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| Subject keyword(s) | Length, Mathematics, Mathematics history, Measurement, Metric, Systems of measurement |
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| Rights | 2000 Sizes, Inc. All rights reserved. |
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meter (metre) Convert cubic meters or cubic centimeters to other major units oflength history of the meter the seconds pendulum the quadrant of the earth measuring the quadrant the meter as a bar the meter defined by light The unit of length in SI, one of the seven base units. Since 1983 the meter has been defined as the distance light travels in avacuum in exactly 1⁄299,792,458th of a second (17th CGPM, Resolution 1). This definition of the meter makes the length of the meter depend on the duration ofthe second; by definition the speed of light is now exactly 299,792,458 meters per second.A measurement of the time it takes light to travel between two points in a vacuum nolonger indicates the speed of light; it indicates the distance between the points! History of the meter In the 1780s, French weights and measures were a mess, withdozens of units, each with dozens or even hundreds of local values. No other nationsuffered from such a disparity between the demands of an industrializing economy and thecapabilities of its system of weights and measures. Long before the French Revolution,persons of all political persuasions were calling for metrological reform. There was alsoa feeling, consonant with the Rousseauistic spirit of the times, that units should be,somehow, “natural.” The seconds pendulum Jean Picard, Olaus Rømer and other astronomers had suggested that a unit of length bedefined as the length of a pendulum with a period of 2 seconds. (A pendulum's period is thetime it takes to make one complete swing back and forth). It was already known thatidentical pendulums set up in different places had different periods, so any such adefinition would have to specify a location for the standard pendulum. In 1790 Talleyrand, then the Bishop of Autun, made a reportto the Constituent Assembly on the state of French weights and measures, and init suggested a new measure of length based on the length of the seconds pendulum at thelatitude of Paris, 45°N. He also suggested that the Academy of Sciences in Pariscollaborate with the Royal Society of London in defining the new unit. The Assembly and subsequently Louis XVIapproved this proposal, but nothing came of it. By the end of 1790 the Academy had placed the matter in thehands of as illustrious a scientific commission as has ever existed: Lagrange, Laplace,Borda, Monge, and Condorcet. In their report to the Academy on March19, 1791, the commission recommended scrapping the seconds pendulum. Instead, theysuggested the new unit of length be one ten-millionth of the distance at sea level fromthe pole to the equator. The quadrant of the earth From a metrological point of view, taking a quadrant of the earth as a standard makesno sense at all. Any two surveys of such a distance are bound differ by much more than theamount of precision demanded of the unit. Nor is there some special relation between thedefinition and the unit's use, as there is, say, for the nautical mile in marinenavigation or the astronomical unit in astronomy. But the idea that the basic unit was tobe a definite fraction of the earth's size appealed to the Enlightenment's desire to tracestandards back to Nature, much as the idea that a food contains only natural ingredientsappeals to some of today's consumers. And there were other reasons. Enormous meridian measuring projects were to the science of the late18th century as space programs or the construction of large particle acceleratorshave been to ours. They challenged the limits of the day's technology and tested thepredictions of the new physics—in the 18th century,Newtonian predictions that the earth was not a sphere. Preeminence in such projects was amatter of national pride, at least among “natural philosophers.” Borda, forexample, a member of the commission, had constructed extremely precise graduated circlesfor measuring angles, just what would be needed for this sort of work. (His circles weregraduated in a new unit, the “grade,” rather thanin degrees, which he sneered at as “Babylonian.”) The Assembly approved the proposed unit on March 26, 1791,and work began on realizing it. To replace the hated “royal foot” until theresults of the survey were in, a provisional meter was defined, two of whichequaled 6 pied, 1 pouce, 10 22/25 lignes of the toise duPerou. Measuring the quadrant Obviously itwould be impossible to survey the distance between the North Pole and the equator, thewhole 90°. No one had ever been to the North Pole. But if one could measure a significantpiece of a meridian, the rest could be calculated. The two ends of the line to be measuredhad to be at sea level, and somewhere near the middle of the pole-to-equator quadrant. Asit happens, there is only one such meridian on earth: from Dunkirk to Barcelona, whichcovers about a tenth of the distance from the pole to the equator. The distance liesalmost entirely in France, which did not escape the French, nor indeed such impartialobservers as Thomas Jefferson. The survey was put in the hands of P. F. A. Méchain and J. B. J.Delambre. (See map; caution! 1.05 MB file.) In thesummer of 1792, Delambre began working his way south from thecoast near Dunkirk, while Méchain started north from the Mediterranean. They would meetat Rodez, 300 miles south of Paris. Méchain's share was shorter, but more difficult, forit crossed the Pyrenees Mountains that separate Spain and France. In September theRepublic was declared. The French revolution was soon in full swing. Within a few months France was at war withGreat Britain, Austria, Prussia, Holland and Spain; Louis XVI had been executed, andParisian mobs were massacring various groups. The Terror was not far off. In such aclimate the surveyors were regularly arrested. The flags on their survey poles werewhite—the color of the royalists! They were from Paris. All they had going for them wasthat their story—we are measuring the distance from Dunkirk to Barcelona—was sounbelievable in the midst of war and revolution that no real spy would have used it. Once when Delambre was seized his captors compelled him to make his explanations in themost republican way, to an audience of volunteers on their way to the war. The troops didnot find the trigonometry lecture entertaining. Delambre was saved from the crowd bya localofficial who took him into protective custody, and was eventually released only becausethe National Convention ordered it. On August 8, 1793, the National Convention abolished theAcademy of Sciences as unrepublican. The Committee of Public Safety, however, remainedintent on doing away with the old feudal measures and needed the help of the Academiciansto do it, so it persuaded the Convention to create a new, independent temporary commission(Commission temporaire des poids et mesures républicains) with the same members. InNovember Lavoisier was arrested; the commission asked for his release; the Committee ofPublic Safety responded by kicking five more members off the commission, includingDelambre. Seeing which way the wind blew, the commission then devoted itself to preparingrevolutionary denunciations of the old weights and measures. Delambre thought they shouldkill the whole meridian-measuring project and just accept the provisional meter. But war requires maps. A military cartographer who was also a Jacobin was put in chargeof map-making. Needing trained staff, he brought Delambre and Méchain back to Paris.(Méchain had prudently withdrawn to Genoa, narrowly escaping pirates.) On April 7, 1795 an order establishing the names now in use(meter, liter, gram) also reestablished the commission (except for Lavoisier, who had beenguillotined the previous year) and ordered resumption of the survey. Delambre finished his portion in the fall of 1797. ButMéchain had yet to reach Rodez. Sick, with winter coming, he wrote to his colleague,“I will sacrifice everything, give up everything, rather than return withoutcompleting my part.” And so the survey stalled. But Méchain recovered and resumedwork; in September 1798 he reached Rodez. To this point, except for the sides of two triangles, only angles had been measured,the angles of contiguous triangles stretching all the way from Dunkirk to Barcelona. Ifany side of only one of these triangles were known, the dimensions of all the others couldbe calculated, and from them the distance along the meridian. While Mechain labored in thesouth, Delambre measured one of the baselines with a special ruler. It took him 33 days. On November 28, 1798, the French convened an internationalmeeting of experts from friendly powers and puppet states. One of the meeting's committeesconsisted of four persons, each of whom independently calculated the length of the meterfrom the measurements made by Delambre and Méchain (and from certain assumptions aboutthe shape of the earth). Their calculations agreed. The meter was established at 0.144lignes of the toise de Perou shorter than than the provisional meter. Today the length of the earth's quadrant can be measured relatively easily by the useof satellites. Such measurements show that the meter is actually about 1/5of a millimeter shorter than one ten-millionth of the earth's quadrant. The startlingthing about this fact is not that the meter does not conform to its original conception,but that two 18th century surveyors should have come so close. The meter as a bar Since 1795 the former royal jeweler had been producing barsof platinum 4 mm thick, 25.3 mm wide and about a provisional meter long, with planeparallel ends. The lengths of these bars were compared with the length of the meter asdetermined by the survey. The one nearest that length (at 0°C) was deposited in theNational Archives on June 22, 1799, and has since been known asthe Mètre des Archives. The metric system itself was legalized on December10, 1799. The Mètre des Archives was, by definition, a meter long, from end to end. Metrologistscall such a standard an end measure. End measure standards are not a good idea, becauseany simple way of measuring their lengths requires touching the ends, which causes wearand shortens the standard. A much better form for a standard of a unit of length is a pairof scratches on a metal bar, because the lines' locations can be determined visually. Sucha standard is called a line measure. International interest in the meter and the French proselytizing spirit led to twointernational conferences (Commission Internationale du Mètre) in 1870and 1872 to discuss international standardization of the meter.The attendees favored replacing the Mètre des Archives with a new prototype which wouldbe a line measure and made of a harder, platinum-iridium alloy (10% iridium, to within0.0001%). They also suggested that the meter be taken as the length of the Mètre desArchives, “in the state in which it is found,” without reference to the quadrantof the earth. In 1875, twenty countries attended the third conference.Eighteen subscribed to a treaty (the Convention du Mètre), which set up the BureauInternational des Poids et Mésures. Production of the meter standard, however, provedvery difficult. Besides having an extremely high melting point (2,443°C), iridium had notyet been produced in purities greater than 50%. The bars from the first casting of thealloy, in 1874, were rejected in 1877,and the problem was turned over to the London firm of Johnson, Matthey and Co. Theysucceeded, and one of the resulting bars was made the provisional standard, even though itwas 0.006 mm shorter than the Mètre des Archives. In 1882France ordered thirty more bars, one of which (No. 6) turned out to be, as nearly as couldbe ascertained, exactly the length of the Mètre des Archives. This bar is the standardwhich was declared to be the International Prototype of the Meter by the First GeneralConference on Weights and Measures (first CGPM) in 1889:“This prototype, at the temperature of melting ice, shall henceforth represent themetric unit of length.” The International Prototype continues to be preserved by theBIPM. As a way of distributing this standard to the countries signing the treaty,“national Meters” were made, which were copies of the International Prototypeplus or minus 0.01 millimeter, supplied with a correction factor obtained by comparingthat particular national meter with the International Prototype. The meter defined by light The idea of defining a unit of length in terms of the wavelength of light had beenfloated early in the 19th century (J. Babinet, 1827), before there was any way of realizing the idea in practice. Bythe end of the century this was no longer so. “White” light is a mixture of light with different wavelengths. To define aunit of length in terms of wavelength, one needs light that is all of the same wavelength.Light consisting of only one wavelength–any wavelength, provided it isvisible–appears to a human to be colored, and is called monochromatic. Fortunately it doesn't seem hard to produce monochromatic light: sprinkle some salt onthe gas flames of a kitchen range. When the sodium atoms in the salt get excited, theygive off a yellow light which is pretty much all the same wavelength. It is the sameyellow as the light from sodium vapor street lamps. The wavelength is characteristic ofthe sodium atom. In 1892-3 A. A. Michelson and J. R. Benoit succeeded inmeasuring the meter in terms of the wavelength of red light given off by excited cadmiumatoms. Benoit and others refined the measurement in 1905-7, andin 1907 the International Solar Union (which is now the IAU)defined the international angstrom, a unit of distance to beused in measuring wavelengths, by making 6438.4696 internationalangstroms equal to the wavelength of the red line of cadmium. This value was taken fromBenoit's experiments, and was chosen so that one angstrom was approximately 10-10meter. (In 1927, the 7th CGPM provisionally sanctioned measuringdistances in terms of the red line of cadmium, taking its wavelength to be 0.643 846 96micrometers.) Meanwhile, much had been learned since 1892. Even in the bestof spectroscopes, the red line of cadmium was somewhat fuzzy. In fact, it turned out to becomposed of many lines (physicists refer to its “hyperfine structure”), whichaffected how precisely the light's wavelength could be determined. When the existence ofisotopes was discovered, it became clear that part of the reason for the fuzziness wasthat the light was not coming from a single kind of atom, but from a mixture of isotopes:cadmium atoms with the same number of protons, but different numbers of neutrons.Investigating light from pure isotopes, it was found that if an atom had an even number ofprotons, and the sum of the numbers of protons and neutrons it contained was also even,the light from it had no hyperfine structure. (Such atoms have no nuclear spin, hence nocoupling of nuclear spin to electron spins–and the light comes from the electrons.) The 9th CGPM (1948) allowed as how the meter might eventuallybe defined in terms of light from such an isotope. Three isotopes were intensivelyinvestigated to see which would be most suitable as the basis for a standard of length:krypton-86 (36 protons), mercury-198 (80 protons), and cadmium-114 (48 protons). Thecommittee in charge of following these developments recommended that any new definition bestated in terms of the wavelength in a vacuum instead of in air, and that the length ofthe wavelength should be specified by comparing it with the already determined wavelengthof the red line of cadmium, not with the International Prototype of the Meter. The 10thCGPM (1954) accepted these recommendations, in effect making theangstrom exactly equal to 10-10 meter and defining the meter in terms of light,although this was not formally acknowledged until 1960. The advisory committee declared krypton-86 the winner in 1957,and in 1960, the 11th CGPM (Resolution 6), noting that “theInternational Prototype does not define the meter with an accuracy adequate for thepresent needs of metrology,” redefined the meter as “the length equal to1 650 763.73 wavelengths in vacuum of the radiationcorresponding to the transition between the levels 2p10 and 5d5 of the krypton 86atom.” Defined this way, it proved impossible to realize the meter with an accuracy betterthan 4 parts in 109, and eventually that was not accurate enough. In themeantime, however, the laser had been invented, and the light it produced–not onlyall one wavelength, but all in phase–opened up new possibilities for metrology. In 1983 the 17th CGPM (Resolution 1) redefined the meter interms of the speed of light in a vacuum. The value for the speed of light, 299,792,458meters per second, had already been recommended in 1975 by the15th CGPM, (Resolution 2). Its use in the meter's definition made the speed of light fallwithin the limits of uncertainty of the best existing measurements. Thus the second, rejected as too arbitrary in 1791, hasbecome the basis of the meter. We have probably not seen the last redefinition of themeter; the current definition may need tuning if even more accuracy becomes necessary. Forexample, the speed of light is affected by the strength of the gravitational field, andthe 1983 definition does not take such factors into account. P. F. A. Méchain and J. B. J. Delambre. Base du système métrique decimal, ou Mesure de l'arc du méridien compris entre lesparallèles de Dunkerque et Barcelone. Paris: Baudoin, 1806–1810. 3 vols. H. Barrell. The Metre. Contemporary Physics 3:415 (1962). home | units index | search | your comments | about | help | privacy terms of use Copyright © 2000 Sizes, Inc. All rights reserved. Last revised: 17 April 2008.