The Measure of All Things

by Ken Alder

  How did Méchain feel about this rising new talent? Did he resent Delambre’s Mercury coup, his one-upmanship on the Uranus data? Was he jealous of his maître’s newfound favorite? Méchain’s feelings mattered to Delambre. Méchain not only sat on the prize committees; as a member of the Academy, he could have blocked his rival’s election. The two astronomers had occasionally observed the stars together. Lalande asked them to collaborate on yet another edition of his Astronomy. And Méchain published Delambre’s work in his astronomical journal. Yet relations between the two remained formal and Delambre still thought it wise to ask his friends to put in a good word about him with Méchain. For his part, Méchain always addressed the up-and-coming astronomer with elaborate courtesy as the “abbé de Lambre.”

  Delambre would later acknowledge that “one can trace certain similarities between the early years of Delambre and Méchain.” Both were men of modest background, sons of provincial Picardy, educated by the Jesuits, rejected by the Ancien Régime’s institutions of higher learning, and later employed as tutors. And from there, their lives converged ever more closely: the same scientific discipline, the same maître, the same expedition. But a career trajectory does not decide one’s fate.

  Lalande’s proposal that the nation adopt the Paris measurement standards received little attention until the juridical revolution of August 1789, when the nobility renounced all its legal privileges, including its authority over weights and measures. From that point onward, a flood of proposals poured in from the members of provincial learned societies, underemployed state engineers, and enthusiastic citizens of all stripes. Each of these pamphleteers had his own pet notions about the form the nation’s new system of measures should take.

  Yet in the end the metric system that emerged was essentially the creation of a core of savants from the Paris Academy of Sciences. The French kings had traditionally referred questions of measurement to their Academy. In the run-up to the Revolution, Lavoisier and other academicians had been invited onto royal commissions to consider the advantages of uniform measures. Now savants such as Condorcet, Lavoisier, Laplace, Borda, and Legendre quickly formed a Commission of Weights and Measures to hammer out the specifics of the metric reform. Some of these men, like Condorcet, themselves sat in the legislative assembly. Other members of the legislature, such as a young engineer named Claude-Antoine Prieur-Duvernois, known as Prieur de la Côte-d’Or, helped promote the reform from within the ranks of officialdom. Over the next four years, these men transformed the citizenry’s simple plea for a uniform system of weights and measures into a hyperrational system, combining features which had long been sought by savants and from them assembling a system of perfect metrical communication. Yet each of these features was proposed independently, and each proved controversial.

  The single demand which united all the savants, legislators, and pamphleteers was the expectation that the new weights and measures would be applied uniformly throughout France. It was true that in 1788 some of the complainants in the Cahiers de doléances had thought it sufficient to demand regional measures based on the standards of provincial market towns. But merely regional measures quickly came to seem inadequate to the leaders of the new national government, and in February 1790 the first proposal for metric reform to reach the National Assembly reiterated Lalande’s plea that the legislators adopt the Paris standards throughout the nation. It was a proposal bound to appeal to a nation newly conscious of its unity. It was also the logical culmination of a thousand years of French centralization. In any other nation at any other time, this proposal would undoubtedly have become the law of the land—in which case the metric system would almost certainly never have existed in anything like its current form.

  But it was not just any nation and it was not just any time. It was a nation conscious of its place at the vanguard of history at a time when history called for actions of universal significance. Even the men who proposed the Paris standard recognized the thrum in the air. They knew that some of their comrades had grander ambitions, and they feared that those ambitions would scuttle any chance for a more limited success. “Do not,” they pleaded, “take us beyond our desires and our hopes.” The savants, however, were determined not to let slip this chance to design a truly rational system of weights and measures.

  One month later, in March 1790, Charles-Maurice de Talleyrand offered the legislature a far grander proposal. While the adoption of the Paris measures might seem expedient, it failed to rise, he said, to “the importance of the matter, nor the aspirations of enlightened and exacting men.” In its place, the former bishop, sometime revolutionary, and perennial master of French foreign policy advanced the proposal favored by the savants, especially by Condorcet. In place of a measure derived from history or the fiat of kings, he asked that the legislature derive its fundamental measure from nature, the common heritage of all mankind. Only a measure derived from nature, he declared, could be eternal because only such a standard could be reconstructed should its man-made physical embodiment suffer the ravages of time. For instance, the Paris toise—which equaled, by definition, six times the length of the royal pied (foot)—was actually a bar of iron mortised into the wall at the foot of the staircase of the great Châtelet courthouse. Yet, as everyone knew, the original bar had become badly bent as the building settled and had been replaced in 1666. By 1758 even the new bar, equal to half the width of the entrance to the royal Palais du Louvre, had begun to show its age. Surely so ephemeral a standard would not suffice for a new régime founded on the rights of man. Only a measure taken from nature could be said to transcend the interests of any single nation, thereby commanding global assent and hastening the day when all the world’s peoples would engage in peaceable commerce and the exchange of information without encumbrance.

  Talleyrand—again, at Condorcet’s prompting—also proposed an additional feature for the new system of measures: that its various units (length, area, capacity, weight, et cetera) be rigorously linked by an interconnected system. The idea was that once the unit of length had been derived from nature, all the other units might be defined in relation to it. This would ease all kinds of calculations and comparisons, especially for those professionals—engineers, doctors, savants, artisans—who transformed nature into useful things. This provision was reiterated in all subsequent proposals, although the savants would themselves disagree about how to define these relationships, especially for the unit of weight. Lavoisier and the crystallographer René-Just Haüy set to work early in 1793 to define the grave (as the gram was then called) as a cubic centimeter of rainwater weighed in a vacuum at the melting point of ice. But without a definitive determination of the meter, their findings were necessarily provisional. Ultimately, in 1799, the chemist Lefèvre-Guineau would define the gram as one cubic centimeter of rainwater weighed in a vacuum at the temperature of maximum density.

  Not longer after Talleyrand’s proposal had been voted into law, the legislature authorized the addition of a third feature, one long desired by savants. They declared that all the metric units would be divided by a decimal scale. The idea for universal decimal measures went all the way back to the proposals of Simon Stevin, the Flemish engineer who had invented the decimal point in the Renaissance. In the seventeenth century the advantages of decimal measures had been echoed by the English philosopher John Locke and the French military engineer Sébastien Le Prestre de Vauban. More recently, in his textbook for the new chemistry, Lavoisier had urged that decimal measurement be adopted by all the world’s savants. Given the near universality of the decimal scale in arithmetic, the savants pointed out, a complementary system of measures would ease calculation, not only for learned folk, but for everyone engaged in trade, commerce, or construction. The decimal system could even be considered a kind of natural scale because human beings have ten fingers. To cap this reform, the National Assembly was also considering a proposal to decimalize the new national currency, as the American republic had done a few years before.

>   Yet even this proposal proved controversial. Several pamphleteers suggested that the metric system be designed around a duodecimal scale. Because of its many divisors, a base-12 system would allow buyers and sellers to divide and subdivide goods easily, enabling butchers to chop sausages into halves, thirds, or quarters. The admitted drawback of the duodecimal system, its incompatibility with the usual arithmetic scale, could be solved by switching our arithmetic to a duodecimal system and adding two new single digits for “10” and “11.” The Revolution was a chance to rethink all old assumptions. Then again, other pamphleteers preferred a scale derived from base 8 because it would enable commodities to be divided in half again and again and again, like a pie. Yet another pamphleteer proposed instead division by base 2. And one great mathematician even toyed with the idea of a scale built around a prime number, like base 11, since from a mathematician’s point of view a fundamental unit ought not itself to be divisible.

  The fourth and final addition made by the savants—and certainly the one that most baffled their countrymen—was their proposal for a nomenclature of prefixes. Only gradually did the Academy come around to the view that the new measures needed new names. In May 1790, the citizen Auguste-Savinien Leblond was the first to propose the neologism “the meter” for the fundamental unit of length, “a name so expressive that I would almost say it was French.” And for the next few years, the reformers continued to assume that the multiples and subdivisions of the meter would go by their own simple names like the perche (10 meters) and stade (100 meters), or the palme (0.1 meters) and doigt (0.01 meters). The idea that one might use Greek and Latin prefixes—kilo-to mean 1000, and milli-to mean 0.001—first surfaced in a report by the Commission on Weights and Measures in May 1793. In spite of a counterproposal that the prefixes would be more authentically French if taken instead from Low Breton, this system of classical prefixes was the final element to be added to the metric system as we currently know it today.

  Each of these features was controversial, added in succession, and debated in turn during the early years of the Revolution. Yet no single feature caused more consternation, frustration, and second-guessing than the proposal to base the fundamental unit of length on the measure of the earth. “Was it really necessary,” one critic asked, “to go so far to find what lay so near?”

  Indeed, Talleyrand had initially proposed that the fundamental unit of length be derived from the length of a pendulum beating one second. This was an idea with a long pedigree, going back to the early seventeenth century when Galileo had first demonstrated that the period of a pendulum’s beat was determined entirely by its length, so long as its swing was not too wide. In the 1620s, the Dutch savant Isaac Beeckman and Father Marin Mersenne of Paris had discussed a natural standard for length calibrated against the length of a pendulum beating at one-second intervals. In 1775, the reform-minded Chief Minister Turgot had asked Condorcet, the rising star of the Academy of Sciences, to draw up a plan for a scientific system of weights and measures based on the one-second pendulum.

  Talleyrand, on Condorcet’s advice, had initially proposed that the French government invite two savants from each of the world’s nations to participate in a joint experiment to determine the length of a pendulum beating one second. Talleyrand further announced that he was in contact with Sir John Riggs Miller, a member of the British Parliament who had introduced similar legislation in the House of Commons. Talleyrand considered this a hopeful sign, and wondered if it were “permissible to see in the concourse of two nations interrogating Nature together the principle of a political union by the mediation of science.” If successful, such a measurement system might extend beyond Europe and around the globe. A savant from France’s young sister republic across the Atlantic had sent word that he too was interested in this project. Thomas Jefferson, in his capacity as the nation’s first Secretary of State, had been asked by President Washington to report on the reform of American weights and measures, and he had likewise agreed to coordinate his proposals with the French. Condorcet privately predicted that the French, the British, and the Americans—“the world’s three most enlightened and active nations”—would all be employing the same measures in short order.

  There was only one catch. In the two centuries since Galileo’s day, the savants had learned that the length of the one-second pendulum was also sensitive to the latitude at which it was measured, because gravity varied slightly with latitude. Hence, Talleyrand reminded the legislators that this pendulum experiment would have to be conducted at some specific location. The equator might have seemed the most natural choice, positioned as it was, equidistant from the poles. But the equator was unfortunately remote from the scientific nations. So the second most natural location, Talleyrand argued (on Condorcet’s advice), would be the midpoint between the pole and the equator—at 45 degrees of north latitude—where the pendulum possessed its average length. And since the experiment ought to be carried out at sea level and far from any disturbing mountains, the most plausible site on earth was on the outskirts of Bordeaux in southwest France.

  Needless to say, this aspect of Talleyrand’s proposal did not meet with international approval. Miller of Britain plumped for a measurement in London. Jefferson of Virginia argued for a measurement on the 38th parallel, both the median latitude of the United States and conveniently downhill from his estate at Monticello. And some Parisians dared to suggest that the experiment might most easily be carried out in Paris. The achievement of universality, it seemed, would require some delicate diplomacy. But Talleyrand was a master diplomat. He saw to it that the law passed by the National Assembly on May 8, 1790, gently suggested the pendulum measurement be taken at 45 degrees, “or whatever other latitude might be preferred,” and invited the Academy of Sciences to form a Commission of Weights and Measures to carry out this plan. In England Miller praised this concession before the House of Commons, and Jefferson redrafted his final report to the U.S. House of Representatives to tout the advantages of cooperating on the measurements at the 45th parallel “with the hope that it will become a line of union with the rest of the world.”

  Yet after all these delicate negotiations were concluded, when the Commission reported back one year later, on March 19, 1791, they urged that the pendulum standard be dropped altogether in place of a meter based on one ten-millionth of the distance from the North Pole to the equator as established by a survey of the meridian that ran from Dunkerque to Barcelona.

  It was Borda, as chairman of the Commission, who justified this change on scientific grounds. The problem with the pendulum, he noted, was that it would make one fundamental unit (the length of the meter) depend upon another unit (a second of time). What would then happen if the units of time were themselves to change? Even as he spoke, the Academy was considering whether the arbitrary division—inherited from the Babylonians—of a day divided into 24 hours of 60 minutes of 60 seconds each should likewise be converted to the decimal scale, so that the day might be more rationally divided into 10 hours of 100 minutes of 100 seconds. By contrast, there could be nothing simpler or more natural than basing the fundamental unit of length (the meter) upon another unit of length (the size of the earth).

  Besides, it was only fitting that a measure for all the world’s people be based on a measure of the world. It was consonant with the universal aspirations of the Revolution. As Laplace would later point out, a meter based on the size of the earth would entitle even the most humble landowner to say, “The field that nourishes my children is a known portion of the globe; and so, in proportion, am I a co-owner of the World.”

  Obviously, the circumference of the entire earth would make an awkward unit of length for ordinary purposes. But a measure of length based on the quarter meridian divided by ten million would come out to very near the length of the aune of Paris, a three-foot length comfortably on the human scale and familiar to many French citizens. To determine that length with the necessary precision, the National Assembly need only to authori
ze a new expedition to measure a meridian—or at least a portion of one.

  Borda explained how the French academicians had selected just such a meridian on the basis of rational criteria that would “exclude all that was arbitrary.” First, the selected arc would have to traverse at least 10 degrees of latitude to allow for a valid extrapolation to the full arc of the earth. Second, the selected arc would have to straddle the 45th parallel, which, as the intermediate distance between the pole and the equator, would minimize any uncertainty caused by the eccentricity of the earth’s shape. Third, its two end points would have to be located at sea level, the natural level of the earth’s figure. And fourth, the meridian would have to traverse a region already well surveyed so that it could be quickly measured. There was only one meridian in the entire world which met all these requirements: the meridian which ran from Dunkerque through Paris to Barcelona. He assured the legislators that “there was nothing in this proposal that would give any nation the least pretext for reproach.” He also assured them that the task could be completed in a year.

  As Borda noted, the idea of basing a natural unit of measurement on the circumference of the earth had long been a cherished dream of savants. Centuries before Columbus set sail west from Spain, learned folk had known that the earth was round. Eratosthenes, director of the fabulous Library of Alexandria in the third century B.C.E., was also the father of geodesy and had measured the earth’s circumference to within 10 percent. Eratosthenes knew that in the Egyptian town of Syène (Aswan), located 5,000 stades due south of Alexandria, the sun stood directly overhead at noon on the spring equinox because its light then reached the bottom of a deep well. So one spring equinox around 240 B.C.E., he simultaneously measured the solar height at noon in Alexandria by means of the shadow cast by an upright stick, and found it to be 7.2 degrees from vertical, or approximately one fiftieth of the total circle of 360 degrees. From this, he deduced that the earth’s circumference was fifty times greater than the 5,000-stade distance between the two towns, or 250,000 stades. Not a bad estimate, given what we know about the length of the stade.