The Measure of All Things: The Seven-Year Odyssey and Hidden Error That Transformed the World , Ken Alder Simon & Schuster, New York, 2002. $27.00 (422 pp.). ISBN 0-7432-1675-X
All things seemed possible in the heady early years of the French Revolution. In 1791, the French Academy of Sciences organized a commission to measure Earth. The goal was to replace the locally defined measuring standards of the old regime with more objective and universal standards. Accordingly, a new measure of length, the meter, was to be defined as one ten-millionth the length of a circular arc from Earth’s pole to its equator.
The academy commissioned the distinguished astronomers J.-B.-J. Delambre and P.-F.-A. Méchain to survey a meridian—that of Paris, naturally—from the North Sea to the Mediterranean. The two astronomers were to use the newly invented “Borda repeating circle,” said to permit angular measurement to one second of arc by accumulating many observations of a specified angle. (Dividing the total angle by the number of observations yielded a more precise estimate of the desired angle than any single measurement.) The latitude difference determined from the Borda circle would be used to scale the measured distance and infer the equator-to-pole arc length. Delambre and Méchain’s ambitious survey would become the foundation of the metric system.
Ken Alder, a historian of science at Northwestern University, has written The Measure of All Things as both a narrative of the expedition and a thoughtful study of the prehistory of error theory. It is a rousing good story whose multifaceted interest greatly exceeds what a brief review can convey.
Delambre and Méchain were men of their age, learned men or savants, not really scientists in the modern sense. Both were astronomers, well suited to craft a standard on which modern science and commerce rely. Their mission, however, soon became far more daunting than the academy had foreseen, as revolutionary France plunged into war with its neighbors.
In the ensuing turmoil, it soon became apparent that, although the meridian survey offered many benefits to science and to large-scale commerce, it did little for the mostly rural inhabitants of France. When Delambre surveyed the northern part of the Paris meridian—in regions agitated by rumors of an imminent Prussian invasion—he sometimes had to explain to a volatile crowd what he was doing. As he spoke eloquently of the need for a single set of measures, shared among all the peoples of the world, “a few voices proposed one of those expeditious methods, so in use in those days, which cut through all difficulties and put an end to all doubts” (p. 34). Those voices were speaking of the guillotine.
Where the Paris meridian crosses Spain’s northern border, Méchain faced even greater obstacles. Spain declared war on France while Méchain was in Barcelona. Spanish authorities were understandably reluctant to allow a French surveyor to work in the border regions. Méchain became entangled in the ebb and flow of the war, and eventually made his way home through Italy. Upon reducing his Spanish observations to usable form, he found an alarming inconsistency and panicked. Hoping to repeat his measurements when circumstances permitted, he concealed the problem from his colleague. The chance never came, and the hidden error festered in his conscience. Decades later, as Delambre reconstructed the work of his late associate, he uncovered Méchain’s deception—but also his peculiar integrity. Méchain had doctored his observational records to make them appear more consistent, but had done so in such a way that the altered observations would appear redundant and therefore would not be used at all. In other words, he fudged his data to protect his personal reputation as an observer, but tried to ensure that the truth would not suffer.
In the end, Delambre and Méchain accomplished their surveying mission but failed in their goal of determining the pole-to-equator arc length along the Paris meridian. Their estimate of the length of a meter differs by 0.2 mm from its target value of 10−7 of that arc length—actually less accurate than a provisional value adopted in 1793 based on an earlier and less precise survey! The extraordinarily precise measurements made with the Borda repeating circle were more than negated by systematic problems such as erroneous assumptions about Earth’s exact shape. We now define the meter in terms of the speed of light in a vacuum and the frequency of light emitted by cesium-133, and thus escape the ambiguities that lurk in a standard so particular and ill-behaved as planet Earth. As Alder points out, though, each new definition has been calibrated to agree with its predecessor. Hence, the modern meter effectively differs by 0.2 mm from the Delambre–Méchain estimate. The expedition of Delambre and Méchain remains among the foundations of today’s standard meter.
Exploring the paradoxical failure of the surveyors’ ambitious attempt at high-precision measurement, Alder opens up a much larger theme: the origins of the modern understanding of scientific measurement. No measurement is without error, so today’s scientist is expected both to reduce measurement error and to estimate its magnitude. Reported measurements are taken not as true values but as statistics, in which one acknowledges the error in order to control it. Although that attitude is second nature to modern scientists, it arose only in the 19th century.
The Measure of All Things offers many rewards to its reader: a great story, colorful characters, a reminder of the messy origins of the tidy metric system, and some thought-provoking considerations about what measurement is and is not. It reads well enough to hold the attention of a non-technical audience, but offers plenty of technical substance.
Bruce Stephenson is curator at Chicago’s Adler Planetarium, whose collection includes a Borda repeating circle. His current research involves astrolabes and synchrotron radiation.
