Measuring the Meter: an Error that Changed the World

In the midst of the French revolution, two scientists were charged by the revolutionary government to measure a quadrant of a meridian arc of the Earth. This universal length would then be the basis for a new measurement system, used today by over 95% of the world: the metric system. This seven-year adventure shows that tenacity, self-confidence and errors were part of the building of early science.

In the midst of the French revolution, two scientists were charged by the revolutionary government to measure a quadrant of a meridian arc of the Earth. This universal length would then be the basis for a new measurement system, used today by over 95% of the world: the metric system. This seven-year adventure shows that tenacity, self-confidence and errors were part of the building of early science.


Some years ago Ken Alder, professor of history of science at Northwestern University (Illinois, near Chicago), got hold of the written notebooks of the two men. He found one at the Observatory of Paris and the second in a library in Utah after a long and complex tracking of the archive long presumed lost. In his book «The Measure of All Things » published in 2004, he relates a historical journey and scientific discoveries through the men’s lives, showing what a human adventure science is. Alder also demonstrates that social context matters to science and that history can set a new way of understanding and questioning the present.

In 1792 Jean-Baptiste Delambre and Pierre Méchain, two renowned astronomers, were sent from Paris in opposite directions to measure the width of the Earth. Indeed, the freshly created revolutionary government of France had commissioned them to precisely measure that piece of meridian arc which ran from Dunkirk through Paris to Barcelona. Why? To reform the unit of length “for all people, for all time.” Its ambitions were to reform the world the French people were living in, with the goal of freeing them from the monarchy. Money, calendar, even the seven-day week and the 60-minute hour were modified. They also needed a unifying unit of length to harmonize the measurement systems, but also to free the trade market. “The people depended on the man that calculated how much they were buying and selling. Condorcet is believed to have said about the meter that: [quote] « the people will not be free as long as they cannot calculate. » Indeed as much as 250, 000 units of weight and length were used: the foot, the point, the inch, the lign, the perch… Some of them even differed between provinces, mostly to fit the lord of the land’s interests. Hence most of the “cahier de doléances” (lists of hopes and grievances drawn up by each village of France to the King) would ask for a global unit of length.


The Borda circle was the instrument used by Delambre and Méchain to estimate the latitudes. source : Abbé J. Loridan, Voyages des Astronomes français à la recherche de la figure de la terre et de ses dimensions
Borda circle and triangulation


Thus, the mission of the two astronomers was important. Alder’s book describes the journey of the two men, their difficulties, their encounters… He describes this story with a human point of view. Indeed human obstacles were the harder to overcome. As the two men climbed domed volcanoes, churches and cathedral towers with bizarre instruments, they were imprisoned as spies, royalists and sorcerers. Méchain also got severely injured. But the most surprising (unexpected) fact occurred when the latter got trapped in Spain when it declared war on France (Mars 7th, 1793). During his imprisonment, he remeasured the latitude of Barcelona. But his second set of data didn’t fit the first. He was never able to make this measurement again. This man of integrity became completely distressed by this mismatch. A mistake that would torture him to the brink of madness so that he would neither finish the task he had been given nor would he hand in his results.


Jean-Baptiste Delambre, French mathematician and astronomer. source : Wikipédia


« Méchain  possessed no conceptual tool to evaluate scientific errors. He did know  that measurements were never perfect but at the time people could not  even make a distinction between precision and accuracy. He thought that  he’d made a mistake that was almost a moral failure, » explains Alder. In  the end he handed in his first set of results but kept the second one  secret. And the meter was calculated as a certain fraction (one ten  millionth) of the distance between the North Pole and the equator*. This  was done by the largest committee of world-leader scientists – Laplace,  Legendre, Lagrange etc– and maybe the first international scientific  congress. A platinum meter was then fabricated to be the basis for a  universal length system. After the revolution, Napoleon Bonaparte is  believed to have said about the meter that: “Conquests will come and go  but this work will endure.”

The  error Méchain might have made would never have been discovered but for a  small note written by hand by Delambre in Méchain’s notebook after the  latter’s death. “Delambre, Alder explains, wrote in the margin that he  chose one of the versions of Méchain’s data and that we would not tell  the public what it didn’t need to know.” “Because after all, does it  matter if it is wrong? And can the meter be wrong? ”

Knowing  this, one could conclude that the two men’s journey had been useless.  But from the actual point of view that Alder’s book gives us, it appears  that many scientific developments date back to this period and are  related to this event. Scientists realized that the Earth was not a  perfect sphere and that it was smaller than they thought.


Pierre Méchain, French astronomer. source : Stoyan R. et al. Atlas of the Messier Objects: Highlights of the Deep Sky


When the notebook of the late Méchain arrived in Paris, Delambre faced a dilemma. But, in the meantime, mathematicians like Legendre and Gauss had developed new ways to treat data, like the “least square method of approximation” for example. The expedition to measure the Earth, therefore, emphasized the importance of the scientific method at a time when statistics did not even exist. It showed great scientific results and was an efficient political tool. It changed how the people thought and it opened an area of for a free-trade market.


Alder recalls: “In 1999 NASA’s Mars climate Orbiter crashed, apparently because two teams working on the project had used different length units and the error checking system failed to detect this.” Since 1983, the meter has been defined as “the length of the path travelled by light in vacuum during a time interval of 1/299 792 458 of a second ” but it is still 0.2 millimeter short of one ten millionth of the quadrant of a meridian arc. But a scientific discovery is never as simple as it sounds. It is built upon errors and approximations. And remembering this, one could consider that all we think is standard and reliable may not be so, nor has it always been.

Ken Alder’s book has been translated to many languages including French (see below). It has won several prizes and received highly positive evaluations from History of Science societies and from newspaper book reviews.


* In the end, the scientists chose to use 50-year-old measurements of a longer meridian. Because if the Earth is not spherical and all meridians are different, then the longer the measurement, the more precise and the better the approximation.

  To know more: Un historique du mètre Prologue of the book



Rory Allen Rory Allen 7 months ago

There seem to be two separate issues with Mechain. One is the discrepancy in the metre, and the other is the much larger (proportionally) difference in the latitudes of the Mont Jouy and Fontana d'Oro measuring points, of around 5%. Nobody to my knowledge has suggested a solution to this, but it seems very likely that it was due to the difference in the direction of gravity in the two locations. If Mechain determined the zenith by finding the local direction of gravity, then the mass of Mont Jouy itself would lead to a difference in the two locations. A plumb bob at the Fontana d'Oro would experience a small Southerly force, making the location appear to be further North than it actually was.