# meter (metre)

For the meaning of any metric prefix, go here.

Convert between meters per second and other major units of velocity.

Convert cubic meters or cubic centimeters to other major units of capacity.

Convert between meters per second per second and other major units of acceleration.

Convert between gigameters or yottameters and other units of astronomical distance.

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 a vacuum 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 of the 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 no longer 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, with dozens of units, each with dozens or even hundreds of local values. No other nation suffered from such a disparity between the demands of an industrializing economy and the capabilities of its system of weights and measures. Long before the French Revolution, persons of all political persuasions were calling for metrological reform. There was also a 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 be defined as the length of a pendulum with a period of 2 seconds. (A pendulum's period is the time it takes to make one complete swing back and forth). It was already known that identical pendulums set up in different places had different periods, so any such a definition would have to specify a location for the standard pendulum.

In 1790 Talleyrand, then the Bishop of Autun, made a report to the Constituent Assembly on the state of French weights and measures, and in it suggested a new measure of length based on the length of the seconds pendulum at the latitude of Paris, 45°N. He also suggested that the Academy of Sciences in Paris collaborate with the Royal Society of London in defining the new unit. The Assembly and subsequently Louis XVI approved this proposal, but nothing came of it.

By the end of 1790 the Academy had placed the matter in the hands of as illustrious a scientific commission as has ever existed: Lagrange, Laplace, Borda, Monge, and Condorcet. In their report to the Academy on March 19, 1791, the commission recommended scrapping the seconds pendulum. Instead, they suggested the new unit of length be one ten-millionth of the distance at sea level from the pole to the equator.

## The quadrant of the earth

From a metrological point of view, taking a quadrant of the earth as a standard makes no sense at all. Any two surveys of such a distance are bound differ by much more than the amount of precision demanded of the unit. Nor is there some special relation between the definition and the unit's use, as there is, say, for the nautical mile in marine navigation or the astronomical unit in astronomy. But the idea that the basic unit was to be a definite fraction of the earth's size appealed to the Enlightenment's desire to trace standards back to Nature, much as the idea that a food contains only natural ingredients appeals to some of today's consumers. And there were other reasons.

Enormous meridian measuring projects were to the science of the late 18th century as space programs or the construction of large particle accelerators have been to ours. They challenged the limits of the day's technology and tested the predictions of the new physics—in the 18th century, Newtonian predictions that the earth was not a sphere. Preeminence in such projects was a matter of national pride, at least among “natural philosophers.” Borda, for example, a member of the commission, had constructed extremely precise graduated circles for measuring angles, just what would be needed for this sort of work. (His circles were graduated in a new unit, the “grade,” rather than in 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 the results of the survey were in, a provisional meter was defined, two of which equaled 6 pied, 1 pouce, 10 22/25 lignes of the toise du Perou.

Obviously it would be impossible to survey the distance between the North Pole and the equator, the whole 90°. No one had ever been to the North Pole. But if one could measure a significant piece of a meridian, the rest could be calculated. The two ends of the line to be measured had to be at sea level, and somewhere near the middle of the pole-to-equator quadrant. As it happens, there is only one such meridian on earth: from Dunkirk to Barcelona, which covers about a tenth of the distance from the pole to the equator. The distance lies almost entirely in France, which did not escape the French, nor indeed such impartial observers 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 the summer of 1792, Delambre began working his way south from the coast near Dunkirk, while Méchain started north from the Mediterranean. They would meet at Rodez, 300 miles south of Paris. Méchain's share was shorter, but more difficult, for it crossed the Pyrenees Mountains that separate Spain and France. In September the Republic was declared.

The French revolution was soon in full swing. Within a few months France was at war with Great Britain, Austria, Prussia, Holland and Spain; Louis XVI had been executed, and Parisian mobs were massacring various groups. The Terror was not far off. In such a climate the surveyors were regularly arrested. The flags on their survey poles were white—the color of the royalists! They were from Paris. All they had going for them was that their story—we are measuring the distance from Dunkirk to Barcelona—was so unbelievable 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 the most republican way, to an audience of volunteers on their way to the war. The troops did not find the trigonometry lecture entertaining. Delambre was saved from the crowd by a local official who took him into protective custody, and was eventually released only because the National Convention ordered it.

On August 8, 1793, the National Convention abolished the Academy of Sciences as unrepublican. The Committee of Public Safety, however, remained intent on doing away with the old feudal measures and needed the help of the Academicians to 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. In November Lavoisier was arrested; the commission asked for his release; the Committee of Public Safety responded by kicking five more members off the commission, including Delambre. Seeing which way the wind blew, the commission then devoted itself to preparing revolutionary denunciations of the old weights and measures. Delambre thought they should kill 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 charge of 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 been guillotined the previous year) and ordered resumption of the survey.

Delambre finished his portion in the fall of 1797. But Méchain had yet to reach Rodez. Sick, with winter coming, he wrote to his colleague, “I will sacrifice everything, give up everything, rather than return without completing my part.” And so the survey stalled. But Méchain recovered and resumed work; 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. If any side of only one of these triangles were known, the dimensions of all the others could be calculated, and from them the distance along the meridian. While Mechain labored in the south, Delambre measured one of the baselines with a special ruler. It took him 33 days.

On November 28, 1798, the French convened an international meeting of experts from friendly powers and puppet states. One of the meeting's committees consisted of four persons, each of whom independently calculated the length of the meter from the measurements made by Delambre and Méchain (and from certain assumptions about the shape of the earth). Their calculations agreed. The meter was established at 0.144 lignes 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 use of satellites. Such measurements show that the meter is actually about 1/5 of a millimeter shorter than one ten-millionth of the earth's quadrant. The startling thing 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 bars of platinum 4 mm thick, 25.3 mm wide and about a provisional meter long, with plane parallel ends. The lengths of these bars were compared with the length of the meter as determined by the survey. The one nearest that length (at 0°C) was deposited in the National Archives on June 22, 1799, and has since been known as the Mètre des Archives. The metric system itself was legalized on December 10, 1799.

The Mètre des Archives was, by definition, a meter long, from end to end. Metrologists call such a standard an end measure. End measure standards are not a good idea, because any simple way of measuring their lengths requires touching the ends, which causes wear and shortens the standard. A much better form for a standard of a unit of length is a pair of scratches on a metal bar, because the lines' locations can be determined visually. Such a standard is called a line measure.

International interest in the meter and the French proselytizing spirit led to two international conferences (Commission Internationale du Mètre) in 1870 and 1872 to discuss international standardization of the meter. The attendees favored replacing the Mètre des Archives with a new prototype which would be a line measure and made of a harder, platinum-iridium alloy (10% iridium, to within 0.0001%). They also suggested that the meter be taken as the length of the Mètre des Archives, “in the state in which it is found,” without reference to the quadrant of the Earth.

In 1875, twenty countries attended the third conference. Eighteen subscribed to a treaty (the Convention du Mètre), which set up the Bureau International des Poids et Mésures. Production of the meter standard, however, proved very difficult. Besides having an extremely high melting point (2,443°C), iridium had not yet been produced in purities greater than 50%. The bars from the first casting of the alloy, in 1874, were rejected in 1877, and the problem was turned over to the London firm of Johnson, Matthey and Co. They succeeded, and one of the resulting bars was made the provisional standard, even though it was 0.006 mm shorter than the Mètre des Archives. In 1882 France ordered thirty more bars, one of which (No. 6) turned out to be, as nearly as could be ascertained, exactly the length of the Mètre des Archives. This bar is the standard which was declared to be the International Prototype of the Meter by the First General Conference on Weights and Measures (first CGPM) in 1889: “This prototype, at the temperature of melting ice, shall henceforth represent the metric unit of length.” The International Prototype continues to be preserved by the BIPM.

As a way of distributing this standard to the countries signing the treaty, “national Meters” were made, which were copies of the International Prototype plus or minus 0.01 millimeter, supplied with a correction factor obtained by comparing that 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 been floated early in the 19th century (J. Babinet, 1827), before there was any way of realizing the idea in practice. By the end of the century this was no longer so.

“White” light is a mixture of light with different wavelengths. To define a unit 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 is visible–appears to a human to be colored, and is called monochromatic.

Fortunately it doesn't seem hard to produce monochromatic light: sprinkle some salt on the gas flames of a kitchen range. When the sodium atoms in the salt get excited, they give off a yellow light which is pretty much all the same wavelength. It is the same yellow as the light from sodium vapor street lamps. The wavelength is characteristic of the sodium atom.

In 1892-3 A. A. Michelson and J. R. Benoit succeeded in measuring the meter in terms of the wavelength of red light given off by excited cadmium atoms. Benoit and others refined the measurement in 1905-7, and in 1907 the International Solar Union (which is now the IAU) defined the international angstrom, a unit of distance to be used in measuring wavelengths, by making 6438.4696 international angstroms equal to the wavelength of the red line of cadmium. This value was taken from Benoit's experiments, and was chosen so that one angstrom was approximately 10⁻¹⁰ meter. (In 1927, the 7th CGPM provisionally sanctioned measuring distances in terms of the red line of cadmium, taking its wavelength to be 0.643 846 96 micrometers.)

Meanwhile, much had been learned since 1892. Even in the best of spectroscopes, the red line of cadmium was somewhat fuzzy. In fact, it turned out to be composed of many lines (physicists refer to its “hyperfine structure”), which affected how precisely the light's wavelength could be determined. When the existence of isotopes was discovered, it became clear that part of the reason for the fuzziness was that 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 of protons, 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 no coupling of nuclear spin to electron spins–and the light comes from the electrons.)

The 9th CGPM (1948) allowed as how the meter might eventually be defined in terms of light from such an isotope. Three isotopes were intensively investigated 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). The committee in charge of following these developments recommended that any new definition be stated in terms of the wavelength in a vacuum instead of in air, and that the length of the wavelength should be specified by comparing it with the already determined wavelength of the red line of cadmium, not with the International Prototype of the Meter. The 10th CGPM (1954) accepted these recommendations, in effect making the angstrom 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 “the International Prototype does not define the meter with an accuracy adequate for the present needs of metrology,” redefined the meter as “the length equal to 1 650 763.73 wavelengths in vacuum of the radiation corresponding to the transition between the levels 2p10 and 5d5 of the krypton 86 atom.”

Defined this way, it proved impossible to realize the meter with an accuracy better than 4 parts in 10⁹, and eventually that was not precise enough. In the meantime, however, the laser had been invented, and the light it produced–not only all one wavelength, but all in phase–opened up new possibilities for metrology.

In 1983 the 17th CGPM (Resolution 1) redefined the meter in terms of the speed of light in a vacuum. The value for the speed of light, 299,792,458 meters per second, had already been recommended in 1975 by the 15th CGPM, (Resolution 2). Its use in the meter's definition made the speed of light fall within the limits of uncertainty of the best existing measurements.

Thus the second, rejected as too arbitrary in 1791, has become the basis of the meter. We have probably not seen the last redefinition of the meter; the current definition may need tuning if even more accuracy becomes necessary. For example, the speed of light is affected by the strength of the gravitational field, and the 1983 definition does not take such factors into account.

## resources

P. F. A. Méchain and J. B. J. Delambre.
Base du système métrique decimal, ou Mesure de l'arc du méridien compris entre les parallèles de Dunkerque et Barcelone.
Paris: Baudoin, 1806–1810. 3 vols.

H. Barrell.
The Metre.
Contemporary Physics, vol. 3, page 415 (1962).