The Mistake in the Meter

In June 1792, two astronomers left Paris in opposite directions to measure the shape of the Earth.

Jean-Baptiste Delambre went north, toward Dunkirk. Pierre Mechain went south, toward Barcelona. Their task, assigned by the newly formed French Republic, was to measure the meridian arc between the two cities with enough precision to define a universal unit of length. The meter would be one ten-millionth of the distance from the North Pole to the equator, calculated from their survey. The idea was elegant: a unit derived from the planet itself, belonging to no king and no nation, permanent as the ground underfoot.

The ground was not cooperative. Delambre spent weeks on church towers and hilltops, waiting for clear weather to sight his triangulation signals. Local militias arrested him repeatedly, suspicious of a man with expensive instruments staring at the countryside during a revolution. His letters of authorization, signed by the king, became liabilities after the king was arrested. He got new ones, signed by the Republic. He kept measuring.

Mechain had it worse. In Barcelona, he fell from an observatory platform and dislocated his shoulder. While recovering, France declared war on Spain. He was trapped behind enemy lines for two years. When he finally returned to the survey, he remeasured the latitude of Barcelona from a different location and got a number that didn't match his earlier observations. The discrepancy was small: 3.24 seconds of arc, roughly a hundred metres on the ground. It should have been reconcilable, but Mechain couldn't reconcile it.

He never told anyone.

The problem was not incompetence. Mechain was one of the finest observational astronomers in Europe. The problem was that the Earth is not a perfect ellipsoid. The local gravitational field in Barcelona, shaped by the density of the rock beneath the city, deflected his plumb line by a tiny, unmeasurable amount. His instruments were telling the truth. The truth was that the planet's shape is irregular in ways that eighteenth-century physics couldn't model, and no amount of rechecking would make two observations from slightly different positions agree exactly.

Mechain knew something was wrong with his data but not what. He adjusted his Barcelona numbers, quietly, in his notebooks. He presented a clean result to the International Commission that met in Paris in 1798 to finalize the meter. Delambre, who reviewed the data after Mechain's death in 1804, eventually found the alterations. He said nothing publicly.

The meter was proclaimed in 1799. A platinum bar was machined to the calculated length and deposited in the Archives of the Republic. It was wrong. Not by much: the meridian-derived meter was about 0.2 millimetres short of the true ten-millionth of a quadrant, an error that came partly from Mechain's hidden adjustments and partly from the genuine difficulty of measuring a planet that refuses to be regular.

The bar was the meter anyway. Once the platinum was cut, the definition detached from the measurement. Nobody went back to the meridian. For the next two centuries, the meter was whatever that bar said it was, then whatever a certain number of wavelengths of krypton-86 light said it was, and now whatever distance light travels in 1/299,792,458 of a second. Each redefinition was more precise. None of them corrected Mechain's error, because there was nothing to correct. The meter had stopped being about the Earth the moment the bar was cut.

Mechain died on a survey expedition in Valencia in 1804, still trying to fix his numbers. He never published the discrepancy. His private notebooks, filled with recalculations and mounting distress, were found after his death and quietly archived. Delambre wrote the official history of the meridian survey. In it, he was generous to his dead colleague, acknowledging the difficulty of the measurements without naming the deception. The kindness may have been self-interested: if Mechain's data was compromised, so was the meter, and so was the entire project to which Delambre had given a decade of his life.

The unit that was supposed to belong to no one began with one man's private anguish over a number that wouldn't come out right. The anguish was unnecessary. The error was smaller than the uncertainty inherent in the method. If Mechain had reported his raw data, the Commission would have averaged it and arrived at a meter within a fraction of a hair's width of the one they got. His silence changed almost nothing about the length. It changed everything about the story.