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Metre

SI unit of length

This article is about the unit of length. For other uses of "metre" or "meter", see Meter (disambiguation).

metre
Metric shoppingdowntown.us

Seal of the International Bureau of Weights and Measures (BIPM) – Use measure (Greek: ΜΕΤΡΩ ΧΡΩ)

Unit systemSI base unit
Unit&#;ofLength
Symbolm[1]
1 m[1]in is equal to
&#;&#;&#;SI units&#;&#;&#;
  • &#;mm
  • &#;km
&#;&#;&#;Imperial/US units&#;&#;&#;
  • ≈&#;&#;yd
  • ≈&#;&#;ft
  • ≈&#;&#;in
&#;&#;&#;Nautical units&#;&#;&#;≈&#;&#;nmi

The metre (Commonwealth spelling) or meter (American spelling; see spelling differences) (from the French unit mètre, from the Greek noun μέτρον, "measure") is the base unit of length in the International System of Units (SI). The SI unit symbol is m.

The metre is currently defined as the length of the path travelled by light in a vacuum in 1/ of a second.

The metre was originally defined in as one ten-millionth of the distance from the equator to the North Pole along a great circle, so the Earth's circumference is approximately &#;km. In , the metre was redefined in terms of a prototype metre bar (the actual bar used was changed in ). In , the metre was redefined in terms of a certain number of wavelengths of a certain emission line of krypton The current definition was adopted in and modified slightly in to clarify that the metre is a measure of proper length.

Spelling[edit]

Metre is the standard spelling of the metric unit for length in nearly all English-speaking nations except the United States[2][3][4][5] and the Philippines,[6] which use meter. Other Germanic languages, such as German, Dutch, and the Scandinavian languages,[7] likewise spell the word Meter or meter.

Measuring devices (such as ammeter, speedometer) are spelled "-meter" in all variants of English.[8] The suffix "-meter" has the same Greek origin as the unit of length.[9][10]

Etymology[edit]

The etymological roots of metre can be traced to the Greek verb μετρέω (metreo) (to measure, count or compare) and noun μέτρον (metron) (a measure), which were used for physical measurement, for poetic metre and by extension for moderation or avoiding extremism (as in "be measured in your response"). This range of uses is also found in Latin (metior, mensura), French (mètre, mesure), English and other languages. The Greek word is derived from the Proto-Indo-European root *meh₁- 'to measure'. The motto ΜΕΤΡΩ ΧΡΩ (metro chro) in the seal of the International Bureau of Weights and Measures (BIPM), which was a saying of the Greek statesman and philosopher Pittacus of Mytilene and may be translated as "Use measure!", thus calls for both measurement and moderation. The use of the word metre (for the French unit mètre) in English began at least as early as [11]

History of definition [edit]

Main article: History of the metre

Pendulum or meridian[edit]

In Jean Picard measured the length of a "seconds pendulum" and proposed a unit of measurement twice that length to be called the universal toise (French: Toise universelle).[12] In , Tito Livio Burattini suggested the term metre for a unit of length based on a pendulum length, but then it was discovered that the length of a seconds pendulum varies from place to place.[14][15][16][17][18][19][20][21][22]

Since Eratosthenes, geographers had used meridian arcs to assess the size of the Earth, which in , Jean Picard determined to have a radius of toises, treated as a simple sphere. In the 18th century, geodesy grew in importance as a means of empirically demonstrating the theory of gravity and because the radius of the Earth was the unit to which all celestial distances were to be referred.[24][25]

Meridional definition[edit]

As a result of the Lumières and during the French Revolution, the French Academy of Sciences charged a commission with determining a single scale for all measures. On 7 October that commission advised the adoption of a decimal system, and on 19 March advised the adoption of the term mètre ("measure"), a basic unit of length, which they defined as equal to one ten-millionth of the quarter meridian, the distance between the North Pole and the Equator along the meridian through Paris.[26][27][28][29][30] On 26 March , the French National Constituant Assembly adopted the proposal.[11][31]

The French Academy of Sciences commissioned an expedition led by Jean Baptiste Joseph Delambre and Pierre Méchain, lasting from to , which attempted to accurately measure the distance between a belfry in Dunkerque and Montjuïc castle in Barcelona at the longitude of the Paris Panthéon (see meridian arc of Delambre and Méchain).[32] The expedition was fictionalised in Denis Guedj, Le Mètre du Monde. Ken Alder wrote factually about the expedition in The Measure of All Things: the seven year odyssey and hidden error that transformed the world. This portion of the Paris meridian was to serve as the basis for the length of the half meridian connecting the North Pole with the Equator. From to France adopted this definition of the metre as its official unit of length based on results from this expedition combined with those of the Geodesic Mission to Peru.[35][36] The latter was related by Larrie D. Ferreiro in Measure of the Earth: The Enlightenment Expedition that Reshaped Our World.[37][38]

In the 19th century, geodesy underwent a revolution with advances in mathematics as well as progress of observation instruments and methods with the taking into account of the personal equation. The application of the least squares method to meridian arc measurements demonstrated the importance of the scientific method in geodesy. On the other hand, the invention of the telegraph made it possible to measure parallel arcs, and the improvement of the reversible pendulum gave rise to the study of the Earth's gravitational field. A more accurate determination of the Figure of the Earth would soon result from the measurement of the Struve Geodetic Arc (–) and would have given another value for the definition of this standard of length. This did not invalidate the metre but highlighted that progresses in science would allow better measurement of Earth's size and shape.[40][41][42]

In , Carl Friedrich Gauss studied the Earth's magnetic field and proposed adding the second to the basic units of the metre and the kilogram in the form of the CGS system (centimetre, gram, second). In , he founded the Magnetischer Verein, the first international scientific association, in collaboration with Alexander von Humboldt and Wilhelm Edouard Weber. The coordination of the observation of geophysical phenomena such as the Earth's magnetic field, lightning and gravity in different points of the globe stimulated the creation of the first international scientific associations. The foundation of the Magnetischer Verein would be followed by that of the Central European Arc Measurement (German: Mitteleuropaïsche Gradmessung) on the initiative of Johann Jacob Baeyer in , and by that of the International Meteorological Organisation whose second president, the Swiss meteorologist and physicist, Heinrich von Wild would represent Russia at the International Committee for Weights and Measures (CIPM).[43][44][45][46][47][48]

International prototype metre bar[edit]

The influence of the intellect trancends mountains and leaps across oceans. At the time when George Washington warned his fellow countrymen against entangling political alliances with European countries, there was started a mouvement of far reaching importance in a small country in the heart of the Alps which (as we shall see) exerted a silent, yet potent scientific influence upon the young republic on the Eastern shores of North America.

—&#;Florian Cajori[49]

In , Ferdinand Hassler was appointed first Superintendent of the Survey of the Coast. Trained in geodesy in Switzerland, France and Germany, Hassler had brought a standard metre made in Paris to the United States in He designed a baseline apparatus which instead of bringing different bars in actual contact during measurements, used only one bar calibrated on the metre and optical contact. Thus the metre became the unit of length for geodesy in the United States.[50][51][52]

Since , Hassler was also head of the Bureau of Weights and Measures which became a part of the Coast Survey. He compared various units of length used in the United States at that time and measured coefficients of expansion to assess temperature effects on the measurements.[53]

In , Friedrich Wilhelm Bessel, taking into account errors which had been recognized by Louis Puissant in the French meridian arc comprising the arc measurement of Delambre and Méchain which had been extended southward by François Arago and Jean-Baptiste Biot, recalculated the flattening of the Earth ellipsoid making use of nine more arc measurements, namely Peruan, Prussian, first East-Indian, second East-Indian, English, Hannover, Danish, Russian and Swedish covering almost 50 degrees of latitude, and stated that the Earth quadrant used for determining the length of the metre was nothing more than a rather imprecise conversion factor between the toise and the metre. Regarding the precision of the conversion from the toise to the metre, both units of measurement were then defined by standards made of different alloys with distinct coefficients of expansion. On the subject of the theoretical definition of the metre, it had been inaccessible and misleading at the time of Delambre and Mechain arc measurement, as the geoid is a ball, which on the whole can be assimilated to an ellipsoid of revolution, but which in detail differs from it so as to prohibit any generalization and any extrapolation. As early as , after Friedrich von Schubert showed that the different meridians were not of equal length, Elie Ritter a mathematician from Geneva deduced from a computation based on eleven meridian arcs covering 86 degrees that the meridian equation differed from that of the ellipse and that the meridian was swelled about the 45th degree of latitude by a layer whose thickness was difficult to estimate because of the uncertainty of the latitude of some stations in particular that of Montjuïc in the French meridian arc. By measuring the latitude of two stations in Barcelona, Méchain had found that the difference between these latitudes was greater than predicted by direct measurement of distance by triangulation. It was an infavourable vertical deflection which gave an innacurate determination of Barcelona's latitude and a metre "too short" compared to a more general definition taken from the average of a large number of arcs.[54][55][56][57][58][59][60]

Nevertheless Ferdinand Rudolph Hassler's use of the metre in coastal survey contributed to the introduction of the Metric Act of allowing the use of the metre in the United States, and possibly also played a role in the choice of the metre as international scientific unit of length and the proposal by the European Arc Measurement (German: Europäische Gradmessung) to “establish a European international bureau for weights and measures”. However, in , the most important concern was that the Toise of Peru, the standard of the toise constructed in for the French Geodesic Mission to the Equator, might be so much damaged that comparison with it would be worthless, while Bessel had questionned the accuracy of copies of this standard belonging to Altona and Koenigsberg Observatories, which he had compared to each other about Indeed when the primary Imperial yard standard was partially destroyed in , a new standard of reference had been constructed using copies of the "Standard Yard, " instead of the pendulum's length as provided for in the Weights and Measures Act of [61][62][63][64][65][66][67]

Swiss baseline measurement with Ibáñezapparatus in

In at the second general conference of the International Association of Geodesy held in Berlin, the question of an international standard unit of length was discussed in order to combine the measurements made in different countries to determine the size and shape of the Earth.[68][69][70] The conference recommended the adoption of the metre in replacement of the toise and the creation of an international metre commission, according to the proposal of Johann Jacob Baeyer, Adolphe Hirsch and Carlos Ibáñez e Ibáñez de Ibero who had devised two geodetic standards calibrated on the metre for the map of Spain.[71][68][70][72]

Ibáñez adopted the system which Ferdinand Rudolph Hassler used for the United States Survey of the Coast, consisting of a single standard with lines marked on the bar and microscopic measurements. Regarding the two methods by which the effect of temperature was taken into account, Ibáñez used both the bimetallic rulers, in platinum and brass, which he first employed for the central baseline of Spain, and the simple iron ruler with inlaid mercury thermometers which was utilized in Switzerland. These devices, the first of which is referred to as either Brunner apparatus or Spanish Standard, were constructed in France by Jean Brunner, then his sons. Measurement traceability between the toise and the metre was ensured by comparison of the Spanish Standard with the standard devised by Borda and Lavoisier for the survey of the meridian arc connecting Dunkirk with Barcelona.[73][72][74][68][75][76][77][78][79]

In , the Saint Petersburg Academy of Sciences sent to the French Academy of Sciences a report drafted by Otto Wilhelm von Struve, Heinrich von Wild and Moritz von Jacobi inviting his French counterpart to undertake joint action with a view to ensuring the universal use of the metric system in all scientific work.[67]

Creating the metre-alloy in at the Conservatoire des Arts et Métiers. Present Henri Tresca, George Matthey, Saint-Claire Deville and Debray

In the s and in light of modern precision, a series of international conferences was held to devise new metric standards. When a conflict broke out regarding the presence of impurities in the metre-alloy of , a member of the Preparatory Committee since and Spanish representative at the Paris Conference in , Carlos Ibáñez e Ibáñez de Ibero intervened with the French Academy of Sciences to rally France to the project to create an International Bureau of Weights and Measures equipped with the scientific means necessary to redefine the units of the metric system according to the progress of sciences. The Metre Convention (Convention du Mètre) of mandated the establishment of a permanent International Bureau of Weights and Measures (BIPM: Bureau International des Poids et Mesures) to be located in Sèvres, France. This new organisation was to construct and preserve a prototype metre bar, distribute national metric prototypes, and maintain comparisons between them and non-metric measurement standards. The organisation distributed such bars in at the first General Conference on Weights and Measures (CGPM: Conférence Générale des Poids et Mesures), establishing the International Prototype Metre as the distance between two lines on a standard bar composed of an alloy of 90% platinum and 10% iridium, measured at the melting point of ice.[80][48][81][82]

Closeup of National Prototype Metre Bar No. 27, made in by the International Bureau of Weights and Measures(BIPM) and given to the United States, which served as the standard for defining all units of length in the US from to

The comparison of the new prototypes of the metre with each other and with the Committee metre (French: Mètre des Archives) involved the development of special measuring equipment and the definition of a reproducible temperature scale. The BIPM's thermometry work led to the discovery of special alloys of iron-nickel, in particular invar, for which its director, the Swiss physicist Charles-Edouard Guillaume, was granted the Nobel Prize for physics in [83]

As Carlos Ibáñez e Ibáñez de Ibero stated, the progress of metrology combined with those of gravimetry through improvement of Kater's pendulum led to a new era of geodesy. If precision metrology had needed the help of geodesy, the latter could not continue to prosper without the help of metrology. It was then necessary to define a single unit in order to express all the measurements of terrestrial arcs, and all determinations of the force of gravity by the mean of pendulum. Metrology had to create a common unit, adopted and respected by all civilized nations. Moreover, at that time, statisticians knew that scientific observations are marred by two distinct types of errors, constant errors on the one hand, and fortuitous errors, on the other hand. The effects of the latters can be mitigated by the least squares method. Constant or regular errors on the contrary must be carefully avoided, because they arise from one or more causes which constantly act in the same way, and have the effect of always altering the result of the experiment in the same direction. They therefore deprive of any value the observations that they impinge. For metrology the matter of expansibility was fundamental; as a matter of fact the temperature measuring error related to the length measurement in proportion to the expansibility of the standard and the constantly renewed efforts of metrologists to protect their measuring instruments against the interfering influence of temperature revealed clearly the importance they attached to the expansion-induced errors. It was thus crucial to compare at controlled temperatures with great precision and to the same unit all the standards for measuring geodetic baselines, and all the pendulum rods. Only when this series of metrological comparisons would be finished with a probable error of a thousandth of a millimetre would geodesy be able to link the works of the different nations with one another, and then proclaim the result of the measurement of the Globe.[84][85][40]

As the figure of the Earth could be inferred from variations of the seconds pendulum length with latitude, the United States Coast Survey instructed Charles Sanders Peirce in the spring of to proceed to Europe for the purpose of making pendulum experiments to chief initial stations for operations of this sort, in order to bring the determinations of the forces of gravity in America into communication with those of other parts of the world; and also for the purpose of making a careful study of the methods of pursuing these researches in the different countries of Europe. In the association of geodesy changed name for the International Geodetic Association, which Carlos Ibáñez e Ibáñez de Ibero presided up to his death in During this period the International Geodetic Association (German: Internationale Erdmessung) gained worldwide importance with the joining of United States, Mexico, Chile, Argentina and Japan.[73][86][87][88][89]

Artist's impression of a GPS-IIR satellite in orbit.

Efforts to supplement the various national surveying systems, which begun in the 19th century with the foundation of the Mitteleuropäische Gradmessung, resulted in a series of global ellipsoids of the Earth (e.g., Helmert , Hayford and ) which would later lead to develop the World Geodetic System. Nowadays the practical realisation of the metre is possible everywhere thanks to the atomic clocks embedded in GPS satellites.[90][91]

Wavelength definition[edit]

In , James Clerk Maxwell suggested that light emitted by an element be used as the standard both for the metre and for the second. These two quantities could then be used to define the unit of mass.[92]

In , the standard metre was first measured with an interferometer by Albert A. Michelson, the inventor of the device and an advocate of using some particular wavelength of light as a standard of length. By , interferometry was in regular use at the BIPM. However, the International Prototype Metre remained the standard until , when the eleventh CGPM defined the metre in the new International System of Units (SI) as equal to wavelengths of the orange-redemission line in the electromagnetic spectrum of the kryptonatom in a vacuum.[93]

Speed of light definition[edit]

To further reduce uncertainty, the 17th CGPM in replaced the definition of the metre with its current definition, thus fixing the length of the metre in terms of the second and the speed of light:[94]

The metre is the length of the path travelled by light in vacuum during a time interval of 1/ of a second.

This definition fixed the speed of light in vacuum at exactly metres per second (≈&#;km/s).[94] An intended by-product of the 17th CGPM's definition was that it enabled scientists to compare lasers accurately using frequency, resulting in wavelengths with one-fifth the uncertainty involved in the direct comparison of wavelengths, because interferometer errors were eliminated. To further facilitate reproducibility from lab to lab, the 17th CGPM also made the iodine-stabilised helium–neon laser "a recommended radiation" for realising the metre.[95] For the purpose of delineating the metre, the BIPM currently considers the HeNe laser wavelength, λHeNe, to be &#;nm with an estimated relative standard uncertainty (U) of ×10−11.[95][96][97] This uncertainty is currently one limiting factor in laboratory realisations of the metre, and it is several orders of magnitude poorer than that of the second, based upon the caesium fountain atomic clock (U = 5×10−16).[98] Consequently, a realisation of the metre is usually delineated (not defined) today in labs as (33) wavelengths of helium-neon laser light in a vacuum, the error stated being only that of frequency determination.[95] This bracket notation expressing the error is explained in the article on measurement uncertainty.

Practical realisation of the metre is subject to uncertainties in characterising the medium, to various uncertainties of interferometry, and to uncertainties in measuring the frequency of the source.[99] A commonly used medium is air, and the National Institute of Standards and Technology (NIST) has set up an online calculator to convert wavelengths in vacuum to wavelengths in air.[] As described by NIST, in air, the uncertainties in characterising the medium are dominated by errors in measuring temperature and pressure. Errors in the theoretical formulas used are secondary.[] By implementing a refractive index correction such as this, an approximate realisation of the metre can be implemented in air, for example, using the formulation of the metre as (33) wavelengths of helium–neon laser light in vacuum, and converting the wavelengths in a vacuum to wavelengths in air. Air is only one possible medium to use in a realisation of the metre, and any partial vacuum can be used, or some inert atmosphere like helium gas, provided the appropriate corrections for refractive index are implemented.[]

The metre is defined as the path length travelled by light in a given time, and practical laboratory length measurements in metres are determined by counting the number of wavelengths of laser light of one of the standard types that fit into the length,[] and converting the selected unit of wavelength to metres. Three major factors limit the accuracy attainable with laser interferometers for a length measurement:[99][]

  • uncertainty in vacuum wavelength of the source,
  • uncertainty in the refractive index of the medium,
  • least count resolution of the interferometer.

Of these, the last is peculiar to the interferometer itself. The conversion of a length in wavelengths to a length in metres is based upon the relation

{\displaystyle \lambda ={\frac {c}{nf}}}

which converts the unit of wavelength &#; to metres using c, the speed of light in vacuum in m/s. Here n is the refractive index of the medium in which the measurement is made, and f is the measured frequency of the source. Although conversion from wavelengths to metres introduces an additional error in the overall length due to measurement error in determining the refractive index and the frequency, the measurement of frequency is one of the most accurate measurements available.[]

Timeline[edit]

DateDeciding bodyDecision
8 May French National AssemblyThe length of the new metre to be equal to the length of a pendulum with a half-period of one second.[35]
30 Mar French National AssemblyAccepts the proposal by the French Academy of Sciences that the new definition for the metre be equal to one ten-millionth of the length of a great circle quadrant along the Earth's meridian through Paris, that is the distance from the equator to the north pole along that quadrant.
Provisional metre bar made of brass and based on Paris meridan arc (French: Méridienne de France) measured by Nicolas-Louis de Lacaillle and Cesar-François Cassini de Thury, legally equal to lines of the toise du Pérou (a standard French unit of length from ).[35][36][74][91] [The line was 1/ of a toise.]
10 Dec French National AssemblySpecifies the platinum metre bar, presented on 22 June and deposited in the National Archives, as the final standard. Legally equal to lines on the toise du Pérou.[91]
24–28 Sept 1st General Conference on Weights and Measures (CGPM)Defines the metre as the distance between two lines on a standard bar of an alloy of platinum with 10% iridium, measured at the melting point of ice.[91][]
27 Sept – 6 Oct 7th CGPMRedefines the metre as the distance, at 0&#;°C (&#;K), between the axes of the two central lines marked on the prototype bar of platinum-iridium, this bar being subject to one standard atmosphere of pressure and supported on two cylinders of at least 10&#;mm (1&#;cm) diameter, symmetrically placed in the same horizontal plane at a distance of &#;mm (&#;cm) from each other.[]
14 Oct 11th CGPMDefines the metre as wavelengths in a vacuum of the radiation corresponding to the transition between the 2p10 and 5d5 quantum levels of the krypton atom.
21 Oct 17th CGPMDefines the metre as the length of the path travelled by light in a vacuum during a time interval of 1/ of a second.[][]
International Committee for Weights and Measures (CIPM)Considers the metre to be a unit of proper length and thus recommends this definition be restricted to "lengths ℓ which are sufficiently short for the effects predicted by general relativity to be negligible with respect to the uncertainties of realisation".[]
Basis of definition Date Absolute
uncertainty
Relative
uncertainty
1/10 part of the quadrant along the meridian, measurement by Delambre and Méchain ( lines) –&#;μm 10−4
First prototype Mètre des Archives platinum bar standard 50–10&#;μm 10−5
Platinum-iridium bar at melting point of ice (1st CGPM) –&#;μm (–&#;nm) 10−7
Platinum-iridium bar at melting point of ice, atmospheric pressure, supported by two rollers (7th CGPM) n.a. n.a.
Hyperfine atomic transition; wavelengths of light from a specified transition in krypton (11th CGPM) 4&#;nm 4×10−9[]
Length of the path travelled by light in a vacuum in 1/ second (17th CGPM) &#;nm 10−10

Early adoptions of the metre internationally[edit]

Main article: Metrication

After the July Revolution of the metre became the definitive French standard from At that time it had already been adopted by Ferdinand Rudolph Hassler for the U.S Survey of the Coast.[35][][71]

"The unit of length to which all distances measured in the Coast Survey are referred is the French metre, an authentic copy of which is preserved in the archives of the Coast Survey Office. It is the property of the American Philosophical Society, to whom it was presented by Mr. Hassler, who had received it from Tralles, a member of the French Committee charged with the construction of the standard metre by comparison with the toise, which had served as unit of length in the measurement of the meridional arcs in France and Peru. It possesses all the authenticity of any original metre extant, bearing not only the stamp of the Committee but also the original mark by which it was distinguished from the other bars during the operation of standardising. It is always designated as the Committee metre" (French&#;: Mètre des Archives).[52]

In President Andrew Jackson mandated Ferdinand Rudolf Hassler to work out new standards for all U.S. states. According to the decision of the Congress of the United States, the British Parliamentary Standard from was introduced as the unit of length.[]

Another geodesist with metrology skills was to play a pivotal role in the process of internationalization of weights and measures, Carlos Ibáñez e Ibáñez de Ibero who would become the first president of both the International Geodetic Association and the International Committee for Weights and Measures.[73]

SI prefixed forms of metre[edit]

SI prefixes can be used to denote decimal multiples and submultiples of the metre, as shown in the table below. Long distances are usually expressed in km, astronomical units ( Gm), light-years (10 Pm), or parsecs (31 Pm), rather than in Mm, Gm, Tm, Pm, Em, Zm or Ym; "30 cm", "30 m", and " m" are more common than "3 dm", "3 dam", and "3 hm", respectively.

The terms micron and millimicron can be used instead of micrometre (μm) and nanometre (nm), but this practice may be discouraged.[]

Equivalents in other units[edit]

Metric unit
expressed in non-SI units
Non-SI unit
expressed in metric units
1 metreyard1 yardmetre
1 metreinches1 inchmetre
1 centimetreinch1 inchcentimetres
1 millimetreinch1 inchmillimetres
1 metre1 × 1010ångström1 ångström1 × 10−10metre
1 nanometre10ångström1 ångströmpicometres

Within this table, "inch" and "yard" mean "international inch" and "international yard"[] respectively, though approximate conversions in the left column hold for both international and survey units.

"≈" means "is approximately equal to";
"≡" means "equal by definition" or "is exactly equal to".

One metre is exactly equivalent to 5 /&#;inches and to 1 /1 &#;yards.

A simple mnemonic aid exists to assist with conversion, as three "3"s:

1 metre is nearly equivalent to 3&#;feet3+3&#;8&#;inches. This gives an overestimate of &#;mm; however, the practice of memorising such conversion formulas has been discouraged in favour of practice and visualisation of metric units.

The ancient Egyptian cubit was about &#;m (surviving rods are –&#;mm).[] Scottish and English definitions of the ell (two cubits) were &#;mm (&#;m) and &#;mm (&#;m) respectively.[][] The ancient Parisian toise (fathom) was slightly shorter than 2&#;m and was standardised at exactly 2&#;m in the mesures usuelles system, such that 1&#;m was exactly 1&#;2&#;toise.[] The Russian verst was &#;km. The Swedish mil was &#;km, but was changed to 10&#;km when Sweden converted to metric units.[]

See also[edit]

Wikimedia Commons has media related to Metre.
Look up metre in Wiktionary, the free dictionary.

Notes[edit]

  1. ^"Base unit definitions: Meter". National Institute of Standards and Technology. Retrieved 28 September
  2. ^"The International System of Units (SI) – NIST". US: National Institute of Standards and Technology. 26 March
  3. ^The most recent official brochure about the International System of Units (SI), written in French by the Bureau international des poids et mesures, International Bureau of Weights and Measures (BIPM) uses the spelling metre; an English translation, included to make the SI standard more widely accessible also uses the spelling metre (BIPM, , p. ff). However, in the U.S. English translation published by the U.S. National Institute of Standards and Technology (NIST) chose to use the spelling meter in accordance with the United States Government Printing Office Style Manual. The Metric Conversion Act of gives the Secretary of Commerce of the US the responsibility of interpreting or modifying the SI for use in the US. The Secretary of Commerce delegated this authority to the Director of the National Institute of Standards and Technology (Turner). In , NIST published the US version (Taylor and Thompson, a) of the English text of the eighth edition of the BIPM publication Le Système international d'unités (SI) (BIPM, ). In the NIST publication, the spellings "meter", "liter" and "deka" are used rather than "metre", "litre" and "deca" as in the original BIPM English text (Taylor and Thompson (a), p. iii). The Director of the NIST officially recognised this publication, together with Taylor and Thompson (b), as the "legal interpretation" of the SI for the United States (Turner). Thus, the spelling metre is referred to as the "international spelling"; the spelling meter, as the "American spelling".
  4. ^Naughtin, Pat (). "Spelling metre or meter"(PDF). Metrication Matters. Retrieved 12 March
  5. ^"Meter vs. metre". Grammarist. Retrieved 12 March
  6. ^The Philippines uses English as an official language and this largely follows American English since the country became a colony of the United States. While the law that converted the country to use the metric system uses metre (Batas Pambansa Blg. 8) following the SI spelling, in actual practice, meter is used in government and everyday commerce, as evidenced by laws (kilometer, Republic Act No. ), Supreme Court decisions (meter, G.R. No. ), and national standards (centimeter, PNS/BAFS ).
  7. ^"– (Nordisk familjebok / Uggleupplagan. Mekaniker – Mykale)" [– (Nordic Family Book / Owl Edition. Mechanic – Mycular)]. Stockholm.
  8. ^Cambridge Advanced Learner's Dictionary. Cambridge University Press. Retrieved 19 September , s.v. ammeter, meter, parking meter, speedometer.
  9. ^American Heritage Dictionary of the English Language (3rd&#;ed.). Boston: Houghton Mifflin. , s.v. meter.
  10. ^"-meter – definition of -meter in English". Oxford Dictionaries.
  11. ^ abOxford English Dictionary, Clarendon Press 2nd ed, shoppingdowntown.us p col
  12. ^texte, Picard, Jean (–). Auteur du (). Mesure de la terre [par l'abbé Picard]. Gallica. pp.&#;3–4. Retrieved 13 September [verification needed]
  13. ^Lucendo, Jorge (23 April ). Centuries of Inventions: Encyclopedia and History of Inventions. Jorge Lucendo. p.&#; Retrieved 2 August
  14. ^Camerini, Valentina (1 December ). Real-Life Superheroes. Black Inc. p.&#; ISBN&#;.
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  20. ^Picard, Jean (–) Auteur du texte (). Mesure de la terre [par l'abbé Picard]. pp.&#;3–5.
  21. ^Bond, Peter, ( ). (). L'exploration du système solaire. Dupont-Bloch, Nicolas. ([Édition française revue et corrigée]&#;ed.). Louvain-la-Neuve: De Boeck. pp.&#;5–6. ISBN&#;. OCLC&#;CS1 maint: multiple names: authors list (link)
  22. ^Badinter, Élisabeth (). Les passions intellectuelles. Normandie roto impr.). Paris: Robert Laffont. ISBN&#;. OCLC&#;
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  24. ^Tipler, Paul A.; Mosca, Gene (). Physics for Scientists and Engineers (5th&#;ed.). W.H. Freeman. p.&#;3. ISBN&#;.
  25. ^('decimalization is not of the essence of the metric system; the real significance of this is that it was the first great attempt to define terrestrial units of measure in terms of an unvarying astronomical or geodetic constant.) The metre was in fact defined as one ten-millionth of one-quarter of the earth's circumference at sea-level.' Joseph Needham, Science and Civilisation in China, Cambridge University Press, vol.4, pt.1, p
  26. ^Agnoli, Paolo (). Il senso della misura: la codifica della realtà tra filosofia, scienza ed esistenza umana (in Italian). Armando Editore. pp.&#;93–94, ISBN&#;. Retrieved 13 October
  27. ^Rapport sur le choix d'une unité de mesure, lu à l'Académie des sciences, le 19 mars (in French). shoppingdowntown.us 15 October Retrieved 25 March : "Nous proposerons donc de mesurer immédiatement un arc du méridien, depuis Dunkerque jusqu'a Bracelone: ce qui comprend un peu plus de neuf degrés & demi." [We propose then to measure directly an arc of the meridian between Dunkirk and Barcelona: this spans a little more than nine-and-a-half degrees."] p. 8
  28. ^Paolo Agnoli and Giulio D’Agostini,'Why does the meter beat the second?,' December, pp.1–
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  34. ^Ferreiro, Larrie D. (25 June ). Measure of the Earth: The Enlightenment Expedition That Reshaped Our World. Basic Books. ISBN&#;.
  35. ^ abIbáñez e Ibáñez de Ibero, Carlos (). Discursos leidos ante la Real Academia de Ciencias Exactas Fisicas y Naturales en la recepcion pública de Don Joaquin Barraquer y Rovira(PDF). Madrid: Imprenta de la Viuda e Hijo de D.E. Aguado. pp.&#;70–
  36. ^"Nomination of the Struve geodetic arc for inscription on the World Heritage List"(PDF). Retrieved 13 May
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  39. ^Géophysique in Encyclopedia Universalis. Encyclopedia Universalis. pp.&#;Vol 10, p. ISBN&#;. OCLC&#;
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  43. ^ abQuinn, T. J. (). From artefacts to atoms&#;: the BIPM and the search for ultimate measurement standards. Oxford. pp.&#;91–92, 70–72, –, – ISBN&#;. OCLC&#;
  44. ^Cajori, Florian (). "Swiss Geodesy and the United States Coast Survey". The Scientific Monthly. Vol.&#;13 no.&#;2. American Association for the Advancement of Science. pp.&#;–
  45. ^Poupard, James (). Transactions of the American Philosophical Society. 2. Philadelphia: Abraham Small. pp.&#;–, –, ,
  46. ^Cajori, Florian (). "Swiss Geodesy and the United States Coast Survey". The Scientific Monthly. 13 (2): – BibcodeSciMoC. ISSN&#;
  47. ^ abClarke, Alexander Ross (), "XIII. Results of the comparisons of the standards of length of England, Austria, Spain, United States, Cape of Good Hope, and of a second Russian standard, made at the Ordnance Survey Office, Southampton. With a preface and notes on the Greek and Egyptian measures of length by Sir Henry James", Philosophical Transactions, London, , p.&#;, doi/rstl
  48. ^Parr, Albert C. (1 April ). "A Tale About the First Weights and Measures Intercomparison in the United States in ". Journal of Research of the National Institute of Standards and Technology. (1): 31–32, doi/jres PMC&#; PMID&#; &#; via NIST.
  49. ^Viik, T (). "F. W. BESSEL AND GEODESY". Struve Geodetic Arc, International Conference, The Struve Arc and Extensions in Space and Time, Haparanda and Pajala, Sweden, August . p.&#; CiteSeerX&#; Retrieved 23 September
  50. ^Bessel, Friedrich Wilhelm (1 December ). "Über einen Fehler in der Berechnung der französischen Gradmessung und seineh Einfluß auf die Bestimmung der Figur der Erde. Von Herrn Geh. Rath und Ritter Bessel". Astronomische Nachrichten. 19 (7): BibcodeANB. doi/asna ISSN&#;
  51. ^Lebon, Ernest (). Histoire abrégée de l'astronomie / par Ernest Lebon, Paris. p.&#;
  52. ^Zuerich, ETH-Bibliothek (). "La méridienne de Dunkerque à Barcelone et la déterminiation du mètre ()". E-Periodica (in French): – doi/seals Retrieved 12 October
  53. ^"c à Paris&#;; vitesse de la lumière "shoppingdowntown.us. Retrieved 12 October
  54. ^Société de physique et d'histoire naturelle de Genève.; Genève, Société de physique et d'histoire naturelle de (). Memoires de la Société de physique et d'histoire naturelle de Genève. 15. Geneve: Georg [etc.] pp.&#;–
  55. ^Société de physique et d'histoire naturelle de Genève.; Genève, Société de physique et d'histoire naturelle de (). Memoires de la Société de physique et d'histoire naturelle de Genève. 16. Geneve: Georg [etc.] p.&#;
  56. ^"Metric Act of – US Metric Association". shoppingdowntown.us. Retrieved 15 March
  57. ^Bericht über die Verhandlungen der vom September bis 7. October zu BERLIN abgehaltenen allgemeinen Conferenz der Europäischen Gradmessung(PDF) (in German). Berlin: Central-Bureau der Europäischen Gradmessung. pp.&#;–
  58. ^Quinn, Terry (). "Wilhelm Foerster's Role in the Metre Convention of and in the Early Years of the International Committee for Weights and Measures". Annalen der Physik. (5): 2. BibcodeAnPQ. doi/andp ISSN&#; S2CID&#;
  59. ^Clarke, Alexander Ross; James, Henry (1 January ). "X. Abstract of the results of the comparisons of the standards of length of England, France, Belgium, Prussia, Russia, India, Australia, made at the ordnance Survey Office, Southampton". Philosophical Transactions of the Royal Society of London. : doi/rstl S2CID&#;
  60. ^Bessel, Friedrich Wilhelm (1 April ). "Über das preufs. Längenmaaß und die zu seiner Verbreitung durch Copien ergriffenen Maaßregeln". Astronomische Nachrichten. 17 (13): BibcodeANB. doi/asna ISSN&#;
  61. ^Britain, Great (). The Statutes of the United Kingdom of Great Britain and Ireland.
  62. ^ abGuillaume, Ed. (1 January ). "Le Systeme Metrique est-il en Peril?". L'Astronomie. 30: BibcodeLAstrG. ISSN&#;
  63. ^ abcHirsch, Adolphe (). "Don Carlos IBANEZ (–)"(PDF). Bureau International des Poids et Mesures. pp.&#;4, 8. Retrieved 22 May
  64. ^"BIPM – International Metre Commission". shoppingdowntown.us. Retrieved 26 May
  65. ^ ab"A Note on the History of the IAG". IAG Homepage. Retrieved 26 May
  66. ^ abRoss, Clarke Alexander; James, Henry (1 January ). "XIII. Results of the comparisons of the standards of length of England, Austria, Spain, United States, Cape of Good Hope, and of a second Russian standard, made at the Ordnance Survey Office, Southampton. With a preface and notes on the Greek and Egyptian measures of length by Sir Henry James". Philosophical Transactions of the Royal Society of London. : – doi/rstl
  67. ^ abBrunner, Jean (). "Comptes rendus hebdomadaires des séances de l'Académie des sciences / publiés par MM. les secrétaires perpétuels". Gallica (in French). pp.&#;– Retrieved 15 May
  68. ^ abcSoler, T. (1 February ). "A profile of General Carlos Ibáñez e Ibáñez de Ibero: first president of the International Geodetic Association". Journal of Geodesy. 71 (3): – BibcodeJGeodS. doi/s ISSN&#; S2CID&#;
  69. ^ abWolf, Charles (–) Auteur du texte (). Recherches historiques sur les étalons de poids et mesures de l'Observatoire et les appareils qui ont servi à les construire / par M. C. Wolf (in French). pp.&#;C–39, C.2–4.
  70. ^Wolf, Rudolf (January ). "Comptes rendus hebdomadaires des séances de l'Académie des sciences / publiés par MM. les secrétaires perpétuels". Gallica. pp.&#;– Retrieved 30 August
  71. ^Brenni, Paolo (). "19th Century French Scientific Instrument Makers - XI: The Brunners and Paul Gautier"(PDF). Bulletin of the Scientific Instrument Society. 49: 3–5 &#; via Universidad de Navarra.
  72. ^Clarke, Alexander Ross; Helmert, Friedrich Robert (). "Geodesy"&#;. In Chisholm, Hugh (ed.). Encyclopædia Britannica. 11 (11th&#;ed.). Cambridge University Press. pp.&#;–
  73. ^Schiavon, Martina (1 December ). "Les officiers géodésiens du Service géographique de l'armée et la mesure de l'arc de méridien de Quito ()". Histoire & mesure (in French). XXI (XXI - 2): 55– doi/histoiremesure ISSN&#;
  74. ^Expériences faites avec l'appareil à mesurer les bases appertant à la commission de la carte d'Espagne /: ouvrage publié par ordre de la reine (in French). J. Dumaine.
  75. ^Pérard, Albert (). "Carlos IBAÑEZ DE IBERO (14 avril – 29 janvier ), par Albert Pérard (inauguration d'un monument élevé à sa mémoire)"(PDF). Institut de France – Académie des sciences. pp.&#;26–
  76. ^Dodis, Diplomatische Dokumente der Schweiz Dodis, retrieved 20 September
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  78. ^"BIPM – la définition du mètre". shoppingdowntown.us. Retrieved 15 May
  79. ^"The Nobel Prize in Physics ". shoppingdowntown.us. Retrieved 13 March
  80. ^Ritter, Élie (). Manuel théorique et pratique de l'application de la méthode des moindres carrés: au calcul des observations (in French). Mallet-Bachelier.
  81. ^"Report from Charles S. Peirce on his second European trip for the Anual Report of the Superintendent of the U. S. Coast Survey, New York, ". shoppingdowntown.us. Retrieved 22 May
  82. ^Faye, Hervé (). "Comptes rendus hebdomadaires des séances de l'Académie des sciences / publiés par MM. les secrétaires perpétuels". Gallica (in French). pp.&#;– Retrieved 22 May
  83. ^Torge, Wolfgang (). Rizos, Chris; Willis, Pascal (eds.). "From a Regional Project to an International Organization: The "Baeyer-Helmert-Era" of the International Association of Geodesy –". IAG Years. International Association of Geodesy Symposia. Springer International Publishing. : 3– doi/__ ISBN&#;.
  84. ^Torge, W. (1 April ). "The International Association of Geodesy to from a regional project to an international organization". Journal of Geodesy. 78 (9): – BibcodeJGeodT. doi/s ISSN&#;
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(30 March ), Bericht der schweizerischen Delegierten an der internationalen Meterkonferenz an den Bundespräsidenten und Vorsteher des Politischen Departements, J. J. Scherer (in French), Diplomatische Dokumente der Schweiz Documenti diplomatici svizzeri

Metre

SI unit of length

This article is about the unit of length. For other uses of "metre" or "meter", see Meter (disambiguation).

metre
Metric shoppingdowntown.us

Seal of the International Bureau of Weights and Measures (BIPM) – Use measure (Greek: ΜΕΤΡΩ ΧΡΩ)

Unit systemSI base unit
Unit&#;ofLength
Symbolm[1]
1 m[1]in is equal to
&#;&#;&#;SI units&#;&#;&#;
  • &#;mm
  • &#;km
&#;&#;&#;Imperial/US units&#;&#;&#;
  • ≈&#;&#;yd
  • ≈&#;&#;ft
  • ≈&#;&#;in
&#;&#;&#;Nautical units&#;&#;&#;≈&#;&#;nmi

The metre (Commonwealth spelling) Express Systems Express Meter v3.0 crack serial keygen meter (American spelling; see spelling differences) (from the French unit mètre, from the Greek noun μέτρον, "measure") is the base unit of length in the International System of Units (SI). The SI unit symbol is m.

The metre is currently defined as the length of the path travelled by light in a vacuum in 1/ of a second.

The metre was originally defined in as one ten-millionth of the distance from the equator to the North Pole along a great circle, so the Earth's circumference is approximately &#;km. Inthe metre was redefined in terms of a prototype metre bar (the actual bar used was changed in ). Inthe metre was redefined in terms of a certain number of wavelengths of a certain emission line of krypton The current definition was adopted in and modified slightly in to clarify that the metre is a measure of proper length.

Spelling[edit]

Metre is the standard spelling of the metric unit for length in nearly all English-speaking nations except the United States[2][3][4][5] and the Philippines,[6] which use meter. Other Germanic languages, such as German, Dutch, and the Scandinavian languages,[7] likewise spell the word Meter or meter.

Measuring devices (such as ammeter, speedometer) are spelled "-meter" in all variants of English.[8] The suffix "-meter" has the same Greek origin as the unit of length.[9][10]

Etymology[edit]

The etymological roots of metre can be traced to the Greek verb μετρέω (metreo) (to measure, count or compare) and noun μέτρον (metron) (a measure), which were used for physical measurement, for poetic metre and by extension for moderation or avoiding extremism (as in "be measured in your response"). This range of uses is also found in Latin (metior, mensura), French (mètre, mesure), English and other languages. The Greek word is derived from the Proto-Indo-European root *meh₁- 'to measure'. The motto ΜΕΤΡΩ ΧΡΩ (metro chro) in the seal of the International Bureau of Weights and Measures (BIPM), which was a saying of the Greek statesman and philosopher Pittacus of Mytilene and may be translated as "Use measure!", thus calls for both measurement and moderation. The use of the word metre (for the French unit mètre) in English began at least as early as [11]

History of definition [edit]

Main article: History of the metre

Pendulum or meridian[edit]

In Jean Picard measured the length of a "seconds pendulum" and proposed a unit of measurement twice that length to be called the universal toise (French: Toise universelle).[12] InTito Livio Burattini suggested the term metre for a unit of length based on a pendulum length, but then it was discovered that the length of a seconds pendulum varies from place to place.[14][15][16][17][18][19][20][21][22]

Since Eratosthenes, geographers had used meridian arcs to assess the size of the Earth, which inJean Picard determined to have a radius of toises, treated as a simple sphere. In the 18th century, geodesy grew in importance as a means of empirically demonstrating the theory of gravity and because the radius of the Earth was the unit to which all celestial distances were to be referred.[24][25]

Meridional definition[edit]

As a result of the Lumières and during the French Revolution, the French Academy of Sciences charged a commission with determining a single scale for all measures. On 7 October that commission advised the adoption of a decimal system, and on 19 March advised the adoption of the term mètre ("measure"), a basic unit of length, which they defined as equal to one ten-millionth of the quarter meridian, the distance between the North Pole and the Equator along the meridian through Paris.[26][27][28][29][30] On 26 Marchthe French National Constituant Assembly adopted the proposal.[11][31]

The French Academy of Sciences commissioned an expedition led by Jean Baptiste Joseph Delambre and Pierre Méchain, lasting from towhich attempted to accurately measure the distance between a belfry in Dunkerque and Montjuïc castle in Barcelona at the longitude of the Paris Panthéon (see meridian arc of Delambre and Méchain).[32] The expedition was fictionalised in Denis Guedj, Le Mètre du Monde. Ken Alder wrote Express Systems Express Meter v3.0 crack serial keygen about the expedition in The Measure of All Things: the seven year odyssey and hidden error that transformed the world. This portion of the Paris meridian was to serve as the basis for the length of the half meridian connecting the North Pole with the Equator. From to France adopted this definition of the metre as its official unit of length based on results from this expedition combined with those of the Geodesic Mission to Peru.[35][36] The latter was related by Larrie D. Ferreiro in Measure of the Earth: The Enlightenment Expedition that Reshaped Our World.[37][38]

In the 19th century, geodesy underwent a revolution with advances in mathematics as well as progress of observation instruments and methods with the taking into account of the personal equation. The application of the least squares method to meridian arc measurements demonstrated the importance of the scientific method in geodesy. On the other hand, the invention of the telegraph made it possible to measure parallel arcs, and the improvement of the reversible pendulum gave rise to the study of the Earth's gravitational field. A more accurate determination of the Figure of the Earth would soon result from the measurement of the Struve Geodetic Arc (–) and would have given another value for the definition of this standard of length. This did not invalidate the metre but highlighted that progresses in science would allow better measurement of Earth's size and shape.[40][41][42]

InCarl Friedrich Gauss studied the Earth's magnetic field and proposed adding the second to the basic units of the metre and the kilogram in the form of the CGS system (centimetre, gram, second). Inhe founded the Magnetischer Verein, the first international scientific association, in collaboration with Alexander von Humboldt and Wilhelm Edouard Weber. The coordination of the observation of geophysical phenomena such as the Earth's magnetic field, lightning and gravity in different points of the globe stimulated the creation of the first international scientific associations. The foundation of the Magnetischer Verein would be followed by that of the Central European Arc Measurement (German: Mitteleuropaïsche Gradmessung) on the initiative of Johann Jacob Baeyer inand by that of the International Meteorological Organisation whose second president, the Swiss meteorologist and physicist, Heinrich von Wild would represent Russia at the International Committee for Weights and Measures (CIPM).[43][44][45][46][47][48]

International prototype metre bar[edit]

The influence of the intellect trancends mountains and leaps across oceans. At the time when George Washington warned his fellow countrymen against entangling political alliances with European countries, there was started a mouvement of far reaching importance in a small country in the heart of the Alps which (as we shall see) exerted a silent, yet potent scientific influence upon the young republic on the Eastern shores of North America.

—&#;Florian Cajori[49]

InFerdinand Hassler was appointed first Superintendent of the Survey of the Coast. Trained in geodesy in Switzerland, France and Germany, Hassler had brought a standard metre made in Paris to the United States in He designed a baseline apparatus which instead of bringing different bars in actual contact during measurements, used only one bar calibrated on the metre and optical contact. Thus the metre became the unit of length for geodesy in the United States.[50][51][52]

SinceHassler was also head of the Bureau of Weights and Measures which became a part of the Coast Survey, Express Systems Express Meter v3.0 crack serial keygen. He compared various units of length used in the United States at that time and measured coefficients of expansion to assess temperature effects on the measurements.[53]

InFriedrich Wilhelm Bessel, taking into account errors which had been recognized by Louis Puissant in the French meridian arc comprising the arc measurement of Delambre and Méchain which had been extended southward by François Arago and Jean-Baptiste Biot, recalculated the flattening of the Earth ellipsoid making use of nine more arc measurements, namely Peruan, Prussian, first East-Indian, second East-Indian, English, Hannover, Danish, Russian and Swedish covering almost 50 degrees of latitude, and stated that the Earth quadrant used for determining the length of the metre was nothing more than a rather imprecise conversion factor between the toise and the metre. Regarding the precision of the conversion from the toise to the metre, both units of measurement were then defined by standards made of different alloys with distinct coefficients of expansion. On the subject of the theoretical definition of the metre, it had been inaccessible and misleading at the time of Delambre and Mechain arc measurement, as the geoid is a ball, which on the whole can be assimilated to an ellipsoid of revolution, but which in detail differs from it so as to prohibit any generalization and any extrapolation. As early asafter Friedrich von Schubert showed that the different meridians were not of equal length, Elie Ritter a mathematician from Geneva deduced from a computation based on eleven meridian arcs covering 86 degrees that the meridian equation differed from that of the ellipse and that the meridian was swelled about the 45th degree of latitude by a layer whose thickness was difficult to estimate because of the uncertainty of the latitude of some stations in particular that of Montjuïc in the French meridian arc. By measuring the latitude of two stations in Barcelona, Méchain had found that the difference between these latitudes was greater than predicted by direct measurement of distance by triangulation. It was an infavourable vertical deflection which gave an innacurate determination of Barcelona's latitude and a metre "too short" compared to a more general definition taken from the average of a large number of arcs.[54][55][56][57][58][59][60]

Nevertheless Ferdinand Rudolph Hassler's use of the metre in coastal survey contributed to the introduction of the Metric Act of allowing the use of the metre in the United States, and possibly also played a role in the choice of the metre as international scientific unit of length and the proposal by the European Arc Measurement (German: Europäische Gradmessung) to “establish a European international bureau for weights and measures”. However, inthe most important concern was that the Toise of Peru, the standard of the toise constructed in for the French Geodesic Mission to the Equator, might be so much damaged that comparison with it would be worthless, while Bessel had questionned the accuracy of copies of this standard belonging to Altona and Koenigsberg Observatories, which he had compared to each other Express Systems Express Meter v3.0 crack serial keygen Indeed when the primary Imperial yard standard was partially destroyed ina new standard of reference had been constructed using copies of the "Standard Yard, " instead of the pendulum's length as provided for in the Weights and Measures Act of [61][62][63][64][65][66][67]

Swiss baseline measurement with Ibáñezapparatus in

In at the second general conference of the International Association of Geodesy held in Berlin, the question of an international standard unit of length was discussed in order to combine the measurements made in different countries to determine the size and shape of the Earth.[68][69][70] The conference recommended the adoption of the metre in replacement of the toise and the creation of an international metre commission, according to the proposal of Johann Jacob Baeyer, Adolphe Hirsch and Carlos Ibáñez e Ibáñez de Ibero who had devised two geodetic standards calibrated on the metre for the map of Spain.[71][68][70][72]

Ibáñez adopted the system which Ferdinand Rudolph Hassler used for the United States Survey of the Coast, consisting of a single standard with lines marked on the bar and microscopic measurements. Regarding the two methods by which the effect of temperature was taken into account, Ibáñez used both the bimetallic rulers, in platinum and brass, which he first employed for the central baseline of Spain, and the simple iron ruler with inlaid mercury thermometers which was utilized in Switzerland. These devices, the first of which is referred to as either Brunner apparatus or Spanish Standard, were constructed in France by Jean Brunner, then his sons. Measurement traceability between the toise and the metre was ensured by comparison of the Spanish Standard with the standard devised by Borda and Lavoisier for the survey of the meridian arc connecting Dunkirk with Barcelona.[73][72][74][68][75][76][77][78][79]

Inthe Saint Petersburg Academy of Sciences sent to the French Academy of Sciences a report drafted by Otto Wilhelm von Struve, Heinrich von Wild and Moritz von Jacobi inviting his French counterpart to undertake joint action with a view to ensuring the universal use of the metric system in all scientific work.[67]

Creating the metre-alloy in at the Conservatoire des Arts et Métiers. Present Henri Tresca, George Matthey, Saint-Claire Deville and Debray

In the s and in light of modern precision, a series of international conferences was held to devise new metric standards. When a conflict broke out regarding the presence of impurities in the metre-alloy ofa member of the Preparatory Committee since and Spanish representative at the Paris Conference inCarlos Ibáñez e Ibáñez de Ibero intervened with the French Academy of Sciences to rally France to the project to create an International Bureau of Weights and Measures equipped with the scientific means necessary to redefine the units of the metric system according to the progress of sciences. The Metre Convention (Convention du Mètre) of mandated the establishment of a permanent International Bureau of Weights and Measures (BIPM: Bureau International des Poids et Mesures) to be located in Sèvres, France, Express Systems Express Meter v3.0 crack serial keygen. This new organisation was to construct and preserve a prototype metre bar, distribute national metric prototypes, and maintain comparisons between them and non-metric measurement standards. The organisation distributed such bars in at the first General Conference on Weights and Measures (CGPM: Conférence Générale des Poids et Mesures), establishing the International Prototype Metre as the distance between two lines on a standard bar composed of an alloy of 90% platinum and 10% iridium, measured at the melting point of ice.[80][48][81][82]

Closeup of National Prototype Metre Bar No. 27, made in by the International Bureau of Weights and Measures(BIPM) and given to the United States, which served as the standard for defining all units of length in the US from to

The comparison of the new prototypes of the metre with each other and with the Committee metre (French: Mètre des Archives) involved the development of special measuring equipment and the definition of a reproducible temperature scale. The BIPM's thermometry work led to the discovery of special alloys of iron-nickel, in particular invar, for which its director, the Swiss physicist Charles-Edouard Guillaume, was granted the Nobel Prize for physics in [83]

As Carlos Ibáñez e Ibáñez de Ibero stated, the progress of metrology combined with those of gravimetry through improvement of Kater's pendulum led to a new era of geodesy. If precision metrology had needed the help of geodesy, the latter could not continue to prosper without the help of metrology. It was then necessary to define a single unit in order to express all the measurements of terrestrial arcs, and all determinations of the force of gravity by the mean of pendulum. Metrology had to create a common unit, adopted and respected Express Systems Express Meter v3.0 crack serial keygen all civilized nations. Moreover, at that time, statisticians knew that scientific observations are marred by two distinct types of errors, constant errors on the one hand, and fortuitous errors, on the other hand. The effects of the latters can be mitigated by the least squares method. Constant or regular Express Systems Express Meter v3.0 crack serial keygen on the contrary must be carefully avoided, because they arise from one or more causes which constantly act in the same way, and have the effect of always altering the result of the experiment in the same direction. They therefore deprive of any value the observations that they impinge. For metrology the matter of expansibility was fundamental; as a matter of fact the temperature measuring error related to the length measurement in proportion to the expansibility of the standard and the constantly renewed efforts of metrologists to protect their measuring instruments against the interfering influence of temperature revealed clearly the importance they attached to the expansion-induced errors. It was thus crucial to compare at controlled temperatures with great precision and to the same unit all the standards for measuring geodetic baselines, and all the pendulum rods. Only when this series of metrological comparisons would be finished with a probable error of a thousandth of a millimetre would geodesy be able to link the works of the different nations with one another, and then proclaim the result of the measurement of the Globe.[84][85][40]

As the figure of the Earth could be inferred from variations of the seconds pendulum length with latitude, the United States Coast Survey instructed Charles Sanders Peirce in the spring of to proceed to Europe for the purpose of making pendulum experiments to chief initial stations for operations of this sort, in order to bring the determinations of the forces of gravity in America into communication with those of other parts of the world; and also for the purpose of making a careful study of the methods of pursuing these researches in the different countries of Europe. In the association of geodesy changed name for the International Geodetic Association, which Carlos Ibáñez e Ibáñez de Ibero presided up to his death in During this period the International Geodetic Association (German: Internationale Erdmessung) gained worldwide importance with the joining of United States, Mexico, Chile, Argentina and Japan.[73][86][87][88][89]

Artist's impression of a GPS-IIR satellite in orbit.

Efforts to supplement the various national surveying systems, which begun in the 19th century with the foundation of the Mitteleuropäische Gradmessung, resulted in a series of global ellipsoids of the Earth (e.g., Express Systems Express Meter v3.0 crack serial keygen, HelmertHayford and ) which would later lead to develop the World Geodetic System. Nowadays the practical realisation of the metre is possible everywhere thanks to the atomic clocks embedded in GPS satellites.[90][91]

Wavelength definition[edit]

InJames Clerk Maxwell suggested that light emitted by an element be used as the standard both for the metre and for the second. These two quantities could then be used to define the unit of mass.[92]

Inthe standard metre was first measured with an interferometer by Albert A. Michelson, the inventor of the device and an advocate of using some particular wavelength of light as a standard of length. Byinterferometry was in regular use at the BIPM. However, the International Prototype Metre remained the standard untilwhen the eleventh CGPM defined the metre in the new International System of Units (SI) as equal to wavelengths of the orange-redemission line in the electromagnetic spectrum of the kryptonatom in a vacuum.[93]

Speed of light definition[edit]

To further reduce uncertainty, the 17th CGPM in replaced the definition of the metre with its current definition, thus fixing the length of the metre in terms of the second and the speed of light:[94]

The metre is the length of the path travelled by light in vacuum during a time interval of 1/ of a second.

This definition fixed the speed of light in vacuum at exactly metres per second (≈&#;km/s).[94] An intended by-product of the 17th CGPM's definition was that it enabled scientists to compare lasers accurately using frequency, resulting in wavelengths with one-fifth the uncertainty involved in the direct comparison of wavelengths, because interferometer errors were eliminated. To further facilitate reproducibility from lab to lab, the 17th CGPM also made the iodine-stabilised helium–neon laser "a recommended radiation" for realising the metre.[95] For the purpose of delineating the metre, the BIPM currently considers the HeNe laser wavelength, λHeNe, to be &#;nm with an estimated relative standard uncertainty (U) of ×10−11.[95][96][97] This uncertainty is currently one limiting factor in laboratory realisations of the metre, and it is several orders of magnitude poorer than that of the second, based upon the caesium fountain atomic clock (U = 5×10−16).[98] Consequently, a realisation of the metre is usually delineated (not defined) today in labs as (33) wavelengths of helium-neon laser light in a vacuum, the error stated being only that of frequency determination.[95] This bracket notation expressing the error is explained in Express Systems Express Meter v3.0 crack serial keygen article on measurement uncertainty.

Practical realisation of the metre is subject to uncertainties in characterising the medium, to various uncertainties of interferometry, and to uncertainties in measuring the frequency of the source.[99] A commonly used medium is air, and the National Institute of Standards and Technology (NIST) has set up an online calculator to convert wavelengths in vacuum to wavelengths in air.[] As described by NIST, in air, the uncertainties in characterising the medium are dominated by errors in measuring temperature and pressure. Errors in the theoretical formulas used are secondary.[] By implementing a refractive index correction such as this, an approximate realisation of the metre can be implemented in air, for example, using the formulation of the metre as (33) wavelengths of helium–neon laser light in vacuum, and converting the wavelengths in a vacuum to wavelengths in air. Air is only one possible medium to use in a realisation of the metre, and any partial vacuum can be used, or some inert atmosphere like helium gas, provided the appropriate corrections for refractive index are implemented.[]

The metre is defined as the path length travelled by light in a given time, and practical laboratory length measurements in metres are determined by counting the number of wavelengths of laser light of one of the standard Express Systems Express Meter v3.0 crack serial keygen that fit into the length,[] and converting the selected unit of wavelength to metres. Three major factors limit the accuracy attainable with laser interferometers for a length measurement:[99][]

  • uncertainty in vacuum wavelength Express Systems Express Meter v3.0 crack serial keygen the source,
  • uncertainty in the refractive index of the medium,
  • least count resolution of the interferometer.

Of these, the last is peculiar to the interferometer itself. The conversion of a length in wavelengths to a length in metres is based upon the relation

{\displaystyle \lambda ={\frac {c}{nf}}}

which converts the unit of wavelength &#; to metres using c, the speed of light in vacuum in m/s. Here n is the refractive index of the medium in which the measurement is made, and f is the measured frequency of the source. Although conversion from wavelengths to metres introduces an additional error in the overall length due to measurement error in determining the refractive Wondershare Video Converter Ultimate 10.4.3 Crack and the frequency, the measurement of frequency is one of the most accurate measurements available.[]

Timeline[edit]

DateDeciding bodyDecision
8 May French National AssemblyThe length of the new metre to be equal to the length of a pendulum with a half-period of one second.[35]
30 Mar French National AssemblyAccepts the proposal by the French Academy of Sciences that the new definition for the metre be equal to one ten-millionth of the length of a great circle quadrant along the Earth's meridian through Paris, that is the distance from the equator to the north pole along that quadrant.
Provisional metre bar made of brass and based on Paris meridan arc (French: Méridienne de France) measured by Nicolas-Louis de Lacaillle and Cesar-François Cassini de Thury, legally equal to lines of the toise du Pérou (a standard French unit of length from ).[35][36][74][91] [The line was 1/ of a toise.]
10 Dec French National AssemblySpecifies the platinum metre bar, presented on 22 June and deposited in the National Archives, as the final standard. Legally equal to lines on the toise du Pérou.[91]
24–28 Sept 1st General Conference on Weights and Measures (CGPM)Defines the metre as the distance between two lines on a standard bar of an alloy of platinum with 10% iridium, measured at the melting point of ice.[91][]
27 Sept – 6 Oct 7th CGPMRedefines the metre as the distance, at 0&#;°C (&#;K), Express Systems Express Meter v3.0 crack serial keygen, between the axes of the two central lines marked on the prototype bar of platinum-iridium, this bar being subject to one standard atmosphere of pressure and supported on two cylinders of at least 10&#;mm (1&#;cm) diameter, symmetrically placed in the same horizontal plane at a distance of &#;mm (&#;cm) from each other.[]
14 Oct 11th CGPMDefines the metre as wavelengths in a vacuum of the radiation corresponding to the transition between the 2p10 and 5d5 quantum levels of the krypton atom.
21 Oct 17th CGPMDefines the metre as the length of the path travelled by light in a vacuum during a time interval of 1/ of a second.[][]
International Committee for Weights and Measures (CIPM)Considers the metre to be a unit of proper length and thus recommends this definition be restricted to "lengths ℓ which are sufficiently short for the effects predicted by general relativity to be negligible with respect to the uncertainties of realisation".[]
Basis of definition Date Absolute
uncertainty
Relative
uncertainty
1/10 part of the quadrant along the meridian, measurement by Delambre and Méchain ( lines) –&#;μm 10−4
First prototype Mètre des Archives platinum bar standard 50–10&#;μm 10−5
Platinum-iridium bar at melting point of ice (1st CGPM) –&#;μm (–&#;nm) 10−7
Platinum-iridium bar at melting point of ice, atmospheric pressure, supported by two rollers (7th CGPM) n.a. n.a.
Hyperfine atomic transition; wavelengths of light from a specified transition in krypton (11th CGPM) 4&#;nm 4×10−9[]
Length of the path travelled by light in a vacuum in 1/ second (17th CGPM) &#;nm 10−10

Early adoptions of the metre internationally[edit]

Main article: Metrication

After the July Revolution of the metre became the definitive French standard from At that time it had already been adopted by Ferdinand Rudolph Hassler for the U.S Survey of the Coast.[35][][71]

"The unit of length to which all distances measured in the Coast Survey are referred is the French metre, an authentic copy of which is preserved in the archives of the Coast Survey Office. It is the Express Systems Express Meter v3.0 crack serial keygen of the American Philosophical Society, to whom it was presented by Mr. Hassler, who had received it from Tralles, a member of the French Committee charged with the construction of the standard metre by comparison with the toise, which had served as unit of length in the measurement of the meridional arcs in France and Peru. It possesses all the authenticity of any original metre extant, bearing not only the stamp of the Committee but also the original mark by which it was distinguished from the other bars during the operation of standardising. It is always designated as the Committee metre" (French&#;: Mètre des Archives).[52]

In President Andrew Jackson mandated Ferdinand Rudolf Hassler to work out new standards for all U.S. states. According to the decision of the Congress of the United States, the British Parliamentary Standard from was introduced as the unit of length.[]

Another geodesist with metrology skills was to play a pivotal role in the process of internationalization of weights and measures, Carlos Ibáñez e Ibáñez de Ibero who would become the first president of both the International Geodetic Association and the International Committee for Weights and Measures.[73]

SI prefixed forms of metre[edit]

SI prefixes can be used to denote decimal multiples and submultiples of the metre, as shown in the table below. Long distances are usually expressed in km, astronomical units ( Gm), light-years (10 Pm), or parsecs (31 Pm), rather than in Mm, Gm, Tm, Pm, Express Systems Express Meter v3.0 crack serial keygen, Em, Zm or Ym; "30 cm", "30 m", and " m" are more common than "3 dm", Express Systems Express Meter v3.0 crack serial keygen, "3 dam", and "3 hm", respectively.

The terms micron and millimicron can be used instead of micrometre (μm) and nanometre (nm), but this practice may be discouraged.[]

Equivalents in other units[edit]

Metric unit
expressed in non-SI units
Non-SI unit
expressed in metric units
1 metreyard1 yardmetre
1 metreinches1 inchmetre
1 centimetreinch1 inchcentimetres
1 millimetreinch1 inchmillimetres
1 metre1 × 1010ångström1 ångström1 × 10−10metre
1 nanometre10ångström1 ångströmpicometres

Within this table, "inch" and "yard" mean "international inch" and "international yard"[] respectively, though approximate conversions in the left column hold for both international and survey units.

"≈" means "is approximately equal to";
"≡" means "equal by definition" or "is exactly equal to".

One metre is exactly equivalent to 5 /&#;inches and to 1 /1 &#;yards, Express Systems Express Meter v3.0 crack serial keygen.

A simple mnemonic aid exists to assist with conversion, as three "3"s:

1 metre is nearly equivalent to 3&#;feet3+3&#;8&#;inches. This gives an overestimate of &#;mm; however, the practice of memorising such conversion formulas has been discouraged in favour of practice and visualisation of metric units.

The ancient Egyptian cubit was about &#;m (surviving rods are –&#;mm).[] Scottish and English definitions of the ell (two cubits) were &#;mm (&#;m) and &#;mm (&#;m) respectively.[][] The ancient Parisian toise (fathom) was slightly shorter than 2&#;m and was standardised at exactly 2&#;m in the mesures usuelles system, such that 1&#;m was exactly 1&#;2&#;toise.[] The Russian verst was &#;km. The Swedish mil was &#;km, but was changed to 10&#;km when Sweden converted to metric units.[]

See also[edit]

Wikimedia Commons has media related to Metre.
Look up metre in Wiktionary, the free dictionary.

Notes[edit]

  1. ^"Base unit definitions: Meter". National Institute of Standards and Technology. Retrieved 28 September
  2. ^"The International System of Units (SI) – NIST". US: National Institute of Standards and Technology. 26 March
  3. ^The most recent official brochure about the International System of Units (SI), written in French by the Bureau international des poids et mesures, International Bureau of Weights and Measures (BIPM) uses the spelling metre; an English translation, included to make the SI standard more widely accessible also uses the spelling metre (BIPM,p. ff). However, in the U.S. English translation published by the U.S. National Institute of Standards and Technology (NIST) chose to use the spelling meter in accordance with the United States Government Printing Office Style Manual. The Metric Conversion Act of gives the Secretary of Express Systems Express Meter v3.0 crack serial keygen of the US the responsibility of interpreting or modifying the SI for use in the US. The Secretary of Commerce delegated this authority to the Director of the National Institute of Standards and Technology (Turner). InNIST published the US version (Taylor and Thompson, a) of the English text of the eighth edition of the BIPM publication Le Système international d'unités (SI) (BIPM, ), Express Systems Express Meter v3.0 crack serial keygen. In the NIST publication, the spellings "meter", "liter" and "deka" are used rather than "metre", "litre" and "deca" as in the original BIPM English text (Taylor and Thompson (a), p. iii). The Director of the NIST officially recognised this publication, together with Taylor and Thompson (b), as the "legal interpretation" of the SI for the United States (Turner). Thus, the spelling metre is referred to as the "international spelling"; the spelling meter, as the "American spelling".
  4. ^Naughtin, Pat (). "Spelling metre or meter"(PDF). Metrication Matters. Retrieved 12 March
  5. ^"Meter vs. metre", Express Systems Express Meter v3.0 crack serial keygen. Grammarist. Retrieved 12 March
  6. ^The Philippines uses English as an official language and this largely follows American English since the country became a colony of the United States. While the law that converted the country to use the metric system uses Express Systems Express Meter v3.0 crack serial keygen (Batas Pambansa Blg. 8) following the SI spelling, in actual practice, meter is used in government and everyday commerce, as evidenced by laws (kilometer, Republic Act No. ), Supreme Court decisions (meter, G.R. No. ), and national standards (centimeter, PNS/BAFS ).
  7. ^"– (Nordisk familjebok / Uggleupplagan. Mekaniker – Mykale)" [– (Nordic Family Book / Owl Edition. Mechanic – Mycular)]. Stockholm, Express Systems Express Meter v3.0 crack serial keygen.
  8. ^Cambridge Advanced Learner's Dictionary. Cambridge University Press. Retrieved 19 September , s.v. ammeter, meter, parking meter, speedometer.
  9. ^American Heritage Dictionary of the English Language (3rd&#;ed.). Boston: Houghton Mifflin. , s.v. meter.
  10. ^"-meter – definition of -meter in English". Oxford Dictionaries.
  11. ^ abOxford English Dictionary, Clarendon Press 2nd ed, shoppingdowntown.us p col
  12. ^texte, Picard, Jean (–). Auteur du (). Mesure de la terre [par l'abbé Picard]. Gallica. pp.&#;3–4. Retrieved 13 September [verification needed]
  13. ^Lucendo, Jorge (23 April ). Centuries of Inventions: Encyclopedia and History of Inventions. Jorge Lucendo. p.&#; Retrieved 2 August
  14. ^Camerini, Valentina (1 December ), Express Systems Express Meter v3.0 crack serial keygen. Real-Life Superheroes. Black Inc. p.&#; ISBN&#.
  15. ^"Appendix B: Tito Livio Burattini's catholic meter". shoppingdowntown.us, Express Systems Express Meter v3.0 crack serial keygen. Retrieved 3 August
  16. ^"Science.l'adoption révolutionnaire du mètre". shoppingdowntown.us (in French). 25 March Retrieved 3 August
  17. ^"The meter, an ingenious intuition from belluno Documents diplomatiques suisses Diplomatic Documents of Switzerland Express Systems Express Meter v3.0 crack serial keygen

    Express Systems Express Meter v3.0 crack serial keygen - opinion

    Documents diplomatiques suisses Documents diplomatiques suisses

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Источник: [shoppingdowntown.us]
Diplomatic Documents of Switzerland Diplomatic Documents of Switzerland Dodis, retrieved 20 September
  • ^National Institute of Standards and Technology ; Historical context of the SI: Unit of length (meter)
  • ^"BIPM – la définition du mètre". shoppingdowntown.us. Retrieved 15 May
  • ^"The Nobel Prize in Physics ". shoppingdowntown.us. Retrieved 13 March
  • ^Ritter, Élie (). Manuel théorique et pratique de l'application de la méthode des moindres carrés: au calcul des observations (in French). Mallet-Bachelier.
  • ^"Report from Charles S. Peirce on his second European trip for the Anual Report of the Superintendent of the U. S. Coast Survey, New York, ". shoppingdowntown.us. Retrieved 22 May
  • ^Faye, Hervé (). "Comptes rendus hebdomadaires des séances de l'Académie des sciences / publiés par MM. les secrétaires perpétuels". Gallica (in French). pp.&#;– Retrieved 22 May
  • ^Torge, Wolfgang (). Rizos, Chris; Willis, Pascal (eds.). "From a Regional Project to an International Organization: The "Baeyer-Helmert-Era" of the International Association of Geodesy –". IAG Years. International Association of Geodesy Symposia. Springer International Publishing. : 3– doi/__ ISBN&#;.
  • ^Torge, W. (1 April ). "The International Association of Geodesy to from a regional project to an international organization". Journal of Geodesy. 78 (9): – BibcodeJGeodT. doi/s ISSN&#;
  • Источник: [shoppingdowntown.us]

    Metre

    SI unit of length

    This article is about the unit of length. For other uses of "metre" or "meter", see Meter (disambiguation).

    metre
    Metric shoppingdowntown.us

    Seal of the International Bureau of Weights and Measures (BIPM) – Use measure (Greek: ΜΕΤΡΩ ΧΡΩ)

    Unit systemSI base unit
    Unit&#;ofLength
    Symbolm[1]
    1 m[1]in is equal to
    &#;&#;&#;SI units&#;&#;&#;
    • &#;mm
    • &#;km
    &#;&#;&#;Imperial/US units&#;&#;&#;
    • ≈&#;&#;yd
    • ≈&#;&#;ft
    • ≈&#;&#;in
    &#;&#;&#;Nautical units&#;&#;&#;≈&#;&#;nmi

    The metre (Commonwealth spelling) or meter (American spelling; see spelling differences) (from the French unit mètre, from the Greek noun μέτρον, "measure") is the base unit of length in the International System of Units (SI). The SI unit symbol is m.

    The metre is currently defined as the length of the path travelled by light in a vacuum in 1/ of a second.

    The metre was originally defined in as one ten-millionth of the distance from the equator to the North Pole along a great circle, so the Earth's circumference is approximately &#;km. In , the metre was redefined in terms of a prototype metre bar (the actual bar used was changed in ). In , the metre was redefined in terms of a certain number of wavelengths of a certain emission line of krypton The current definition was adopted in and modified slightly in to clarify that the metre is a measure of proper length.

    Spelling[edit]

    Metre is the standard spelling of the metric unit for length in nearly all English-speaking nations except the United States[2][3][4][5] and the Philippines,[6] which use meter. Other Germanic languages, such as German, Dutch, and the Scandinavian languages,[7] likewise spell the word Meter or meter.

    Measuring devices (such as ammeter, speedometer) are spelled "-meter" in all variants of English.[8] The suffix "-meter" has the same Greek origin as the unit of length.[9][10]

    Etymology[edit]

    The etymological roots of metre can be traced to the Greek verb μετρέω (metreo) (to measure, count or compare) and noun μέτρον (metron) (a measure), which were used for physical measurement, for poetic metre and by extension for moderation or avoiding extremism (as in "be measured in your response"). This range of uses is also found in Latin (metior, mensura), French (mètre, mesure), English and other languages. The Greek word is derived from the Proto-Indo-European root *meh₁- 'to measure'. The motto ΜΕΤΡΩ ΧΡΩ (metro chro) in the seal of the International Bureau of Weights and Measures (BIPM), which was a saying of the Greek statesman and philosopher Pittacus of Mytilene and may be translated as "Use measure!", thus calls for both measurement and moderation. The use of the word metre (for the French unit mètre) in English began at least as early as [11]

    History of definition [edit]

    Main article: History of the metre

    Pendulum or meridian[edit]

    In Jean Picard measured the length of a "seconds pendulum" and proposed a unit of measurement twice that length to be called the universal toise (French: Toise universelle).[12] In , Tito Livio Burattini suggested the term metre for a unit of length based on a pendulum length, but then it was discovered that the length of a seconds pendulum varies from place to place.[14][15][16][17][18][19][20][21][22]

    Since Eratosthenes, geographers had used meridian arcs to assess the size of the Earth, which in , Jean Picard determined to have a radius of toises, treated as a simple sphere. In the 18th century, geodesy grew in importance as a means of empirically demonstrating the theory of gravity and because the radius of the Earth was the unit to which all celestial distances were to be referred.[24][25]

    Meridional definition[edit]

    As a result of the Lumières and during the French Revolution, the French Academy of Sciences charged a commission with determining a single scale for all measures. On 7 October that commission advised the adoption of a decimal system, and on 19 March advised the adoption of the term mètre ("measure"), a basic unit of length, which they defined as equal to one ten-millionth of the quarter meridian, the distance between the North Pole and the Equator along the meridian through Paris.[26][27][28][29][30] On 26 March , the French National Constituant Assembly adopted the proposal.[11][31]

    The French Academy of Sciences commissioned an expedition led by Jean Baptiste Joseph Delambre and Pierre Méchain, lasting from to , which attempted to accurately measure the distance between a belfry in Dunkerque and Montjuïc castle in Barcelona at the longitude of the Paris Panthéon (see meridian arc of Delambre and Méchain).[32] The expedition was fictionalised in Denis Guedj, Le Mètre du Monde. Ken Alder wrote factually about the expedition in The Measure of All Things: the seven year odyssey and hidden error that transformed the world. This portion of the Paris meridian was to serve as the basis for the length of the half meridian connecting the North Pole with the Equator. From to France adopted this definition of the metre as its official unit of length based on results from this expedition combined with those of the Geodesic Mission to Peru.[35][36] The latter was related by Larrie D. Ferreiro in Measure of the Earth: The Enlightenment Expedition that Reshaped Our World.[37][38]

    In the 19th century, geodesy underwent a revolution with advances in mathematics as well as progress of observation instruments and methods with the taking into account of the personal equation. The application of the least squares method to meridian arc measurements demonstrated the importance of the scientific method in geodesy. On the other hand, the invention of the telegraph made it possible to measure parallel arcs, and the improvement of the reversible pendulum gave rise to the study of the Earth's gravitational field. A more accurate determination of the Figure of the Earth would soon result from the measurement of the Struve Geodetic Arc (–) and would have given another value for the definition of this standard of length. This did not invalidate the metre but highlighted that progresses in science would allow better measurement of Earth's size and shape.[40][41][42]

    In , Carl Friedrich Gauss studied the Earth's magnetic field and proposed adding the second to the basic units of the metre and the kilogram in the form of the CGS system (centimetre, gram, second). In , he founded the Magnetischer Verein, the first international scientific association, in collaboration with Alexander von Humboldt and Wilhelm Edouard Weber. The coordination of the observation of geophysical phenomena such as the Earth's magnetic field, lightning and gravity in different points of the globe stimulated the creation of the first international scientific associations. The foundation of the Magnetischer Verein would be followed by that of the Central European Arc Measurement (German: Mitteleuropaïsche Gradmessung) on the initiative of Johann Jacob Baeyer in , and by that of the International Meteorological Organisation whose second president, the Swiss meteorologist and physicist, Heinrich von Wild would represent Russia at the International Committee for Weights and Measures (CIPM).[43][44][45][46][47][48]

    International prototype metre bar[edit]

    The influence of the intellect trancends mountains and leaps across oceans. At the time when George Washington warned his fellow countrymen against entangling political alliances with European countries, there was started a mouvement of far reaching importance in a small country in the heart of the Alps which (as we shall see) exerted a silent, yet potent scientific influence upon the young republic on the Eastern shores of North America.

    —&#;Florian Cajori[49]

    In , Ferdinand Hassler was appointed first Superintendent of the Survey of the Coast. Trained in geodesy in Switzerland, France and Germany, Hassler had brought a standard metre made in Paris to the United States in He designed a baseline apparatus which instead of bringing different bars in actual contact during measurements, used only one bar calibrated on the metre and optical contact. Thus the metre became the unit of length for geodesy in the United States.[50][51][52]

    Since , Hassler was also head of the Bureau of Weights and Measures which became a part of the Coast Survey. He compared various units of length used in the United States at that time and measured coefficients of expansion to assess temperature effects on the measurements.[53]

    In , Friedrich Wilhelm Bessel, taking into account errors which had been recognized by Louis Puissant in the French meridian arc comprising the arc measurement of Delambre and Méchain which had been extended southward by François Arago and Jean-Baptiste Biot, recalculated the flattening of the Earth ellipsoid making use of nine more arc measurements, namely Peruan, Prussian, first East-Indian, second East-Indian, English, Hannover, Danish, Russian and Swedish covering almost 50 degrees of latitude, and stated that the Earth quadrant used for determining the length of the metre was nothing more than a rather imprecise conversion factor between the toise and the metre. Regarding the precision of the conversion from the toise to the metre, both units of measurement were then defined by standards made of different alloys with distinct coefficients of expansion. On the subject of the theoretical definition of the metre, it had been inaccessible and misleading at the time of Delambre and Mechain arc measurement, as the geoid is a ball, which on the whole can be assimilated to an ellipsoid of revolution, but which in detail differs from it so as to prohibit any generalization and any extrapolation. As early as , after Friedrich von Schubert showed that the different meridians were not of equal length, Elie Ritter a mathematician from Geneva deduced from a computation based on eleven meridian arcs covering 86 degrees that the meridian equation differed from that of the ellipse and that the meridian was swelled about the 45th degree of latitude by a layer whose thickness was difficult to estimate because of the uncertainty of the latitude of some stations in particular that of Montjuïc in the French meridian arc. By measuring the latitude of two stations in Barcelona, Méchain had found that the difference between these latitudes was greater than predicted by direct measurement of distance by triangulation. It was an infavourable vertical deflection which gave an innacurate determination of Barcelona's latitude and a metre "too short" compared to a more general definition taken from the average of a large number of arcs.[54][55][56][57][58][59][60]

    Nevertheless Ferdinand Rudolph Hassler's use of the metre in coastal survey contributed to the introduction of the Metric Act of allowing the use of the metre in the United States, and possibly also played a role in the choice of the metre as international scientific unit of length and the proposal by the European Arc Measurement (German: Europäische Gradmessung) to “establish a European international bureau for weights and measures”. However, in , the most important concern was that the Toise of Peru, the standard of the toise constructed in for the French Geodesic Mission to the Equator, might be so much damaged that comparison with it would be worthless, while Bessel had questionned the accuracy of copies of this standard belonging to Altona and Koenigsberg Observatories, which he had compared to each other about Indeed when the primary Imperial yard standard was partially destroyed in , a new standard of reference had been constructed using copies of the "Standard Yard, " instead of the pendulum's length as provided for in the Weights and Measures Act of [61][62][63][64][65][66][67]

    Swiss baseline measurement with Ibáñezapparatus in

    In at the second general conference of the International Association of Geodesy held in Berlin, the question of an international standard unit of length was discussed in order to combine the measurements made in different countries to determine the size and shape of the Earth.[68][69][70] The conference recommended the adoption of the metre in replacement of the toise and the creation of an international metre commission, according to the proposal of Johann Jacob Baeyer, Adolphe Hirsch and Carlos Ibáñez e Ibáñez de Ibero who had devised two geodetic standards calibrated on the metre for the map of Spain.[71][68][70][72]

    Ibáñez adopted the system which Ferdinand Rudolph Hassler used for the United States Survey of the Coast, consisting of a single standard with lines marked on the bar and microscopic measurements. Regarding the two methods by which the effect of temperature was taken into account, Ibáñez used both the bimetallic rulers, in platinum and brass, which he first employed for the central baseline of Spain, and the simple iron ruler with inlaid mercury thermometers which was utilized in Switzerland. These devices, the first of which is referred to as either Brunner apparatus or Spanish Standard, were constructed in France by Jean Brunner, then his sons. Measurement traceability between the toise and the metre was ensured by comparison of the Spanish Standard with the standard devised by Borda and Lavoisier for the survey of the meridian arc connecting Dunkirk with Barcelona.[73][72][74][68][75][76][77][78][79]

    In , the Saint Petersburg Academy of Sciences sent to the French Academy of Sciences a report drafted by Otto Wilhelm von Struve, Heinrich von Wild and Moritz von Jacobi inviting his French counterpart to undertake joint action with a view to ensuring the universal use of the metric system in all scientific work.[67]

    Creating the metre-alloy in at the Conservatoire des Arts et Métiers. Present Henri Tresca, George Matthey, Saint-Claire Deville and Debray

    In the s and in light of modern precision, a series of international conferences was held to devise new metric standards. When a conflict broke out regarding the presence of impurities in the metre-alloy of , a member of the Preparatory Committee since and Spanish representative at the Paris Conference in , Carlos Ibáñez e Ibáñez de Ibero intervened with the French Academy of Sciences to rally France to the project to create an International Bureau of Weights and Measures equipped with the scientific means necessary to redefine the units of the metric system according to the progress of sciences. The Metre Convention (Convention du Mètre) of mandated the establishment of a permanent International Bureau of Weights and Measures (BIPM: Bureau International des Poids et Mesures) to be located in Sèvres, France. This new organisation was to construct and preserve a prototype metre bar, distribute national metric prototypes, and maintain comparisons between them and non-metric measurement standards. The organisation distributed such bars in at the first General Conference on Weights and Measures (CGPM: Conférence Générale des Poids et Mesures), establishing the International Prototype Metre as the distance between two lines on a standard bar composed of an alloy of 90% platinum and 10% iridium, measured at the melting point of ice.[80][48][81][82]

    Closeup of National Prototype Metre Bar No. 27, made in by the International Bureau of Weights and Measures(BIPM) and given to the United States, which served as the standard for defining all units of length in the US from to

    The comparison of the new prototypes of the metre with each other and with the Committee metre (French: Mètre des Archives) involved the development of special measuring equipment and the definition of a reproducible temperature scale. The BIPM's thermometry work led to the discovery of special alloys of iron-nickel, in particular invar, for which its director, the Swiss physicist Charles-Edouard Guillaume, was granted the Nobel Prize for physics in [83]

    As Carlos Ibáñez e Ibáñez de Ibero stated, the progress of metrology combined with those of gravimetry through improvement of Kater's pendulum led to a new era of geodesy. If precision metrology had needed the help of geodesy, the latter could not continue to prosper without the help of metrology. It was then necessary to define a single unit in order to express all the measurements of terrestrial arcs, and all determinations of the force of gravity by the mean of pendulum. Metrology had to create a common unit, adopted and respected by all civilized nations. Moreover, at that time, statisticians knew that scientific observations are marred by two distinct types of errors, constant errors on the one hand, and fortuitous errors, on the other hand. The effects of the latters can be mitigated by the least squares method. Constant or regular errors on the contrary must be carefully avoided, because they arise from one or more causes which constantly act in the same way, and have the effect of always altering the result of the experiment in the same direction. They therefore deprive of any value the observations that they impinge. For metrology the matter of expansibility was fundamental; as a matter of fact the temperature measuring error related to the length measurement in proportion to the expansibility of the standard and the constantly renewed efforts of metrologists to protect their measuring instruments against the interfering influence of temperature revealed clearly the importance they attached to the expansion-induced errors. It was thus crucial to compare at controlled temperatures with great precision and to the same unit all the standards for measuring geodetic baselines, and all the pendulum rods. Only when this series of metrological comparisons would be finished with a probable error of a thousandth of a millimetre would geodesy be able to link the works of the different nations with one another, and then proclaim the result of the measurement of the Globe.[84][85][40]

    As the figure of the Earth could be inferred from variations of the seconds pendulum length with latitude, the United States Coast Survey instructed Charles Sanders Peirce in the spring of to proceed to Europe for the purpose of making pendulum experiments to chief initial stations for operations of this sort, in order to bring the determinations of the forces of gravity in America into communication with those of other parts of the world; and also for the purpose of making a careful study of the methods of pursuing these researches in the different countries of Europe. In the association of geodesy changed name for the International Geodetic Association, which Carlos Ibáñez e Ibáñez de Ibero presided up to his death in During this period the International Geodetic Association (German: Internationale Erdmessung) gained worldwide importance with the joining of United States, Mexico, Chile, Argentina and Japan.[73][86][87][88][89]

    Artist's impression of a GPS-IIR satellite in orbit.

    Efforts to supplement the various national surveying systems, which begun in the 19th century with the foundation of the Mitteleuropäische Gradmessung, resulted in a series of global ellipsoids of the Earth (e.g., Helmert , Hayford and ) which would later lead to develop the World Geodetic System. Nowadays the practical realisation of the metre is possible everywhere thanks to the atomic clocks embedded in GPS satellites.[90][91]

    Wavelength definition[edit]

    In , James Clerk Maxwell suggested that light emitted by an element be used as the standard both for the metre and for the second. These two quantities could then be used to define the unit of mass.[92]

    In , the standard metre was first measured with an interferometer by Albert A. Michelson, the inventor of the device and an advocate of using some particular wavelength of light as a standard of length. By , interferometry was in regular use at the BIPM. However, the International Prototype Metre remained the standard until , when the eleventh CGPM defined the metre in the new International System of Units (SI) as equal to wavelengths of the orange-redemission line in the electromagnetic spectrum of the kryptonatom in a vacuum.[93]

    Speed of light definition[edit]

    To further reduce uncertainty, the 17th CGPM in replaced the definition of the metre with its current definition, thus fixing the length of the metre in terms of the second and the speed of light:[94]

    The metre is the length of the path travelled by light in vacuum during a time interval of 1/ of a second.

    This definition fixed the speed of light in vacuum at exactly metres per second (≈&#;km/s).[94] An intended by-product of the 17th CGPM's definition was that it enabled scientists to compare lasers accurately using frequency, resulting in wavelengths with one-fifth the uncertainty involved in the direct comparison of wavelengths, because interferometer errors were eliminated. To further facilitate reproducibility from lab to lab, the 17th CGPM also made the iodine-stabilised helium–neon laser "a recommended radiation" for realising the metre.[95] For the purpose of delineating the metre, the BIPM currently considers the HeNe laser wavelength, λHeNe, to be &#;nm with an estimated relative standard uncertainty (U) of ×10−11.[95][96][97] This uncertainty is currently one limiting factor in laboratory realisations of the metre, and it is several orders of magnitude poorer than that of the second, based upon the caesium fountain atomic clock (U = 5×10−16).[98] Consequently, a realisation of the metre is usually delineated (not defined) today in labs as (33) wavelengths of helium-neon laser light in a vacuum, the error stated being only that of frequency determination.[95] This bracket notation expressing the error is explained in the article on measurement uncertainty.

    Practical realisation of the metre is subject to uncertainties in characterising the medium, to various uncertainties of interferometry, and to uncertainties in measuring the frequency of the source.[99] A commonly used medium is air, and the National Institute of Standards and Technology (NIST) has set up an online calculator to convert wavelengths in vacuum to wavelengths in air.[] As described by NIST, in air, the uncertainties in characterising the medium are dominated by errors in measuring temperature and pressure. Errors in the theoretical formulas used are secondary.[] By implementing a refractive index correction such as this, an approximate realisation of the metre can be implemented in air, for example, using the formulation of the metre as (33) wavelengths of helium–neon laser light in vacuum, and converting the wavelengths in a vacuum to wavelengths in air. Air is only one possible medium to use in a realisation of the metre, and any partial vacuum can be used, or some inert atmosphere like helium gas, provided the appropriate corrections for refractive index are implemented.[]

    The metre is defined as the path length travelled by light in a given time, and practical laboratory length measurements in metres are determined by counting the number of wavelengths of laser light of one of the standard types that fit into the length,[] and converting the selected unit of wavelength to metres. Three major factors limit the accuracy attainable with laser interferometers for a length measurement:[99][]

    Of these, the last is peculiar to the interferometer itself. The conversion of a length in wavelengths to a length in metres is based upon the relation

    {\displaystyle \lambda ={\frac {c}{nf}}}

    which converts the unit of wavelength &#; to metres using c, the speed of light in vacuum in m/s. Here n is the refractive index of the medium in which the measurement is made, and f is the measured frequency of the source. Although conversion from wavelengths to metres introduces an additional error in the overall length due to measurement error in determining the refractive index and the frequency, the measurement of frequency is one of the most accurate measurements available.[]

    Timeline[edit]

    DateDeciding bodyDecision
    8 May French National AssemblyThe length of the new metre to be equal to the length of a pendulum with a half-period of one second.[35]
    30 Mar French National AssemblyAccepts the proposal by the French Academy of Sciences that the new definition for the metre be equal to one ten-millionth of the length of a great circle quadrant along the Earth's meridian through Paris, that is the distance from the equator to the north pole along that quadrant.
    Provisional metre bar made of brass and based on Paris meridan arc (French: Méridienne de France) measured by Nicolas-Louis de Lacaillle and Cesar-François Cassini de Thury, legally equal to lines of the toise du Pérou (a standard French unit of length from ).[35][36][74][91] [The line was 1/ of a toise.]
    10 Dec French National AssemblySpecifies the platinum metre bar, presented on 22 June and deposited in the National Archives, as the final standard. Legally equal to lines on the toise du Pérou.[91]
    24–28 Sept 1st General Conference on Weights and Measures (CGPM)Defines the metre as the distance between two lines on a standard bar of an alloy of platinum with 10% iridium, measured at the melting point of ice.[91][]
    27 Sept – 6 Oct 7th CGPMRedefines the metre as the distance, at 0&#;°C (&#;K), between the axes of the two central lines marked on the prototype bar of platinum-iridium, this bar being subject to one standard atmosphere of pressure and supported on two cylinders of at least 10&#;mm (1&#;cm) diameter, symmetrically placed in the same horizontal plane at a distance of &#;mm (&#;cm) from each other.[]
    14 Oct 11th CGPMDefines the metre as wavelengths in a vacuum of the radiation corresponding to the transition between the 2p10 and 5d5 quantum levels of the krypton atom.
    21 Oct 17th CGPMDefines the metre as the length of the path travelled by light in a vacuum during a time interval of 1/ of a second.[][]
    International Committee for Weights and Measures (CIPM)Considers the metre to be a unit of proper length and thus recommends this definition be restricted to "lengths ℓ which are sufficiently short for the effects predicted by general relativity to be negligible with respect to the uncertainties of realisation".[]
    Basis of definition Date Absolute
    uncertainty
    Relative
    uncertainty
    1/10 part of the quadrant along the meridian, measurement by Delambre and Méchain ( lines) –&#;μm 10−4
    First prototype Mètre des Archives platinum bar standard 50–10&#;μm 10−5
    Platinum-iridium bar at melting point of ice (1st CGPM) –&#;μm (–&#;nm) 10−7
    Platinum-iridium bar at melting point of ice, atmospheric pressure, supported by two rollers (7th CGPM) n.a. n.a.
    Hyperfine atomic transition; wavelengths of light from a specified transition in krypton (11th CGPM) 4&#;nm 4×10−9[]
    Length of the path travelled by light in a vacuum in 1/ second (17th CGPM) &#;nm 10−10

    Early adoptions of the metre internationally[edit]

    Main article: Metrication

    After the July Revolution of the metre became the definitive French standard from At that time it had already been adopted by Ferdinand Rudolph Hassler for the U.S Survey of the Coast.[35][][71]

    "The unit of length to which all distances measured in the Coast Survey are referred is the French metre, an authentic copy of which is preserved in the archives of the Coast Survey Office. It is the property of the American Philosophical Society, to whom it was presented by Mr. Hassler, who had received it from Tralles, a member of the French Committee charged with the construction of the standard metre by comparison with the toise, which had served as unit of length in the measurement of the meridional arcs in France and Peru. It possesses all the authenticity of any original metre extant, bearing not only the stamp of the Committee but also the original mark by which it was distinguished from the other bars during the operation of standardising. It is always designated as the Committee metre" (French&#;: Mètre des Archives).[52]

    In President Andrew Jackson mandated Ferdinand Rudolf Hassler to work out new standards for all U.S. states. According to the decision of the Congress of the United States, the British Parliamentary Standard from was introduced as the unit of length.[]

    Another geodesist with metrology skills was to play a pivotal role in the process of internationalization of weights and measures, Carlos Ibáñez e Ibáñez de Ibero who would become the first president of both the International Geodetic Association and the International Committee for Weights and Measures.[73]

    SI prefixed forms of metre[edit]

    SI prefixes can be used to denote decimal multiples and submultiples of the metre, as shown in the table below. Long distances are usually expressed in km, astronomical units ( Gm), light-years (10 Pm), or parsecs (31 Pm), rather than in Mm, Gm, Tm, Pm, Em, Zm or Ym; "30 cm", "30 m", and " m" are more common than "3 dm", "3 dam", and "3 hm", respectively.

    The terms micron and millimicron can be used instead of micrometre (μm) and nanometre (nm), but this practice may be discouraged.[]

    Equivalents in other units[edit]

    Metric unit
    expressed in non-SI units
    Non-SI unit
    expressed in metric units
    1 metreyard1 yardmetre
    1 metreinches1 inchmetre
    1 centimetreinch1 inchcentimetres
    1 millimetreinch1 inchmillimetres
    1 metre1 × 1010ångström1 ångström1 × 10−10metre
    1 nanometre10ångström1 ångströmpicometres

    Within this table, "inch" and "yard" mean "international inch" and "international yard"[] respectively, though approximate conversions in the left column hold for both international and survey units.

    "≈" means "is approximately equal to";
    "≡" means "equal by definition" or "is exactly equal to".

    One metre is exactly equivalent to 5 /&#;inches and to 1 /1 &#;yards.

    A simple mnemonic aid exists to assist with conversion, as three "3"s:

    1 metre is nearly equivalent to 3&#;feet3+3&#;8&#;inches. This gives an overestimate of &#;mm; however, the practice of memorising such conversion formulas has been discouraged in favour of practice and visualisation of metric units.

    The ancient Egyptian cubit was about &#;m (surviving rods are –&#;mm).[] Scottish and English definitions of the ell (two cubits) were &#;mm (&#;m) and &#;mm (&#;m) respectively.[][] The ancient Parisian toise (fathom) was slightly shorter than 2&#;m and was standardised at exactly 2&#;m in the mesures usuelles system, such that 1&#;m was exactly 1&#;2&#;toise.[] The Russian verst was &#;km. The Swedish mil was &#;km, but was changed to 10&#;km when Sweden converted to metric units.[]

    See also[edit]

    Wikimedia Commons has media related to Metre.
    Look up metre in Wiktionary, the free dictionary.

    Notes[edit]

    1. ^"Base unit definitions: Meter". National Institute of Standards and Technology. Retrieved 28 September
    2. ^"The International System of Units (SI) – NIST". US: National Institute of Standards and Technology. 26 March
    3. ^The most recent official brochure about the International System of Units (SI), written in French by the Bureau international des poids et mesures, International Bureau of Weights and Measures (BIPM) uses the spelling metre; an English translation, included to make the SI standard more widely accessible also uses the spelling metre (BIPM, , p. ff). However, in the U.S. English translation published by the U.S. National Institute of Standards and Technology (NIST) chose to use the spelling meter in accordance with the United States Government Printing Office Style Manual. The Metric Conversion Act of gives the Secretary of Commerce of the US the responsibility of interpreting or modifying the SI for use in the US. The Secretary of Commerce delegated this authority to the Director of the National Institute of Standards and Technology (Turner). In , NIST published the US version (Taylor and Thompson, a) of the English text of the eighth edition of the BIPM publication Le Système international d'unités (SI) (BIPM, ). In the NIST publication, the spellings "meter", "liter" and "deka" are used rather than "metre", "litre" and "deca" as in the original BIPM English text (Taylor and Thompson (a), p. iii). The Director of the NIST officially recognised this publication, together with Taylor and Thompson (b), as the "legal interpretation" of the SI for the United States (Turner). Thus, the spelling metre is referred to as the "international spelling"; the spelling meter, as the "American spelling".
    4. ^Naughtin, Pat (). "Spelling metre or meter"(PDF). Metrication Matters. Retrieved 12 March
    5. ^"Meter vs. metre". Grammarist. Retrieved 12 March
    6. ^The Philippines uses English as an official language and this largely follows American English since the country became a colony of the United States. While the law that converted the country to use the metric system uses metre (Batas Pambansa Blg. 8) following the SI spelling, in actual practice, meter is used in government and everyday commerce, as evidenced by laws (kilometer, Republic Act No. ), Supreme Court decisions (meter, G.R. No. ), and national standards (centimeter, PNS/BAFS ).
    7. ^"– (Nordisk familjebok / Uggleupplagan. Mekaniker – Mykale)" [– (Nordic Family Book / Owl Edition. Mechanic – Mycular)]. Stockholm.
    8. ^Cambridge Advanced Learner's Dictionary. Cambridge University Press. Retrieved 19 September , s.v. ammeter, meter, parking meter, speedometer.
    9. ^American Heritage Dictionary of the English Language (3rd&#;ed.). Boston: Houghton Mifflin. , s.v. meter.
    10. ^"-meter – definition of -meter in English". Oxford Dictionaries.
    11. ^ abOxford English Dictionary, Clarendon Press 2nd ed, shoppingdowntown.us p col
    12. ^texte, Picard, Jean (–). Auteur du (). Mesure de la terre [par l'abbé Picard]. Gallica. pp.&#;3–4. Retrieved 13 September [verification needed]
    13. ^Lucendo, Jorge (23 April ). Centuries of Inventions: Encyclopedia and History of Inventions. Jorge Lucendo. p.&#; Retrieved 2 August
    14. ^Camerini, Valentina (1 December ). Real-Life Superheroes. Black Inc. p.&#; ISBN&#;.
    15. ^"Appendix B: Tito Livio Burattini's catholic meter". shoppingdowntown.us. Retrieved 3 August
    16. ^"Science. , l'adoption révolutionnaire du mètre". shoppingdowntown.us (in French). 25 March Retrieved 3 August
    17. ^"The meter, an ingenious intuition from belluno

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