The meter was supposed to belong to everyone, and for a brief, strange moment in the 1790s, it almost did.
I have spent a long time with the documents from the expedition that produced it, and I will admit something I do not say often in print: I find Pierre Méchain's letters difficult to read without flinching. He is writing from Barcelona, then from a Spanish prison cell when the war catches up with him, then from the Balearic Islands, then from southern France on the long return north, and he is, in nearly every letter, lying. Not about politics. About a number. A number he took at Mont-Jouy in 1792, an early reading of the latitude there, which he later realised did not agree with his subsequent measurements. The discrepancy was small. He could not bring himself to declare it. He carried the error in his luggage, across borders, through quarantines, into the final calculations, and finally into his grave in 1804, where it stayed buried until Delambre, sorting through his dead colleague's papers, found the original notes and understood what had happened.
This is how the meter began. Not with the clean revolutionary geometry one reads about in textbooks. With a sick, conscientious astronomer hiding a rounding error from his nation.
The official story is tidier. Talleyrand, the bishop-turned-diplomat who survived every regime France could throw at him, proposed to the National Assembly in 1790 that France ought to have a new system of measures, derived not from the body of a king or the foot of a magistrate but from the body of the earth itself. The unit of length, he suggested, should be one ten-millionth of the distance from the equator to the North Pole, measured along the meridian that passes through Paris. The Academy of Sciences took the idea up. Two astronomers were chosen to measure the relevant portion of that meridian — the stretch from Dunkirk on the Channel to Barcelona on the Mediterranean — by triangulation. Delambre would take the north. Méchain would take the south. They set out in June 1792.
What followed was seven years. Seven years of climbing church steeples to take sightings, of being detained as spies by suspicious local committees during the Terror, of waiting out wars and fevers and lost equipment, of arguing by letter about angles. By the time they finished, the regime that commissioned them had been replaced twice. The platinum bar they produced — the mètre des Archives, deposited in the French National Archives on the 22nd of June, 1799 — was meant to be a copy of nature. It was, in fact, slightly short. The earth was not as oblate as their calculations had assumed, and Méchain's hidden error was sitting quietly inside the final number. The meter that was supposed to belong to everyone began its life as a flawed approximation of a planet that nobody had finished measuring.
What strikes me, reading the expedition journals two centuries later, is how little this seems to have mattered. The bar was the bar. The standard was the standard. Once you have a thing on a shelf in Paris, the philosophical question of whether it correctly represents a quarter of a meridian becomes, for most practical purposes, an academic one. The meter had become an object.
It stayed an object for a long time. In 1875, seventeen nations met in Paris and signed the Convention of the Metre, which established the BIPM — the Bureau International des Poids et Mesures — out at the Pavillon de Breteuil in Sèvres, on a small piece of internationally administered land in a Paris suburb. I have walked the grounds. They are quieter than you expect. The pavilion is small and yellow and looks like a country house, which is what it was before it became the address of the world's measurements. In 1889, the first General Conference on Weights and Measures approved a new standard: a bar of ninety percent platinum and ten percent iridium, X-shaped in cross-section to resist bending, with two fine lines scratched near its ends. The distance between those lines, at zero degrees Celsius, was now the meter. Thirty copies were cast. They were distributed to the signatory nations by lot. The United States, drawing badly, received Prototype Number 27.
Charles Sanders Peirce — the American philosopher, who in his other life was a working scientist for the US Coast and Geodetic Survey — had spent the 1870s swinging pendulums in basements on three continents trying to make American measurements compatible with European ones, and corresponding with the new bureau at Sèvres about the maddening sensitivity of length to temperature, to vibration, to the way a man set down his foot near the apparatus. Peirce, who was difficult and brilliant and would die in poverty in Pennsylvania, understood something about the meter that the engineers did not quite want to. Every measurement is a negotiation. Every standard is a temporary peace treaty between the world and the people trying to write it down.
The platinum-iridium bar reigned for seventy-one years. Then, in 1960, the CGPM did something that in retrospect was the first real break with the revolutionary dream. They redefined the meter as 1,650,763.73 wavelengths of the orange-red emission line of krypton-86. The bar at Sèvres became, overnight, a souvenir. The meter no longer lived in a vault. It lived in any laboratory that could excite the right isotope.
This was made possible, in large part, by the interferometry of Albert Michelson, who had spent decades at the end of the nineteenth century learning to count light waves with unreasonable accuracy. Michelson is more famous for failing to detect the luminiferous ether, which was the more important failure, but his quieter success was teaching the world that wavelengths were more stable than artifacts. A bar can be scratched. A bar can be stolen. A bar can be slightly the wrong length because a Spanish astronomer in 1792 was too proud to publish his uncertainty. A wavelength is the same in Paris and in Tokyo and on the moon.
In 1983, the meter retreated one further step from the physical world. It is now defined as the distance light travels in a vacuum during 1 / 299,792,458 of a second. There is no krypton lamp. There is no bar. The meter is a consequence of two other things — the speed of light, which is now defined as exact, and the second, which is defined by the cesium atom. To realise a meter, you must run a clock and a beam of light and do arithmetic. The meter no longer exists anywhere in particular. It exists wherever you bother to construct it.
I am not sure how to feel about this, and I have stopped pretending I am sure. The 1983 definition is more accurate, more democratic in a deep sense, more durable against fire and theft and the slow oxidation of platinum, than anything Delambre and Méchain could have hoped for. It is also, in a way the revolutionaries would have found suspicious, completely invisible. The meter that was supposed to be the property of all peoples is now the property of anyone with a frequency-stabilised laser and a working knowledge of metrology, which is a smaller group than the framers had in mind.
Whether the 1983 definition is the end of the story I do not know. There are physicists at Sèvres who will tell you the speed of light is the speed of light and the matter is settled. There are others who point out that we said the same about the platinum bar, and about the krypton lamp, and that the history of measurement is the history of provisional certainties being replaced by better ones, on a schedule we do not get to set.
What I am sure of is this. We no longer keep the meter on a shelf in Paris. The meter keeps us — keeps our satellites in orbit, our chips in tolerance, our bridges from falling — and we have agreed, mostly without noticing, to live inside a length we can no longer point to. Delambre would, I think, have found this acceptable. Méchain, I suspect, would have found it a relief.