The Measure of All Things

by Ken Alder

  To some extent, even this startling discovery was not entirely unanticipated. Laplace himself, the foremost theoretician of geodesy, had occasionally wondered whether the earth was in fact a perfect spheroid of revolution, as all his models supposed. And Roger Boscovich, the Jesuit geodeser who had surveyed the Papal States in the middle of the eighteenth century, had already suggested that the meridian through Rome did not have the same curvature as the meridian through Paris. Indeed, this doubt had been one of the secret motives for the meridian expedition in the first place, and why the savants had added the “superfluous” latitude points. Not that the savants had ever admitted as much. “Sometimes to serve the people,” one savant privately acknowledged, “one must resolve to deceive them.”

  There was only one problem. This great discovery invalidated the guiding premise of the entire mission.

  Delambre and Méchain had been sent out to measure the world on the assumption that their meridian, standing in for all the earth’s meridians, could furnish an invariant and universal measure. Now they discovered that the world was too irregular to serve as its own measure. To be sure, Delambre and Méchain had surveyed only one meridian. That one meridian, however, was sufficiently irregular to suggest that every other meridian would also be irregular, each in its own way. In any case, there would be no simple way to extrapolate from their one small sector of the meridian to the whole, which was the task they now confronted.

  In that sense, the results were a scandal. But then again, truly new knowledge almost always is.

  The members of the International Commission now faced a stark choice. They could extrapolate from the Dunkerque–Mont-Jouy arc to the full quarter meridian using either the new eccentricity of 1/150, or the older eccentricity of 1/334. They had every reason to believe that the eccentricity of 1/150 offered the best description of the arc as it passed through France, but they knew that the older data offered a more plausible picture of the overall curve of the earth. They could choose consistency or plausibility. And after some heated discussion, they chose plausibility and the old data. Delambre and Méchain had been sent out to remeasure the world with supreme accuracy, and in the end the single factor that made the greatest difference to the final determination of the meter was based on the very data they had been sent to supersede.

  The decision shaved a thin slice off the length of the meter. Where the provisional meter had measured 443.44 lignes, the definitive meter measured 443.296 lignes. The difference of 0.144 lignes (or about 0.325 millimeters, or 0.013 inches) may seem insignificant, about the thickness of three sheets of paper. But it was considerably more than the uncertainty Borda had anticipated. And as paper stacks, so did that difference: it added up to a change of some two miles (3.25 kilometers) in the total quarter meridian. It was also, we now know, a step in the wrong direction. The definitive meter deviates twice as much from what we now know to be the size of the earth as does the provisional meter. Seven years of labor had only succeeded in making the meter less accurate.

  The final step was to embody the meter in a permanent physical standard. Copper had been sufficient for the provisional meter, but for the definitive meter only the ultimate metal would do. Long despised as a contaminant by South American prospectors, platinum was impossible to melt, difficult to purify, and nearly indestructible. For just that reason it had acquired a lustrous reputation among savants. It promised to outlast time. Just before the Revolution, an arsenic process had been discovered that made platinum sufficiently malleable to shape into snuffboxes and ornamental vases. After the Revolution, a grander purpose had been found for the new metal: the creation of permanent metrical standards. The Commission of Weights and Measures spent one fifth of its budget buying and refining some one hundred pounds of pure platinum. Even so, the Commission nearly missed its quota. The final shipment from Spain had been short-weighted by 15 percent, and the commissioners had to scramble to replace the loss.

  It fell to Lenoir to make the final cut. The dwarfish artist was now fifty-five. His repeating circles had made him world famous, a peer of the best instrument-makers of London. In April 1799 he was supplied with the calculated value of the definitive meter and four bars of pure platinum, and told to shape four standards of precisely one meter each. For this purpose he employed a “comparator” of his own invention, which could gauge objects to within one millionth of a toise (0.000072 inches). The task was “diabolically tricky.” Of the four bars, the one that came closest—within 0.001 percent of the proper length—was selected as the definitive meter.

  In a grand ceremony held on June 22, 1799, this platinum bar was presented to the French legislative assemblies so that the people’s elected representatives could add the consecration of man’s law to that of nature. It was a solemn ceremony, the occasion for speeches of global import. Laplace reminded his audience that a meter based on the size of the earth made every landowner a “co-owner of the World.” And the Dutch astronomer Van Swinden expressed gratitude for the iron facsimile that each foreign savant would carry back to his homeland to help “tie together” the peoples of Europe “with fraternal bonds.”

  Needless to say, no one mentioned the unexpected discovery of the eccentricity of the world, nor its subversion of the seven-year project. And no one mentioned the fact that the platinum meter bar and kilogram weight would have to be whisked back to Lenoir’s workshop after the ceremony for further preparation and not returned to their triple-locked box in the National Archives for another nine months. The making of science—like the making of laws and sausages—was best kept out of public view.

  But beneath the grandiloquence, it was easy to detect an undertone of plaintive hectoring. Everyone in the chamber that day knew the French people had yet to embrace the new measures. The problem, they all agreed, was not that the people were secretly loyal to the Ancien Régime. The problem was that the people were still attached to their old routines. The president of the Assembly sadly cited this wise saying of Jean-Jacques Rousseau: “Men will always prefer a worse way of knowing to a better way of learning.”

  In the months that followed, the legislature ordered its citizens to start learning. This task of instruction fell mainly to the Agency of Weights and Measures. The Agency’s directors included the gifted mathematician Legendre, plus administrators committed to a free-market economy. For several years now they had sought to inspire their fellow citizens with their own passion for the new measures. Even bureaucrats can believe in what they are doing. “I dream only of weights and measures now,” one said.

  Over the previous five years, the Agency had distributed tens of thousands of pamphlets to persuade citizens of the law’s simplicity: some a hundred pages long, others broadsheets for shopkeepers’ windows. Prieur de la Côte-d’Or designed conversion graphs for those citizens who could read graphs. Commercial publishers had also sold guides to the new measures, including almanacs, paper dial-up “converters,” and educational playing cards. The Agency had also mortised marble-encased meters into the walls of prominent Paris buildings. (The last surviving example can still be seen on the rue de Vaugirard across from the Palais du Luxembourg.) The Agency had even hired a blind man named Duverny to lecture on the metric system under the archways of the Louvre. His message was simple: Justice is blind, the scales must balance, and the metric system is easy.

  THE FIVE OF HEARTS

  This Revolutionary playing card—the five of hearts—is named Quintidi after the fifth day of the week. The card informs us that when the sun is due south on the meridian the time will no longer read twelve o’clock, but five o’clock. It explains: “We reckon by 1, 2, 3, 4, 5 o’clock.” These cards were made by Jean-Pierre Bézu in 1792 in the town of Château-Thierry, then known as Egalité-sur-Marne. (From the Bibliothèque Nationale de France, Paris, Estampes)

  Finally, to help citizens cross into the new metric world, the Agency ordered each département in France to draw up a table to translate its old measures into the new. Lengthy as they were,
these tables overlooked much of the diversity of the Ancien Régime measures. Local administrators admitted that they had been unable to locate all the old “master” measures; that they had barely broached the multiplicity of land measures; and that they had necessarily suppressed all mention of the anthropometric practices that defined most Ancien Régime measurement. From these hundred or so tables, the Agency then compiled an abbreviated national summary so that “at last the French will no longer be strangers in France.” But the real danger was that they would no longer feel at home in their own parish. Where citizens had once needed a dictionary to travel from one town to the next, they now needed one to travel into the future.

  The Agency recognized it was not enough to produce pamphlets, marble-encased standards, and numerical tables; 25 million French men and women also needed to be able to lay their hands on ordinary rulers. Paris alone needed 500,000 meter sticks. Yet one month after the meter became the sole legal standard there, the Agency had only 25,000 sticks in storage. To spur production, it contracted with private manufacturers and transformed churches into factories. They promised to reward citizens who would invent machinery capable of cutting meter sticks “with precision and promptitude.” If anything was amenable to mass production, surely it was identical standards. But when citizens finally did track down meter sticks for sale, they found that rulers from the same shop differed by a millimeter or more.

  So far, the metric system applied only to the city of Paris. Yet even in the capital undercover police reported that merchants still sold cloth by the aune, if only because their customers preferred the slightly longer measure. Enforcement was impossible. Every time the police confiscated an aune and referred the violator to a criminal court, the criminal courts sent the case back to the police, who could only impose minor fines.

  One story making the rounds was the exception that proved the rule. Apparently, a woman from the Pelletier district of Paris had returned home one day from shopping for fabric thinking she had bought an aune of cloth, only to discover that she had received a meter. She went to Judge Delorme to complain.

  THE WOMAN: Monsieur—

  THE JUDGE (interrupting): What do you say? I am no Monsieur.

  THE WOMAN: I beg your pardon, Citizen! Last Sunday—

  THE JUDGE (impatient): What do you call Sunday? We have no such thing now.

  THE WOMAN: Well then, the—the—the Quintidi of the week.

  THE JUDGE (angry): You tire me with your nonsense! I know nothing of weeks.

  THE WOMAN: But, Mons—Citizen, I mean to say—the décade in the month of—of—April.

  THE JUDGE: Again your nonsense! April!

  THE WOMAN: Of floréal, I should say. I bought two ells.

  THE JUDGE (furious): Enough! You mean a meter. Go your ways. You still have your Sundays, your weeks, your months of April, your ells, and your Monsieurs! Get out of my court. You are an aristocrat!

  After September 1799, when the legislature introduced the metric system to the region surrounding Paris, complete confusion reigned. Police inspectors insisted on the new measures; customers preferred the old measures; and storekeepers stocked both. This invited the very abuses the new system was supposed to eradicate, giving shopkeepers yet another means of shorting customers. The Almanach des gourmands, the city’s premier guide to fine restaurants and up-market grocers, warned its clientele that butchers and bakers—especially by the Port de Saint-Honoré—were using the new measures to cheat customers, rounding up prices or dishing out smaller portions.

  Yet the savants still could not understand how the common people could reject the new measures. The new measures were derived from nature and reason; the entire system formed a logical whole. The members of the Agency warned its critics not to quibble with the new system:

  You cannot attack a part of the system without endangering the whole. Otherwise many different objections will follow: some will want a new nomenclature; others will want the meter to be based on the full circumference of the earth; still others will prefer the pendulum; and still others will revisit the idea of a duodecimal system to ease division, etc. . . . Now that the law is promulgated (after long deliberation), it is best not to attack it, but to give it the respect it is due. . . . There must not be any doubt about the goodness of the law.

  However slow their progress, the savants held out hope—the perennial hope of those already enlightened—that the next generation would see the light. They made instruction in the metric system obligatory in the nation’s schools, including the Ecole Normale, where the nation’s teachers themselves were trained. They assured their fellow citizens that the metric system would never be imposed by force or become an instrument of tyranny. The metric system, they said, “is simply a police measure to ensure the social order. . . . Neither our good pleasure, nor our full power are part of the lexicon of a reasonable people, whose enduring obedience will only follow if they are enlightened and convinced.”

  THE USE OF THE NEW MEASURES

  These cheerful Republican citizens are demonstrating (clockwise from top left) the proper use of the liter, the gram, the meter, the stere (the cubic meter), the franc, and the double meter. (From the Photothèque des Musées de la Ville de Paris, photograph by Svartz)

  This liberal creed, however, did allow for the possibility that public opinion was something the nation’s leaders could both interpret and direct. That is why the Minister of the Interior saw no paradox in his simultaneous assurance that “uniformity of measures has always been desired by the people” and his boast that the metric system, as designed by the nation’s leading savants, “would be a splendid instrument for molding public reason.” The goal remained the same: the metric system would transform the French economy and ease administration by transforming the thinking of French citizens, making them into rational calculators who conceived of their interests in a new way. No wonder this transformation was slow in coming. It was also vulnerable to shifting politics, as successive French governments reconsidered the role of the state in the economic life of the nation.

  Paradoxically, the only way the state could enforce the metric system was to reregulate the nation’s marketplaces. In 1799, a few months after the meter had been declared definitive, the government authorized each major market town to set up its own Bureau of Weights and Measures. Just as the state licensed pharmacists to prevent poisoning, so would the state now license a Bureau of Weights and Measures to prevent the metrical mistrust which was poisoning commerce. In return, each privately owned Bureau might charge a small fee for its services. To some, this signaled a return to the hated feudal dues of the Ancien Régime and a restriction on the absolute right to trade wherever and however one pleased. The Paris Bureau, run by Brillat and Company, was denounced as “despotic” and “tyrannical” after it sent hundreds of government troops into Les Halles to drive out the old-time weighers. Critics warned that the metric system would never take hold if the people were forced to use it at bayonet point. For their part, Brillat and Company claimed that these actions were needed to restore confidence to commerce, make trade fair, and prevent the metric system from being held up to ridicule. In this way, the new weights and measures became the wedge by which the government revived the distinction, familiar to the Ancien Régime, between the regulated public marketplace (limited in time and location, so that all might have equal access) and the unregulated free market.

  The metric system was not in itself a guarantor of free commerce (though some kind of uniform measurement system is usually a prerequisite). The metric system could just as easily be used to enforce the state’s regulation of trade. But in either case it was designed to break the hold of the old anthropometric measures and the old just-price economy.

  The French savants consistently overlooked the rational motives ordinary citizens had for rejecting the metric system: the disruption it caused to community norms, plus the fear of opening local markets to outside competition. In many cases the old units could not even be ad
equately translated into the new terms, since that would involve thinking of objects apart from the labor and materials that had gone into their making. This was something that many peasant and artisanal producers were understandably reluctant to do, whatever gain they might expect as consumers from transparency in business dealings.

  Indeed, it was not only conniving merchants and ignorant peasants who rejected the metric system. The nation’s most educated citizens clung to their old measures just as tenaciously. The old units had permeated the work routines of all French people, including government officials and professionals. For the numerate, it is worth repeating, numbers matter. Many French physicians, having just switched from a “medical pound” to a “commercial pound,” worried they would have to relearn all their dosages. In 1796 provincial notaries had yet to switch to the new system. In 1797 state surveyors had to be scolded for not using the meter. In 1798 accountants in the Department of the Treasury were still refusing to use the decimal system for sums of money. And in 1799 Paris administrators were still employing the old measures in their official correspondence. Even the national legislators continued to publish new laws in the old measures, in violation of their own laws. The ultimate irony came when the central Office of Weights and Measures shipped a set of the new metric standards to a provincial branch office and informed them that the total package weighed sixty livres, poids de marc (or sixty pounds, old-style).

  And as for those sectors of the economy where the change in measures meant retooling machinery or altering bureaucratic practice, resistance there was adamant. The artillery service, the branch of the military most committed to uniformity, precision, and modern manufacturing—and Napoleon’s old corps—had initially planned to publish a metric edition of their cannon blueprints, but the War Office called the publication too expensive. By 1801, the shoe was on the other foot, and the War Office was pleading with the artillery to adopt the metric units. But metric units, the artillery now complained, would ruin the mathematically precise ratio between the cannonball’s weight and its caliber, and would undo the uniformity of matériel they had taken such pains to establish.