The Measure of All Things

by Ken Alder

  The remaining clues to the mystery lay elsewhere, scattered not only across France and the sources Delambre preserved, but also in the records of the savants’ many correspondents in Spain, Holland, Italy, Germany, Denmark, England, and the United States, including a cache of Delambre’s papers which had mysteriously vanished from a French archive—along with the garbage, said the archivists—to find its way, via a London auction house, to the library of Brigham Young University in Provo, Utah. And finally, I tracked down something long presumed lost: Delambre’s own copy of his magisterial work, the Base du système métrique décimal.

  Those volumes are located today in the private home of David Karpeles, a collector of rare books and manuscripts in Santa Barbara, California. There, on the title page, in his angular hand, Delambre had inscribed Napoleon’s grand prophesy: “ ‘Conquests will come and go, but this work will endure,’ words of Nap. Bonaparte to the author of the Base.” Yet the title page was not the only page on which he had recorded his marginal comments.

  Together, these documents reveal a remarkable story. They reveal that Méchain—despite his extreme caution and exactitude—committed an error in the early years of the expedition, and worse, upon discovering his mistake, covered it up. Méchain was so tormented by the secret knowledge of his error that he was driven to the brink of madness. In the end, he died in an attempt to correct himself. The meter, it turns out, is in error, an error which has been perpetuated in every subsequent redefinition of its length, including our current definition of the meter in terms of the distance traveled by light in a fraction of a second.

  According to today’s satellite surveys, the length of the meridian from the pole to the equator equals 10,002,290 meters. In other words, the meter calculated by Delambre and Méchain falls roughly 0.2 millimeters short, or about the thickness of two pages of this book. It may not seem like much, but it is enough to feel with your fingers, enough to matter in high-precision science, and in that slender difference lies a tale of two men sent out in opposite directions on a Herculean task—a mission to measure the world—who discovered that integrity could carry them in directions as contrary as their carriages. Both were men in their mid-forties, men of humble origins from the French provinces who had risen to prominence on the basis of talent and a mind-numbing capacity for work. Both had been trained by the same astronomer, Jérôme Lalande, and elected to the Academy of Sciences in time for the Revolution to hand them the career opportunity of a lifetime: the chance to sign their names to the world’s measure. But during their seven years of travels, the two men came to have a different understanding of their metric mission and the allegiance it commanded. That difference would decide their fates.

  DELAMBRE’S BASE, KARPELES EDITION

  On the title page of his own copy of the Base du système métrique décimal, Delambre wrote: “ ‘Les conquêtes passent et ces opérations restent.’ Paroles de Nap. Bonaparte à l’auteur de la Base.” This may be translated as: “ ‘Conquests will come and go, but this work will endure.’ Words of Nap. Bonaparte to the author of the Base.” (From the Karpeles Museum, Santa Barbara, California; photograph by David Karpeles)

  This then is a tale of error and its meaning: how people strive for utopian perfection—in their works and in their lives—and how they come to terms with the inevitable shortcomings. What does it feel like to make a mistake, and in a matter of such supreme importance? Yet even in failure, Delambre and Méchain succeeded, for by their labor they rewrote not only our knowledge of the shape of the earth, but our knowledge of error as well. In the process, scientific error was transformed from a moral failing into a social problem, forever altering what it meant to be a practicing scientist. And the consequences of their labor resonated far outside the realm of science. We can trace the impact of their work in the globalization of economic exchange, and in the way ordinary people have come to understand their own best interest. In the end, even the French countryside they traversed has been transformed.

  To come to terms with this history, I set out to retrace their journey. In the year 2000, at a time when France was celebrating the millennium along the Meridienne Verte—a six-hundred-mile row of evergreen trees which was meant to mark out the national meridian, but which was somehow never planted—I set out on the zigzag trail of Delambre and Méchain. I climbed the cathedral towers and mountain peaks from which they conducted their survey, and combed the provincial archives for traces of their passage. It was my own Tour de France. Delambre and Méchain had demonstrated that the judicious application of scientific knowledge might, as Archimedes once boasted, move the world. Where they traveled by carriage and on foot, I substituted a bicycle. After all, what is a bicycle but a lever on wheels?—a lever which allows the cyclist to move along the surface of the world, or, which is much the same thing, move the world.

  CHAPTER ONE

  The North-Going Astronomer

  Fabrice showed them his passport indicating he was a barometer salesman travelling with his wares. “Are they fools!” cried the border-guard, “This goes too far!”

  —STENDHAL, The Charterhouse of Parma

  The countryside was strangely silent, the roads deserted. The local militia had been ordered to stop “any unknown person travelling by foot, horse, or carriage, and with the amiability which Equality and Liberty prescribe, check their identity against their passports, and if the passports prove false, conduct them to the town hall to be judged according to the law.” That afternoon, a gendarme told a man traveling by carriage with his wife and daughter to hurry home. The fortress of Verdun had fallen and eighty thousand Prussian soldiers were crossing the plains of Champagne, marching toward Paris to restore the French king to his throne. Everything was in readiness for the onslaught. A proclamation had gone out from the capital that the people of the surrounding hamlets should prepare themselves to “share with their fellow citizens the honor of saving their fatherland—or of dying in its defense.” Inside the Paris walls, the gendarme told the traveler, patriots had begun to massacre all the city’s prisoners lest they rise in aid of the aristocrats.

  That same day—September 4, 1792—in the highest reaches of a château set on top of the region’s most elevated prominence, a man was bent over a strange apparatus, sighting across the horizon. The man—a savant by all appearance—had set up an observatory inside a lofty twenty-two-foot pyramid that normally served as a belvedere where diners might admire the delightful prospect. At intervals, he lifted his head from the instrument to manipulate the two telescopes on their interlaced brass rings, pivoting them first one way, then the other, as if solving a mechanical puzzle. Then he bent his eye to the eyepiece to take another sighting, while one assistant verified the gauge and another recorded the value. It was a delicate operation, sensitive to the least vibration. The men dared not shift their weight lest the floorboards transmit their motion to the instrument and perturb those values destined to serve as the unique and permanent measure of all things.

  The Château de Belle-Assise was aptly named. It was indeed “beautifully situated,” famous for its view over the fertile valley of Brie. A château had stood on the hill since the thirteenth century. The current owner, the comte de Vissec, had permitted the expedition to labor in his pleasure pavilion. On the western horizon, the savant could pick out twin domes rising from the gray jumble of Paris: the leaden dome of the new Panthéon and the golden dome of the old Invalides. On the southern horizon he could make out the Gothic church at Brie-Comte-Robert. And on the northern horizon he could identify the church belfry of Dammartin, due to be demolished. Nearer to his position he could see the medieval dungeon of Montjai, from which he had originally hoped to conduct his measurements. His task was to measure the horizontal angle separating these sites with a precision never before achieved.

  That evening, just as the savant completed his fourth and final day of observations at Belle-Assise—night had fallen and his assistants were packing their instruments into their carriages
in preparation for the post-horses they had ordered from the town of Lagny—a party of militiamen arrived instead. They were well armed with muskets and well fortified with wine. They had secured permission from the local municipal council to search all the surrounding châteaux. Rumors of treason were circulating through the countryside. It was widely suspected that the four visitors to Belle-Assise were spying for the Prussians. Was it not true they had paid the local carpenter Petit-Jean to build a platform on the ruined tower at Montjai, which, as everyone knew, was haunted by the demons of a murderous priest? And why had they been peering across the valley in the direction of the Prussian advance? They would have to show their papers.

  The savant presented his passport. It identified him as Jean-Baptiste-Joseph Delambre, “jointly charged by the National Assembly to carry out, in conjunction with Monsieur Méchain, the mathematical measurement of the meridian from Dunkerque to Barcelona.” Delambre was a solid, well-set man of forty-two, of average height for that time—he was five foot four—with a round face, a strong nose, blue eyes, and brown hair swept back from his forehead. It was a frank and open countenance, yet curiously observant, with a mouth inclined toward irony. His blue eyes were disarmingly naked, and on closer inspection it was clear why: Delambre had no eyelashes. He was an observer rather than a man readily observed.

  His assistants presented their papers as well. The first was Michel Lefrançais, a twenty-six-year-old apprentice astronomer, nephew of the illustrious astronomer Jérôme Lalande. The second was Benjamin Bellet, a thirty-two-year-old instrument-maker, an apprentice to Etienne Lenoir, whose workshop had built the expedition’s newfangled “Borda repeating circle,” the instrument that was to bring unrivaled precision to their survey. And the third was a manservant named Michel.

  The leader of the militia seemed satisfied by these documents. But his followers did not agree. They complained that the passports had expired—or more precisely, had been issued by a political authority which had itself expired. In the four months since they had been signed, an uprising had deposed Louis XVI and installed a republic.

  Delambre tried to explain that he had been sent on a mission to measure the size of the world. He was a practitioner of geodesy, the science of measuring the size and shape of the earth. Improbable as it sounded at a time of national emergency, the government had assigned his mission its highest priority. His mission was to travel up and down the meridian of France. The Academy of Sciences—

  “There is no more ’Cademy,” interrupted one of the militiamen, “the Cademy is no more. We’re all equal now. You’ll come with us.”

  It was not true, not yet; the Academy still existed, as far as Delambre knew. Earlier that week, Antoine-Laurent Lavoisier, the great chemist and treasurer of the Academy, had admonished him not to quit his mission until he had “exhausted every reserve of strength within him.” Any halt or failure would have to be justified to the National Assembly itself. But at the moment, further resistance seemed pointless. As Delambre wrote to a friend, “They were armed and we had only reason; the parties were not equal.”

  So Delambre and his team accepted the militia’s “invitation” to accompany them across the nighttime fields. The mud was thick, the sky black. A heavy rain had begun to fall. “Luckily I had time to place a frock coat over my clothes,” Delambre wrote. “And as we marched, we could talk to the men and make them see reason, so that they began to show us some courtesy, warning us of treacherous footing ahead, and giving us a hand when we needed to be pulled out of the muck.” For the next four hours they accompanied the militia on their rounds, searching houses for arms and requisitioning horses. After struggling for six miles through the dark, they finally arrived in Lagny shortly before midnight, just as a squall soaked them to the bone.

  CASSINI MAP: THE REGION EAST OF PARIS

  This portion of the great Cassini map of France (1740–95) shows the area around the Château de Belle-Assise. The château is here labeled Belleassise, southeast of Lagny on the way to Villeneuve. After the Revolution the château came into the possession of the Baron de Rothschild and it was demolished at the end of the nineteenth century. Its formal gardens (pictured on the map) are today a tangle of muddy forest. Only the windmill (likewise indicated) still stands. The town of Lagny is now a suburb of Paris, and the land to the east of the town is today the valley of Euro Disney. (From the Earth Sciences Library, University of California, Berkeley)

  The municipal council was in candlelight session. The town was on a wartime footing. Mayor Aublan, a former financial agent for the local abbey (now abolished), had recently congratulated his constituents for overthrowing the “odious king” and unmasking the “perfidious proclamations of the corrupt ministers and other vampires of the realm.” Delambre presented his papers to the assembled officialdom. One alderman recognized the signature of the district official on the papers, and argued that Delambre should be released. But Mayor Aublan was more suspicious. He ordered all four members of the expedition escorted by armed guard to the Hôtellerie de l’Ours (the Inn of the Bear), where they were “not to consider themselves arrested, but merely detained.” In the meantime, Delambre should send a message to the district office so that they might vouch for the legitimacy of his mission.

  “That night we had nothing to change into, no nightclothes, nothing; and to dry ourselves, only a few sticks of firewood and a couple of glasses of bad wine.” Their two guards had a worse night of it, however; they had to spend all night in a drafty corridor, detaining men who had no intention of escaping. As Delambre noted in his expedition logbook: “Consigned to the Hôtellerie de l’Ours, two sentinels on guard at the exits; September 4, 1792, the second year of liberty and the first of equality.”

  In the morning, when confirmation came from the district office that the mission was indeed sanctioned by the highest authority in the land, Delambre thought it advisable before leaving town to thank the municipal council in person for their overnight hospitality. As he entered the town hall, the mayor rushed over from his office to apologize for the “little trouble” of the previous evening—while the impatient militiaman who despised academies stood by with a sullen expression, having apparently slept off his wine. According to the municipal records, Delambre then “thanked the municipality for so promptly allowing him to continue on his way.”

  “And so ends the true and tragicomic history of the memorable arrest of the former Cademician,” Delambre wrote that evening to a friend—as if his troubles had not just begun.

  Delambre’s wry equanimity seems to have been due in part to his late start in science. He did not take up astronomy until his mid-thirties—an age when many scientists are either at the height of their powers or already on the downhill slope. He was born in the cathedral town of Amiens on September 16, 1749, the eldest child of cloth-sellers of modest means. The family name Delambre probably derives from lambeau, meaning “rag.” When he was still an infant, fifteen months old, he was stricken with smallpox, which nearly cost him his eyesight and permanently denuded him of eyelashes. If the latter loss ultimately made it easier for him to take up the telescope (lashes tend to get in the way of beginners), his weak eyesight hardly presaged a promising career in observational astronomy. Until the age of twenty he was acutely sensitive to sunlight, and could hardly read his own handwriting. He grew up assuming he would one day go blind. For just that reason, he devoured every book he found. He learned English and German, and studied with the Jesuits until the order was expelled from France, at which point the town brought in three replacement teachers from Paris.

  Delambre might have aspired at most to a position as a local curé had not one of these teachers put him up for a scholarship at du Plessis, a famous Paris school where adolescent boys absorbed Roman virtues through an endless diet of Latin classics. Graduates included devout theologians, atheist physicians, military republicans, and illustrious savants. The high hopes for young Delambre were not fulfilled at exam time, however. He failed his finals
because he could not read his exam papers. Without a scholarship for a university, his parents urged him to return to Amiens and take up holy orders.

  Instead Delambre stayed in the capital, living on bread and water, studying ancient Greek by day and carousing with demimonde literati by night. It was the high tide of the Enlightenment. While the elderly Voltaire issued epigrams from Ferney, and the moody Rousseau wrote diatribes from the country, their would-be usurpers plotted utopias in cafés and wrote subversive pamphlets in garrets. Delambre and his friends formed their own literary club. To support himself he took a temporary position tutoring a nobleman’s son in nearby Compiègne; to instruct his pupil he was obliged to learn mathematics himself. He read Milton’s Paradise Lost in the original, and composed his own English primer, which included such homilies as: “To love riches is the property of a base and groveling soul, as to live [poorly] in comparison of virtue is the property of a noble and generous mind.”

  He was certainly poor enough. At the age of twenty-two he returned to Paris to tutor the son of Jean-Claude Geoffroy d’Assy, a member of the prosperous elite who managed the kingdom’s finances. For the next thirty years, Delambre remained a part of the d’Assy household. The grateful parents even offered him a sinecure in their financial offices, but Delambre accepted a more modest annuity that would enable him to devote the rest of his life to study. Thus did many a promising young man from the provinces set himself up as a lay cleric in the Ancien Régime, a bachelor scholar on a small pension. In those days, Delambre styled himself the “abbé de Lambre.” It was his dream fulfilled. He was a cosmopolitan humanist, rigorous in his learning, tolerant in his poverty, a connoisseur of human absurdity. He had narrow eyes, quizzical eyebrows, and a mouth framed by skeptical curves. Already in his mid-thirties, he still had no career.