The most magnificent prizes are reserved
For those whom mathematics serve.
For triangles connected at enormous cost,
Never to be renounced, whether true or false.
. . . . . . . . . . . . . . . . . . . . . . . . . .
Have they decreed new weights and measures?
Subjected old folks to the latest tortures?
To hoist a pint, or cut a yard of cloth,
Or adjust the hands on the family clock
Was the arc of the meridian really worth it?
We can cut our fabric without measuring the earth;
And if our calculations are not free of error,
To break old habits is still false rigor.
—LOUIS SÉBASTIEN MERCIER, Satires on Astronomers, 1803
Méchain returned to a hero’s welcome. He scarcely had time to clean himself up before he and Delambre were ushered in to a formal banquet hosted by the President of the Directory, the Minister of the Interior, the Minister of Foreign Affairs, and the entire Academy of Sciences, all of whom were lined up to offer their collective (if belated) greetings to their prodigal expedition leaders and the visiting savants, obliging Méchain to accept their heartfelt congratulations, “which they presumed I deserved,” he remarked, “for the completion of my mission.” It almost pained him to admit it, but his colleagues even offered him “a demonstration of their most tender friendship, expressing satisfaction with the accomplishments of the past and confidence for the future.” And this was not all. In the days that followed, they confirmed his elevation to the directorship of the Observatory, the highest honor in French astronomy. They elected him temporary president of the Bureau of Longitudes. They crowned his head so high with laurels that he dared not look behind him.
“The first days are always glorious and festive,” Méchain confided to his friends in Carcassonne. “Those that follow will be the days of trial. . . . Will I then be able to fulfill the expectations for which they honor me now?”
In his absence, Paris had changed. If its buildings were recognizable, their inner purpose had been reconsecrated. The same might be said for its inhabitants. The Panthéon had become a national mausoleum; the old nobility had given way to a new notability; and the Méchain family had moved out of the little house on the edge of the gardens and into the redecorated Cassini apartments in the main Observatory, where Méchain now ruled in the Cassinis’ place. His children had grown up. His youngest boy had been six when he left; he was now thirteen and wanted to be an astronomer like his father. His oldest son had departed on a geodesic expedition of his own, working as an astronomical aide on Napoleon’s expedition to Egypt. While Méchain had been traveling far from home for seven years, those he had left behind had traveled further still.
After months of delay, the world’s first international scientific conference could begin. The preeminent savants of all the nations of Western Europe—all those nations, that is, allied to France by conquest or watchful neutrality—had gathered in Paris to settle together the true length of the meter. These were not men who could be easily fooled, and who would try?
It was Laplace—the most eminent of them all—who had first proposed the conference. It would guarantee, he said, the metric system’s universality. Let the final determination of the meter be set by an International Commission, and it would dissipate any lingering “jealousies” caused by the decision to base the meter on a meridian that ran through France alone. Let the foreign savants consider the metric system their own work, and they would ensure its spread to foreign lands. Privately, of course, Laplace assured Delambre that the gathering was a “mere formality.” As the basic parameters of the metric system had all been set in advance, the foreign savants would come to Paris simply to rubber-stamp the preordained results.
Not all the French expected their guests to be so docile. Commander Borda, the prime mover behind the meridian expedition, objected to the conference. If the meridian expedition had produced a meter based in nature, why did it need the imprimatur of the savants of all Europe? The truth did not care who spoke on its behalf.
But Laplace’s proposal found two powerful backers. Minister Talleyrand, the perennial master of French foreign policy, was still committed to metric reform as a tool of international diplomacy, although France was now in a position to command rather than beseech. Where Talleyrand had once proposed that Britain and France cooperate on the new measures, his Foreign Office now invited only savants having “at heart not only the progress of the arts and sciences, but also the glory of the nations prepared to collaborate in this undertaking.” The British were pointedly excluded.
Laplace’s other ally was the most junior member of the Academy of Sciences. Ordinarily, a young academician would not dare to intervene in such a momentous controversy between his seniors only one month after his election, but Napoleon Bonaparte was an extraordinary academician on several counts. For one thing, he had never published a scientific paper. His main claim to scientific fame was the fact that he had been Laplace’s examination pupil at artillery school. He had no pretensions to original invention or research. Rather, Laplace had advanced his candidacy (over the marvelous Lenoir, among others) in the hope of allying the Academy to France’s rising political star.
For his part, the general had political ambitions, and science was part of his campaign. He did not merely cultivate the sciences, he cultivated the savants. He returned from his Italian conquests bearing Renaissance art and the latest theorems. He strode into Academy meetings to the applause of men and the cheers of women. He was no wilting Méchain, cowering from praise. In the throng after the meeting, Delambre expressed surprise that the general was back in town again so soon. “I am indeed, and will dine with you tomorrow if you so desire.” Over dinner, he spread his napkin on the table to diagram a new geometric proof from Italy. “My dear General,” fawned Laplace, “we have come to expect everything from you, except a lesson in mathematics.” He was the universal man: blending thought and action, science and romance, inspiration and planning. He was as delighted as a child with his election to the Academy, and intervened immediately in its affairs. An international scientific conference on the meter dovetailed nicely with his own vision of a Europe unified under French leadership.
Invitations had gone out in June 1798 to savants from the Netherlands, Denmark, Switzerland, Spain, and the Italian republics; those nations, in other words, which would form the nucleus of the League of Armed Neutrality directed against Britain. None of the savants of Britain, America, or the German states was invited.
From the beginning, the French had expected America—their sister republic—to be the first country to join the metric system. They had been delighted when Jefferson dropped his preference for a pendulum standard at the 38th parallel (near Monticello) in place of a standard at the 45th (near Bangor, Maine), clearing the way for trilateral Franco-British-American cooperation. In 1792 a committee of the United States Senate even recommended this pendulum standard as the national unit of length. But when the French savants switched to a meridian standard that traversed France alone, Jefferson became convinced that the French show of internationalism was a sham. Congress put off any consideration of the legislation.
The French did not give up so easily on America, however. Soon after the passage of the metric law of 1793, they dispatched the naturalist-explorer Joseph Dombey to convey the new (provisional) standards to the United States in the form of a copper meter stick and a kilogram weight. In January 1794 Dombey set sail from Le Havre on the American vessel The Soon. Unfortunately a storm drove him to the Caribbean, to the fractious French colony of Guadeloupe. From there, his mission went from bad to worse. Local plantation owners imprisoned Dombey as an emissary of the radical Jacobin government. Released upon threat of violence by those loyal to Paris, he disguised himself as a Spanish sailor and boarded a Swedish schooner, only to be captured by British corsairs and escorted to the prison island of Montserrat. There he died of illness in April.
Miraculously, Dombey’s papers and the precious copper meter bar and kilogram weight arrived safely in the United States (where they are still preserved in the Museum of the National Institute of Standards and Technology) and the French ambassador took up Dombey’s mission with enthusiasm. Ambassador Fauchet said he was delighted to learn of the metric reform and expressed his confidence that “an enlightened and free people would receive with pleasure one of the discoveries of the human mind, the most beautiful in theory, and the most useful in application.” By this he meant the French people. He also hoped the adoption of the metric system in America would “cement the political and commercial connexions of the two nations.” His hopes were echoed in newspaper editorials urging all Americans—or at least, all educated Americans—to adopt the rational French measures voluntarily.
For a time, success seemed within reach. Fauchet was friendly with President Washington, who was friendly toward France, and the President asked Congress to reconsider the metric system. Washington had stressed the great importance of uniform measures in all three of his earliest State of the Union addresses. Although this sort of repetition is almost always a bad omen, Fauchet still held out hope. In a coded letter sent back to Paris, he noted that American adherence to the metric system might well prove advantageous to France. “Would it not make the People here more French if they shared in our knowledge; would it not bind them closer to us with commercial ties if they were subjected to our System of weights and measures?” He did worry, however, that Congress, having learned that the measures were merely “provisional,” would deliberate and delay “as they so like to do.”
While Congress dithered and America began a diplomatic rapprochement with Britain, Fauchet recklessly supported the Whiskey Rebellion, as a prelude to a great Jacobin revolution in the United States. This infuriated President Washington and prompted Fauchet’s recall to Paris. Six months later the House of Representatives voted to adopt national standards based on a modified version of the English foot and pound. These were not the ordinary foot and pound, but standards fixed by scientific experiment, and divisible into subunits of ten. The Speaker of the House urged passage. So long as each former colony had its own standards of weights and measures, national commerce would remain uncertain. This time, it was the Senate that killed the legislation by inaction.
Would it have helped if Delambre and Méchain had completed their mission in 1794 as planned, and the meter had been declared “definitive”? Or if Fauchet had been more prudent? It is hard to imagine that anything could have saved Americans from two hundred years of fruitless debate. Jefferson understood this very well. The United States Congress, he acknowledged, was dominated by a mercantile class hostile to France and fearful of surrendering their customary English units. On a question so immediate to their commercial interests, their views would always predominate.
For its part, the British Crown had been trying to reform its weights and measures for as long as the French, with as little to show for its pains. The Magna Carta’s lofty promise of uniform measures had been buttressed by stern parliamentary decrees and reaffirmed by the Article of Union between Scotland and England, without curbing a diversity as confounding as the languages of Babel. Travelers needed to learn a new language in every parish or market town, one which “no Dictionary will enable us to acquire.” The apothecary, the silversmith, and the wool merchant all spoke distinct measurement dialects. The county of Hampshire alone had three different acres, plus a different bushel in each market town. This diversity produced “cabal, delay, fraud, anxiety, and indeed everything hostile to the good faith and confidence which ought ever to subsist between buyer and seller, agent and principal.” “Knaves and cheats” forced the poor to sell wheat in a large bushel and buy back bread in a small one. Indignant administrators condemned these practices as iniquities—which by the rules of transparent exchange they no doubt were—although the local people undoubtedly considered them integral to the just-price economy, which prevailed in much of Britain as well.
British men of science, like their Continental brethren, added their voices to the call for uniform measures. Since the days of John Locke and Christopher Wren, members of the Royal Society had proposed standards based on nature, such as a new “yard” defined as a pendulum beating at one-second intervals in the Tower of London (equal to 39.2 inches). And in the eighteenth century the new thinkers called “economists” likewise championed uniform measures as a spur to commerce.
Then in 1789 an obscure Member of Parliament named Sir John Riggs Miller urged the House of Commons to coordinate its metric reform with the French National Assembly. Miller convinced Talleyrand to allow the pendulum to be measured at a site jointly determined by British and French savants. In Europe’s antique universal language, he expressed this antique universal dream.
Una fides, pondus, mensura, moneta, fit una,
Et flatus illaesus totius orbis erit.
One faith, one weight, one measure, and one coin,
Would all the world in harmony conjoin.
The hard part about harmony, of course, is getting everyone to sing in tune. Since almost any standard will do equally well, so long as everybody agrees on it, everybody prefers that someone else make the change. Miller faced this obstacle both at home and abroad. Each of Miller’s learned allies within Britain had his own idiosyncratic view of which standard would be best. And collectively, Parliament expected the French to follow Britain’s lead, especially now that the French embrace of constitutional monarchy would cause them to be “emancipated from national prejudices.”
So when the French switched to the meridian standard, it killed the enthusiasm of even the most sympathetic British savants. Charles Blagden, Méchain’s collaborator in the 1788 Greenwich–Paris survey, saw the Dunkerque-Barcelona project as a transparent bid to exclude all other countries from any say in the new measure. Once the war broke out, the British press began mocking the metric system as another instance of Republican rationalism run amuck. Miller’s proposal died in Parliament.
The same problem kept the Germans at home. The patchwork sovereignty of principalities that had multiplied measures in what later became Germany also precluded any centralized solution there. Besides, the German savants likewise preferred a standard based on the pendulum to one based on a meridian whose value, they noted, depended on who conducted the measurements, and where, and with what instruments. It was just this sort of discontent that the international conference was supposed to pacify.
War kept the British, American, and German savants at home, but France’s victories on the Continent made it impolitic for her neighbors to refuse her invitation. Bonaparte had brought the Italian peninsula under French rule. French occupation had reconstituted the Low Countries as the Batavian Republic. Spain had been forced into a sullen neutrality. Switzerland had been refashioned by the French as the Helvetian Republic. And the left bank of the Rhine had been rechristened the départements réunis, “reunited” to greater France first militarily, then politically, and now cartographically through the geodetic labors of engineer Tranchot.
With meter sticks and maps, the French would manage an empire, uniting the tools of commerce and military might in the form of a geodetic meter based on the size of the earth. A transnational metric system would mold the European economy into a Continental bloc, while “an army of astronomers,” outfitted with repeating circles, would assimilate all the nations of Europe to a single grid. As Delambre put it: “Now that the use of the repeating circle has spread throughout the Continent, one may hope that all Europe will soon be covered with triangles.” Indeed, the French were determined to extend their new metric revolution right around the globe.
Bonaparte was not in Paris for the conference he had helped to convene. The modern Alexander the Great—the world conqueror and world civilizer—had left France on the most exotic metric expedition of all: the invasion of Egypt. At the core of his force of 54,000 soldiers and sailors was an “academy” of 167 savants, including mathematicians, naturalists, chemists, and geodesers. Their goal was both imperial and geo-scientific: to supplant a British Levant with the French civilizing mission and to reclaim antique civilization with the tools of modern science. Among the savants was the twenty-year-old Jérôme-Isaac Méchain, an astronomical assistant to abbé Nouet, the former monk Méchain had trained at the Observatory. Lenoir’s son had come along, too, to make any repairs needed on the team’s repeating circle. While Méchain the father triangulated his way through the south of France, Méchain the son mapped an empire: from Marseille to Malta to Alexandria, then up the Nile to Cairo. While the father sighted wooden pyramids in the Montagnes Noires, the son triangulated the Great Pyramid at Giza. While the father agonized in his monastic retreat at Saint-Pons, the son struck out with an expeditionary force for the fount of all scientific knowledge.
In the summer of 1799, a team of Napoleon’s savants headed up the Nile to Syène (Aswan), famous, as the expedition leader noted, for “its proximity to the Tropic of Cancer and the measurement of the earth conducted by Eratosthenes.” There, on the island of Philae, where the cataracts of the Nile poured from red granite cliffs, the savants carved their global position on the wall of the Temple of Isis:
LONGIT. DEPUIS PARIS, 30°34'16"
LATITUDE BOREALE, 24°1'34"
Among the sixteen savants who scratched their name below was the young MÉCHAIN.
Geodesy would not only colonize the globe, it would colonize time. Built into the embankment of the nearby island of Elephantine, the expedition discovered the “Nilometer,” an ancient standard of length that gauged the great river’s height. Comparing this ancient measure with the new meter seemed to suggest that Eratosthenes’ estimate for the size of the earth had come within 0.4 percent of the modern value. And when they looked even further back in time, to the origins of Egyptian civilization a full three millennia earlier, the French discovered something more remarkable still: evidence that the ancient Egyptians had also derived their standard measures from geodesy, building them into the design of the Great Pyramid at Giza. There really is nothing new under the sun. Already some Ancien Régime astronomers had speculated that the Egyptians had derived their standard unit of length from the base of the pyramid, itself said to be 1/500 of one degree of the circumference of the earth. Now the expeditionary savants had discovered evidence that the perimeter of the Great Pyramid measured 1,842 meters, which came to within a miniscule 0.5 percent of the value of one minute of the earth’s meridian. Peering into antiquity, the savants saw their own origins reflected back at them. Whether this was a coincidence or not, no one was prepared to say.
The invasion was an imperial fiasco. Nelson destroyed the French fleet at the Bay of Abukir, Napoleon slouched back to Paris, and his geodesers were left up the Nile. But the invasion proved a scientific success. The expedition mapped a possible canal through the isthmus of Suez. French archeologists unearthed the Rosetta stone. And by agreement with the British, the remnants of the expedition, young Méchain among them, sailed back to France in October 1801, with their invaluable logbooks.
Other Frenchmen, meanwhile, were extending their metric rule even further afield. Where the diversity of measures had once hampered colonial trade, the metric system would coordinate a new overseas empire. During the Ancien Régime, the residents of then-French New Orleans had complained that ship captains often shorted their deliveries of flour, beef, lard, and wine. The captains had always responded that these were not short measures, merely different measures. Not to be outdone, the colonists ran the deceit in reverse. Merchandise often arrived short-weighted from the Americas “where they say trickery and bad faith are contagious.” The Crown ordered all parties to use standard barrels, filled to within one sixteenth of true weight. But the official measurement bureaus—established to levy taxes and stop smuggling—never monitored more than a tiny portion of the colonial traffic. The metric system now promised to integrate the Caribbean colonies with the mother country, rationalizing transatlantic trade, just as the meter would tame the world.
Already the French state had dispatched circumnavigators armed with Borda’s repeating circles to chart the globe. Between 1785 and 1788, the Crown sent La Pérouse to explore the Pacific coast from Alaska to California, and then across to Asia and Australia. He sent back reams of precision data before ultimately vanishing in the Indian Ocean. Between 1791 and 1794, the Republic sent Entrecasteaux on a mission to learn the fate of La Pérouse. He charted the Indian Ocean and some of the South Pacific archipelagoes before succumbing to disease. In the short run the French metric empire failed, but it would return.
This project of global coordination depended on making the meter “definitive.” Making the meter definitive meant that the International Commission had to guarantee its precision. So the Commission focused its attention on the exactitude of Delambre and Méchain’s seven-year mission.
But as yet Delambre and Méchain were not ready to present their data—or at least Méchain was not. In the meantime, then, as a pledge of their exactitude, the French offered to stage a “theater of precision” under the Commission’s supervision, pitting Delambre against Méchain in a friendly competition to determine the latitude of Paris. Paris was one of those “superfluous” latitudes chosen to exhibit the curvature of the earth as it arced from Dunkerque to Barcelona. Each astronomer would measure the capital’s latitude from his respective site: Delambre from the rooftop of 1, rue de Paradis, and Méchain from the rooftop of the National Observatory, which he now directed. Both men would then adjust their measurements to converge on the Panthéon: offering “authentic proof” of the excellence of the repeating circle and the skills of the savants who wielded it.
The great dome remained essentially unchanged, a testament to the royal state’s engineering prowess and magnificent investment. But the meaning of the building had been altered—again—along with slight changes in the decor. Delambre’s old crow’s-nest observatory had been torn down. The 52,000-pound statue of Fame had been declared too burdensome for the dome to support. Mirabeau, the first man to be panthéonized—and the first to be de-panthéonized—was now supposed to be re-panthéonized—except that no one could find his body. Descartes, France’s greatest savant, was also being reconsidered for the honor.
Delambre and Méchain both began observing on December 7, although they did not embrace their roles with equal enthusiasm. In addition to the faithful Bellet, Delambre was also assisted by Charles de Pommard, the son of Elisabeth-Aglaée Leblanc de Pommard, a longtime intimate of Delambre and a gifted scholar of Latin in her own right, “learned . . . , but not pedantic.” She and her son now resided on the rue de Paradis with Delambre, who doted on the boy. He was already six feet tall, with gray eyes and chestnut hair, and Delambre thought he combined “much intelligence with a great love of work.” The young man hoped to become an astronomer—or at least that was Delambre’s fond hope. Each night that winter, they climbed to the rooftop above the Marais to observe the stars. Each morning, Delambre handed down their nighttime observations to the International Commission.
Méchain did no such thing. He held fast to his data, as he always did—and in return the data tortured him, as they always did. After twenty nights and five hundred sightings, he announced that he would have to start from scratch. His data were inconsistent. This time it was the wintry cold of northern France that was apparently to blame, rather than the heat of Catalonia. His assistant seemed incapable of maintaining the level of the instrument. Or perhaps the refraction correction was askew. In any case, it was all too much. He was despondent, distressed, desperate. To Delambre, he complained that if he did not get acceptable results soon, he would “renounce it all.” To Borda, he admitted that his results were unacceptable, while “Delambre obtains results that are as consistent as one could wish.”
The self-doubt that had stalked Méchain through the mountains of southern France had followed him to Paris. Melancholic comparisons sapped his confidence. Every morning he learned that Delambre’s results had arrived on the Commission’s desk. And every evening he searched for“the hidden defect” within his data and within himself. He began to avoid his colleagues. He skipped meetings of the Academy of Sciences and the Bureau of Longitudes, over which he nominally presided. He even stopped attending sessions of the International Commission. He announced he was too busy gathering new data to discuss old results.
The Commission began to schedule its meetings at the Observatory so that Méchain could not avoid them. Delambre had to stall to protect his colleague. In an attempt to drag out the process, he revisited observations long after the results had stabilized. Méchain, meanwhile, refused to hand his data over for others to sort out. No matter how great his anguish, he insisted on bearing the burden of precision himself. Anything else was an abdication of his responsibility. He was not some lackey who had been sent to gather chestnuts, but a savant entrusted to make delicate judgments. He was not a menial technician, but an emissary of the Academy, whose integrity underwrote his observations. He knew better than anyone which values were valid and which were not. It was his duty to choose. . . . But which would he choose: Mont-Jouy or the Fontana de Oro? A full confession or an admission of failure?
As the delays piled up, rumors began to circulate. The foreign delegates were not as docile as Laplace supposed. The Danish Royal Astronomer, Thomas Bugge, had been the first foreign savant to arrive in Paris. For three months, while he waited for Delambre and Méchain, he had been forbidden to begin his own calculations. The Academy expressly forbade all savants to publicly release their own estimates of the meter in advance of the official report. Bugge had begun to feel he was being used. He heard Lalande privately dismiss the whole operation as “a charlatanism of Borda.” Now, three months after Delambre and Méchain had returned, the Frenchmen had yet to present their geodetic data. Whisperers made slanderous accusations: the data were wretched, the mission had been botched. If the conference was not concluded by January, Bugge declared, he would return to his duties back home.
When rumors circulate through the world of cosmopolitan science, they circulate far and fast. A German astronomer wrote to Lalande with evident schadenfreude of “the scandal of the new measurements.” He had heard from Bugge that the expedition’s value for the curvature of the earth was apparently implausible and its geodesic measurements were “worthless, poorly executed, inconclusive, and untrustworthy—which pains me greatly.” “These shameful aspects of astronomy are best kept hidden,” he purred with thinly disguised glee. Nearer to home, an obscure amateur astronomer from the French provinces wrote to Delambre to express condolences that his “zeal and skill had not produced satisfactory results.” Although he did not know the astronomer personally, he offered him this consolation: “You have been poorly seconded.”
When January ended without Delambre or Méchain presenting their data, Bugge acted on his threat. No sooner had he left for Copenhagen than he was attacked in the Paris press for “ridiculing” the metric project. Yet his departure provoked the French into action. Delambre stopped covering for his colleague and formally presented his own data to the International Commission on February 2, 1799. It was an all-day ordeal. The Commissioners went through each page of his logbook, querying each station, vetting each observation. In the end, they accepted almost all his data, including some results Delambre himself doubted. But as he himself noted, once data were recorded they became a sacred thing. At this remove from the time and place of observation, it was no mean feat to distinguish a flawed from a valid result. The commissioners had no choice but to trust the logbook and accept its inky assertions, no matter what the author himself now said. By the day’s end, Delambre’s triangles from Dunkerque to Rodez had been officially endorsed, as had his latitude data for the northern anchor at Dunkerque. Méchain was next.
A few days later, Laplace himself paid a private visit to the Observatory. He had come to deliver an ultimatum. Méchain had ten days to hand over all his data. No further delay could be tolerated.
It is easy to picture Méchain’s reaction: his eyebrows hitched high in supplication, his eyes searching for some sign of sympathy from a man who could see right down to the whirling nebula of dust that had formed the solar system. There was nowhere left to hide. Every excuse was worn out, every academic courtesy exhausted. Méchain’s moment of trial had come. So he agreed to present his data “without fail” in ten days, under one condition. Rather than supply his original logbooks—which he admitted were in a state of disarray—he would present the summary results for each station as corrected by the usual formulas. To this, Laplace secretly agreed. That was how badly the Commission needed Méchain’s data.
In the intervening ten days, Méchain discovered that a loose screw on his lower scope had been responsible for his erratic data, or so he informed the Commission. His results had now begun to converge, and he promised to make his presentation ten days hence. Indeed, they were approaching within 0.13 seconds of Delambre’s. It was a stunning display of observational prowess. By locating his position on the surface of the earth to within thirteen feet, Méchain had demonstrated that, in the right hands, the precision of the repeating circle was limited only by the observer’s patience. Naturally, the Commission agreed to wait.
Ten days later he was still not ready to present his data. And ten days after that, he postponed the meeting again. Then, finally, on March 22, Méchain presented the results of the southern expedition.
He arrived for the all-day session with his results copied out in a beautiful scribal hand. The commissioners subjected his results to the same ordeal that Delambre had faced. The angles for each station from Mont-Jouy to Rodez were vetted individually before being officially accepted. At times, Méchain considered the review “a bit severe.” But in the end the Commission was compelled to congratulate Méchain for the remarkable consistency of his triangles. As for his latitude data from Mont-Jouy and the Fontana de Oro, they too were found to be in superb order, and in remarkable conformity with one another. Indeed, their conformity was so great that, at Méchain’s request, the International Commission agreed to set the Fontana de Oro data aside as redundant, and use only the data from Mont-Jouy.
Just like that, the nightmare lifted. His anxieties, his fears, and his sense of inadequacy, all evaporated like phantasms. The International Commission had recognized his work as a masterpiece of astronomical precision. Indeed, one of the foreign commissioners privately approached Delambre to ask him why his results were not as precise as Méchain’s. The tables had turned. Méchain had triumphed.
All that remained was to boil down those concatenated results into a single number: the meter. For the next few weeks, each commissioner calculated independently, using his own preferred method. The mathematician Legendre deployed refined calculations using ellipsoid geometry. The Dutch astronomer Jan Hendrik Van Swinden made use of traditional geodetic techniques. Delambre employed improved methods that he had recently published.
Borda was not present for these final calculations. The inventor of the repeating circle and the guiding force behind the meridian project did not live to see the meter become definitive. During Méchain’s final procrastination the old commander, after a long illness, died. In a pounding rain, a cortège of international savants bore his body up a muddy road for burial below Montmartre. His legacy was a conundrum.
As each savant completed his geodetic calculations, it became increasingly clear that the rumors were justified: something was wrong. The meridian results were shocking, unexpected, inexplicable. Against all odds, the meridian expedition had produced something unanticipated: genuine scientific novelty.
This had never been their intention. Delambre and Méchain had not been sent out to unearth new knowledge. They had been sent out to refine to a nicer degree of exactitude what was already known. But the world, they had now discovered, was more eccentric than anyone supposed. Was it a scandal, or a discovery?
According to the data gathered fifty years earlier in Peru and Lapland, and confirmed by Cassini III in France, the eccentricity of the earth was approximately 1/300—which is to say that the earth’s radius at the poles was 1/300 (or 0.3 percent) shorter than its radius at the equator. By contrast, Delambre and Méchain’s data for the arc from Dunkerque to Barcelona suggested that the eccentricity was 1/150, or twice as great. Even more startling, when the Commission plotted the curve tracked by the intervening “superfluous” latitude measures at Dunkerque, Paris, Evaux, Carcassonne, and Barcelona, they discovered that the surface of the earth did not even follow a regular arc, but shifted with every segment. It was a stunning discovery. But what did it mean?
The reversal clearly delighted Méchain. It was a vindication of sorts. His colleagues would now regret their refusal to let him triangulate as far as the Balearic Islands or take additional latitude measures. He took the experimentalist’s perverse joy in baffling his theoretical colleagues—Laplace most of all. He gloated that “the earth has refused to conform to the formulas of my mathematical colleagues, who have insisted until now, with absolute certainty, that it is a perfectly regular spheroid of revolution.” It was perhaps Méchain’s one true moment of joy in the entire expedition. It was also a moment of great discovery, as he wrote to his Carcassonne friends.
Our observations show that the earth’s curve is nearly circular from Dunkerque to Paris, more elliptical from Paris to Evaux, even more elliptical from Evaux to Carcassonne, then returns to the prior ellipticity from Carcassonne to Barcelona. So why did He who molded our globe with his hands not take more care . . . ? That is what they cannot comprehend. How did it happen that by the laws of motion, weight, and attraction, which the Creator presumably decreed before He set to work, He allowed this ill-formed earth to take this irregular shape for which there is no remedy, unless He were to begin anew?
Progress, as so often happens, had slipped in sideways where least anticipated. Unexpectedly, the meridian project had produced new and baffling knowledge. Instead of a spherical orange of an earth, or even an oblate tomato of an earth, the geodesers now discovered that they lived on a lumpy squash of an earth.
Everyone knew that the earth was not a perfectly smooth surface, everywhere becalmed at sea level. For a hundred years, savants had known that the figure of the earth was not a perfect sphere but was flattened at the poles. For the past few decades, they had begun to suspect that its figure was not even an ellipsoid but rather some more complex form of ovoid. Now they had discovered that its shape was not even that of a curve of rotation, a well-defined figure turned symmetrically on an axial lathe. They had discovered that we live on a fallen planet, a world buckled, bent, and warped. And they had discovered this only because they were seeking perfection. Examined from a great enough distance the earth appeared to be a sphere. Move in closer and it appeared flattened at the poles. Closer still—at the stunning level of precision achieved by Delambre and Méchain—and the earth was not even symmetrical enough to be approximated by a curve rotated through space. Delambre and Méchain had discovered that not all meridians were equal. The meridian that ran through Paris was not the same length as the meridians that ran through Greenwich or Monticello or Rome.
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 anaune 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 thethinking 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 adequately 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.
As for Napoleon, he refused to learn the metric system. Inspecting a gunpowder factory in Essonnes, he quizzed the plant’s manager about the chemical processes in considerable detail. But every time the manager supplied him with a weight in kilograms, Napoleon insisted that he restate the formula in poids de marc (old-style pounds). He said he could not think in the new units.
Faced with this obstinacy, the government temporized even as it persisted. One year after the meter was made definitive, the first compromise was made. On November 4, 1800, the metric system was at last declared to be the sole measurement system for the entire nation, and the use of the nomenclature of compound words—decimeter, kilometer—was abolished. The meter was still the meter, and its use would be obligatory throughout the nation as of September 1801. But the Greek and Latin prefixes “which frightened the people” were replaced with “ordinary names.” After consultation with Laplace and Delambre, the decimeter was renamed the palme (the hand-breadth), the centimeter the doigt (the finger-breadth), the millimeter the trait (the trace), and so on.
The instigator of this compromise was none other than Napoleon Bonaparte, back from Egypt. To honor their colleague’s return, the Academy had struck a commemorative medal from the residual platinum left over from the making of the meter. That way, they said, the medal would last“almost as long as your glory.” Thirteen days after accepting the medal, Napoleon seized absolute power in the coup d’état of 18 brumaire—and held it for the next sixteen years. One of his first acts was to make his old mathematics examiner, Pierre-Simon Laplace, Minister of the Interior, with responsibility for enforcing the nation’s laws and the metric system. The savants, it appeared, had bet on the right general. Imagine their dismay, then, when they learned of his compromise. Laplace tried to reassure his colleagues: a retreat on the nomenclature did not imply that the entire system would fail. Lalande smirked, “Monsieur Laplace is not in his place.” After only forty days in office he was turned out in favor of Napoleon’s brother. Other retreats were to follow.
The French were not only the first nation to invent the metric system; they were also the first to reject it.