by Ken Alder
Two days later, on 9 fructidor of the year V of the Revolution—otherwise known as August 26, 1797—Delambre arrived in Rodez and wrote in his logbook this epigraph from Virgil’s Aeneid:
Hic labor extremus, longarum haec meta viarum.
This is the final labor and the end of long travels.
Then he, Bellet, and Tranchot climbed the 397 steps of the cathedral tower to observe the surrounding stations. Statues of the four archangels watched from the corners. On a central pedestal, higher than any other point for fifty miles around, stood the statue of the Virgin Mary. After a lightning strike in 1588, the bronze figure had been replaced by a statue in the same red stone as the rest of the tower. Some Revolutionaries now wanted to replace her with a statue of Liberty. Others insisted that the entire tower be razed. But the local Revolutionary Society had voted instead to reconsecrate the cathedral as a Temple of Reason. Like the basilica at Saint-Denis, the past had been preserved to serve new ends.
The wind was blowing hard; the horizon was clear. They completed the sightings in two days, then packed to return to Paris. Delambre was almost done.
RODEZ CATHEDRAL
The Renaissance belfry of Rodez Cathedral served as the liaison between Delambre’s and Méchain’s triangulations. The head of the statue of the Virgin Mary, which they used as their common signal, is the most elevated point in the center of the tower. (Photograph by Roman Stansberry)
CHAPTER EIGHT
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.
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.
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.