On 20 May 2019 the definition of the kilogram changed, and not one scale anywhere gave a different reading. That was the requirement. Meeting it was the difficult part.

Julian Ashworth follows the twenty-year project that removed the last physical object from the International System of Units.

The object had an odd property: it could not be in error. Every mass on earth was referred to it, which left nothing to refer it to. Contamination or a cleaning simply carried the world's masses along. What the record shows is more cautious than the usual telling — across a century, the prototype and its official copies separated by something on the order of fifty micrograms, with no way to say which had moved, and a fair chance they were drifting together.

Two experiments had to succeed before the change was possible. In one, a mass is weighed against the force felt by a current-carrying coil sitting in a magnetic field; the same coil is then set moving and the voltage it generates is read off, so that the quantity nobody can measure cancels between the two steps. The other counts atoms in a sphere of silicon-28 finished to such a degree that the thin oxide layer on its outside became a term in the arithmetic, to be gauged and taken off before any total was worth stating.

Neither was allowed to define the unit alone. Agreement between two methods sharing no systematic error was worth more than one method with a smaller uncertainty.

The chain downward gets its own chapters: why weighing in air is corrected for the air, why a certificate states density alongside mass, and what the tolerance classes are really rationing.

The cylinder is still in its vault, incidentally, and still has a mass of about a kilogram — but that is now something to measure rather than something to assume.