The modern tape measure found in toolboxes is 0.197 millimeters shorter than the original meter defined by the French Convention in the late 18th century. This small but significant difference traces back to a major scientific effort between 1792 and 1798, when astronomers Jean-Baptiste Delambre and Pierre Méchain measured a section of the Earth's meridian from Dunkerque to Barcelona. The goal was to define the meter as one ten-millionth of a quarter of the Earth's meridian, a task requiring extreme precision. Delambre measured from Dunkerque to Rodez, while Méchain measured from Rodez to Barcelona. Méchain discovered a discrepancy of 3 arc seconds in Barcelona but kept it secret for a long time. This error, when accumulated, results in a difference of over 1 millimeter over 5 meters of tape.
Méchain, who had previously been a comet hunter and an elected member of the Academy of Sciences in 1782, was responsible for writing the Connaissance des Temps, an annual astronomical almanac, in 1788. He collaborated with Charles Messier, a fellow astronomer, in discovering many deep sky objects. In 1792, the two men left Paris in opposite directions, with Delambre accompanied by engineer Bellet and Méchain by engineer Tranchot, as recorded by the French Association for the Advancement of Sciences. The journey was challenging, as geodetic instruments were not always welcomed by local revolutionary committees. Despite these obstacles, the measurements continued until 1798.
In March 1793, Spain declared war on France, and Méchain was in Barcelona at the time. He was ordered to remain there and found himself under surveillance. During a technical visit, a pump lever struck him violently, causing several days of unconsciousness, a fractured clavicle, and broken ribs. According to the French Association for the Advancement of Sciences, he never fully recovered from the incident. While held in place, he continued his latitude calculations and noticed a discrepancy of 3 arc seconds in Barcelona, depending on whether he used the point in Barcelona or the nearby Montjuïc station. The two sites are only 2 kilometers apart, according to the Paris Observatory. Méchain chose not to share his second set of measurements upon returning to France. Historian Ken Alder, who wrote about this period in a book, noted that at the time, scientists did not clearly distinguish between precision and accuracy. Méchain viewed the discrepancy as a moral failure and revealed only the first set of measurements. He returned to Spain and died in Castellón de la Plana on September 20, 1804, likely from malaria, though some sources suggest yellow fever. He had been directing the Paris Observatory since 1794.
Delambre later retrieved Méchain's records and uncovered the discrepancy in the Barcelona measurements. He compiled a detailed 2,400-page report on the six years of measurements, completed in 1807, which did not conceal the anomaly. In 1799, the definitive length of the meter was set at 3 feet 11.296 lines of the Academy's toise, represented by platinum standards. With the benefit of hindsight, it is known that this value is 0.197 millimeters shorter than the original definition. The Wikipedia article on the history of the meter attributes this primarily to a deviation in the vertical direction at the southern end of the meridian, which was not considered. The Paris Observatory mentions the accumulation of small errors, such as local deviations of the vertical, instrumental inaccuracies, and imprecise star refractions. None of these sources quantify Méchain’s exact contribution to the 0.197 millimeters, and it would be unfair to attribute the entire discrepancy to him alone. On a tape measure, the smallest division is 1 millimeter, and the discrepancy is about one fifth of that. It is roughly the thickness of two standard sheets of paper. Over 5 meters of tape, the cumulative discrepancy approaches 1 millimeter. In 1993, a plaque was placed on the tower of Montjuïc Castle in Barcelona to commemorate the 200th anniversary of the meter, noting that Méchain conducted his observations there in 1792 and 1793. The astronomer is buried in Castellón de la Plana, in Ribalta Park.
Historical Discrepancy in the Definition of the Meter Revealed
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