Talk:Centimetre–gram–second system of units/Archive 1

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Archive 1

Is this system still in use?

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

Not quite true! First of all, gauss is part of EMU, and statV/m is part of ESU, so they should not be mixed freely. Only in Gaussian and Heaviside-Lorentz variants, the B and E fields have the same units, — this is where this particular confusion could have come from (statV/m is a unit of electric field in ESU).Xenonice (talk) 17:50, 14 May 2009 (UTC)

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)

Math formatting does not seem to be working. Does anyone know why?

Wikipedia seems to convert simple math to greek font + subscripts.Xenonice (talk) 17:50, 14 May 2009 (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) .

Grams are very much a part of SI. Where'd you ever get the idea they are not? There is no lack of SI units for the quantities you mentioned, either. In fact, the SI unit corresponding to the gauss is the tesla, like the gauss with a special one-word name. The SI unit of dynamic viscosity is the pascal second. Gene Nygaard 04:04, 30 March 2006 (UTC)

The SI unit for mass is the kilogram, not the gram, just as for length it is the meter instead of the centimeter. Furthermore, while you are correct that the Tesla is the SI unit for magnetic flux density, mks/SI has no unit for the magnetic field strength H (equivalent to the cgs Oersted). -Athaler (talk) 20:35, 3 June 2008 (UTC)

This is quite sterile, one can also say that the gauss=oersted=statvolt/cm=statcoulomb/cm^2. It's like counting energy in petrol Barrels or TNT kilotons, It's the same thing but called differently according to the context. A system of unit, in my opinion, should not have to different names for the same thing. Braice (talk) 11:42, 4 December 2008 (UTC)

Braice, the philosophy of dimensionally-equivalent units is described here. You're right that gaussian-cgs does that. SI does it too, e.g. becquerel = hertz, Newton metre = Joule, etc. The idea is that people are less likely to get confused, although it does sometimes feel like an insult to one's intelligence. :-) --Steve (talk) 22:55, 23 December 2008 (UTC)

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)

Definition of the centimetre

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)

I also remember it being radius 1cm, but didn't check just now.

See Gaussian units for some more explanation...The unit of charge in gaussian units (in base units) is g^1/2 cm^3/2 s⁻¹ , and the unit of voltage (in base units) is cm^1/2 g^1/2 s⁻¹. Since capacitance is charge divided by voltage, the unit of capacitance is cm. :-) --Steve (talk) 19:33, 6 January 2012 (UTC)

Capacitance in the esu and gaussian has the dimensions of length. One finds a capacitance and then derives a matching length, and supposes that is what is meant. A 1-cm sphere is in common parlence a sphere of 1 cm diameter. The capacitance of a sphere is the same as its radius in these systems. Note the HLU has a different capacitance, corresponding to a capacitance of opposite faces of a 1 cm cube. Wendy.krieger (talk) 10:28, 30 November 2014 (UTC)

Gauss

Would anyone object to my removing the 'not used' from Gauss? I, and many others astronomers, use them every day.

More Gauss

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).

Done. Markus Kuhn 13:17, 7 August 2005 (UTC)

Various cgs systems

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 erg^1/2·cm^1/2) 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)

Well, it was a big pain, but it is mostly done. Please take a look.Xenonice (talk) 17:50, 14 May 2009 (UTC)

relation of constants

What's wrong: k_1/k_2=c^2 or k_2 in the electrostatic cgs system?

That whole section was quite a mess! The problem is, there are about a dozen conflicting definitions of CGS electro-magnetic systems, and a lot of people "mix and match" units from different definitions. Lack of named units (such as Volt, Ampere) doesn't help at all! I tried to fix the mess, but more work is needed to bring together all the conflicting definitions, sources citing them, and to sort this all out! Xenonice (talk) 14:13, 20 October 2008 (UTC)

Fixed now, to the best of my knowledge.Xenonice (talk) 17:50, 14 May 2009 (UTC)

From PNA/Physics

Oersted,Centimetre gram second system of units in my humble opinion those article should at least contain the same information as the appendix of Jackson's electrodynamic --LN2 05:46, 18 February 2006 (UTC)

Proposal: Spin-off article on the Gaussian System of Units

I propose a separate spin-off article, Gaussian units (or cgs-Gaussian units or Gaussian-cgs units). My reasoning:

Gaussian-cgs is much more common (in my experience) than the other cgs types. It would be nice to have a less-cluttered article focusing on just that unit system.
Tons of wikipedia electricity/magnetism articles discuss "cgs units" when they actually mean "cgs-Gaussian units". There's an ambiguity there, and it would be very nice to be able to fix that ambiguity by going through and (where appropriate) replacing links that point to cgs units with links that point to cgs-Gaussian units. That would be easier than changing the text of all those different articles to clarify "cgs-Gaussian". Especially when "cgs" is in those contexts a legitimate synonym for cgs-Gaussian.

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)

I think it is a great idea, Steve! That way, we can keep the discussion of the reasoning behind and the differences between all the related cgs systems here, and refer to your new page for quick answers about unit conversion, where appropriate. I would call the new article "Gaussian System of Units", similar to International System of Units. Also take note of this compendium of less-known gaussian unit names from hypertextbook.com. Xenonice (talk) 20:52, 15 January 2009 (UTC)

This article seems way too "pro-CGS"

This article repeatedly praises CGS/Gaussian units for reducing pre-factors in Maxwell's Equations and giving ${\vec {E}}$ and ${\vec {B}}$ 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 (ǝɹʎℲxoɯ | contrib) 16:54, 29 April 2009 (UTC)

I agree with most of what you said, but I think we cannot just dismiss the CGS out of hand. We need to establish clarity where it is most sorely needed. One thing that would be nice, is to have two more tables that compare the following aspects of the three systems (SI, ESU and EMU) or maybe even including Gaussian and Heaviside-Lorentz: (1) Dimensional analysis (e.g. Current is I in SI, L^1/2M^3/2T^-2 in ESU, etc.), and (2) Equations and laws of electromagnetism in each system, with the prefactors explicitly written.Xenonice (talk) 17:50, 14 May 2009 (UTC)

When I read it, it seems neither pro-cgs nor anti-cgs throughout almost the whole article, except for the little "pro and contra" section at the end. That section definitely is bad right now...for one thing, it has no sources, for another it spends ~1 sentence pro-cgs and ~0 contra, rather than ~5 and ~5 which is what it should be. What are the other parts of the article that you see as "pro"?

Yeah, that's reasonable. The intro and history mention that CGS is no longer used in most fields, but don't really explain why. I guess I would point that out as well. Moxfyre (ǝɹʎℲxoɯ | contrib) 22:58, 29 April 2009 (UTC)

By the way, if you have a problem with measuring capacitance in cm, just imagine "cm" stands for "capacitance measurement" or something, with the conversion 1 capacitance measurement equals 1 centimeter! You're not the first one to have a problem with units taking on multiple physical meanings...Someone once had a problem with measuring radiation in Hz, so they made up a new name "becquerel" to be the unit of radiation, with the conversion 1 Bq = 1 Hz! :-) --Steve (talk) 18:55, 29 April 2009 (UTC)

True, the symbol "cm" could represent anything in principle. The problem, in my mind, is not the definition of any one particular unit, but the relationships among them. It seems that SI and CGS are based on two fundamentally distinct premises, which are outlined somewhat confusingly in this article. I would describe them as follows:

SI begins with the observation that electric charge (or current if you prefer) measures a physical quantity that is fundamentally distinct from any of the other base units of mass, length, or time. Thus a new base unit of Coulombs (or Amperes) is posited. This allows us to determine the units of all other EM quantities without any wiggle room. For example, k in $F_{e}=kq_{1}q_{2}/r^{2}$ must have units of $\mathrm {Force} \times \mathrm {Length} ^{2}/\mathrm {Charge} ^{2}$ . Likewise $k_{A}$ in Ampere's Law must have the units of $\mathrm {Force} /\mathrm {Current} ^{2}$ . Any time an EM relation gives an answer with purely mechanical units, it can be directly related to a purely mechanical quantity.
On the other hand, CGS begins with the notion that no new base units should be introduced to describe EM phenomena. Perhaps this was historically justifiable, but today seems extremely justifiable. Thus an equation like that of electrostatic force, $F_{e}=kq_{1}q_{2}/r^{2}$ , is very ambiguous. We do not know the units of either $q$ or $k$ . One of infinite possible choices would be to say that $k$ has units of Force, and thus $q$ has units of Length. This might yield an internally consistent system, but it invites apples-to-oranges comparisons with non-EM units. In such a system, the electron could have a "charge" of, say, "1 meter". There would not, however, be any physically plausible reason to compare the electron charge with any real measurable length, despite their equivalent units. We could equally choose to equate the units of Charge with those of Time, still without obtaining any physical insight that would allow us to compare charge with measurable periods of time. Furthermore, the ambiguity of this approach encourages the proliferation of multiple sub-systems of CGS, none of which is physically any more justifiable than any other, and yet all of which are incompatible.

And, that, in my mind, is why CGS is a nasty relic. When I was learning EM in a CGS-based course, I would often try to work out the units of my answers to locate math mistakes and pin down the physical relationships between things. Often I'd get the units of some seemingly mechanical quantity (length, time, speed, etc.) and try to relate it to the mechanical properties of the system. And of course, this might be totally wrong, since in the Gaussian system, length and capacitance have the same units, so working out units of "cm" cannot help a confused student figure out what they're dealing with.

So I'm wondering if anyone knows of any reliable sources that explain these difficulties, hopefully better than I do, so that I can refer to them in the article. Moxfyre (ǝɹʎℲxoɯ | contrib) 22:58, 29 April 2009 (UTC)

I added a few more references and explanations. Also, notice that the much-praised SI system is 90% plain old EMU in disguise (that is factors of 10ⁿ from cm->m and g->kg conversions, and the fact that 1 A is defined with a somewhat artificial prefactor 10^-7. The only substantial difference between SI and EMU is all the units related to H and D fields, where factors of 4π pop up in unexpected places.Xenonice (talk) 17:50, 14 May 2009 (UTC)

Quoting from above: "[In SI] Any time an EM relation gives an answer with purely mechanical units, it can be directly related to a purely mechanical quantity. [...] On the other hand, CGS begins with the notion that no new base units should be introduced to describe EM phenomena. Perhaps this was historically justifiable, but today seems extremely justifiable."

Light can hardly be called "purely mechanical", although the speed of light (which pops out of Maxwell's equations) can certainly be related to other mechanical phenomena. But more generally, relating EM and mechanical quantities is exactly what equations like Coulomb's law do. So the rationale behind CGS could be expressed by saying that if it is possible to describe EM phenomena without introducing any new dimensions then such new dimensions should be avoided because they generate spurious quantities like "the permittivity of free space" which one may be confused into thinking is a physical property of the vacuum but from the CGS viewpoint is more like an artefact of SI. Of course the same argument can be used to justify c = 1 too, going from CGS to natural units. It's a theorist's argument; the main factor it ignores is the desire to have sensible-sized numbers (i.e. of order 1) for everyday quantities. —Preceding unsigned comment added by 194.81.223.66 (talk) 16:29, 12 August 2009 (UTC)

Also, I think Bq/Hz may be the opposite problem. The same physical quantity (average frequency with which some event occurs) is expressed with TWO DIFFERENT NAMES. The frequency of a sample experiencing a decay could be reasonably compared with, say, the ticking of a pendulum. On the other hand, a 10 cm long ruler cannot reasonably be compared with "10 cm of capacitance" in Gaussian units. :-) Moxfyre (ǝɹʎℲxoɯ | contrib) 19:27, 30 April 2009 (UTC)

I added a quick explanation for why some purely electrical units become "cm" and "s/cm". But I agree, the main, biggest problem of CGS is having ONE NAME for DIFFERENT quantities (e.g. infamous "e.m.u." in place of a unit name for virtually any electromagnetic quantity).Xenonice (talk) 17:50, 14 May 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 (ǝɹʎℲxoɯ | contrib) 23:07, 29 April 2009 (UTC)

You're welcome to add that to the article, as long as the result stays neutral. Remember, a lot of informed people think cgs leads to clearer thinking and better understanding...the article shouldn't come across as taking a stand one way or the other.

I think the biggest argument against cgs is that more and more people use SI, and whatever the advantages or disadvantages of one or the other, there's an obvious advantage to having everyone communicate using the same system. That's the argument I've seen the most in textbooks etc., so I think that one should be most emphasized in a "pro and contra" section. I can provide textbook references for this. --Steve (talk) 06:42, 30 April 2009 (UTC)

Thanks, Sbyrnes. I'll definitely be careful to stay NPOV! And it's a good point that a lot of accomplished physicists, especially theorists, prefer the CGS units for emphasizing the absolute equivalence of E and B fields. And it's true that their usage is declining nonetheless. Moxfyre (ǝɹʎℲxoɯ | contrib) 19:22, 30 April 2009 (UTC)

Gaussian units now spun off

As I proposed above, I just made a dedicated article for Gaussian units. --Steve (talk) 07:25, 4 August 2009 (UTC)

Impedance of free space

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)

Definitely E=B for a light wave in Heaviside-Lorentz units. I'm not sure how permeability is defined in H-L, but I think it's a safe bet that B=H in vacuum, i.e. that vacuum permeability is 1, like it is in Gaussian. Therefore, E=B=H so E/H=1, not 4π.

A more important question question is whether E/H for a light wave is really the correct general definition for impedance of free space. What's your reasoning behind this? Is this what you get by thinking about impedance matching, e.g. making an rf signal pass from a wire to vacuum without reflection? --Steve (talk) 04:25, 13 August 2009 (UTC)

You are right about Heaviside-Lorentz. I failed to take account of the difference between Heaviside-Lorentz rationalization and MKS rationalization (the latter called Fessenden rationalization in D.L. Cohen, Demystifying Electromagnetic Equations).

As for E/H, I was merely indicating that it is the basis for the stated values. In fact, I have failed to find any reference in a selection of textbooks to "the impedance of free space" other than in SI units. Note that in SI, circuit impedance V/I and wave impedance E/H both have the same units as resistance, whereas in Gaussian units the former still does but the latter is dimensionless. So in Gaussian units it is at best confusing to call both quantities impedance. It would certainly be worth attempting to interpret 377 Ω in SI physically, as you suggest, and then asking what the corresponding physics is in Gaussian. --194.81.223.66 (talk) 09:43, 13 August 2009 (UTC)

Towards a physical interpretation. Transmission line impedance may also be written Z = √(L/C), where L and C are the inductance and capacitance per unit length. Like V/I, √(L/C) retains units of resistance even in Gaussian units. A cable "impedance-matched to the vacuum" with √(L/C) = Z₀ in SI units would have √(L/C) = 4π/c in Gaussian units (or ESU). The 4π discrepancy with the given value for Z₀ in ESU is due to the 4π in the conversion factor for H, but not for E, L or C. Likewise, the dimensionless Gaussian Z₀ is because E is taken from ESU (as are L, C, V and I) whereas H is taken from EMU. —Preceding unsigned comment added by 194.81.223.66 (talk) 11:20, 13 August 2009 (UTC)

This is interesting. But it should be said...if no one ever talks about the impedance of free space outside of SI, it shouldn't be in the table in the first place! :-) --Steve (talk) 19:01, 13 August 2009 (UTC)

The impedance of free space sounds like a contradiction in terminology. Or is the implication that the so called "free space" must have something in it, like maybe 1 nucleon/cubic meter?WFPM (talk) 20:08, 24 August 2009 (UTC)

OK, 194.81.223.66, I've taken it out of the table, since it seems not to be commonly used except within SI. WFPM, free space has 0 nucleons/cubic meter. Your question is why some people think that cgs-Gaussian units are better than SI units...in cgs-Gaussian units the "impedance of free space", such as it is, equals 1. It's more intuitive to say that the impedance of free space is 1, than that the impedance of free space is 377 ohms, the SI value. :-) --Steve (talk) 07:24, 25 August 2009 (UTC)

Prefix

The units gram and centimetre remain useful as prefixed units within the SI system, What's the prefix on "gram" ? Very logical system, this SI system. Base units don't have prefixes, except for the kilogram. --Wtshymanski (talk) 16:32, 16 July 2010 (UTC)

The milligram, microgram, nanogram, etc remain in use of course, as does the centimetre. The former to avoid "microkilogram" and the latter simply because it is a convenient size for everyday use in, for example, carpentry. We don't decide what's correct at WP, we merely report other writings in reliable sources. LeadSongDog come howl! 18:25, 11 August 2010 (UTC)

The 1873 BA standard that created the CGS (with descent from Prof Stoney), clearly stated the correct style of creating multiples of the CGS. The style is ancient, dating back to Stevins in the XVI century. One use prepended ordinals for divisions, and postpended cardinals for the multiples. An angstrom is a tenth-metre: that is, the tenth column to the right of a metre. A joule is an erg-seven, that is, seven columns to the left of an erg. The same scheme, with a different base, serves the basis of the minute, second, and third divisions of the degree and hour.

The prefixes of micro and mega were the last until 1947, it is for this reason that electrical units run by powers of six, viz µµF = picofarid, and µµH is microhenry. Length baulks at the kilometre, since this is the ordinary non-scientific unit. Wendy.krieger (talk) 12:12, 21 July 2016 (UTC)

Defining "c"

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)

The main reason they put c without units, is because the theory of dimensions as taught in schools is broken. Quantities do not have dimensions = they have scales, and scales have dimensions. When for example, you write 1 lb = 32.175 pdl, there is a dimensioned unity floating around being 1 = 32.175 ft/s². If we multiply this by 1 lb, the unit becomes 32.175 lb. ft/s² = 32.175 pdl. Likewise, in the gaussian system, there is a dimensioned unity that connects the esu and emu. These individual systems have different units, but a conversion is possible between them by the relation '1 = 29.979245800 cm/s'. So, for example, 1 emu = 1 Bi.s = 1 Bi.s * 3e10 cm/s = 3e10 Bi.cm, but the Bi,cm here is the Fr (ie the charge a biot delivers in the time light travels 1 cm).

The primary gaussian units in electrostatics and magnetistatics, all have units that have dimensions dyn^a cm^b. The esu and emu that are not gaussian have a unit in the form with 's', where 1 s = 29979245800 cm. So, eg charge is Fr = Bi.cm, to get Bi.s, then 1 s = c cm. Wendy.krieger (talk) 08:39, 1 December 2014 (UTC)

Why the kilogram is more convenient for practical puposes

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)

The cgs was chosen over the older MGS, because it has the density of water = 1, something that Maxwell specifically requested. The electric units were defined in terms of MGS, specifically, decade units of the mgs emu that were nearest the siemens unit and the daniels cell. Maxwell showed that these belong to a system based on the quadrant (10,000 km) and a unit of mass of 10 pg. Gustav Mie constructed a similar system on the cgs, using the cm dekaton second. But you can construct these sort of units on any fourth measure, such as the foot or inch. Volts / inch is not unknown, and not an admixture of systems any more than V/cm were.

The Giorgi was based on the volt-ohm-second-metre, with a derived kilogram. The formulation of the definition of the ampere as a base unit is because legal theory requires that you describe an experiment with values, rather than simply give a formula. Since the legal standards are based on the pre-metric national units of length-mass-capacity (eg foot, pound, gallon), the base unit, once established, does not seem to change, even if the purpose is define something like "the speed of light is 299792458 metres per second". The original intent was to define µ as in cgs-theory to 10^-7 H/m. Wendy.krieger (talk) 08:48, 1 December 2014 (UTC)

Omitted units

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)

Well, they are all in the table at Centimetre–gram–second_system_of_units#Electromagnetic_units_in_various_CGS_systems ... they are only listed by abbreviation (G, Mx, Oe), not the full names ... --Steve (talk) 01:18, 1 September 2012 (UTC)

Units like the gauss and maxwell, belong to the "CGS practical" or Hansen system, the system that SI displaced. This system consisted of the practical electrical units (volt - ohm - second), the unmodified CGS emu, and a generous helping of powers of 10's to convert between them. The IEEE were coerced into approving the gauss etc in 1930. Gauss gets a lot of currency, because it is about the size of the earth's mgnetic field. reference = 'System of units in electromagnetism' Leo Young, Oliver and Boyd, Edinborough, 1969.

The Franklin and Biot were approved in 1947 to permit supposed dimensional analysis of the cgs esu and cgs emu, in an attempt to prevent having to approve the ab- and stat- units.

When one detangles artificial constraints of the SI from CGS naming, it is possible to use most of the existing units to completely cover the gaussian units with simple names. A franklin is a unit pole as well. A gilbert is both V and U, an oersted is E and H, a gauss D and B, a maxwell the flux units of \Psi and \Phi, A Biot is still I_a, but the esu does not have a unit around there. You then have a millijar (jar = Lieden jar = 10 Dm capacitance), a millimic (a mic = microhenry = 10 Dm induction), and a milliper (a new unit, so that the permittivity and permeability are both 1 mper/cm. A dimensioned interscalar of 376.730313462 ohms operates in the conversions. Wendy.krieger (talk) 08:59, 1 December 2014 (UTC)

Problems with the section "Relations between ESU and EMU units"

In the sections "Electrostatic units (ESU)" and "Electromagnetic units (EMU)", we have the definitions

\mathrm {1\,Fr=1\,statcoulomb=1\,esu\;charge=1\,cm{\sqrt {dyne}}=1\,g^{1/2}\cdot cm^{3/2}\cdot s^{-1}}

and

\mathrm {1\,Bi\cdot s=1\,abcoulomb=1\,emu\,charge=1\,s\cdot {\sqrt {dyne}}=1\,g^{1/2}\cdot cm^{1/2}} .

It would seem that

\mathrm {\frac {1\,statcoulomb}{1\,abcoulomb}} =1\,\mathrm {cm} \,\mathrm {s} ^{-1}\neq c^{-1},

where $c\equiv 29979245800\,\mathrm {cm} \,\mathrm {s} ^{-1}\equiv C\,\mathrm {cm} \,\mathrm {s} ^{-1}$ . It is true by definition that

1\,\mathrm {dyn} ={\frac {(1\,\mathrm {statcoulomb} )^{2}}{1\,\mathrm {cm} ^{2}}},

and it can be readily checked that

C^{2}\,\mathrm {dyn} =c^{2}\,{\frac {(1\,\mathrm {abcoulomb} )^{2}}{1\,\mathrm {cm} ^{2}}}

and

C^{2}\times 10^{-11}\,\mathrm {N} ={\frac {1}{4\pi \epsilon _{0}}}\,{\frac {(1\,\mathrm {coulomb} )^{2}}{1\,\mathrm {m} ^{2}}}.

A direct comparison of the three equations would argue that

{\frac {\mathrm {coulomb} }{\sqrt {4\pi \epsilon _{0}}}}={\frac {C}{10}}\,\mathrm {statcoulomb} ={\frac {c}{10}}\,\mathrm {abcoulomb} .

This also illustrates that $\mathrm {coulomb} /{\sqrt {4\pi \epsilon _{0}}}$ should always be considered as an inseparable whole when dealing with unit transformations.

Machina Lucis (talk) 03:07, 19 June 2013 (UTC)

The arguments that you discuss are well-known. Are you advocating that they be incorporated into this article or that an article should be written dedicated to Giorgi's work on the fourth base unit. Martinvl (talk) 06:21, 19 June 2013 (UTC)

It is unsurprising that this argument is well-known, but it would be useful to beginners to this SI/CGS mess, and I personally think my last equation is more palatable than the wishy-washy way of saying one coulomb "corresponds" to so-and-so many statcoulombs. The main point is that I am merely suggesting that the section I refer to seems to give the wrong ratio of statcoulomb to abcoulomb: it should be

\mathrm {cm} \,\mathrm {s} ^{-1}

, not

c^{-1}\equiv (29979245800\,\mathrm {cm} \,\mathrm {s} ^{-1})^{-1}

. Furthermore, I agree with LeadSongDog above that in some parts of the article

c\equiv 29979245800\,\mathrm {cm} \,\mathrm {s} ^{-1}

, while in other parts

c\equiv 29979245800

. I was hoping someone more knowledgeable than I am can clear up this issue. Machina Lucis (talk) 16:38, 19 June 2013 (UTC)

This is one of the things on my "to-do" list, but it is quite far down the list. I also need to do a little reading first. If however someboidy has more time on their hands, feel free to extend the article (or possibly write a new article "Comparison of SI and GGS electrical units"). Martinvl (talk) 18:00, 19 June 2013 (UTC)

I agree with (I would say) all the equations Machina Lucis has written.

Above all I agree on the fact that it is crucial to state clearly that statC, statA, abC, and abA, being derived units, are indeed trivial products of powers of cm, g and s, involving no numeric factor.

The main points, imho, to understand "correspondences" and "conversions" between different systems are the following two:

let's say: i[ESU] and i[EMU] "are the same current" (i.e. imply the same dynamic effect) in the ESU and EMU systems respectively (analogously for ESU-SI and EMU-SI, and/or other physical quantities); from the dynamic law (in this case Ampère) one has: i[EMU] = i[ESU] / c, where c is the speed of light (a physical constant, dimensioned as a velocity, almost equal to 299792458 m/s or 29979245800 cm/s); this sets also the correct relationship between units of measures: statA = abA cm/s;
then if i[EMU] = x abA and i[ESU] = y statA, with x and y pure numbers (one could say the measurements, in EMU and ESU respectively, of the same current), then we have: x abA = y statA / c = y abA cm/s /c = y/C abA, being C = c / cm/s ≈ 29979245800 (i.e. the measurement in cgs of the speed of light, the pure number that multiplied for cm/s gives the speed of light) so that the relation between the numbers that, when multiplied for their respective units of measurement, express the same current in the two systems (which is not a relation between units of measurement) is: x = y / C or x / y = 1 / C.

Sorry for my english, and for not using the equation editor (which I'm not acquainted with). Rocco. — Preceding unsigned comment added by 188.217.210.27 (talk) 20:44, 23 May 2014 (UTC)

The proper way to think of units and dimensions is as 'algebraic blobs'. This means that one can think of a unit like (foot) as (12 inch), and then move numbers into and out of the equation.

The relation here is that '1 (Bi.s) = C (Fr)'. In any gaussian system, such as the fps or cgs, 'c' is the speed of light measured in the appropriate units, eg C(ft/s) or C(cm/s), and C adjusted accordingly (ie 983574900 or 29979245800). One can suppose that there is a unit of time 'cm', representing the time that light takes to travel 1 cm. Then, 1 Bi.s = C Fr = C Bi.cm, and hence 1 = C cm/s.

But supposing that CGS must conform to SI dimensional analysis is simply plain wrong: charge and flux have the same dimensions, but different conversion factors between these, because the dimensional analysis does not take care of quantities SI sets to unity. One of these constants is in gaussian and hlu, not just not unity, but has dimensions too.Wendy.krieger (talk) 10:45, 30 November 2014 (UTC)

CGS Systems of units.

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.

Ref: http://www.colorado.edu/physics/phys3320/phys3320_sp12/AJPPapers/AJP_E&MPapers_030612/Mendelson_StoryOfC.pdf

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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