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CHAPTER EIGHT

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Triangulation

Tis the same, he would say, throughout the whole circle of the sciences;—the great, the established points of them, are not to be broke in upon.—The laws of nature will defend themselves;—but error—(he would add, looking earnestly at my mother)—error, Sir, creeps in thro’ the minute holes and small crevices which human nature leaves unguarded.

—LAURENCE STERNE, The Life and Opinions of Tristram Shandy

Where was Méchain?

That spring and summer of 1797, as Delambre triangulated from Evaux to Rodez, and Tranchot unfurled his chain of signals from Carcassonne to Rodez, no one heard from the leader of the southern expedition. In early August, as he approached Rodez, Delambre had become sufficiently worried to contact Madame Méchain at the Paris Observatory. Perhaps she knew her husband’s whereabouts.

While Méchain worked his way slowly through the remote mountains of southern France, his wife had moved from her little home on the edge of the grounds into the “big house” of the Observatory, into the grand apartment once occupied by four generations of Cassinis. She had been offered the apartment while her husband was in Marseille. But practical Thérèse wanted to make a few improvements before moving in, as the rooms had been damaged during the Revolution. It must have been a glorious day when the Méchain family entered their new home. Their eldest son, Jérôme-Isaac, now seventeen years old and named after his godfather Lalande, intended to follow his father’s profession of astronomer. Already he had been hired as an Observatory assistant. The younger boy also showed scientific promise. The daughter was perhaps the brightest of the three. Who knew? With the Cassinis in eclipse, perhaps the Méchain clan would rule the Observatory for the next few generations. Of course, their father first had to found an honorable line.

Thérèse Méchain expressed surprise that her husband had not been in contact with his esteemed colleagues. His last letter to her, dated July 21, had indicated that he was about to begin his triangles in the Montagnes Noires north of Carcassonne, and that he hoped to complete his mission by summer’s end. Now the summer was over, and the race—if that is what it was—was over. The only question now was whether Méchain could salvage his honor.

When a letter from Méchain finally did arrive, it was winter and Delambre was back in Paris, preparing to measure the northern baseline near Melun. The letter was dated November 10, 1797, and had been mailed from the town of Pradelles, where, by his own admission, Méchain had made little progress. The problem was the weather. He had not been able to squeeze in more than two hours of observations in the past two months. And while waiting for the skies to clear he had been agonizing over his Barcelona results. He revisited his perennial obsession with Mizar. “It has caused me nothing but despair and disappointment; I regret that I ever observed that star.” He also now worried about the looming moment when he would have to present his data to his fellow savants. He had done some preliminary calculations and they had revealed some shameful comparisons. When Delambre’s geodetic and astronomical data were combined, the values for Dunkerque and Evaux matched to within one second. When he performed the same operation with his own data, he found an inconsistency of nearly five seconds in his values for Barcelona and Carcassonne. His analysis was admittedly premature, perhaps even forbidden. (Were the savants allowed to peek ahead at the final result while the expedition was still in progress?) But he had made the calculations, and they had convinced him that he must return to Barcelona that winter. For this, he needed the assent of both the French and Spanish governments, and he feared that Borda would not approve. Might Delambre approach the old physicist-commander on his behalf?

It was the same old obsession, with an ominous new tone. No matter what the cost, Méchain informed Delambre, he was determined to complete his mission. “In this situation, I have chosen to remain in the horrific exile I have long bewailed, far from my other duties, far from all I hold dear, and far from my own best interests. I will make every sacrifice, renounce everything, rather than return to Paris without having finished my portion of the labor . . . and if I am not allowed to complete it, I will never return.” Méchain saw only two options. “Either I will soon recover the strength and energy I should never have lost, or I will soon cease to exist.”

To Delambre, this smacked of a suicide note. And where, in the name of Cassini, was Pradelles? Delambre could not locate the town on any map. Presumably it lay somewhere in the Montagnes Noires of Languedoc, which suggested that Méchain had not completed even a single station for the second year in a row.

Delambre decided to consult Borda. He sent the commander excerpts of Méchain’s letter as a sign of the “moral state” of their colleague. “I don’t like it when he says, I will recover my energy or I will soon cease to exist.” Personally, he would have liked to see Méchain return to Paris for the winter so that the two expedition leaders might compare data and check over each other’s calculations. Delambre had so far shared all his data with Méchain, yet Méchain had refused to reciprocate. “Not only do I really wish to see his data, but I think this precaution necessary. If Méchain returns to Spain, who knows if he’ll ever come back, or if his data will ever be recovered?” It was essential that they find some way to “heal his mind and return him to his right senses, to his family, to astronomy, and to his colleagues.” To that end, Delambre urged that they enlist Madame Méchain.

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All that winter, while Delambre soaked in the hot springs of Evaux, Méchain had been holed up in the southern citadel of Carcassonne. It was one of the coldest winters on record; even the Canal du Midi had frozen over. The citadel had been fortified since Roman times, and repaired many times since. Méchain spent the season taking latitude measurements from the tower of the Saint-Vincent church in the basseville, a “modern” town of the thirteenth century, with clean straight streets, decent sanitation, a hospital, a courthouse, and a theater. It also housed the cloth merchants and professionals who had prospered since the Canal du Midi had connected the Atlantic and the Mediterranean.

Amateur astronomers had long haunted the Saint-Vincent tower. During the Revolution, the church had been put to more mundane uses. A factory for artillery carriages had been established in the nave, with forges in the side chapels. Restored to its traditional functions in late 1795, the tower once again became the site of astronomical observations. In Carcassonne, Méchain found a pair of amateur stargazers eager to assist him.

Raymond de Rolland and Gabriel Fabre were local magistrates who shared a passion for the heavens. Like Méchain, both men were approaching fifty, their careers and families up-ended by the Revolution. Rolland, the son of a wealthy manufacturer, had become the region’s chief judge and a partisan of 1789, only to lose his post in the judicial reforms of that year. Fabre was the principal author of Carcassonne’s Cahier de doléance, which had called for uniformity of measures and many other enlightened laws. He now presided over a criminal court, where he had a reputation for combining legal analysis with sympathy for the unfortunate. His personal motto came from Seneca, the Stoic philosopher and astronomer: Res est sacra miser, or “A suffering man is a sacred being.”

These men welcomed Méchain into their homes with honor and sympathy. His mission made sense to them. They admired him. Their hearts went out to him. It was a glorious opportunity for two amateurs to assist one of astronomy’s elite practitioners. Méchain considered his stay in Carcassonne the most gratifying period of his life. His personal comfort and sympathetic new friends also combined to make it the most miserable.

In mid-April, shortly after Delambre set out from Evaux, Méchain wrote to his northern colleague to inform him that he would be heading into the Montagnes Noires the following month, or as soon as the snows melted. On clear days, he could make out his next station, the forbidding Pic de Nore, the highest peak in the range. He made a final plea to Delambre that he be allowed to extend his triangles north of Rodez to atone for his shameful performance of the previous season. But it was too late; Delambre was already on mission.

Then, instead of heading north, Méchain stayed in Carcassonne all that spring and summer. He was comfortably lodged near Fabre’s home, not far from the civic theater. He often dined at the house of Rolland, whose wife was a charming hostess. Among these sympathetic friends, Méchain was overwhelmed by guilt.

Precision is an obsession. Why else would anyone sharpen the blade of knowledge to its ultimate fineness? Precision is a quest on which travelers, as Zeno foretold, journey halfway to their destination, and then halfway again and again and again, never reaching finality. We generally expect our heroes to possess virtues we might envy: courage, generosity, insight, honesty. The heroism that Méchain was expected to display was more prosaic: the ability to focus his attention for numberless days and nights on a repetitive task while he worked toward an ever-receding goal. Scientific knowledge is a prize which recedes as we advance. They are also heroic who practice self-abnegation. The price they pay is equally prosaic: anxiety, the abyss of self-doubt, and a certain fastidiousness. Precision is an obsession, and the sharp edge of Méchain’s exactitude was cutting him up inside. He was terrified of being caught, of being accused, of being blamed. His results “oppressed him day and night.” Endlessly he replayed the events of the past.

He confessed his anxiety, but would not reveal the data. He confessed his pain, but not its cause. He appeased his conscience with self-reproach, without quite admitting what he had to reproach himself for. Every letter he wrote to Delambre alluded to the Barcelona latitude without explaining exactly what was wrong. He was not ready to turn over his logbooks, he said, not even to General Calon, his administrative patron and military superior, despite the general’s promise that they would not be shown to others. Still Méchain refused. He needed more time to correct his corrections, he said.

Error was the great enemy of enlightenment, the loathsome infâme the philosophes had journeyed forth to slay. In that battle, mathematical science was their most fearsome weapon. For four millennia, astronomy had been the supreme quantitative science, gathering more and more of the world under its domain. Ptolemy’s geocentric model had been an orrery of mathematical refinement. Galileo, Kepler, and Newton had shown that God’s geometric perfection existed on earth as well as in heaven. And now Laplace and the other eighteenth-century savants were using mathematical analysis to show how the very dust of creation had formed our solar system, while they were simultaneously engaged in an epic struggle to direct their great mathematical weapon against the corrupt society around them. The metric system was another extension of this program to bring mathematical rigor down from the heavens so as to reorder the most mundane of earthly affairs.

Yet none of these great minds had ever treated their own data as rigorously as they treated the movements of the heavens or the shape of the earth. They averaged results, they looked for discrepancies, and they tossed out the data they considered unworthy of nature’s perfection. The question they asked one another was not which data to trust, but whose. An honorable savant made himself personally responsible for the consistency of nature’s data, without defining what that consistency consisted of. What counts as an error? Who is to say when you have made a mistake? How close is close enough? Neither Méchain nor his colleagues could have answered these questions with any degree of confidence. They were completely innocent of statistical method.

In their more reflective moments, the savants did acknowledge that the paths of error were multiple, that investigators could hardly express the degree of their error without first having access to the truth, and that the acquisition of truth was a voyage through a labyrinth. For six years now, Méchain had been wandering in a maze of mountains and regrets. At the core of his agony lay a tight cluster of doubts. Whom could he trust? Could he trust Delambre? If he told his colleague his secret, would his colleague betray him? Did his colleague trust him? Could he trust himself? With whom did his allegiance lie?

With his acute self-awareness, Méchain posed this question directly to Delambre. “Can I always be assured that when I write to you I am addressing a friend and absolutely him alone?” Sometimes, he made every pretense of trusting his colleague. “I throw myself into the arms of a friend and can only hope he will not fold his arms against me; I confide in him and in him alone.” Other times, he pleaded for compassion, leniency, and forgiveness. “If you treat me with rigor, I won’t know whom to turn to; my position is abominable.” Still other times, he begged Delambre to conceal everything that passed between them. “If you still have any friendship for me, you will throw this letter in the fire.”

That letter survived—albeit under seal.

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Pradelles was and is a hillside hamlet on the southern slope of the Pic de Nore. The village was even marked on Cassini’s map. It had 561 inhabitants and twelve times as many sheep. Before the Revolution, it had filed a complaining Cahier de doléance, like tens of thousands of other French villages, demanding fairer taxes, more reliable justice, the end of road tolls, regular meetings of the National Assembly, and “individual and civil liberty for every citizen.” In short, it was a typical mountain village in rural France.

While in Pradelles Méchain lodged with the richest man in town, Joseph-Louis de Lavalette, sieur de Fabas, a young former nobleman, whose Pailhès manor house is now a resort hotel with a dining room and a swimming pool. Several caches of Fabas’ treasure of gold and silver coins have been unearthed over the centuries. In all that time the town population has hardly varied. The mountain that dominates the village is today itself dominated by a factory-sized meteorological station, whose red-and-white-striped tower rises another 150 feet into the atmosphere like a giant barber pole. It is a felicitous perch for those who wish to peer into the distance or predict the future—and only a ten-minute drive up the paved road, or a stiff one-hour hike from Pradelles. From the summit, Méchain could see the citadel of Carcassonne to the south, the round blue bowl of the Mediterranean to the east, and the forest peaks he had yet to measure up north.

Not that clear days are common in the Montagnes Noires. By the time Méchain arrived in October, the summit was already inhospitable. “The unhappy Pic de Nore is redoubtable for its cold and fogs,” he wrote to his Carcassonne friends. He was still in Pradelles in late November when three feet of snow fell on the mountain in one night. It was the biggest storm of the decade. He considered calling a halt. “I will cede the terrain to the snow, the icy winds, and the wolves, which are not uncommon in these parts.” The long trough from the Atlantic to the Mediterranean funneled alternating winds against the mountainside; the western cers brought icy chills, and the eastern autun induced “aches and nervous afflictions . . . , sapping strength and vitality.” Méchain finally retreated to Carcassonne in mid-January, after climbing the mountain more than thirty times. In two years of campaigning it was the only station he had measured. Méchain seemed to have lost interest in finishing the mission.

At that same moment, the Paris Academy of Sciences made a momentous decision for the future of the metric system. The assembled academicians decided to convoke a meeting of the world’s most capable savants to review the meridian data and prepare the final determination of the meter. The idea was to give a global imprimatur to the metric system, to demonstrate that it was not merely a French reform, but was truly “for all people, for all time.” The decision was made in January 1798; the meeting was scheduled for September. This meant that the expedition data had to be assembled for examination in nine months at the latest. It was to be the first international scientific conference in history.

For the conference to succeed—for the provisional meter to be rendered “definitive”—it was essential that Méchain complete his triangles that year, while Delambre measured the two baselines—the one in the north near Paris and the other that Méchain had already prepared in the south. As spring rolled around, Méchain again made promises. He did not need Tranchot to complete the survey. His friends had found a local lad named Marc Agoustenc to assist him. This year he would start at Rodez, and work his way back south toward Carcassonne. That way he could measure the temperate tablelands around Rodez in the spring, and then return to the frigid Montagnes Noires in the summer. As of June, however, he had yet to leave Carcassonne.

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After years of quest, time had suddenly contracted. Delambre hurried to measure the northern baseline, a straight stretch of the king’s highway near Melun, known today as the N6. In the company of Laplace and the nation’s chief engineer, he had scouted the terrain and requested the construction of two masonry markers, each containing a copper plug that would define the exact terminal point. Above each stone foundation, he now erected a sixty-one-foot wooden tower. Yet even from this high platform, the beautiful twin rows of plane trees along the highway blocked his line of sight. Over the next six weeks he had workmen prune back some six hundred trees, while he triangulated the two ends of the baseline from the roof of the farmhouse at nearby Malvoisine. Six years earlier, the proprietors there had let him raise their chimney so that he might sight the d’Assy country château, thereby weaving his own life story into the making of the impersonal meter. Since then his patron had been executed, and the world turned upside down. Now, back on the same farmhouse roof, Delambre and Bellet took their final geodesic measurements.

At eleven o’clock on the morning of April 24, the team laid down the first of their high-precision rulers to measure the baseline. Each of their four rulers was two toises (twelve feet) long and a marvel of artifice. Lenoir’s workshop had fashioned them out of pure platinum, the newest and most expensive metal on earth. Borda had then calibrated each one against a one-second pendulum and set it in a wooden sleeve alongside a strip of copper so that the relative expansion of the two metals could be read with microscopic precision. The routine was this: Bellet laid the rulers, Tranchot checked their alignment and level, Delambre read the temperature gauge, and each man recorded the results in his own separate logbook. An additional logbook was kept by a tall gray-eyed young man of seventeen named Achille-César-Charles de Pommard, the son of Delambre’s widow-companion. After the fourth ruler was placed, the first was removed and attached to the end of the fourth, and the process resumed. It took them all of the first day to advance 528 feet. At night they marked their point of progress by driving a lead-topped stake into a hole in the road and marking the extremity of the final ruler with a plumb line. They then covered the hole with heavy planks to shield the marker from passing carriages. It took them forty-one days, working from dawn till dusk, to traverse the six miles.

Eminent visitors came to watch their tedious crawl across the earth. Lalande rode down from Paris for the afternoon. A party of savants arrived on June 3 to celebrate the final measurements: among them Louis-Antoine de Bougainville, a seventy-year-old circumnavigator who had been the first European to discover Tahiti, and the youthful German geographer Alexander von Humboldt, on the threshold of a world tour that would make him the most famous explorer of the age. Both were impressed with Delambre’s approach. “Delambre’s personal character inspires as much confidence as the excellence of his instruments,” Humboldt wrote. “To complete such a task in the face of so many physical, moral, and political obstacles, it is essential that the expedition leader have this calm temperament, this tranquil joy, this perseverance.”

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THE BASELINE OF MELUN

Masonry pyramids were placed at the terminal points of the Melun baseline, a six-mile stretch of the Paris-Melun highway now known as the N6. The pyramids were completed in 1798, in time for Delambre’s measurements. They were replaced in the 1880s when the baseline was remeasured. Later they were damaged in a road accident and subsequently destroyed. (From J.-B.-J. Delambre, Base du système métrique décimal, 3, plate VI; photograph by Roman Stansberry)

High-precision instruments mean nothing unless you trust those who wield them. Humboldt had secured one of Lenoir’s precious repeating circles for his own world tour. His first stop would be Barcelona, where he hoped to take latitude measurements and send Delambre his data. Trust, but verify.

The next order of business was the southern baseline at Perpignan. This was originally to have been Méchain’s baseline, linked to his chain of triangles, and so Delambre invited his colleague to join the measurement party. Méchain refused. Three years ago the Commission had not trusted him to measure the baseline on his own, and had insisted that he finish his triangles first. Well, he had yet to finish them. And there was another reason. He refused to have anything to do with Tranchot. The fact that the Commission had allowed Tranchot to assist Delambre proved that his colleagues trusted Tranchot more than Méchain. Let Tranchot have all the glory, then. Méchain should have surrendered command of the southern expedition to him long ago. Instead, he had botched his mission, failed his colleagues, and besmirched his reputation. Shame was all he felt. Painful, acute, and deserved shame. “After all that has happened,” he wailed, “I can no longer show myself anywhere and my only wish is to be annihilated.”

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Madame Méchain agreed to help bring her husband to his senses. As he had refused to come and visit her in Paris, she would track him down in southern France. And once she found him, she assured Delambre, she would convince him to join his colleague at Perpignan for the measurement of the baseline. She would stay with him until his mission was accomplished, assisting him with his observations, as she had done in the halcyon days before the Revolution. In return, she had only one request. Scientific Paris was full of gossips; no one must know that Pierre-François-André Méchain, member of the Academy and joint commissioner for the measurement of the world, had been unable to complete his mission without the help of a woman, not even if that woman were his wife. She wrote to Delambre in the strictest confidence.

Paris, May 30, 1798

Monsieur,

You ask me to induce my husband to put the final touches on the important work with which you are conjointly charged. No one takes a greater interest in this than I, and I have long considered joining him myself, so that I might bring him words of consolation and peace. Until recently, diverse circumstances have prevented me from carrying out this plan. I now leave immediately for Rodez. I have notified my husband of my trip without awaiting his reply, so as to give him no opportunity to dissuade me. As I suspect he is no longer in Rodez, I have asked him to indicate a place where we might meet. Do not think that I will waste his time. On the contrary, my goal is to accelerate the measure of the triangles.

I have told him emphatically not to accommodate me by proposing a rendezvous in a town appropriate to a lady. I will not waste even a quarter-hour of his time, because he does not have the time to waste. I have told him that I will gladly meet him on the mountaintops, sleep in a tent or a stable, and live on cheese and milk; that with him, I will be content anywhere. I have told him that we will work together by day, and let the nights suffice for conversation. I am hopeful that the esteem and absolute trust he places in me will allow me to dissipate the unwholesome thoughts which devour his spirit, and which, against his will, distract him from his purpose. When I am done with him, he will be ready to be delivered into your hands. Perhaps I will wait until you have joined us before handing him over to you, so that we may together regenerate his spirits. You may judge for yourself, Monsieur, if the signs of your friendship for me have won for you my esteem and my gratitude.

This, regrettably, is all that it is in my power to do, my final effort for the good of the service, for the interests of my husband, and for glory. Needless to say, all of this must remain between you, me, and Monsieur Borda, who entirely approves of this plan. For all the world, I beg you to keep this all a secret. I have announced that I am going on a visit to the country and no one knows the purpose of my voyage, so as to give no one grounds to say, “She has gone to fetch her husband.”

I’ve not heard from him since the letter of 16 floréal [May 5, 1798], in which he says he is leaving for Rodez. I’ve waited until the last minute to find out whether he has resumed his triangles. As soon as I have joined him, I will inform you of the exact state of affairs. I will also ask him why he has not sent the document releasing Tranchot from his employ. All this will soon come to an end.

I have the honor to be, with feelings of the highest esteem, your very humble servant,

Madame Méchain

One month later, on July 7, 1798, in the red-cathedral town of Rodez, Monsieur and Madame Méchain met for the first time in six years.

What did they talk about, Monsieur and Madame Méchain, upon seeing each other for the first time in six years? We do not know. There is no record of their conversation, just as there is no trace of the scores of letters they sent one another during his travels. What we want to know, of course, is whether he told her what was torturing him. Again, we do not know. All we know is that he was a man given to confession, and he had already confessed his error to at least one person (Giuseppe Slop). We also know that his wife had sufficient astronomical knowledge to grasp the import of his error. And we may presume that having traveled so far to lure him out of exile, heal his affliction, and talk some sense into him, she would have felt entitled to some kind of explanation. So it is quite possible that he told her. Indeed, Madame Méchain may have had sufficient astronomical knowledge to put Méchain’s error in perspective. Such knowledge, after all, did not depend on subtle mathematics, but on a grasp of the perils of observational science and the practical goals of the meridian mission. And Madame Méchain was a practical woman. . . .

Why had he not come home once in six years? It was not that far to travel. Paris was only a week away by carriage. Delambre had been back a dozen times, and although his northern sector lay closer to Paris, he had also traveled as far as Rodez, returned home, and then set out again for Perpignan—whereas in six long years Méchain had not found two spare weeks to visit his wife or his children (who hardly knew him) or to confer with his colleagues, not even during the dark winters, when all geodesy stopped. Think how much easier it would have been for him to visit her than for her to visit him.

And now that she had come all that distance, all he wanted to talk about was how they were measuring his baseline without him, how Tranchot was plotting a revolution to usurp his leadership of the southern expedition. What harm had Tranchot ever done him, anyway? The engineer was an honorable man, an able geodeser who had labored hard on this expedition. After a year of working together, Delambre had only words of praise for him. According to Delambre, Tranchot was hard-working, exact in his measurements, intelligent, never presumptuous; in short, an ideal collaborator. Moreover, Tranchot had never spoken a single word against Méchain in Delambre’s presence. To be sure, he lacked Méchain’s education and his skills in calculation. All the more reason to be generous with him. Had he insulted Méchain? Raised a hand against him? (Méchain had called Tranchot a violent man, and claimed that he had once threatened him. And for his part, Tranchot had admitted that once or twice, in Genoa and Marseille, he had expressed, perhaps “intemperately,” his frustration with Méchain’s delays and Méchain’s tight-fisted control over the mission’s purse-strings.) Well, if Tranchot had insisted that Méchain resume his mission, he was right to do so. Any further sulking would forever keep Méchain from the recognition he deserved.

As for this error Méchain kept worrying about: Who was to say whose fault that was? It could be a problem with the instrument (no matter what Borda said). Or it could be a flaw in the formulas or the correction tables. Or it might even have some natural cause. In a sense, it was presumptuous of Méchain to take all the blame. The burden of the mission—like its success—was great enough to be shared by all. No one’s work is perfect. And a relatively minor and inadvertent error was nothing to be ashamed of. His colleagues would not hold it against him, not even Laplace. They weren’t as judgmental as they sometimes seemed. They had no intention of replacing Méchain, nor of assigning someone else to finish his sector for him—provided he finished it. They were simply desperate to see the job done before the foreign savants arrived in Paris, and desperate to please the politicians who had committed such huge sums to the mission.

Or perhaps Méchain’s refusal to return to Paris and his self-reproach were just a roundabout way of casting the blame on others. Yes. By accusing himself of so small (and inadvertent) a sin, he underscored the guilt of all those who had accepted the Revolution, as if those who lived in Paris were somehow complicit in the crimes of those dark years. Well, this was not acceptable. The Méchain family had survived the awful year of 1789, when both of Thérèse’s parents had died and the mob had invaded their home in the Observatory. Méchain himself had missed the horrors of 1794, when so many honorable men and women went to prison or death—and thank God he missed it, because who knew whether he would have been among them. But in the end, things had not turned out so badly for the Méchain clan. Instead of their little house, they lived in the Observatory apartment. (And Cassini was perfectly content on his estate in Thury; he said himself that he wanted nothing more to do with science.) Now that inflation had settled down, Méchain’s salary was worth more than Thérèse’s inheritance ever was. And their new rights and liberties were nothing to belittle. So why did Méchain continue to hide in these remote provincial towns as if Paris were tainted, or as if he could somehow turn back the clock?

She could see he was suffering, that he was exhausted by his travels, by the tedium and terrible burden of his guilt. But he had to think of his children’s future, even if he could not contemplate his own. He always analyzed everything from every angle, turning things over in his mind, working himself into a state. It was all so counterproductive. As he himself wrote to Delambre, their sufferings were nothing alongside the horrible fate of “the millions of people who would have given their whole fortune to be in our shoes, not having suffered for an instant the dire needs which have befallen so many of our fellow citizens.” Consider their sufferings then, complete the mission, and come home. . . .

Of course we do not know what he told her, or whether he told her his secret—all his secrets, for what man spends six years away from his wife and does not amass a multitude of secrets? (And what of her secrets—a wife who was conspiring with her husband’s colleague to “hand him over”?)

All we know we know by triangulation. All our knowledge of nature, of history, of one another, or even (some might say) of ourselves, comes to us by mediation. Delambre and Méchain investigated the shape of the earth by measuring angles along a portion of its surface. We investigate their relationship by taking angular measurements of their letters to one another, their letters to their maître, their letters to third parties. They learned about one another through a similar angular measurement: a colleague triangulates the relationship between a husband and a wife; a wife triangulates the relationship between her husband and his colleague; and a husband triangulates the relationship between his colleague and his wife. We learn about ourselves by comparing ourselves with others, sometimes with others from the eighteenth century.

All we know is that Madame Méchain spent the next five weeks by her husband’s side, and that when they parted in the gloomy village of Rieupeyroux, he still refused to join Delambre at Perpignan. Her husband had rebuked her, she said, even lied to her. Or so she informed Delambre when she wrote to him, as promised, on her way home via Carcassonne.

Carcassonne, September 1, 1798

Citizen,

Having completely failed in my mission, and with a heart pierced by a thousand griefs, I return to Paris. As some business obliged me to pass through Carcassonne, Citizen Fabre has shown me your recent letter, which has disturbed me yet again. I will make every effort to relieve your worry. I informed you in May that I would soon be leaving Paris to take my place beside my husband. I promised you then to send you news as soon as I had joined him. A thousand fatal accidents conspired to prevent us from meeting in Rodez until July 7. Since that time, I have begged him in vain to write to you and to agree to measure the baseline of Perpignan with you. Not wishing to upset me, he always answered vaguely. For the first time, my husband has dissimulated with me. Not knowing his intentions, what could I tell you? I realized I was wronging you, but the situation dictated my actions. I only know that Citizen Tranchot, who knows perfectly well what he is doing, informed all my husband’s acquaintances here that he alone would measure the baseline, not Méchain.

I told my husband that only a barroom savant would think a T—could replace a M—, that everyone knew who was the best man for the job, and that the matter would have to be resolved by the Academy. Above all, I urged him not to throw away the fruits of all his years of suffering and sacrifice for something so idiotic. I decided to force the issue. I insisted that I would not leave his side until he had finished all his triangles and had been reunited with you. He thereupon renounced the baseline irrevocably, and vowed that he would concede all the glory to those whom fortune had favored. He said that he would never show up unless Tranchot had been set aside, that in any case his presence in Perpignan would hardly be agreeable, and that he would rather be sent to his death than go to Perpignan. I lacked the will to oppose him further. But forgive me if even now I lack the courage to address any longer a subject that is killing me.

In the end, I managed to make him promise to inform you himself of his resolve. I wrote to Borda and explained my situation, no longer able to withstand the horrific blows which assail my heart. I know my husband to be a man of talent and virtue. I affirm and attest that his abilities and faculties have not been alienated in any way, that they remain unchanged, only his heart has been ulcerated by a man who has sworn to bring him down, to bring an entire family down. In my mind’s eye, I have seen my husband covered with glory and public acclaim. You put it well, Monsieur, when you say that a moment which should be the happiest of his life may yet consign us to oblivion. I do not complain. I accuse no one, least of all my husband. It is the extreme sensitivity of his soul which has ruined him. He is more unhappy than blamable.

I have obtained from Citizen Méchain a promise that he will not break off his labor until his triangles are complete and the results sent to you and Borda. It’s all I could do. My family calls me back to Paris, and I cannot stay here until the mission is done. When I left him on the first of this month, the stations of Rodez, Rieupeyroux, and Lagaste were done. Puy St. Georges, Montredon, [Combatjou], and Montalet are, I believe, all that remain. You can currently write to him at Lacaune in the Tarn.

Citizen Fabre would be glad to grant you the rendezvous that The Measure of All Things you wish to have with him. I hope with all my heart that it takes place. I will urge my husband to join you here.

I have the honor to be, with the most distinguished sentiments, your fellow citizen,

Madame Méchain

She had failed, she said, to convince her husband to join Delambre at Perpignan. She had failed, she said, to stay by his side until his triangles were done. Most tragically, she had failed, she said, to bring him to his senses. Méchain remained bitter and melancholic. Yet she had succeeded—despite her gloomy prognostication—in the central task. News of her impending arrival had shamed him into leaving Carcassonne to meet her at Rodez. And once she arrived at Rodez, she had restored him to his mission. Méchain was triangulating again. Though her name nowhere appears in the expedition logbooks—an invisibility she undoubtedly sought—it is quite likely that husband and wife observed together the angles at the cathedral of Rodez and the chapel of Rieupeyroux, the two stations that linked Méchain’s southern chain with the northern chain of Delambre.

So did Madame Méchain dissimulate with Delambre? Did she hide, even from him, her role in her husband’s revival? It cannot have been easy for her to work behind her husband’s back, in league with men he considered his persecutors. She told Delambre that Méchain had refused to come to Perpignan because of Tranchot. And Méchain, when he wrote to Delambre, told him much the same story. But in his letters to his friends in Carcassonne, Méchain suggested that this was not the entire truth. Méchain considered the Perpignan baseline “his.” To join his colleague there now, he said, would be to submit himself to “the authority and supervision of Citizen Delambre.”

For his part, Delambre promised Madame Méchain that he would bring her husband back to Paris, come what may.

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The International Conference was to begin two months hence and Méchain had five stations left to measure, which was just about possible. At the Puy de Combatjou site, he observed from a fertile hilltop, then as now under cultivation. At the Montredon site, he observed from a ruined castle all overgrown with trees, now a lover’s lane for teenagers. At Puy Saint-Georges, he observed from the ruins of a medieval abbey, with its freestanding Gothic arches that still open onto the empty air—although a quaint orientation table placed on the site in 1907 thoughtfully directs your attention toward Paris (535 kilometers), Tokyo (14,050 kilometers), Madagascar (9,285 kilometers), and New York (7,350 kilometers).

Three stations down, two to go. All well and good, except that it was already mid-September, the savants had begun to arrive in Paris, and the two remaining stations—Montalet and Saint-Pons—were located in the rough Montagnes Noires of Languedoc, where “malevolent persons” had pulled down the signals Tranchot had erected the previous year. All through the season he had been doing battle with the locals and the weather. One signal had been sawn off, another burned to the ground, another dismantled for nails, another toppled by storms. In one town, a village joker told the peasants that a nearby signal was a new kind of guillotine, so the peasants tore that one down, too. Even some local officials seemed to fear that the signals might serve as a secret aid to the Republic’s enemies. For his part, Méchain said, he feared the “fanaticism” of the people.

His fears were not groundless. Thirty-five years before, a young cartographer working for Cassini III had been surveying from a church tower in the Montagnes Noires, not fifty miles away, when he had been hauled down from his ladder and all but hacked to death by a crowd who claimed that his “sorcery” was sowing death among the villagers. He managed to escape, blood streaming from his head and hands, but the town officials were too intimidated to help him, as were the few strangers he met on the road. Only at nightfall did he manage to stagger into a neighboring town and find asylum in an inn run by the widow Jullia, where a doctor and surgeon tended his wounds. This story was well known to all geodesers and illustrated, sadly, a continuing hazard of the job. It was not so much that the young cartographer was a sorcerer, but that his sorcery was the sorcery of numbers. When surveyors came to measure the earth, peasants had reason to be fearful. In the judicial investigation into the attack, one villager explained that the cartographer was “a sorcerer who had come to harm them and was the agent of taxes, and had come to increase the income tax, ruining them, and causing them to die of hunger.” The court obliged the village to pay reparations and sent the ringleaders to prison. Local priests were told to command their flocks to leave cartographers in peace. But suspicion persisted. And the rough countryside, long famous for its bandits, now sheltered many new fugitives: refractory priests, unrepentant royalists, army deserters, draft dodgers, and rebels of all sorts, all reviled as bandits.

They are still there. This is the country of José Bové, the present-day peasant-activist with the walrus moustache whose rebellion against globalization has become world famous. Bové lives on the eastern slopes of the Montagnes Noires. He grabbed the attention of the international media when he arrived in Seattle for the 1999 World Trade Organization talks bearing a smelly package of his hometown Roquefort cheese, banned in America in retaliation for the European ban on hormone-treated beef. Bové was already notorious in France for bulldozing a local McDonald’s because its standardized food—la malbouffe—was an affront to his region’s produce. That particular “McDo,” since rebuilt, is the world’s most famous, and certainly the most charming I have ever seen, with glossy wooden tables, packs of happy children, leather-clad teens on cell phones, and a soothing view over a bucolic valley. Yet Bové’s message stands: it is standards that define what we eat and who we are. Standards may not make us identical, but they set the menu for our permissible differences. Bové and his cronies pulled up surveyors’ stakes and bulldozed that McDonald’s for much the same reasons that peasants in the 1790s pulled down Méchain’s geodetic signals.

As an agent of progress in this region, Méchain was obliged to call on official protection to ensure his safety. After local ruffians tore down his signal at Montalet for the fourth time, he asked that a garrison of militia post a seven-man guard at the site. The jagged Roc de Montalet rises from the pine forests like a shattered cathedral. Blueberry thickets grow at its perimeter. A plaque there commemorates Méchain’s visit, and proudly records his troubles with the locals. Méchain spent ten days at Montalet, sleeping in a tent at the edge of the rock and scratching out daily letters, his fingers numb with cold. Behind his armed guard, he had slipped back into a dark melancholy. He poured out his soul on the page. “I renounce it all,” he told his friends in Carcassonne, “and the instant I complete my assignment I will abandon everything to seek, if I can find it, some refuge of obscurity and peace, the sole balm my lacerated and broken soul can bear.” He feared he was losing his mind. How do you measure the world when the earth is turning beneath your feet? As he told Delambre, “I have spent all my time in the cruelest anxiety, unable to concentrate on what I am doing, continually reproaching myself for the past because the present is unbearable and because I tremble for the future.”

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At the time, Delambre was waiting on the other side of the Montagnes Noires, no more than sixty miles away as the crow flies. He had arrived in Perpignan with his team in late July to prepare the baseline. Tranchot was of great assistance here, having laid the markers along the Grande Route back in 1796 and having already gauged the distance with a surveyor’s chain. The Grande Route ran just to the west of an ancient Roman road, the Domitia, which two thousand years ago had served as Hannibal’s invasion route. It had been shifted slightly by the medieval Catalan rulers of Perpignan. Then in the middle of the eighteenth century the Ancien Régime engineers had transformed it into one of the king’s magnificent highways, laying it straight and true from Perpignan to Salses, between dry vineyards on the left and the salt lagoon on the right. And just as Delambre arrived the Republican engineers had begun reinforcing the road in anticipation of heavier traffic. In another hundred years, modern engineers would pave it with macadam and then asphalt. Today, it is known as the N9 and it still runs straight and true, except where it swerves to accommodate a shopping mall.

Geodesy may be a natural science, one which measures the size and shape of the earth, but it is also a science which depends on human history and human works. To measure a baseline for their triangles, the geodesers needed a straight stretch of terrain, and what could be straighter than a Roman road, adjusted by medieval surveyors, rectified by Ancien Régime engineers, and finalized by rational Republicans?

On August 6 Delambre, Tranchot, Bellet, and Pommard laid the first ruler. Because they could not afford overnight guards for the rulers (they were, after all, made of the world’s most valuable metal), Delambre had retrieved Méchain’s carriage from storage to ferry the equipment and the team to and from the work site every day. Their goal was the fortress of Salses, an impregnable ochre bastion which blended into the stony red terrain. An English traveler had called this “the most barren country on earth.” Suffocating heat alternated with the winds of the sirocco. The rulers had to be shielded from the sun to prevent them from overheating, lest they expand. Fiery gusts of desiccated air pushed them out of alignment. A flash rainstorm forced the savants to take shelter. Then, toward evening on the thirty-sixth day, a pack of wild dogs charged their camp and scattered the rulers, overturning an entire day’s work. While his assistants labored in the angry sun, Delambre sat in the shaded carriage, reworking the calculations. He had to correct for deficiencies in the thermometers on Rulers 1 and 2, for a slight kink in the road line, for the bridge over the Agly River, and for the forty-eight-foot increase in elevation from one terminus to the other. The price of precision is continual vigilance.

The southern baseline took two days longer to survey than the northern baseline. But the results corroborated one another to a remarkable degree—proof, the savants said, of the care with which they had been measured. On September 19, the tedious operation completed, Tranchot and Bellet began packing the instruments into Méchain’s carriage for their return to Paris. “Only one obstacle holds me back in spite of myself . . . ,” Delambre wrote, “Méchain.”

Lalande had predicted as much. “Our poor Méchain cannot finish,” he wrote to Delambre, “and it is up to you to repair the damage done by his illness, or else two months from now we will be no further along than we were last year.” With the conference about to begin, there was no time to spare their colleague’s feelings. Lalande told Delambre to take over and complete Méchain’s triangles for him. “You keep telling me you don’t want to distress him, but when you deny he is ill it’s as if some nut case were to go around denying that you were an astronomer.”

It was true. Méchain seemed to have taken the only honorable course for a savant who had failed in a mission whose purpose was perfection. He had had a nervous breakdown. His letters had become inchoate, inconsistent, obsessive. Every day he offered another reason why he had yet to finish, why he could not come down from the mountains, why he refused to return to Paris—ever. “The truth is,” he wrote, “that anyone who does not have cause to shed tears for the loss of those dear to them, fearing the loss of their own life and liberty, could hardly be sorry to leave this theater of misery, except for those sick souls who crowd around the guillotine.”

Delambre traveled to Narbonne, then to Carcassonne, to be as near his colleague as possible. The signal at Saint-Pons, Méchain’s final observation point, was a remote mountain station, an arduous three-hour trek up from the ancient abbey town of the same name. But it was only a day’s ride away. Delambre offered to come and assist his colleague with his measurements if he so desired. He could be by his side by evening.

By return post, Méchain warned Delambre to stay away. Delambre should not waste his time coming to Saint-Pons when the foreign savants were waiting for him in Paris. “As it is,” he said, “there is barely enough time for you to make the journey in good time. I will send you my results there as soon as I am done.”

Delambre neither returned to Paris nor charged up the mountain to finish the triangles. Instead he politely requested that the two men meet. He would wait for his colleague to finish, he said.

He was working as fast as he could, Méchain replied. “But I cannot see through clouds, nor stand up to hurricanes that carry everything before them.” He had arrived at the Saint-Pons station in early October, and taken lodgings in the abandoned Moulinet manor house, a half-hour walk to his signal. Moulinet had belonged to the archbishopric before the Revolution. The setting is spectacular. The mountain slopes are densely forested: fallen leaves form a moist October bed around the mossy rocks. Fox, deer, and wild boar flash through the woods. When the view is clear you can see a fourth of territorial France from the peak: from the ragged blue-and-white bands of the Pyrénées to the south, to the black-and-green ridges of Auvergne to the north. It would be a lovely place to make one’s hermitage, if the affairs of the world allowed it.

The days slipped by: ten days, twenty days, thirty days, forty days. . . . Still Delambre persisted. He persisted when Méchain promised on October 4 to send all his data the next day, and was still sending summaries a week later. He persisted when Méchain promised on October 13 to finish tomorrow, and then wrote on October 19 to say he was still wrapping up. He persisted when Méchain wrote on October 22 to say he would be in Carcassonne the day after tomorrow, and then again on October 28 to say the muleteer had canceled the trip because a three-day storm had flooded the roads. He persisted, although the foreign savants were waiting and their French hosts had their reputations on the line. He persisted because Méchain had the data without which a definitive meter was impossible.

Méchain was running out of excuses. “It would be an infinite pleasure to meet you,” he wrote, “though I should fear the occasion.” He kept advising Delambre to leave. You are missing your moment of glory, he reminded his colleague, your chance to present the fruits of your seven-year labor. Which was why, in the end, Méchain had to come down. He could risk his own reputation, but he could not risk Delambre’s, not when Delambre seemed so willing to risk his own moment of glory just to ensure that Méchain shared it. Delambre had let Méchain complete his mission alone—and in that sense, they had done it together. It was a remarkable act of friendship. Delambre’s restraint brought Méchain down the mountain.

They met in Carcassonne in early November 1798 at the home of Gabriel Fabre, the criminal-court judge whose motto came from Seneca: “A suffering man is a sacred being.” In Fabre’s view, there was no man who deserved his fate less than Pierre-François-André Méchain, “but it does not always lie within us to master our feelings.” And Méchain was certainly a man of feeling.

For three arduous days, Delambre labored to convince his colleague to return with him to Paris. Méchain tried every evasion. “I am unshaken in my resolve not to return to Paris this winter,” he said. He had repeated this as many times, in as many ways as he could think of. “I will not change my resolution for anything in the world.” He came up with half a dozen alternatives. He might spend the winter in Rodez collecting more latitude data. He could seclude himself in a mountain hermitage and polish up his calculations. “In the springtime, we will see if my existence is still of some use somewhere.” Perhaps he would return to Barcelona to verify his latitude data. Nor had he given up on the idea of extending his triangles as far as the Balearic Islands. To his Carcassonne friends he admitted that he now regretted turning down the job offers from abroad, and that he might yet “seek his fortune elsewhere.” Under no condition would he return to Paris. What kind of greeting could he expect there except “reproaches, disdain, and contempt”? His shameful behavior was already public knowledge throughout France; must it now be paraded before all the savants of the world? “I will not expose myself to this final humiliation,” he said. Let Tranchot take all the credit. (He now referred to his former assistant as “my director.”) He would accept any punishment the Academy doled out. He deserved no less. As for his family, his return could only aggravate their problems, “burdened as I am with myself.”

Yet once he had come down the mountain, what choice did he really have? Delambre would not return without the southern data, Méchain would not let go of his data, and Méchain could not allow Delambre to delay his own departure any longer. Ergo: Méchain had to go.

If the meter was a social convention, then the social conventions would have to be observed. If two savants had been sent on a mission to measure the world, then two savants must return—together. Science is a collective enterprise: its highest achievement is to “make a contribution.” If Delambre wanted to claim his contribution, he needed to let Méchain make his. He needed to bring Méchain back to Paris with him—along with his data. Delambre also had one final card up his sleeve, and on the third day he played it. He showed Méchain a letter from the Bureau of Longitudes importuning him to return and promising him the directorship of the Observatory when he got back.

They left in early November. Delambre had waited fifty days in all.

Although they had lied about Méchain’s date of departure from Paris, there was no way to disguise the date of his return. The foreign savants had been waiting for two months. It was Lalande who trumpeted the news to his colleagues on November 14. He had just received a message by mail: Delambre and Méchain had arrived at the d’Assy country home in Bruyères-le-Châtel. Tomorrow they would be in the capital. The last triangle had been closed.

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