1.
International System of Units
–
The International System of Units is the modern form of the metric system, and is the most widely used system of measurement. It comprises a coherent system of units of measurement built on seven base units, the system also establishes a set of twenty prefixes to the unit names and unit symbols that may be used when specifying multiples and fractions of the units. The system was published in 1960 as the result of an initiative began in 1948. It is based on the system of units rather than any variant of the centimetre-gram-second system. The motivation for the development of the SI was the diversity of units that had sprung up within the CGS systems, the International System of Units has been adopted by most developed countries, however, the adoption has not been universal in all English-speaking countries. The metric system was first implemented during the French Revolution with just the metre and kilogram as standards of length, in the 1830s Carl Friedrich Gauss laid the foundations for a coherent system based on length, mass, and time. In the 1860s a group working under the auspices of the British Association for the Advancement of Science formulated the requirement for a coherent system of units with base units and derived units. Meanwhile, in 1875, the Treaty of the Metre passed responsibility for verification of the kilogram, in 1921, the Treaty was extended to include all physical quantities including electrical units originally defined in 1893. The units associated with these quantities were the metre, kilogram, second, ampere, kelvin, in 1971, a seventh base quantity, amount of substance represented by the mole, was added to the definition of SI. On 11 July 1792, the proposed the names metre, are, litre and grave for the units of length, area, capacity. The committee also proposed that multiples and submultiples of these units were to be denoted by decimal-based prefixes such as centi for a hundredth, on 10 December 1799, the law by which the metric system was to be definitively adopted in France was passed. Prior to this, the strength of the magnetic field had only been described in relative terms. The technique used by Gauss was to equate the torque induced on a magnet of known mass by the earth’s magnetic field with the torque induced on an equivalent system under gravity. The resultant calculations enabled him to assign dimensions based on mass, length, a French-inspired initiative for international cooperation in metrology led to the signing in 1875 of the Metre Convention. Initially the convention only covered standards for the metre and the kilogram, one of each was selected at random to become the International prototype metre and International prototype kilogram that replaced the mètre des Archives and kilogramme des Archives respectively. Each member state was entitled to one of each of the prototypes to serve as the national prototype for that country. Initially its prime purpose was a periodic recalibration of national prototype metres. The official language of the Metre Convention is French and the version of all official documents published by or on behalf of the CGPM is the French-language version

2.
SI base unit
–
The International System of Units defines seven units of measure as a basic set from which all other SI units can be derived. The SI base units form a set of mutually independent dimensions as required by dimensional analysis commonly employed in science, thus, the kelvin, named after Lord Kelvin, has the symbol K and the ampere, named after André-Marie Ampère, has the symbol A. Many other units, such as the litre, are not part of the SI. The definitions of the units have been modified several times since the Metre Convention in 1875. Since the redefinition of the metre in 1960, the kilogram is the unit that is directly defined in terms of a physical artifact. However, the mole, the ampere, and the candela are linked through their definitions to the mass of the platinum–iridium cylinder stored in a vault near Paris. It has long been an objective in metrology to define the kilogram in terms of a fundamental constant, two possibilities have attracted particular attention, the Planck constant and the Avogadro constant. The 23rd CGPM decided to postpone any formal change until the next General Conference in 2011

3.
SI derived unit
–
The International System of Units specifies a set of seven base units from which all other SI units of measurement are derived. Each of these units is either dimensionless or can be expressed as a product of powers of one or more of the base units. For example, the SI derived unit of area is the metre. The degree Celsius has an unclear status, and is arguably an exception to this rule. The names of SI units are written in lowercase, the symbols for units named after persons, however, are always written with an uppercase initial letter. In addition to the two dimensionless derived units radian and steradian,20 other derived units have special names, some other units such as the hour, litre, tonne, bar and electronvolt are not SI units, but are widely used in conjunction with SI units. Until 1995, the SI classified the radian and the steradian as supplementary units, but this designation was abandoned, International System of Quantities International System of Units International Vocabulary of Metrology Metric prefix Metric system Non-SI units mentioned in the SI Planck units SI base unit I. Mills, Tomislav Cvitas, Klaus Homann, Nikola Kallay, IUPAC, Quantities, Units and Symbols in Physical Chemistry. CS1 maint, Multiple names, authors list

4.
Defining equation (physics)
–
In physics, defining equations are equations that define new quantities in terms of base quantities. This article uses the current SI system of units, not natural or characteristic units, physical quantities and units follow the same hierarchy, chosen base quantities have defined base units, from these any other quantities may be derived and have corresponding derived units. Defining quantities is analogous to mixing colours, and could be classified a similar way, primary colours are to base quantities, as secondary colours are to derived quantities. Mixing colours is analogous to combining quantities using mathematical operations, the choice of a base system of quantities and units is arbitrary, but once chosen it must be adhered to throughout all analysis which follows for consistency. It makes no sense to mix up different systems of units, choosing a system of units, one system out of the SI, CGS etc. is like choosing whether use paint or light colours. Much of physics requires definitions to be made for the equations to make sense, theoretical implications, Definitions are important since they can lead into new insights of a branch of physics. Two such examples occurred in classical physics, ease of comparison, They allow comparisons of measurements to be made when they might appear ambiguous and unclear otherwise. Example A basic example is mass density and it is not clear how compare how much matter constitutes a variety of substances given only their masses or only their volumes. Making such comparisons without using mathematics logically in this way would not be as systematic, functions may be incorporated into a definition, in for calculus this is necessary. Quantities may also be complex-valued for theoretical advantage, but for a measurement the real part is relevant. For more advanced treatments the equation may have to be written in an equivalent, often definitions can start from elementary algebra, then modify to vectors, then in the limiting cases calculus may be used. The various levels of maths used typically follows this pattern, for vector equations, sometimes the defining quantity is in a cross or dot product and cannot be solved for explicitly as a vector, but the components can. Examples Electric current density is an example spanning all of these methods, see the classical mechanics section below for nomenclature and diagrams to the right. Elementary algebra Operations are simply multiplication and division, equations may be written in a product or quotient form, both of course equivalent. Vector algebra There is no way to divide a vector by a vector, elementary calculus The arithmetic operations are modified to the limiting cases of differentiation and integration. Equations can be expressed in these equivalent and alternative ways, vector calculus Tensor analysis Vectors are rank-1 tensors. The formulae below are no more than the equations in the language of tensors. Sometimes there is still freedom within the chosen units system, to one or more quantities in more than one way

5.
Grave (unit)
–
The grave was the original name of the kilogram, in an early version of the metric system between 1793 and 1795. The modern kilogram has its origins in the pre-French Revolution days of France, in 1791, the Commission of Weights and Measures, appointed by the French Academy of Sciences, chose one ten-millionth of the quarter meridian as the unit of length, and named it meter. Initially a provisional value was used, based on the old meridian measurement by Lacaille, in 1793 the commission defined the unit of mass as a cubic decimeter of distilled water at 0°C, and gave it the name grave. The mass of a volume of water at 0°C was accurately determined by Lavoisier. A prototype of the grave was made in brass, in 1795 a new law replaced the three names gravet, grave and bar by a single generic unit name, the gram. The new gram was equal to the old gravet, four new prefixes were added to cover the same range of units as in 1793. The brass prototype of the grave was renamed to provisional kilogram, in 1799 the provisional units were replaced by the final ones. Delambre and Méchain had completed their new measurement of the meridian, hence the final kilogram, being the mass of one cubic decimeter of water, was 0. 09% lighter than the provisional one. In addition, the specification of the water was changed from 0°C to 4°C. This change of temperature added 0. 01% to the final kilogram, in 1799 a platinum cylinder was made, and stored in the Archives of Paris, that served as the prototype of the final kilogram. It was called the Kilogramme des Archives, and this stood for the next ninety years

6.
History of the metre
–
In the aftermath of the French Revolution, the traditional units of measure used in the Ancien Régime were replaced. The livre monetary unit was replaced by the franc. Indeed, as the measures were used as the basis for taxation. However, it was discovered that the length of a seconds pendulum varies from place to place. Little practical progress was made towards the establishment of the measure until the French Revolution of 1789. The question of measurement reform was placed in the hands of the Academy of Sciences, the task of surveying the meridian arc fell to Pierre Méchain and Jean-Baptiste Delambre, and took more than six years. In the meantime, the commission calculated a value from older surveys of 443.44 lignes. This value was set by legislation on 7 April 1795, Delambre used a baseline of about 10 km in length along a straight road between Melun and Lieusaint. In an operation taking six weeks, the baseline was measured using four platinum rods. Thereafter he used, where possible, the points used by Cassini in his 1744 survey of France. Méchains baseline, of a length, and also on a straight section of road between Vernet and Salces. Although Méchains sector was half the length of Delambre, it included the Pyrenees, after the two surveyors met, each computed the others baseline in order to cross-check their results and they then recomputed the kilometre. Their result came out at 0.144 lignes shorter than the provisional value, while Méchain and Delambre were completing their survey, the commission had ordered a series of platinum bars to be made based on the provisional metre. This standard metre bar became known as the mètre des Archives, the metric system, that is the system of units based on the metre, was officially adopted in France on 10 December 1799 and became the sole legal system of weights and measures from 1801. In the meantime, the Netherlands had adopted the system from 1816. It soon became apparent that Méchain and Delambres result was too short for the meridional definition of the metre. The modern value, for the WGS84 reference spheroid, is 1.00019657 m or 443.38308 lignes. Nevertheless, the mètre des Archives remained the legal and practical standard for the metre in France, when it was decided to create a new international standard metre, the length was taken to be that of the mètre des Archives in the state in which it shall be found

7.
Length measurement
–
Length measurement is implemented in practice in many ways. The most commonly used approaches are the methods and the interferometer methods based upon the speed of light. For objects such as crystals and diffraction gratings, diffraction is used with X-rays, measurement techniques for three-dimensional structures very small in every dimension use specialized instruments such as ion microscopy coupled with intensive computer modeling. For a discussion of methods for determining cosmological distances, see the article Cosmic distance ladder. The ruler the simplest kind of length measurement tool, lengths are defined by printed marks or engravings on a stick, the meter was initially defined using a ruler before more accurate methods became available. Gauge blocks are a method for precise measurement or calibration of measurement tools. For small or microscopic objects, microphotography where the length is calibrated using a graticule can be used, a graticule is a piece that has lines for precise lengths etched into it. Graticules may be fitted into the eyepiece or they may be used on the measurement plane, the basic idea behind a transit-time measurement of length is to send a signal from one end of the length to be measured to the other, and back again. The time for the trip is the transit time Δt. If light is used for the signal, its speed depends upon the medium in which it propagates, an additional uncertainty is the refractive index correction relating the medium used to the reference vacuum, taken in SI units to be the classical vacuum. A refractive index of the larger than one slows the light. Transit-time measurement underlies most radio navigation systems for boats and aircraft, for example, radar, for example, in one radar system, pulses of electromagnetic radiation are sent out by the vehicle and trigger a response from a responder beacon. The time interval between the sending and the receiving of a pulse is monitored and used to determine a distance. In the global positioning system a code of ones and zeros is emitted at a time from multiple satellites. Assuming the receiver clock can be related to the clocks on the satellites. Receiver clock error is corrected by combining the data from four satellites, such techniques vary in accuracy according to the distances over which they are intended for use. Generally, transit time measurements are preferred for longer lengths, the figure shows schematically how length is determined using a Michelson interferometer, the two panels show a laser source emitting a light beam split by a beam splitter to travel two paths. The light is recombined by bouncing the two components off a pair of corner cubes that return the two components to the beam splitter again to be reassembled

8.
Proposed redefinition of SI base units
–
The metric system was originally conceived as a system of measurement that was derivable from nature. When the metric system was first introduced in France in 1799 technical limitations necessitated the use of such as the prototype metre. In 1960 the metre was redefined in terms of the wavelength of light from a source, making it derivable from nature. If the proposed redefinition is accepted, the system will, for the first time. The proposal can be summarised as follows, There will still be the seven base units. The second, metre and candela are already defined by physical constants, the new definitions will improve the SI without changing the size of any units, thus ensuring continuity with present measurements. Further details are found in the chapter of the Ninth SI Units Brochure. The last major overhaul of the system was in 1960 when the International System of Units was formally published as a coherent set of units of measure. SI is structured around seven base units that have apparently arbitrary definitions, although the set of units form a coherent system, the definitions do not. The proposal before the CIPM seeks to remedy this by using the quantities of nature as the basis for deriving the base units. This will mean, amongst other things, that the prototype kilogram will cease to be used as the replica of the kilogram. The second and the metre are already defined in such a manner, the basic structure of SI was developed over a period of about 170 years. Since 1960 technological advances have made it possible to address weaknesses in SI. Specifically, the metre was defined as one ten-millionth of the distance from the North Pole to the Equator, although these definitions were chosen so that nobody would own the units, they could not be measured with sufficient convenience or precision for practical use. Instead copies were created in the form of the mètre des Archives, in 1875, by which time the use of the metric system had become widespread in Europe and in Latin America, twenty industrially developed nations met for the Convention of the Metre. They were, CGPM —The Conference meets every four to six years, CIPM —The Committee consists of eighteen eminent scientists, each from a different country, nominated by the CGPM. The CIPM meets annually and is tasked to advise the CGPM, the CIPM has set up a number of sub-committees, each charged with a particular area of interest. One of these, the Consultative Committee for Units, amongst other things, the first CGPM formally approved the use of 40 prototype metres and 40 prototype kilograms from the British firm Johnson Matthey as the standards mandated by the Convention of the Metre