\chapter{A Unit Taken from the Earth}

If a new unit is going to replace every old one, it has to come from somewhere
that nobody owns. The king's foot will not do, because the next king has a
different foot and the neighboring country has a king of its own. What the
reformers of the 1790s wanted was a length that any competent person could
recover from nature, without asking permission from anyone.

\section{The proposal of 1791}

Several candidates were on the table. One was the seconds pendulum, the length
of a pendulum that takes one second to swing. It is easy to reproduce and easy
to explain, and it has one flaw: the answer depends on where you stand, because
gravity is not the same everywhere. Choosing a latitude would have meant
choosing a country, and that was exactly the argument the commission was trying
to avoid.

The proposal that won, put to the National Assembly in 1791, took the unit from
the size of the planet instead. The meter would be one ten millionth of the
distance from the North Pole to the equator, measured along the meridian that
runs through Paris. The Earth belonged to everyone, or at least to nobody in
particular, and the definition could be stated in a sentence.

It also required somebody to go and measure the meridian, which is where the
trouble started \cite{alder2002}.

\section{Seven years between Dunkirk and Barcelona}

The survey was split between two astronomers. Jean Baptiste Joseph Delambre
took the northern arc from Dunkirk to Rodez, and Pierre M\'echain took the
southern arc from Rodez to Barcelona. Both worked by triangulation: pick two
points whose distance apart is known precisely, measure the angles to a third
point from each end, and the geometry gives you the two new distances. Repeat
across the country, chain of triangles by chain of triangles, and you have the
length of the arc.

The work was expected to take a year. It took seven. The two men were surveying
across a country at war, carrying brass instruments up church towers at night,
in a period when a stranger with a telescope and official papers was assumed to
be a spy. Both were detained more than once. Sightlines were blocked by weather
for weeks. M\'echain, stuck in Barcelona and later in Italy, could not get home
for years.

He also found a discrepancy. His latitude measurements at Barcelona did not
agree with each other as closely as his instruments should have allowed, and he
never resolved it. He hid the inconsistency, kept two sets of notes, and spent
the rest of his life trying to justify the number he had published. The story
was reconstructed from his papers long afterward, and it is the most human part
of the whole enterprise: the definition of the meter carries a small error that
one exhausted man could not bring himself to admit \cite{alder2002}.

The final number was deposited in 1799 as a platinum bar, the meter of the
Archives. Later work showed that the arc calculation had used a value for the
flattening of the Earth that was slightly off, so the bar came out about two
tenths of a millimeter shorter than the definition intended. Nobody has
proposed fixing it. By then the bar was the unit, and the definition had become
a historical note.

\section{From a bar to a constant}

Adoption was slower than the reformers hoped, including at home. France itself
went back to older units under Napoleon and only made the metric system
compulsory again in 1840. The international turn came in 1875, when seventeen
states signed the Metre Convention and set up a permanent bureau to hold the
standards and distribute copies. In 1889 a new international prototype, an
alloy of platinum and iridium with a cross section shaped like an X for
stiffness, replaced the bar from the Archives.

A metal bar is still an object. It can be dropped, it can corrode, and it has
to be compared against copies by people traveling to one building outside
Paris. The twentieth century replaced it twice. In 1960 the meter was redefined
as a number of wavelengths of orange red light from krypton 86, which any
properly equipped laboratory could reproduce. In 1983 it was tied to the speed
of light: the meter is the distance light travels in vacuum in one part in
299,792,458 of a second \cite{bipm2019}.

That last move is worth pausing on. The speed of light is no longer measured.
It is fixed by definition, and the meter follows from it. After two centuries,
the unit finally arrived where the commission of 1791 wanted it: available to
anyone, anywhere, without a trip to Paris and without asking a king.
