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64-555: The CGS system has been largely supplanted by the MKS system based on the metre , kilogram , and second, which was in turn extended and replaced by the International System of Units (SI). In many fields of science and engineering, SI is the only system of units in use, but CGS is still prevalent in certain subfields. In measurements of purely mechanical systems (involving units of length, mass, force , energy , pressure , and so on),

128-606: A community , then different units of the same quantity (for example feet and inches) were given a fixed relationship. Apart from Ancient China where the units of capacity and of mass were linked to red millet seed , there is little evidence of the linking of different quantities until the Enlightenment . The history of the measurement of length dates back to the early civilization of the Middle East (10000 BC – 8000 BC). Archaeologists have been able to reconstruct

192-411: A chosen set of base units , is a product of powers of base units, with the proportionality factor being one. If a system of quantities has equations that relate quantities and the associated system of units has corresponding base units, with only one unit for each base quantity, then it is coherent if and only if every derived unit of the system is coherent. The concept of coherence was developed in

256-407: A coherent derived unit. The numerical factor of 100 cm/m is needed to express m/s in the cgs system. The earliest units of measure devised by humanity bore no relationship to each other. As both humanity's understanding of philosophical concepts and the organisation of society developed, so units of measurement were standardized—first particular units of measure had the same value across

320-435: A coherent system the units of force , energy and power be chosen so that the equations hold without the introduction of constant factors. Once a set of coherent units have been defined, other relationships in physics that use those units will automatically be true— Einstein 's mass–energy equation , E  =  mc , does not require extraneous constants when expressed in coherent units. Isaac Asimov wrote, "In

384-414: A constant that depends on the units used. Suppose that the metre (m) and the second (s) are base units; then the kilometer (km) and the hour (h) are non-coherent derived units. The metre per second (mps) is defined as the velocity of an object that travels one metre in one second, and the kilometer per hour (kmph) is defined as the velocity of an object that travels one kilometre in one hour. Substituting from

448-447: A convention of normalizing quantities with respect to some system of natural units . For example, in particle physics a system is in use where every quantity is expressed by only one unit of energy, the electronvolt , with lengths, times, and so on all converted into units of energy by inserting factors of speed of light c and the reduced Planck constant ħ . This unit system is convenient for calculations in particle physics , but

512-408: A definition. It does not imply that a unit of velocity is being defined, and if that fact is added, it does not determine the magnitude of the unit, since that depends on the system of units. In order for it to become a proper definition both the quantity and the defining equation, including the value of any constant factor, must be specified. After a unit has been defined in this manner, however, it has

576-539: A fourth unit to be taken from the practical units of electromagnetism , such as the volt, ohm or ampere, be used to create a coherent system using practical units. This system was strongly promoted by electrical engineer George A. Campbell . The CGS and MKS systems were both widely used in the 20th century, with the MKS system being primarily used in practical areas, such as commerce and engineering. The International Electrotechnical Commission (IEC) adopted Giorgi's proposal as

640-575: A non-coherent set of units. In 1874, the British Association for the Advancement of Science (BAAS) introduced the CGS system , a coherent system based on the centimetre , gram and second. These units were inconvenient for electromagnetic applications, since electromagnetic units derived from these did not correspond to the commonly used practical units , such as the volt , ampere and ohm . After

704-569: A separate abbreviation "esu", and similarly with the corresponding symbols. In another variant of the CGS system, electromagnetic units ( EMU ), current is defined via the force existing between two thin, parallel, infinitely long wires carrying it, and charge is then defined as current multiplied by time. (This approach was eventually used to define the SI unit of ampere as well). The EMU unit of current, biot ( Bi ), also known as abampere or emu current ,

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768-451: A system of units of electromagnetism, in which the dimensions of all electric and magnetic quantities are expressible in terms of the mechanical dimensions of mass, length, and time, is traditionally called an 'absolute system'. All electromagnetic units in the CGS-ESU system that have not been given names of their own are named as the corresponding SI name with an attached prefix "stat" or with

832-416: A way that the equations relating the numerical values expressed in the units of the system have exactly the same form, including numerical factors, as the corresponding equations directly relating the quantities. It is a system in which every quantity has a unique unit, or one that does not use conversion factors . A coherent derived unit is a derived unit that, for a given system of quantities and for

896-404: Is a coherent derived unit for speed or velocity but km / h is not a coherent derived unit. Speed or velocity is defined by the change in distance divided by a change in time. The derived unit m/s uses the base units of the SI system. The derived unit km/h requires numerical factors to relate to the SI base units: 1000 m/km and 3600 s/h . In the cgs system, m/s is not

960-444: Is a special aspect of electromagnetism units. By contrast it is always correct to replace, e.g., "1 m" with "100 cm" within an equation or formula.) Lack of unique unit names leads to potential confusion: "15 emu" may mean either 15 abvolts , or 15 emu units of electric dipole moment , or 15 emu units of magnetic susceptibility , sometimes (but not always) per gram , or per mole . With its system of uniquely named units,

1024-428: Is a statement that determines the ratio of any instance of the quantity to the unit. This ratio is the numerical value of the quantity or the number of units contained in the quantity. The definition of the metre per second above satisfies this requirement since it, together with the definition of velocity, implies that v /mps = ( d /m)/( t /s); thus if the ratios of distance and time to their units are determined, then so

1088-403: Is impractical in other contexts. MKS system of units The metre, kilogram, second system of units , also known more briefly as MKS units or the MKS system , is a physical system of measurement based on the metre , kilogram , and second (MKS) as base units. Distances are described in terms of metres, mass in terms of kilograms and time in seconds. Derived units are defined using

1152-425: Is indistinguishable from the four-unit system, since what is a proportionality constant in the latter is a conversion factor in the former. The relation among the numerical values of the quantities in the force law is { F } = 0.031081 { m } { a }, where the braces denote the numerical values of the enclosed quantities. Unlike in this system, in a coherent system, the relations among the numerical values of quantities are

1216-494: Is less straightforward. Formulas for physical laws of electromagnetism (such as Maxwell's equations ) take a form that depends on which system of units is being used, because the electromagnetic quantities are defined differently in SI and in CGS. Furthermore, within CGS, there are several plausible ways to define electromagnetic quantities, leading to different "sub-systems", including Gaussian units , "ESU", "EMU", and Heaviside–Lorentz units . Among these choices, Gaussian units are

1280-439: Is now based entirely on fundamental physical constants , but still closely approximates the original MKS units for most practical purposes. By the mid-19th century, there was a demand by scientists to define a coherent system of units . A coherent system of units is one where all units are directly derived from a set of base units, without the need of any conversion factors. The United States customary units are an example of

1344-440: Is related to the SI base units of length, mass, and time: Expressing a CGS derived unit in terms of the SI base units, or vice versa, requires combining the scale factors that relate the two systems: The conversion factors relating electromagnetic units in the CGS and SI systems are made more complex by the differences in the formulas expressing physical laws of electromagnetism as assumed by each system of units, specifically in

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1408-539: Is the numeric value of the speed of light in vacuum when expressed in units of centimetres per second. The symbol "≘" is used instead of "=" as a reminder that the units are corresponding but not equal . For example, according to the capacitance row of the table, if a capacitor has a capacitance of 1 F in SI, then it has a capacitance of (10  c ) cm in ESU; but it is incorrect to replace "1 F" with "(10  c ) cm" within an equation or formula. (This warning

1472-527: Is the pure number one. Asimov's conclusion is not the only possible one. In a system that uses the units foot (ft) for length, second (s) for time, pound (lb) for mass, and pound-force (lbf) for force, the law relating force ( F ), mass ( m ), and acceleration ( a ) is F = 0.031081 ma . Since the proportionality constant here is dimensionless and the units in any equation must balance without any numerical factor other than one, it follows that 1 lbf = 1 lb⋅ft/s . This conclusion appears paradoxical from

1536-409: Is the ratio of velocity to its unit. The definition, by itself, is inadequate since it only determines the ratio in one specific case; it may be thought of as exhibiting a specimen of the unit. A new coherent unit cannot be defined merely by expressing it algebraically in terms of already defined units. Thus the statement, "the metre per second equals one metre divided by one second", is not, by itself,

1600-468: Is the volt per centimetre, which is one hundred times the SI unit. The system is electrically rationalized and magnetically unrationalized; i.e., 𝜆 = 1 and 𝜆′ = 4 π , but the above formula for 𝜆 is invalid. A closely related system is the International System of Electric and Magnetic Units, which has a different unit of mass so that the formula for 𝜆′ is invalid. The unit of mass

1664-518: Is therefore defined as follows: The biot is that constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross-section, and placed one centimetre apart in vacuum , would produce between these conductors a force equal to two dynes per centimetre of length. Therefore, in electromagnetic CGS units , a biot is equal to a square root of dyne: The unit of charge in CGS EMU is: Dimensionally in

1728-522: The Akkadian emperor Naram-Sin rationalized the Babylonian system of measure, adjusting the ratios of many units of measure to multiples of 2, 3 or 5, for example there were 6 she ( barleycorns ) in a shu-si ( finger ) and 30 shu-si in a kush ( cubit ). Non- commensurable quantities have different physical dimensions , which means that adding or subtracting them is not meaningful. For instance, adding

1792-606: The American Physical Society and the International Astronomical Union . SI units are predominantly used in engineering applications and physics education, while Gaussian CGS units are still commonly used in theoretical physics, describing microscopic systems, relativistic electrodynamics , and astrophysics . The units gram and centimetre remain useful as noncoherent units within the SI system, as with any other prefixed SI units. In mechanics,

1856-574: The M.K.S. System of Giorgi in 1935 without specifying which electromagnetic unit would be the fourth base unit. In 1939, the Consultative Committee for Electricity (CCE) recommended the adoption of Giorgi's proposal, using the ampere as the fourth base unit. This was subsequently approved by the CGPM in 1954. The rmks system ( rationalized metre–kilogram–second ) combines MKS with rationalization of electromagnetic equations . The MKS units with

1920-580: The Metre Convention of 1875, work started on international prototypes for the kilogram and the metre, which were formally sanctioned by the General Conference on Weights and Measures (CGPM) in 1889, thus formalizing the MKS system by using the kilogram and metre as base units. In 1901, Giovanni Giorgi proposed to the Associazione elettrotecnica italiana (AEI) that the MKS system, extended with

1984-601: The ampere as the units of voltage and current respectively. Doing this avoids the inconveniently large and small electrical units that arise in the esu and emu systems. This system was at one time widely used by electrical engineers because the volt and ampere had been adopted as international standard units by the International Electrical Congress of 1881. As well as the volt and ampere, the farad (capacitance), ohm (resistance), coulomb (electric charge), and henry (inductance) are consequently also used in

Centimetre–gram–second system of units - Misplaced Pages Continue

2048-440: The electrostatic units variant of the CGS system, (CGS-ESU), charge is defined as the quantity that obeys a form of Coulomb's law without a multiplying constant (and current is then defined as charge per unit time): The ESU unit of charge, franklin ( Fr ), also known as statcoulomb or esu charge , is therefore defined as follows: two equal point charges spaced 1 centimetre apart are said to be of 1 franklin each if

2112-482: The mass of an object to its volume has no physical meaning. However, new quantities (and, as such, units) can be derived via multiplication and exponentiation of other units. As an example, the SI unit for force is the newton , which is defined as kg⋅m⋅s . Since a coherent derived unit is one which is defined by means of multiplication and exponentiation of other units but not multiplied by any scaling factor other than 1,

2176-443: The pascal is a coherent unit of pressure (defined as kg⋅m ⋅s ), but the bar (defined as 100 000  kg⋅m ⋅s ) is not. Note that coherence of a given unit depends on the definition of the base units. Should the standard unit of length change such that it is shorter by a factor of 100 000 , then the bar would be a coherent derived unit. However, a coherent unit remains coherent (and a non-coherent unit remains non-coherent) if

2240-462: The CGS-EMU system, charge q is therefore equivalent to ML. Hence, neither charge nor current is an independent physical quantity in the CGS-EMU system. All electromagnetic units in the CGS-EMU system that do not have proper names are denoted by a corresponding SI name with an attached prefix "ab" or with a separate abbreviation "emu". The practical CGS system is a hybrid system that uses the volt and

2304-620: The SI removes any confusion in usage: 1 ampere is a fixed value of a specified quantity, and so are 1 henry , 1  ohm , and 1 volt. In the CGS-Gaussian system , electric and magnetic fields have the same units, 4 π 𝜖 0 is replaced by 1, and the only dimensional constant appearing in the Maxwell equations is c , the speed of light. The Heaviside–Lorentz system has these properties as well (with ε 0 equaling 1). In SI, and other rationalized systems (for example, Heaviside–Lorentz ),

2368-487: The ampere as a fourth base unit is sometimes referred to as the MKSA system . This system was extended by adding the kelvin and candela as base units in 1960, thus forming the International System of Units . The mole was added as a seventh base unit in 1971. Coherence (units of measurement) A coherent system of units is a system of units of measurement used to express physical quantities that are defined in such

2432-470: The appropriate combinations, such as velocity in metres per second. Some units have their own names, such as the newton unit of force which is the combination kilogram metre per second squared. The modern International System of Units (SI), from the French Système international d'unités , was originally created as a formalization of the MKS system. The SI has been redefined several times since then and

2496-423: The base units are redefined in terms of other units with the numerical factor always being unity. The concept of coherence was only introduced into the metric system in the third quarter of the nineteenth century; in its original form the metric system was non-coherent – in particular the litre was 0.001 m and the are (from which we get the hectare ) was 100 m . A precursor to the concept of coherence

2560-443: The cgs system, a unit force is described as one that will produce an acceleration of 1 cm/sec on a mass of 1 gm. A unit force is therefore 1 cm/sec multiplied by 1 gm." These are independent statements. The first is a definition; the second is not. The first implies that the constant of proportionality in the force law has a magnitude of one; the second implies that it is dimensionless. Asimov uses them both together to prove that it

2624-412: The definitions of the units into the defining equation of velocity we obtain, 1 mps = k m/s and 1 kmph = k km/h = 1/3.6 k m/s = 1/3.6 mps. Now choose k = 1; then the metre per second is a coherent derived unit, and the kilometre per hour is a non-coherent derived unit. Suppose that we choose to use the kilometre per hour as the unit of velocity in the system. Then the system becomes non-coherent, and

Centimetre–gram–second system of units - Misplaced Pages Continue

2688-505: The differences between CGS and SI are straightforward: the unit-conversion factors are all powers of 10 as 100 cm = 1 m and 1000 g = 1 kg . For example, the CGS unit of force is the dyne , which is defined as 1 g⋅cm/s , so the SI unit of force, the newton ( 1 kg⋅m/s ), is equal to 100 000  dynes . On the other hand, in measurements of electromagnetic phenomena (involving units of charge , electric and magnetic fields, voltage , and so on), converting between CGS and SI

2752-427: The effect of identifying the pound-force with the pound. The pound is then both a base unit of mass and a coherent derived unit of force. One may apply any unit one pleases to the proportionality constant. If one applies the unit s /lb to it, then the foot becomes a unit of force. In a four-unit system ( English engineering units ), the pound and the pound-force are distinct base units, and the proportionality constant has

2816-525: The electrostatic force between them is 1 dyne . Therefore, in CGS-ESU, a franklin is equal to a centimetre times square root of dyne: The unit of current is defined as: In the CGS-ESU system, charge q is therefore has the dimension to MLT. Other units in the CGS-ESU system include the statampere (1 statC/s) and statvolt (1  erg /statC). In CGS-ESU, all electric and magnetic quantities are dimensionally expressible in terms of length, mass, and time, and none has an independent dimension. Such

2880-522: The field of science. Starting in the 1880s, and more significantly by the mid-20th century, CGS was gradually superseded internationally for scientific purposes by the MKS (metre–kilogram–second) system, which in turn developed into the modern SI standard. Since the international adoption of the MKS standard in the 1940s and the SI standard in the 1960s, the technical use of CGS units has gradually declined worldwide. CGS units have been deprecated in favor of SI units by NIST , as well as organizations such as

2944-442: The general adoption of centimetre, gram and second as fundamental units, and to express all derived electromagnetic units in these fundamental units, using the prefix "C.G.S. unit of ...". The sizes of many CGS units turned out to be inconvenient for practical purposes. For example, many everyday objects are hundreds or thousands of centimetres long, such as humans, rooms and buildings. Thus the CGS system never gained wide use outside

3008-417: The g⋅cm /s ) could bear a coherent relationship to the base units. By contrast, coherence was a design aim of the SI, resulting in only one unit of energy being defined – the joule . Each variant of the metric system has a degree of coherence—the various derived units being directly related to the base units without the need of intermediate conversion factors. An additional criterion is that, for example, in

3072-482: The mid-nineteenth century by, amongst others, Kelvin and James Clerk Maxwell and promoted by the British Science Association . The concept was initially applied to the centimetre–gram–second (CGS) in 1873 and the foot–pound–second systems (FPS) of units in 1875. The International System of Units (SI) was designed in 1960 around the principle of coherence. In the SI system, the derived unit m/s

3136-547: The most common today, and "CGS units" is often intended to refer to CGS-Gaussian units. The CGS system goes back to a proposal in 1832 by the German mathematician Carl Friedrich Gauss to base a system of absolute units on the three fundamental units of length, mass and time. Gauss chose the units of millimetre, milligram and second. In 1873, a committee of the British Association for the Advancement of Science , including physicists James Clerk Maxwell and William Thomson recommended

3200-445: The nature of the constants that appear in these formulas. This illustrates the fundamental difference in the ways the two systems are built: In each of these systems the quantities called "charge" etc. may be a different quantity; they are distinguished here by a superscript. The corresponding quantities of each system are related through a proportionality constant. Maxwell's equations can be written in each of these systems as: In

3264-421: The numerical value equation for velocity becomes { v } = 3.6 { d }/{ t }. Coherence may be restored, without changing the units, by choosing k = 3.6; then the kilometre per hour is a coherent derived unit, with 1 kmph = 1 m/s, and the metre per second is a non-coherent derived unit, with 1 mps = 3.6 m/s. A definition of a physical quantity is a statement that determines the ratio of any two instances of

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3328-424: The point of view of competing systems, according to which F = ma and 1 lbf = 32.174 lb⋅ft/s . Although the pound-force is a coherent derived unit in this system according to the official definition, the system itself is not considered to be coherent because of the presence of the proportionality constant in the force law. A variant of this system applies the unit s /ft to the proportionality constant. This has

3392-399: The practical system and are the same as the SI units. The magnetic units are those of the emu system. The electrical units, other than the volt and ampere, are determined by the requirement that any equation involving only electrical and kinematical quantities that is valid in SI should also be valid in the system. For example, since electric field strength is voltage per unit length, its unit

3456-400: The quantities in the CGS and SI systems are defined identically. The two systems differ only in the scale of the three base units (centimetre versus metre and gram versus kilogram, respectively), with the third unit (second) being the same in both systems. There is a direct correspondence between the base units of mechanics in CGS and SI. Since the formulae expressing the laws of mechanics are

3520-418: The quantity. The specification of the value of any constant factor is not a part of the definition since it does not affect the ratio. The definition of velocity above satisfies this requirement since it implies that v 1 / v 2 = ( d 1 / d 2 )/( t 1 / t 2 ); thus if the ratios of distances and times are determined, then so is the ratio of velocities. A definition of a unit of a physical quantity

3584-399: The same as the relations among the quantities themselves. The following example concerns definitions of quantities and units. The (average) velocity ( v ) of an object is defined as the quantitative physical property of the object that is directly proportional to the distance ( d ) traveled by the object and inversely proportional to the time ( t ) of travel, i.e., v = kd / t , where k is

3648-401: The same in both systems and since both systems are coherent , the definitions of all coherent derived units in terms of the base units are the same in both systems, and there is an unambiguous relationship between derived units: Thus, for example, the CGS unit of pressure, barye , is related to the CGS base units of length, mass, and time in the same way as the SI unit of pressure, pascal ,

3712-414: The system by dividing the units of magnetic pole strength and magnetization by 4 π . The units of the first two quantities are the ampere and the ampere per centimetre respectively. The unit of magnetic permeability is that of the emu system, and the magnetic constitutive equations are B = (4 π /10) μ H and B = (4 π /10) μ 0 H + μ 0 M . Magnetic reluctance is given a hybrid unit to ensure

3776-449: The unit lbf⋅s /(lb⋅ft). All these systems are coherent. One that is not is a three-unit system (also called English engineering units) in which F = ma that uses the pound and the pound-force, one of which is a base unit and the other, a non-coherent derived unit. In place of an explicit proportionality constant, this system uses conversion factors derived from the relation 1 lbf = 32.174 lb⋅ft/s . In numerical calculations, it

3840-532: The unit of current was chosen such that electromagnetic equations concerning charged spheres contain 4 π , those concerning coils of current and straight wires contain 2 π and those dealing with charged surfaces lack π entirely, which was the most convenient choice for applications in electrical engineering and relates directly to the geometric symmetry of the system being described by the equation. Specialized unit systems are used to simplify formulas further than either SI or CGS do, by eliminating constants through

3904-604: The units of measure in use in Mesopotamia , India , the Jewish culture and many others. Archaeological and other evidence shows that in many civilizations, the ratios between different units for the same quantity of measure were adjusted so that they were integer numbers. In many early cultures such as Ancient Egypt , multiples of 2, 3 and 5 were not always used—the Egyptian royal cubit being 28 fingers or 7 hands . In 2150 BC,

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3968-530: The validity of Ohm's law for magnetic circuits. In all the practical systems ε 0 = 8.8542 × 10 A⋅s/(V⋅cm), μ 0 = 1 V⋅s/(A⋅cm), and c = 1/(4 π × 10 ε 0 μ 0 ). There were at various points in time about half a dozen systems of electromagnetic units in use, most based on the CGS system. These include the Gaussian units and the Heaviside–Lorentz units . In this table, c = 29 979 245 800

4032-460: Was chosen to remove powers of ten from contexts in which they were considered to be objectionable (e.g., P = VI and F = qE ). Inevitably, the powers of ten reappeared in other contexts, but the effect was to make the familiar joule and watt the units of work and power respectively. The ampere-turn system is constructed in a similar way by considering magnetomotive force and magnetic field strength to be electrical quantities and rationalizing

4096-416: Was however present in that the units of mass and length were related to each other through the physical properties of water, the gram having been designed as being the mass of one cubic centimetre of water at its freezing point. The CGS system had two units of energy, the erg that was related to mechanics and the calorie that was related to thermal energy , so only one of them (the erg, equivalent to

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