Field Book: The Frozen Error

The frozen error is this site's name for a historical measurement error that was later written into a definition and stopped being treated as an error. The measurement was off; the definition kept the result anyway; and from then on the result was simply the unit.

Three things it takes

A case is called a frozen error only when all three of these are present:

1. An error you can point to: a specific mistake or shortfall in a specific measurement.
2. A basis for comparison: what the measurement was meant to match, stated outright.
3. Evidence: a source for the error and a source for the comparison.

If any of the three is missing, the case is described in plain terms, without the label.

The meter's fifth of a millimeter

In 1791 the meter was proposed as one ten-millionth of the distance from the North Pole to the Equator. From 1792, Delambre and Méchain surveyed the arc from Dunkirk to Barcelona to pin that distance down, and in 1799 the result became a platinum bar. Their estimate of Earth's curvature was off.

The basis for comparison is that original design target. Computed on the WGS 84 ellipsoid, whose semi-major axis is 6,378,137 m [exact by definition] and whose inverse flattening is 298.257223563 [exact by definition], the pole-to-equator quadrant comes to about 10,001.966 km. That is about 1.966 km more than the 10,000 km the design assumed. Shared out over the ten million meters, it means the meter falls short of the 1791 target by about 0.1966 mm, roughly a fifth of a millimeter.

Nobody fixed the gap. The 1889 bar, the 1960 krypton line and the 1983 speed-of-light definition each kept the length already in use. That is what makes it frozen: the error stopped being an error and became the definition.

The comparison is with the design target of 1791. It does not mean today's meter is wrong: today's meter is defined through the speed of light, and the gap is measured against what the 1791 plan aimed for, not against that definition.

What does not count

Adopting a reference point is not a frozen error. When the second was tied to the tropical year 1900 in 1956 and 1960, that choice fixed a baseline; it did not preserve a measurement mistake. This site calls that kind of choice an inherited baseline, as a plain description rather than a term of its own.

The frozen error is one of three terms in this site's field book, with the remainder and the unstated per. It is a special case of the remainder's measurement-error kind.