postpenend by a cardinal. An Angstrom is 10^{-10} metres, is a 'tenth-metre', while a quadrant of 10,000 km, is a 'metre-seven'. Stevins (1580, La Disma) first proposed the use of pre-pended cardinals to describe decimal fractions. The system, with base sixty, is the current source of 'second', 'minute', of both time and angle, the 'third' is occasionally met in this context.
Former bodies of equations describe the technical gravitational, and thermal units, these were implemented in the foot-pound-second, and copied into the cgs, to the extent of seperate scales of mass, force, and energy (slug, pound, ft.pound, copied to glug, gram = pond, and gram.cm), the thermal units copied from Btu (which is what James Prescott Joule converts into 778 foot.pounds) into calories, and lb.mole into g.mole. The loss of these bodies of equations in modern teaching leads to a lot of confusion as to what is going on. This process has been ongoing to those who slavishly apply Gauss's LMT theory to where it does not apply. (eg 'foot-slug-second', when in fact, the slug is derived from mass at gMT^2/L in all systems.)
ELECTRIC AND MAGNETIC UNITS
Separate electric and magnetic units exist long before Maxwell's work. These are extensions on CGS, where we find Gauss defining the units of charge, ie 'electrical mass' and 'magnetic mass' as those quantities which, placed at unit length, exit unit force. From this, magnetism is developed parallel with electric fields, which leads to the parallel names when set out this way. F = QE = PH (where P is a 'unit pole'). Gauss and Maxwell used (mm,mg,s) units, but the theory gives units in the foot-pound-second (fpse, fpsm), the cgs (cgse, cgsm), and metre-gram-second (mgse, mgsm).
The theory evolved (with sidelines), into the electromagnetic system. Since electromagnetism is connected, there is a constant governing electricity from magnetism etc. The unifying constant is what we shall call the 'electro-magnetic velocity constant', or EMV. A common all-system definition of the EMV follows.
If one takes two infinite wires as per the definition of the ampere, one can calculate on one case, the force due to magnetism, F, due to currents Q/T. In a second case, calculate the electric force, due to a charge F and Q/L. When F and Q are set equal in these equations, then L/T is the EMV, and is independent of the setup, arising purely from the constants of space. Weber and Kohlrausch measured this value in 1856.
Maxwell derived his theory of electromagnetism from the dynamics of a viscousless fluid, and among the twenty equations, we find the basis of modern electromagnetism. Among other things, he showed that the charge-free solution to the fields is a wave traveling at the EMV, and compared Weber and Kohlrauch's value with Fizeau's speed of light, concluding that light travels in the same ether as the EM waves.
CGS inherited all of this. The electrostatic and electromagnetic units differ by powers of the EMV, which is normally written as 'c', when electric units are measured in esu, and magnetic stuff in emu.
PRACTICAL ELECTRICAL UNITS
The same BA 1873 annual report that created the CGS system, talks of practical units. Until 1861, the style of creating electrical units was to construct a voltaic cell, a resistor of wire, or a capacitor, whose dimensions were given in feet or metres. The units using natural media to transfer dimension, such as a 'gallon = 10 lb water' were designated as 'Practical'. A unit constructed in theory, as 'gallon = 231 cu in', are 'absolute'.
Because no 'absolute' implementations of the electrical units were forthcoming, the pattern was to continue with 'practical' definitions, but define the experimental setup in units derived from 'decade' units of the metric electromagnetic units. The 'volt' is the decade unit nearest the potential of the Daniell's cell, the 'ohm' is the decade unit nearest the resistance of a metre 'wire' of mercury, one square millimetre in section (Siemens Unit). The definitions and names would be extended and amended, national systems giving way to an 'international' set of 'practical units'.
The system was never complete, and used with the regular length-mass-time system, so it's not unusual to see 'volts per inch', or 'ampere-centimetres'. Unlike the esu and emu (which never had names), this system always had names.
The Hansen system of 1904 is the co-junction of the practical electric units with the CGS mechanical system, the cgs-emu were of sufficient size for the IEEE to be reluctantly coerced to provide names for the gauss, maxwell, gilbert and oersted. The 1947 SI system provides names tesla, weber for the first two.
THE KENNELEY SYSTEM
The common, but unapproved system, was to prepend stat- and ab- to the practical units, to create the electrostatic and electromagnetic units. The system provides all sorts of names for the erstwhile unnamed CGS units, the Gaussian can be regarded as a mix of esu and emu. Simply knowing the gaussian unit gives already the cgse, the cgsm, the practical unit, and the Hansen unit, eg statcoulomb, abcoulomb, coulomb, coulomb.
The system fails under rationalisation, which is why it was unapproved.
RATIONALISATION
Oliver Heaviside wrote a system of electricty, wherein the displacement current is directly associated with the reduction of flux, thereon saguinely crossing barriers where a 4pi had existed. Half way through volume one of 'electromagnetic papers', is a section on the 'eruption of 4pi's'. Rationalisation only really appears when one starts from something that resembles Maxwell's equations. Rationalised Gravity has gravity-style maxwell's equations.
Rationalisation can as readily be accomidated by a kenneley style suffix, where an 'unrationalised' system is a mixture of two or three different 'rationalised' systems. When one takes to account the Kenneley prefix handles 'c', and a suffix would handle '4pi', the basic Gaussian theory is a mixture of no fewer than seven different systems.
This has not been done this way. Instead, the process is to rely on dimensional analysis, and to write a body of equations that will reduce to the desired systems, and the conversions by dimensions, then correctly handles all systems.
SIX BASE UNITS
The common theory supposes that one adds unit constants in one's "home" theory, and then allow these to assume non-unit values in other theories. Leo Young (1961: System of Units in Electromagnetism), 'proves' that two constants suffice. It suffices to use CGS Gaussian and an SI sources, and add to SI constants S and U (as Young does), such that in SI, S=U=1, and in Gausian S=4pi, U=1/c. These are given various physical interpretations, but Young advises against this.
Whereapon, it is possible, to allow S and U to assume various values that one directly derives the Heaviside Lorentz formulae, the unrational theory of the CGSE, CGSM, etc. In terms of the SI+SU theory, we get Maxwell's equations at follows, where
S=U=1 in SI S=4pi, U=1/c Gaussian.
Ampere Scalar \nabla \cdot D = \rho S Ampere Vector \nabla \times H = U dD/dt + J SU Faraday Scalar \nabla \cdot B = 0 Faraday Vector \nabla \times E = -U dB/dt
\epsilon \mu c^2 U^2 = 1
One could then use lower case 's', 'u' for the various cgs systems, giving modern rational theory as S=U=1, HLU puts S=u=1, gaussian s=u=1.
Of \epsilon\mu c^2 U^2 = 1, one can set any two to one (except c), to get esu (\mu=1/c^2), emu (\epsilon = 1), and gaussian (U=1/c).
U, u is always handled in dimensions, since in the CGS, U is dimensionless, and u has the dimensions of T/L. Even without this, one can restore all values of c, present or absent, simply by assuming SI dimensions and any missing L/T becomes a 'c'.
S, s is always dimensionless. Indeed, the susceptability constant, and equations like D = \epsilon E + SP, and B = \mu H + SJ are now taken as the definitions of these measures, but no-one explains how the 4pi creeps in.
RATIONALISATION
As noted above, the unrationalised system can be treated as a mixture of rationalised systems, the variations cause the appearence of factors like 4pi etc. In practice, the dimensional analysis supposes that SI Q or I, can be replaced by IU, IS, IUS, etc to generate a number of the constituant systems.
Rationalisation is about replacing s (which occurs in Ampere's and Coulomb's equations), with S (as in maxwell's equations).
ampere equation F/L = 2(s\mu) I.I/ R = 2(\mu S/4pi) I I / R coulomb equation F = (s/\epsilon) Q^Q R^2 = (S/ 4\pi espilon) QQ/R^2.
In an unrationalised system, s=1, and coulomb's constant is equal to the inverse permittivity. Ampere's constant is then equal to the permeability.
In a rationalised system, one preserves \epsilon, \mu [as Heaviside and Lorentz suggests], or Q and I [as Giorgi does]. Since charge is elsewhere defined, this is why the second choice won out.
We can now derive what constants belong to each of the seven modern-style systems, from gaussian. Since all other systems fit in between, bu adjusting S or U respectively, this covers all the systems that have been used. Note that with QQS etc, the additional dimensions only appear when the power of Q is even.
esu: Q E, P, Q, I, Coulomb-constant K_c [stat] QS D, \phi [stat-ade] QQS \epsilon [stat-ero] emu: QU B, M, ampere current I, Ampere-constant K_A [ab] QUS H, J, Unit-pole, [ab-ade] QQUUS \mu [ab-ero] other: QQUS Z (impedence of free space) [nen-ero]
You use this table to replace the SI dimension Q or I with the extra base units. For example, the magnetic pole is measured in webers (ML^2/TQ), as an emu. It becomes ML^2/TQUS. Unit pole Permeability M 1 gram = 1e-3 kg 1e-3 M 1 gram 1e-3 kg 1e-3 L 1 cm = 1e-2 m 1e-4 L 1 cm 1e-2 m 1e-2 T 1 s = 1 s 1e 0 T 1 s 1e0 s 1e0 QU 1 Bi.s = 10 A 1e-1 QU 1 Bi.s 10 C 1e-2 S s=1/4pi S 4pi S s 1/4pi S 4pi 1 Unit Pole 4pi E-8 Wb µ = 4pi * 10^-7 H/m
So for example, consider the units measured in SI at 'ampere'
1. Q/T I franklin/second as 10/c Amperes, c in cm/s. 2. QU/T biot (measured as an emu) for U => c 3. QUS/T oersted (10/4pi Amperes) for S => 1/4pi 4. QS line of flux as 10/4pi c, Coulombs.
The HLU units here puts QQS (unrationalised), = qqs rationalised, and putting S=4pi, makes q=1/sqrt(4pi). S=1, and U=c as before,
Wendy.krieger ( talk) 14:56, 21 July 2016 (UTC)
This page is an archive of past discussions. Do not edit the contents of this page. If you wish to start a new discussion or revive an old one, please do so on the current talk page. |
This page is an archive of past discussions. Do not edit the contents of this page. If you wish to start a new discussion or revive an old one, please do so on the current talk page. |
Is this system still in use. To my knowledge nowadays international standards recommend people to use SI which is done in Europe.
It's used primarily in physics E&M textbooks because the coulomb and tesla are rediculously large, and in SI they are different units. In CGS, the Gauss is the same as a statvolt/meter. I suppose that it is primarily an informational peice, mainly for completeness.--BlackGriffen
The equations for the force due to magnetic field and other magnetic equations are slightly different in CGS units than SI becuase it includes the speed of light rahter than a constant. CGS units are used in E&M textbooks becuase when using CGS units it is more obvious that magnetic forces are simply a consequence of relativity rather than a phenomena on their own.
They were used not so long ago in physics papers (20-30 years) and they are still used by people which works with magnetic fields. Braice ( talk) 11:37, 4 December 2008 (UTC)
It should be mentioned that chemists only recently converted from cgs to SI units. I suspect that it will be a long time before people who work in the lab use kilograms instead of grams.
Even today the lack of mks units for such quantities as magnetic flux density and viscosity leads people to continue using the gauss and the centipoise. —The preceding unsigned comment was added by 71.250.142.249 ( talk • contribs) .
So, much as I hate to throw anything new in here after a few months, I thought it was prudent to note that astronomers still use CGS units. I'm taking classes and trying to deal with the electromagnetic units are more of a headache than anything else, but every astronomy class that I've had has only grudgingly accepted MKS units instead of CGS. And sometimes its more of a headache trying to figure out how to modify equations written for CGS into MKS anyway. But yeah, astronomers haven't switched yet. Adrieth ( talk) 07:55, 26 March 2009 (UTC)
A centimeter is the capacitance between a 1-cm sphere in vacuum and infinity. Is this true in the CGS system? It doesn't make sense to someone raised on SI units. Could this sentence be better worded to explain why a unit normally used for distance is also a unit of capacitance, please? -- Heron
Yes, it is true, although it is a 1 cm radius sphere I think. The concept of capacitance being used in this case is this: if you start out with this sphere and some charge Q at a distance of infinity from the sphere, then you force that charge to come from infinity to the sphere, little by little, then the energy required to do this is E, where E=0.5*Q^2/C. In other words, the energy required to compress a charge Q from infinitely spread-out down into a sphere of radius 1 cm.
72.70.42.173 (
talk) 19:00, 6 January 2012 (UTC)
Would anyone object to my removing the 'not used' from Gauss? I, and many others astronomers, use them every day.
He's far better known for his contributions to mathematics IMO he should be referred to as a mathematian rather than an astronomer (readers can read about his many other talents on the Gauss page).
In his recent edit summary, Crissov stated "clearer distinction between mechanical and electromechanic CGS is needed".
Even allowing for the fact that edit summaries are often cryptic, that is not what is needed. These aren't what need to be "distinguished". The likely reason that the mechanical units are listed separately is not because they need to be distiguished, but rather that they are pretty much common to all the various cgs systems. It is the electrical and magnetic units, and the electromagnetic system, the electromagnetic system, and the hybrid Gaussian system which need to be better distinguished (all sharing the same mechanical units). Another distinction can be made between three-base-unit (with, for example, electrical charge measured in units of erg1/2·cm1/2) and four-base-unit systems using a franklin or a biot as a base unit, and between rationalized and non-rationalized systems. It hurts my head to even try to figure them all out; thank God for the International System of Units. Gene Nygaard 21:30, 24 September 2005 (UTC)
What's wrong: k_1/k_2=c^2 or k_2 in the electrostatic cgs system?
I propose a separate spin-off article, Gaussian units (or cgs-Gaussian units or Gaussian-cgs units). My reasoning:
The article would list out the units and their conversions, Maxwell's equations and the Lorentz force law in Gaussian units, physical constants in Gaussian, something like the SI-Gaussian translation guide from the appendix of Jackson's E&M textbook, and where it's used in the world. Obviously it would link to this article as the place to learn about cgs in general, and also for more general notes on unit systems.
Thoughts? :-) -- Steve ( talk) 23:11, 23 December 2008 (UTC)
This article repeatedly praises CGS/Gaussian units for reducing pre-factors in Maxwell's Equations and giving and fields the same units. So, those things may make the equations easier to read and write, but they generally make it an absolute NIGHTMARE to figure out what those equations actually mean, and to do unit analysis.
For example, electrostatic units posit that the basic unit of charge is the statcoulomb, which is = √(g·cm3/s2). Likewise the unit of resistance is s/cm and that of capacitance, cm. These are quite unintuitive and disagree with the intuitive notion of electric charge as a unit distinct from other physical quantities like mass, time, and distance. And a the article itself explains, there are multiple choices for the basic units, further complicating things.
In my experience, only theoretical physicists prefer CGS units (and not all of them). Experimentalists who have to compare values from equations to actual measurable quantities typically hate them with a passion, since they make it so hard to relate E&M and mechanical quantities in an intuitive, consistent way. So I'd like to rewrite the article to reflect these issues. Can anyone suggest a good approach, or any good sources?? Moxfyre ( ÇɹʎℲxoɯ | contrib) 16:54, 29 April 2009 (UTC)
Woohoo, found one! Here is a very good explanation by a German professor of why CGS units are horribly ambiguous and yield the temptation to compare to mechanical units in nonsensical ways. Moxfyre ( ÇɹʎℲxoɯ | contrib) 23:07, 29 April 2009 (UTC)
As I proposed above, I just made a dedicated article for Gaussian units. -- Steve ( talk) 07:25, 4 August 2009 (UTC)
I added a note to clarify the meaning of impedance of free space. It would appear to be correct (i.e. E/H by definition) for ESU, EMU and Gaussian, but should the value not then be 4π instead of 1 for Heaviside-Lorentz units? —Preceding unsigned comment added by 194.81.223.66 ( talk) 15:41, 12 August 2009 (UTC)
The units gram and centimetre remain useful as prefixed units within the SI system, What's the prefix on "gram"Â ? Very logical system, this SI system. Base units don't have prefixes, except for the kilogram. -- Wtshymanski ( talk) 16:32, 16 July 2010 (UTC)
We presently have " c = 29,979,245,800 ≈ 3·1010 " used as if it were a dimensionless number rather than a speed in cm/s. This is at best confusing. LeadSongDog come howl! 18:41, 11 August 2010 (UTC)
A thread in Physics Forums discusses how this wikipedia article explains the replacement of the cgs- by the mks-system: "The values (by order of magnitude) of many cgs units turned out to be inconvenient for practical purposes. For example, many everyday length measurements yield hundreds or thousands of centimetres, such as those of human height and sizes of rooms and buildings" and "The units gram and centimetre remain useful .., especially for instructional physics and chemistry experiments, where they match the small scale of table-top setups". That does not make sense, does it? Lengths and masses are expressed identically in cgs and mks, when using the prefixes properly: 5 meters is 5 meters and 7 kilograms is 7 kilograms.
An alternative explanation is given elsewhere in the thread: Cgs was replaced by mks because mks turned out to be the only system of units in which volt, ohm, and ampere are coherent with our units of length, mass, and time. The cgs, which was adopted by the 1881 International Electrical Congress (IEC), contained three electrical quantities with a prototype: voltage, resistance and current. The coherent cgs-units were abvolt, abohm and abampere. The prototypes were called volt (a specification using a chemical cell), ohm (a thin, long column of mercury), and ampere (current which deposits silver by electrolysis at a certain rate). The cgs-units abvolt and abohm were unpractically small, 1 abvolt = 10-8 volt and 1 abohm = 10-9 ohm. Because of the large difference between these electrical base units and their prototypes, the cgs was unsatisfactory. Giorgi discovered that the prototype units were coherent in another unit system, mksA. Ampere's Force Law, which relates current to force, got a new coefficient in the mksA system (2·10-7 instead of 2). The mksA system was adopted some time later by the IEC. Fortuitously, in the new unit system, the base units for mass and length coincided with the prototypes from 1799 (kilogram and meter). Just lucky, not on purpose.
In my opinion the alternative explanation is better. Ceinturion ( talk) 16:56, 1 September 2011 (UTC)
It seems strange to me that this section does not even mention the units of the
gauss,
maxwell (unit), and
oersted. Those contain statemts like "two charges one centimeter apart". That sounds like CGS to me.
`=
98.67.108.12 (
talk) 23:06, 31 August 2012 (UTC)
In the sections "Electrostatic units (ESU)" and "Electromagnetic units (EMU)", we have the definitions
and
It would seem that
where . It is true by definition that
and it can be readily checked that
and
A direct comparison of the three equations would argue that
This also illustrates that should always be considered as an inseparable whole when dealing with unit transformations.
Machina Lucis ( talk) 03:07, 19 June 2013 (UTC)
One might first note that the great confusions with the CGS comes from the use of the incorrect theories applied to SI, and that there really is only one CGS system. The fault is not in these systems, but incorrect terminology applied in dimensional analysis.
Quantities have 'scales', and it is the scales that have 'dimensions', when these numbers are set in a body of equations. The number, choice and use of the base quantities is purely arbitary.
CGS was accepted at the 1873 meeting of the British Association for the Advancement of Science, (ie BA). The system was accepted on the assumption of 'length, density of water, second'. Maxwell insisted the density of water ought be one. The system we have is not the Gauss-weber (mm, mg, s) or Thompson (lord Kelvin's) dm, kg, s, but the cm,g,s. With this system, one moves away from calling systems 'metric' vs 'imperial', to base units in line with Gauss's paper "mass, length, time", which provided the 'body of equations' necessary for dimensional analysis.
Concurrent with this, two units that Prof Preece had suggested in 1861 for the foot,pound,second were used to represent the CGS units of the same scale, ie dyne, erg. The sub-multiples are prepended by an ordinal, the super-multiples postpenend by a cardinal. An Angstrom is 10^{-10} metres, is a 'tenth-metre', while a quadrant of 10,000 km, is a 'metre-seven'. Stevins (1580, La Disma) first proposed the use of pre-pended cardinals to describe decimal fractions. The system, with base sixty, is the current source of 'second', 'minute', of both time and angle, the 'third' is occasionally met in this context.
Former bodies of equations describe the technical gravitational, and thermal units, these were implemented in the foot-pound-second, and copied into the cgs, to the extent of seperate scales of mass, force, and energy (slug, pound, ft.pound, copied to glug, gram = pond, and gram.cm), the thermal units copied from Btu (which is what James Prescott Joule converts into 778 foot.pounds) into calories, and lb.mole into g.mole. The loss of these bodies of equations in modern teaching leads to a lot of confusion as to what is going on. This process has been ongoing to those who slavishly apply Gauss's LMT theory to where it does not apply. (eg 'foot-slug-second', when in fact, the slug is derived from mass at gMT^2/L in all systems.)
ELECTRIC AND MAGNETIC UNITS
Separate electric and magnetic units exist long before Maxwell's work. These are extensions on CGS, where we find Gauss defining the units of charge, ie 'electrical mass' and 'magnetic mass' as those quantities which, placed at unit length, exit unit force. From this, magnetism is developed parallel with electric fields, which leads to the parallel names when set out this way. F = QE = PH (where P is a 'unit pole'). Gauss and Maxwell used (mm,mg,s) units, but the theory gives units in the foot-pound-second (fpse, fpsm), the cgs (cgse, cgsm), and metre-gram-second (mgse, mgsm).
The theory evolved (with sidelines), into the electromagnetic system. Since electromagnetism is connected, there is a constant governing electricity from magnetism etc. The unifying constant is what we shall call the 'electro-magnetic velocity constant', or EMV. A common all-system definition of the EMV follows.
If one takes two infinite wires as per the definition of the ampere, one can calculate on one case, the force due to magnetism, F, due to currents Q/T. In a second case, calculate the electric force, due to a charge F and Q/L. When F and Q are set equal in these equations, then L/T is the EMV, and is independent of the setup, arising purely from the constants of space. Weber and Kohlrausch measured this value in 1856.
Maxwell derived his theory of electromagnetism from the dynamics of a viscousless fluid, and among the twenty equations, we find the basis of modern electromagnetism. Among other things, he showed that the charge-free solution to the fields is a wave traveling at the EMV, and compared Weber and Kohlrauch's value with Fizeau's speed of light, concluding that light travels in the same ether as the EM waves.
CGS inherited all of this. The electrostatic and electromagnetic units differ by powers of the EMV, which is normally written as 'c', when electric units are measured in esu, and magnetic stuff in emu.
PRACTICAL ELECTRICAL UNITS
The same BA 1873 annual report that created the CGS system, talks of practical units. Until 1861, the style of creating electrical units was to construct a voltaic cell, a resistor of wire, or a capacitor, whose dimensions were given in feet or metres. The units using natural media to transfer dimension, such as a 'gallon = 10 lb water' were designated as 'Practical'. A unit constructed in theory, as 'gallon = 231 cu in', are 'absolute'.
Because no 'absolute' implementations of the electrical units were forthcoming, the pattern was to continue with 'practical' definitions, but define the experimental setup in units derived from 'decade' units of the metric electromagnetic units. The 'volt' is the decade unit nearest the potential of the Daniell's cell, the 'ohm' is the decade unit nearest the resistance of a metre 'wire' of mercury, one square millimetre in section (Siemens Unit). The definitions and names would be extended and amended, national systems giving way to an 'international' set of 'practical units'.
The system was never complete, and used with the regular length-mass-time system, so it's not unusual to see 'volts per inch', or 'ampere-centimetres'. Unlike the esu and emu (which never had names), this system always had names.
The Hansen system of 1904 is the co-junction of the practical electric units with the CGS mechanical system, the cgs-emu were of sufficient size for the IEEE to be reluctantly coerced to provide names for the gauss, maxwell, gilbert and oersted. The 1947 SI system provides names tesla, weber for the first two.
THE KENNELEY SYSTEM
The common, but unapproved system, was to prepend stat- and ab- to the practical units, to create the electrostatic and electromagnetic units. The system provides all sorts of names for the erstwhile unnamed CGS units, the Gaussian can be regarded as a mix of esu and emu. Simply knowing the gaussian unit gives already the cgse, the cgsm, the practical unit, and the Hansen unit, eg statcoulomb, abcoulomb, coulomb, coulomb.
The system fails under rationalisation, which is why it was unapproved.
RATIONALISATION
Oliver Heaviside wrote a system of electricty, wherein the displacement current is directly associated with the reduction of flux, thereon saguinely crossing barriers where a 4pi had existed. Half way through volume one of 'electromagnetic papers', is a section on the 'eruption of 4pi's'. Rationalisation only really appears when one starts from something that resembles Maxwell's equations. Rationalised Gravity has gravity-style maxwell's equations.
Rationalisation can as readily be accomidated by a kenneley style suffix, where an 'unrationalised' system is a mixture of two or three different 'rationalised' systems. When one takes to account the Kenneley prefix handles 'c', and a suffix would handle '4pi', the basic Gaussian theory is a mixture of no fewer than seven different systems.
This has not been done this way. Instead, the process is to rely on dimensional analysis, and to write a body of equations that will reduce to the desired systems, and the conversions by dimensions, then correctly handles all systems.
SIX BASE UNITS
The common theory supposes that one adds unit constants in one's "home" theory, and then allow these to assume non-unit values in other theories. Leo Young (1961: System of Units in Electromagnetism), 'proves' that two constants suffice. It suffices to use CGS Gaussian and an SI sources, and add to SI constants S and U (as Young does), such that in SI, S=U=1, and in Gausian S=4pi, U=1/c. These are given various physical interpretations, but Young advises against this.
Whereapon, it is possible, to allow S and U to assume various values that one directly derives the Heaviside Lorentz formulae, the unrational theory of the CGSE, CGSM, etc. In terms of the SI+SU theory, we get Maxwell's equations at follows, where
S=U=1 in SI S=4pi, U=1/c Gaussian.
Ampere Scalar \nabla \cdot D = \rho S Ampere Vector \nabla \times H = U dD/dt + J SU Faraday Scalar \nabla \cdot B = 0 Faraday Vector \nabla \times E = -U dB/dt
\epsilon \mu c^2 U^2 = 1
One could then use lower case 's', 'u' for the various cgs systems, giving modern rational theory as S=U=1, HLU puts S=u=1, gaussian s=u=1.
Of \epsilon\mu c^2 U^2 = 1, one can set any two to one (except c), to get esu (\mu=1/c^2), emu (\epsilon = 1), and gaussian (U=1/c).
U, u is always handled in dimensions, since in the CGS, U is dimensionless, and u has the dimensions of T/L. Even without this, one can restore all values of c, present or absent, simply by assuming SI dimensions and any missing L/T becomes a 'c'.
S, s is always dimensionless. Indeed, the susceptability constant, and equations like D = \epsilon E + SP, and B = \mu H + SJ are now taken as the definitions of these measures, but no-one explains how the 4pi creeps in.
RATIONALISATION
As noted above, the unrationalised system can be treated as a mixture of rationalised systems, the variations cause the appearence of factors like 4pi etc. In practice, the dimensional analysis supposes that SI Q or I, can be replaced by IU, IS, IUS, etc to generate a number of the constituant systems.
Rationalisation is about replacing s (which occurs in Ampere's and Coulomb's equations), with S (as in maxwell's equations).
ampere equation F/L = 2(s\mu) I.I/ R = 2(\mu S/4pi) I I / R coulomb equation F = (s/\epsilon) Q^Q R^2 = (S/ 4\pi espilon) QQ/R^2.
In an unrationalised system, s=1, and coulomb's constant is equal to the inverse permittivity. Ampere's constant is then equal to the permeability.
In a rationalised system, one preserves \epsilon, \mu [as Heaviside and Lorentz suggests], or Q and I [as Giorgi does]. Since charge is elsewhere defined, this is why the second choice won out.
We can now derive what constants belong to each of the seven modern-style systems, from gaussian. Since all other systems fit in between, bu adjusting S or U respectively, this covers all the systems that have been used. Note that with QQS etc, the additional dimensions only appear when the power of Q is even.
esu: Q E, P, Q, I, Coulomb-constant K_c [stat] QS D, \phi [stat-ade] QQS \epsilon [stat-ero] emu: QU B, M, ampere current I, Ampere-constant K_A [ab] QUS H, J, Unit-pole, [ab-ade] QQUUS \mu [ab-ero] other: QQUS Z (impedence of free space) [nen-ero]
You use this table to replace the SI dimension Q or I with the extra base units. For example, the magnetic pole is measured in webers (ML^2/TQ), as an emu. It becomes ML^2/TQUS. Unit pole Permeability M 1 gram = 1e-3 kg 1e-3 M 1 gram 1e-3 kg 1e-3 L 1 cm = 1e-2 m 1e-4 L 1 cm 1e-2 m 1e-2 T 1 s = 1 s 1e 0 T 1 s 1e0 s 1e0 QU 1 Bi.s = 10 A 1e-1 QU 1 Bi.s 10 C 1e-2 S s=1/4pi S 4pi S s 1/4pi S 4pi 1 Unit Pole 4pi E-8 Wb µ = 4pi * 10^-7 H/m
So for example, consider the units measured in SI at 'ampere'
1. Q/T I franklin/second as 10/c Amperes, c in cm/s. 2. QU/T biot (measured as an emu) for U => c 3. QUS/T oersted (10/4pi Amperes) for S => 1/4pi 4. QS line of flux as 10/4pi c, Coulombs.
The HLU units here puts QQS (unrationalised), = qqs rationalised, and putting S=4pi, makes q=1/sqrt(4pi). S=1, and U=c as before,
Wendy.krieger ( talk) 14:56, 21 July 2016 (UTC)
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