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CHAPTER SEVEN

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Convergence

And every Space that a Man views around his dwelling-place Standing on his own roof, or in his garden on a mount Of twenty-five cubits in height, such space is his Universe: And on its verge the Sun rises & sets, the Clouds bow To meet the flat Earth & the Sea in such an order’d Space: The Starry heavens reach no further but here bend and set On all sides & the two Poles turn on their valves of gold; And if he move his dwelling-place, his heavens also move Where’er he goes, & all his neighbourhood bewail his loss. Such are the Spaces called Earth & such its dimension.

—WILLIAM BLAKE, Milton: Book the First

When Delambre and Méchain resumed their mission in the summer of 1795, the red-stone cathedral town of Rodez, where they had promised to meet, lay roughly halfway between them, some two hundred miles away. Delambre, who had come farther, still had the slightly longer route to run. He had put the northern lowlands behind him, though to the extreme north the latitude at Dunkerque remained unmeasured. To the south, Méchain had come through Catalonia, though he had yet to join the Pyrénées peaks to the Cassini triangles of France. As the two savants turned at last to face each other, they looked across la France profonde, the ancient provinces of Auvergne, Rouergue, Languedoc, and Roussillon, a mountainous high plateau dominated by the Massif Central, a series of ranges studded with domed volcanoes and laced with icy rivers.

The Revolution had carved these lands into quasi-geometric départements and uprooted the Ancien Régime’s aristocratic and religious rulers, yet the great geographic center of France still lived by the ancient rhythms: subsistence farming, up-country summer pastures, and market days in the villages. From this high plateau, Paris was a remote metropolitan rumor. The two centers—the political center and the geographical center—were joined in a perpetual struggle to define France. The political center, with its universalistic pretensions, strained after the linear progress of science and empire; while the geographical center, with its pride in its particularity, labored just to get by. The spokesmen of the political center condescended to the geographical center and urged the rustics to emulate them; while the inhabitants of the geographical center, apart from a few official emissaries, did their best to ignore Paris and its fantastical plans—such as the absurd proposal for a new metric system and the impossible mission to measure the world. From their point of view, Delambre and Méchain were just a new kind of emissary sent from the political center to traverse the geographical center and, in the name of number, tame it.

Before resuming his mission, however, Méchain wanted to coordinate with his northern colleague. He wrote to Delambre to inquire how his colleague kept his logbook. Did he record his data in order of observation, or in an order fit for calculation? Did he record every observation, or just the summary values? Did he group the data by station, or by triangle? How many times did he observe each angle? How did he construct his signals? “I ask you all these questions,” Méchain explained, “so that I may follow the same sequence as you, and so that we may present our results uniformly. You have already measured a great many triangles; I have completed far fewer. So it will not cost me as much to redo all my logbooks in the manner you have chosen.” And while he was at it, might he know how Delambre handled expenses? Did he pay for his assistants? Prices were rising in the south of France; the government’s assignats had lost almost all their value.

The world’s preeminent scientific nation had equipped a mission to measure the size of the earth with the greatest precision in human history; yet the expedition leaders, two of the world’s most meticulous astronomers, had not coordinated their methods of recording data. The savants of the eighteenth century might wish to subject the world to the dominion of uniformity, but they were wary of placing themselves under the same rule.

By the time Delambre received this letter (via Paris), he was triangulating his way through the autumn marshes of Sologne. He gladly detailed his methods for his colleague. He always recorded all his observations in the exact order he took them, in a logbook kept in ink with each page numbered. Only then did his assistant copy the data into another notebook in a sequence more convenient for calculation. He always noted who performed the observation, the instrument he used, as well as the time, the weather, and any other relevant circumstances, including a hand-drawn sketch of the site with all its features labeled. He did so with the conviction that as an emissary of the state he was leading a mission of national importance. “The Commission will ultimately decide what to publish; in the meantime, I suppress nothing.”

That went for his expenses too, especially now that the cost of food, lodging, and transport had reached astronomical levels. His assistants’ salaries were insufficient to put food in their bellies, and Delambre paid all their costs out of general funds. So far the administration had refused to reimburse his receipts, and his own salary was several months in arrears. But Calon had lately promised to compensate him. Méchain could likewise rely on a sympathetic hearing if he encountered any problems. In return, Delambre had one question of his own. As he was about to travel to Dunkerque to determine the northern latitude, might Méchain tell him which stars he had observed at Mont-Jouy, and what steps he had taken to assure the precision of his measurements?

No innocent question could have prompted such contradictory reactions from Méchain. There was no subject more painful—and none he was more anxious to discuss. Méchain’s response was longer than most scientific articles. It was certainly longer than any article he had ever published. It covered nine pages in his crabbed script and took him twelve days to compose; it was begun in Perpignan and finished in Estagel, halfway up the mountains.

He began by expressing gratitude for Delambre’s guidance. “Your information offers me the most instructive lessons, from which I will endeavor to profit. I only regret that the circumstances, conditions, and my own inadequate know-how have made it impossible for me to bring our work into concert; but henceforth, guided by you, as well as by the canvas mapped out by Cassini in 1740, I will endeavor to follow a more reliable method.” He then described the precautions he had taken at Mont-Jouy to obtain the most precise results possible—while hinting simultaneously that he had doubts about their trustworthiness. He was concerned, he confessed, about the correction he had used for refraction. His discordant data for Mizar were troubling. Why did his results for that one star diverge from the average value three times as much as the others? He had even contemplated a return to Barcelona to doublecheck his data. He only wished that Delambre had already completed his Dunkerque observations so that “the comparison of results from the same stars would be complete, and the judgment on my case rendered.”

He neglected to mention the contradictory measurements he had taken the following winter at the Fontana de Oro.

Courtesy can be formulaic: an opening flourish to honor an esteemed colleague, a closing embrace “with all my heart.” In between come the data, the conjectures, the counterhypotheses, and the criticisms of the work of third parties. Scientific life in the Ancien Régime had been guided by such formulas, with variations as subtle as the formula for the refraction of light: gradations of respect from token to veneration, and shades of affection from feigned to heartfelt. Seniority, scientific eminence, and social standing bent the spectrum one way or another, as did friendship, camaraderie, and the rivalry of the schools. The new age called for sterner stuff. Manly citizens only had time for frank exchange. Overnight, the formal “you” (vous) became the Republican’s informal “you” (tu). Everyone was equal, at least for the time being. Yet the old forms were already reasserting themselves, and some people had never wholly given them up. Méchain and Delambre never addressed one another as tu.

Méchain’s elaborate courtesy came in many hues. Courtesy is a camouflage, even when sincere. Avowals of respect and affection are pleas for reciprocity. Even an embrace “with all my heart” warily seeks its return. Méchain rarely published or addressed public sessions of the Academy, except to report comet sightings or to contibute to the ephemerides, the annual tables of celestial events. Already, in a career one third as long, Delambre had published three times as much, as if his late scientific bloom had finally given him something to trumpet. Méchain recoiled from the cold finality of the printed page, with its anonymous audience. He preferred the personal letter, specifically crafted for its one sympathetic recipient, a human engagement with a like-minded mind. He corresponded with savants around the world, sharing data and disappointments with men who sympathized with the self-abnegation that went into the making of new knowledge: Bugge of Copenhagen, Zach of Gotha, Maskelyne of Greenwich, and now his compatriot, Delambre of Paris.

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LUCKLESS MAN ON A PILE OF ASSIGNATS

This stack of assignats, paper money issued during the early years of the French Revolution, shows bills ranging in nominal value from 50 francs to 10,000 francs. The assignats lost value with staggering speed during the hyperinflation of the years 1794–97. They were never popular outside of the major towns. (From the Photothèque des Musées de la Ville de Paris; photograph by Briant)

Méchain and Delambre were not friends, not yet. They were cherished colleagues who had once observed the stars together at their maître’s behest, but who had not seen one another for three years. They were former fellows of the Academy (Méchain with ten years’ seniority) who had been sent in opposite directions to measure the world, and were now Republican comrades in a world destroyed and remade since their mission began. They were skilled savants who had been asked to assemble thousands of pages of numerical data in locations up and down the length of France, all the while pitted against one another to gather that data with the greatest dispatch and precision. They were collaborators who would soon be expected to boil that mass of unorganized data down to a single quantity, the length of one meter.

There was no guidebook through this high plateau of cooperation and competition, just as there is no primer for friendship or betrayal. To guide them, Delambre and Méchain had only the codes of etiquette they had absorbed from the Ancien Régime and the new egalitarian codes they were learning as they went. By combining the two, they would have to fashion a new form of integrity.

Méchain’s self-deprecation tapped a vein of sympathy in Delambre, who responded (as he was meant to respond) with praise for Méchain’s talents and virtues. He offered words of reassurance.

Why do you speak of the “judgment of my case”? If there is a judgment to be rendered, it is with regard to Bradley’s tables of refraction. You will be the judge and I think he will lose his suit. Nothing could be more precise than your observations. I would give much to be assured of making ones as good, and I care little whether they conform to a theory widely known to be inadequate, and which has recently been criticized with a vigor that is far from your excessive modesty.

Méchain needed to put more faith in his own exacting observations and precision instruments, Delambre admonished. He then showed Méchain how he might reanalyze his summary Mont-Jouy data, demonstrating how the results varied with different assumptions about the relationship of refraction to temperature, altitude, and angle. None of these assumptions made the data for Mizar accord with the rest, but Delambre promised to look into the matter further when he conducted his own observations at Dunkerque. In the meantime, “I make so bold as to urge you to calm yourself about your observations. I consider them definitive. There is no need for you to return to Barcelona. . . . I hardly flatter myself to think I will do as well.”

Finally, Delambre offered comfort of a more practical nature. He conceded every advantage to Méchain as to salary and position. Times were tough and funds were scarce, but Delambre reassured his colleague. “I am a bachelor; your situation is quite different. Any preferment should fall to you for many reasons, not to mention your seniority and lengthy labors.” Most of all, he hoped Méchain would return to Paris that winter, so they might together mourn the losses they shared—Lavoisier, Condorcet, and the other savants executed by the Jacobin régime, now, fortunately, fallen from power. But even if they did not meet in Paris, he looked forward to the day that he and his esteemed colleague finally joined their triangles together in Rodez, for “that day will mark an epoch in both our lives.”

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On his way to Dunkerque to measure its latitude—his last task in the north—Delambre passed through Paris. He dined with Lalande and Calon, and participated in the inaugural assembly of the new Academy of Sciences, where he heard the metric system extolled as the centerpiece of the Academy’s mission. The morning after, he continued on his way, arriving in Amiens in time to celebrate Christmas Eve (3 nivôse of the year IV), and in Dunkerque five days later.

For the next three months Delambre took the latitude measurements that were the northern counterpart to Méchain’s measurements at Mont-Jouy. These were the most delicate observations of the entire mission because any error here would translate directly into an error in the final length of the meter. The equivalent observations had absorbed Méchain’s attention for two full winters. Yet Lalande suggested that Delambre expend no more than a week on them. Four nights, his maître advised, would be enough to close to within one second of the correct latitude, “and you should satisfy yourself with that.” The old astronomer did not share his former students’ fetish for precision. From his point of view, these superfine measurements wasted time and effort. The standard meter could be established by legal fiat and if scientific window-dressing were needed, a few adequate measurements would suffice. Either way his pupils ought to return to the real business of astronomy, cataloguing the heavens.

Instead, Delambre took pains to match Méchain’s precautions. He set up his observatory in the attic of the Intendance, a military building within sight of the belfry. He pierced a hole in the ceiling (with permission) and slept one story below. The only drawback to this cozy astronomical arrangement was the unsteady floorboards. Even though he calculated that their maximum disturbance caused a deviation of only 0.001 seconds, he built a wooden platform to stand on, just to ensure that his movements would not perturb the instrument.

Precision is painstaking work. It demands meticulous precautions, stratagems planned like war. Delambre used astronomical theory to prepare his observations. He verified the verticality of his circle by three different methods. He drew up formulas to correct his data for refraction and temperature. He estimated in advance the best precision he could expect. And only then did he begin his sightings of Polaris, a star particularly suitable for assessing latitude because its proximity to the pole meant that its angular height as it crossed the celestial meridian would, with only minimal correction, supply the angular distance of the observer from the equator—or in other words, his latitude.

His thirty-eight observations of Polaris as it transited the celestial meridian below the pole gave him a latitude of 51°2'16.66", which shifted by a miniscule 0.06 seconds when he removed his least reliable data. The two hundred results for its transit above the pole were trickier, due to the cloud cover, and differed by one full second from the earlier results. But when he excluded the less reliable data, the difference narrowed to within 0.5 seconds. And when he summed up all his Polaris data, his total differed from his best data by only 0.25 seconds (or some twenty-five feet). It was another demonstration of the repeating circle’s precision, as well as a testament to Delambre’s preparation, skill, and integrity.

Throughout these latitude measurements, Delambre followed the same procedure he had followed for his geodesic measurements. He always recorded all his data, and he and Bellet signed the bottom of every page of his logbook, so that anyone who examined his records would see that nothing had been altered or suppressed. He had decided he did not have the authority to reject data unilaterally. As he later explained: “Once an observation was taken, I considered it a sacred thing: whether good or poor I faithfully recorded it.”

Delambre then set out to verify his Polaris results with the nearby star known as Kochab, also located in northerly Ursa Minor and hence likewise suitable for latitude measurements. Unfortunately, he found the dim star difficult to pinpoint. “It was never completely in focus for me,” he admitted, even though he had Bellet file down the scope to increase the magnification. This had happened during the geodetic sightings as well. At such times, Delambre relied on his assistant, who observed with “much zeal and exactitude.” As he noted occasionally in his logbook: “Bellet thinks he can see the signal; I, who could not see it, took absolutely no part in these observations.” The results for Kochab were mixed: those taken on the lower passage were of especially poor quality because of the cloud cover, and came in three seconds short of the Polaris data—a rather discordant result. Those for the upper passage, however, agreed to within a stunning 0.02 seconds.

At this point, Delambre might have left Dunkerque with a clear conscience. His overall results agreed to within one second. January had been temperate; February was cold with clear skies; but in March the cloud cover worsened. The weather over the English Channel could never rival the skies of Catalonia. Yet when budget woes stranded Delambre for an extra three weeks in Dunkerque, he decided to take supplementary observations. Imagine his horror when the new results radically diverged from the old. For nearly a month, Delambre felt the anguish that so tormented Méchain—until he identified the problem as two loose screws on the lower scope of the circle. Once the scope had been repaired, the new results matched his old ones. He left Dunkerque, satisfied, on March 29.

Delambre had promised Méchain a full report of his latitude measurements, but so far all Méchain had received was a preliminary report from Lalande, which spoke of Polaris and Kochab. This left Méchain bewildered. “No doubt,” he wrote to Delambre in May, “you have since observed the others.” He was counting on Delambre’s results to help him solve the refraction problem and fix the outer limits of his error. He requested a full report “if you can spare me a few moments.” In the formula of courtesy, this was a plea. “Adieu, my dear colleague, I depend upon your friendship and indulgence, which I claim with insistence, while I await your response as a token of them both. I embrace you with all my heart, wishing you perfect health.”

Delambre responded to this plea with a lengthy letter, the core of which he had already read to a public session of the Academy of Sciences. As he explained to Méchain (and to the Academy), he had not observed the four additional stars Méchain had sighted at Barcelona because each presented disqualifying difficulties. The star known as Capricornus only came into position during daylight; it might be observed in Barcelona, but not in gray Dunkerque. The star Mizar, which had caused Méchain so much anxiety, passed too low on the horizon to be observed with confidence on the North Sea coast. And so on. Delambre declared himself satisfied with only the two stars. “Indeed, these are perhaps the only stars a savant ought to observe if he wishes to seek the certainty he needs, rather than to foster doubts.”

A public paper for the Academy is not the same as a letter to a colleague. So Delambre appended a personal note for Méchain. He lauded Méchain’s superior skills at observation, his ability to pick out faint stars that eluded others. “I could never claim to compete with you.” As for Méchain’s doubts about refraction, he assured his colleague that the problem was not worrisome. None of Méchain’s data suggested that the correction for refraction should differ at different latitudes. All their colleagues—Borda included—agreed that Bradley’s tables were inaccurate, and that Méchain’s Mont-Jouy data should be considered definitive, “the most perfect that could be hoped for.” By general acclamation, he told Méchain, his Paris colleagues had declared the astronomical portion of their mission complete. “That task is done,” he said.

Two savants defer to one other. Each denies he is competing. Each concedes the other’s superiority. Yet the same phrases in different mouths have different meanings. Delambre’s formulas rang with self-assurance. Méchain’s formulas quivered with self-doubt. The formulas of polite society—like the formulas of nature—can convey a great variety of meanings.

Delambre appended a final postscript. He informed Méchain that he would be dining two nights hence in the company of Madame Méchain, and hoped that he would likewise embrace his colleague soon. Méchain was missed in Paris, and he would find a warm welcome there. The new Academy was just like the old one; the new Bureau of Longitudes was staffed by their dearest colleagues. The government—now called the Directory—was still dealing with the aftershocks of Revolution and hoped to stabilize the currency by creating a new paper money called mandats.Delambre himself had arrived in the capital just in time to witness the suppression of the “conspiracy of equals,” a revolt led by Gracchus Babeuf, his old political sparring partner from Amiens. Currently he was assembling funds to resume his triangles to the south of Bourges. By midsummer he expected to be back on mission, advancing rapidly toward Méchain.

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All this time, Méchain had been stalled in the mountains outside Perpignan, struggling to advance a few triangles north. The region was in turmoil. French soldiers, back from their Spanish conquests (bargained away by the diplomats), were being billeted in every spare room in town. Prices were soaring. The 24,000 assignats supplied by Calon fetched less than 800 francs in hard currency; a month later they were worth half as much. Not even Méchain’s parsimony could keep pace. His team members could barely afford their daily pound of bread and half pound of meat. Wine and any other “succor” had to be paid for out of their own pockets. Conditions were even worse in the mountains, where his assistants were setting up signals for observation. Villagers would not accept assignats at any price. No one would rent them horses or mules. The equipment had to be carried on foot, and porters were demanding wages of 100 francs a day. The workmen who built the signals expected still more. The bill for the two masonry pyramids that Méchain proposed as markers for the ends of the baseline near Perpignan came to 24,000 francs, his entire budget for the year.

To help out, Tranchot offered to transfer his three years of back pay to the expedition budget. This calculated generosity meant that Tranchot’s daily expenditures had to come out of general funds. To cope with inflation, the Bureau of Longitudes multiplied its pay scale eighteenfold that winter. But even Méchain’s astronomical salary of 144,000 francs (in assignats) did not match the inflation rate. If the Republican government had wanted to teach its people that price was the paramount variable, they could hardly have picked a more painful lesson plan. It was the world’s first experience of hyperinflation. Méchain noted that he and his collaborators would have died of hunger in the mountains without the hard currency he had put away from the sale of his repeating circle, “and that’s no jeremiad, but the truth.”

Tranchot’s first task was to reestablish the frontier signals, destroyed by two years of warfare. He revisited Puig d’Estella, where he had been ambushed by miquelets two years before. He replaced the signals at Mont Bugarach and Forceral. Meanwhile, Méchain assured General Calon of his determination. “Never believe, Citizen, that I am disposed to abandon the mission; I will exhaust every resource.”

Among those resources was his physical stamina, diminished by his accident but unexpectedly robust. Méchain decided not to reclaim his customized carriage, stored in Perpignan these past three years. The terrain was too rough for carriage travel, and horses were prohibitively expensive. He headed into the mountains on foot, alone. The assistants Calon had sent him were more trouble than help. With only one circle, he had nothing for them to do; so he sent them back to Paris—all except Tranchot. He did have one guiding light, however: Cassini’s triangles of 1740. The problem was that Méchain was trying to operate at a level of precision that was itself a kind of uncharted country.

The first stations around Perpignan were relatively benign. The summit of Mont Forceral, a barren cone-shaped hill to the immediate west of the town, overlooked a spectacular panorama of dusty vineyards, salt lagoons, and the Mediterranean coast. Méchain slept under the stars there because he could not afford a guardian to watch over the circle at night. Mont d’Espira, to the immediate north, stands in the foothills of the Corbières range, where the terrain became more forbidding—a landscape of stony valleys dominated by ruined castles. In the interior of this range stands an isolated, twin-peaked mountain, used in Cassini’s 1740 survey, and which Méchain would use as well: Mont Bugarach, known in local dialect as the Pech de Bugarach.

The Pech de Bugarach nearly broke Méchain’s spirit. This enormous limestone rock was considered sacred by the inhabitants of the valley. The town at its foot sheltered eight hundred inhabitants, a general store, three water mills, and a nearby mine that produced jet, a dense black coal that the locals fashioned into jewelry. Méchain had hoped to camp on the summit, but the twelve-foot-wide peak could not accommodate both his signal and his tent. So he lodged in a farm on the mountain’s flank and tackled the two-hour climb every day, scrambling up the slope on his hands and knees, hanging onto shrubs and dwarf trees for balance, then sidestepping his way warily across the bare rock of the final ascent, while loose pebbles underfoot rattled into the abyss below. One misstep and all was lost. He could cite a “thousand examples” of men who had plunged to their death, he informed Lalande. But at least he climbed unencumbered. “I trembled with fear for the men who carried the case for the circle and the timbers for the signal.”

Nothing would induce these men to repeat the performance. They also refused to guard the instruments overnight, or to sit watch over them during the day. The shark’s-tooth summit was scoured by fearsome winds. The new signal was the third on the site. A violent storm a month earlier had destroyed the signal Tranchot had built to replace the one he had built two years before. The place was precarious. Villagers spoke of the sinagries, spirits whose malevolent glance was enough to strike men dead.

Even today, a zone of mystery surrounds the mountain. The name Bugarach derives from Arabic, and means either “father of all rocks” or “the banished father,” signifying a high place where exiles are sent to die. The mountain still attracts mystics, who believe it to be the navel of the world, or a place extraterrestrials will one day land, or a crypt for ancient gods and suppressed human memories. It is a stiff climb to the top. From the farmhouse where Méchain lodged, a climber in a hurry needs nearly two hours to reach the peak. Above the pasturelands, the trail takes a series of switchback turns through a steep scrub of beech trees and mineral springs. The earth is clinging and heavy. After the vegetation clears, the trail passes through a cleft in the twin-toothed peak for the final ascent to the summit. At the top, if the atmosphere is still clear, one can see the cool blue curtain of the Pyrénées drawn across the far southern horizon, and nearer in, a half-dozen ruined fortresses at strategic intervals along the receding ridges, their broken ramparts an extension of the broken hills. To the north, guarding the broad green trough that runs from the Atlantic to the Mediterranean, the citadel of Carcassonne, Méchain’s destination, is barely visible. Yet such clear days are an exception. In the old Occitan dialect of the local shepherds:

Quand Lauro porto cinto

et Bugarach mantelino

Aben pleijo sur l’esquino

When Mount Lauro wears his belt

and Mount Bugarach his cloak

Then it rains on the slopes

Imagine what it was like, Méchain asked Lalande, to set out on a clear morning and reach the top only to find that the surrounding signals had been obscured. Clouds advanced like armies between the ridges, or they flew in at a high altitude, smothering the entire region and lingering for days. Méchain slept in the farmhouse, and every day he had to climb the mountain to check his circle, left unguarded on the summit. Every morning he reassembled it for observations. Every evening he packed it back in its case and secured it under an oilcloth weighted down by stones, with only the sinagries to watch over it at night.

Then, when the weather cleared, Méchain saw a full panorama, including a view of the trail of his ascent. He could trace it back with his eye as it traversed the steep ridge, slipped through the rocky saddle, then emerged on the other side, before plunging into the tangled brush. It was the trail of his immediate past—and his future—the only way up or down the mountain. From the peak, time stretched out before him, like the view toward Carcassonne. Already it was late October. Each series on the repeating circle took an hour, and he needed a dozen series. The wind was cold. The clouds were closing in—then, just like that, his future was obscured.

This was not the sort of life he had envisaged when he took up astronomy. Astronomers are generally sedentary folk. They keep odd hours, to be sure: midnight vigils and predawn discoveries. But after a certain age they stay put and trade information by mail. In the ceremonious days of the Ancien Régime Méchain had held a sinecure as capitaine-concierge of the Royal Observatory. Until his survey across the English Channel in 1788, he had never left the dense soil of northern France. The Ancien Régime had been the fixed backdrop against which time advanced, like a fine chronometer. Every night he had strolled across the midnight gardens of the Observatory to the starry roof, and every dawn he had returned to his neat little house. But the Revolution had broken time, reset the clocks, and torn down the calendars, filling the days with events so rapid he could no longer hear the beat of the pendulum clock. The Revolution had cast him out into the periphery, where time had slowed to a crawl and his days were filled with repetitive ado. Now he slept in decrepit inns in provincial towns: the pork roasted to a chip, the servants always late, no parlor to write in, chairs that defied all notion of rest, doors that gave windy music as well as entrance, whitewashed walls, and tapestries so old as to be a “fit [nest] for moths and spiders.” When he was lucky he slept in the manor houses of the local gentry, or even better, in the homes of amateur savants, such as the Arago household in Estagel near Perpignan. When he was unlucky, he slept in the straw of an up-country cowshed, without candlelight to verify his calculations, or in a windy tent on an icy summit.

Yet he lived in an age when voyagers had approached the ends of the world, returning with sperm whale oil from Antarctic shores, breadfruit from Tahitian Edens, and visions of the Northern Lights. What glory was there then in traversing France, a nation which tens of thousands of ordinary French men and women crossed every year, only to bring back some numbers? One might just as well ask what challenge Thoreau faced in his two years at Walden Pond while tens of thousands of ordinary Americans braved a savage frontier a thousand miles west. For the men of Paris, their nation’s interior was a foreign land, as exotic in its way as any Andean highland. The people of the central provinces did not speak French, but a gamut of Occitan dialects more closely allied to Catalan or Provençal. The village mayor might understand French, but he would not speak it. The local measures enclosed each village in its own economy. The challenge was not whether France could be traversed, but how, by whom, and to what end.Shepherds might herd their flocks to up-country slopes. Brigands might hide in the mountains. Only a man of science would climb a peak to prove a point.

Ten days later, when Bugarach was done, Méchain moved to Mont Alaric, just as a storm knocked down the adjacent signal at Tauch. Tranchot was sent to repair it. Then it was Tauch’s turn. By the time he had finished with Tauch it was late December and bitterly cold. He had climbed each mountaintop station fifteen or twenty times, and each had required some eighty miles of travel through snow-covered fields over ice an inch thick, while violent northwest winds blew. The grease in the repeating circle clotted in the cold. His fingers were too numb to tighten the screws. And despite his efforts he had only extended his arc from Perpignan to Carcassonne, laying down three pitiful triangles in six months.

This might have been an opportunity for him to return to Paris for some much needed rest with his family. Certainly none of his colleagues would have begrudged him a break during the geodetic off-season. But Méchain had once again decided to winter in the south. He told Calon he wanted to choose a site for his baseline, a place he might best measure one of the sides of his triangles from end to end. For this, he needed a straight stretch of level terrain at least five miles long, whose terminal points could be triangulated from a nearby station. In 1740 Cassini had used the beach near Perpignan, but Méchain considered the shifting sands there too unstable. Instead, he picked a segment of the Grande Route that ran from Perpignan to the fortress of Salses. Tranchot directed the army engineers to build a masonry pyramid at each terminus, and Méchain linked them by triangulation to his station at Mont d’Espira. He also wanted to conduct the actual baseline measurement right then and there—Tranchot even assayed a preliminary run with a surveyor’s chain—but his colleagues in Paris insisted that he finish his geodetic angle-measurements first. The baseline measurement would have to be postponed until the special equipment could be prepared in Paris.

Méchain took this refusal to mean that his colleagues did not trust him. His spirits, after a temporary respite, had darkened. In March he admitted to Lalande that “my strength no longer matches my courage.” The cold weather had aggravated the old injury to his arm, but he himself admitted that the accident’s long-term effect had been more mental than physical. He was despondent, and did not quite know why. “All that remains now is to cure my head. I will make every effort. I still have hopes that I will conquer the apathy and lethargy that alienate me from my true self, and that chill my spirit the moment I am at rest or alone with myself, enervating the few faculties I ever had.” His melancholy had begun to overwhelm him. He felt paralyzed.

Then, in the next breath, he wrote to Delambre to offer to triangulate north of Rodez onto his partner’s side of the arc. The extra work would not strain him, he said, but simply allow him to make up for his inadequacies and balance their respective contributions. Delambre never answered this request. Spring came and went. The summer slipped away. Méchain remained in Perpignan taking latitude measurements.

Friendly bureaucrats there let him set up his observatory in the courtyard garden of the district office, where he also constructed a sundial. These measurements were doubly superfluous. The triangles, the baseline measurements, and the latitudes of Dunkerque and Barcelona were all that was needed to calculate the meter. But recently Borda, Laplace, and the other physicists on the Commission of Weights and Measures had decided that a series of intermediate latitude measurements along the arc would fine-tune their knowledge of the curvature of the earth, and hence improve the final extrapolation from the French meridian to the whole. They asked the two expedition leaders to gather this additional latitude data at three other sites: in Paris, within Delambre’s arc; in Evaux, at the halfway point of the meridian arc; and in Carcassonne, within Méchain’s arc. And they urged Méchain to join Delambre in Evaux to take the supplementary latitude measurements there together.

Méchain declined. He thought it best that Delambre measure alone at Evaux. That would ensure, he said, the accuracy of the latitude. “I know all too well that my results are far inferior to yours with regard to their exactitude!”

This remark, conveyed to Borda, prompted a sharp rebuke. This was no way for a self-respecting man of science to talk. When Méchain denigrated himself, he denigrated the mission. Borda set aside the usual courtesies and spoke frankly to the astronomer. The commander’s advanced age, his eminence, and his regard for Méchain gave him the right. “I have good cause to be angry with you,” he wrote. “Where did you get the notion that Delambre’s results, either for the latitude or the triangulation, are better than yours? Why do you deprecate your own work—or rather, the Commission’s work—when everyone else finds it excellent?” The discordant data for Mizar simply proved that Bradley’s old refraction tables were inadequate. If Méchain’s results did not match Cassini’s findings of 1740, then it was “tough luck for them.” “You were not sent out to find the same results as your predecessors,” he reminded Méchain, “but to find the truth.” Armed as he was with superior instruments, and thanks to the precautions he had taken in light of his mission’s supreme importance, his new results would undoubtedly differ from the old. If not, the entire mission would hardly have been worth the effort. In the meantime, Borda would use Méchain’s results to derive a new formula for refraction.

For his part, Delambre advised Méchain to leave the resolution of his problems to the superior theoretical skills of Borda and Laplace. He could take pride in the fact that the world’s preeminent physicists would be constructing their theory from his superb Catalan data, “the best and most certain that exist.” Méchain’s integrity and meticulousness were legendary. Yet Delambre reminded Méchain that he must not try to accomplish the impossible. “No matter how much effort we put in, it will always be difficult to surpass one second of precision. You and I have reached that goal, I think, by avoiding exaggerated claims and contenting ourselves with the art of the possible.” Minor errors were inevitable in any operation of this magnitude, and would hardly affect the overall results. “Anyone with the least notion of the difficulties we have faced will take them into account when they consider the exactitude we have achieved.”

These words of solace do not seem to have given Méchain much comfort. Having let an entire geodetic season pass without closing a single triangle, Méchain shifted his operations to Carcassonne that winter, so that he would be ready to advance on Rodez come the spring. But at the same time, he admitted to Lalande, he was on the verge of collapse. “After having withstood so many tests, my courage has given out, just when there are no more major difficulties to conquer. . . .” Weighing upon his mind was an unflattering comparison with his distant partner. While he stalled in the south, he noted, “Delambre works his way towards us with the swiftness of an eagle, having already traversed almost the entire length of France.”

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In the summer and fall of 1796, Delambre measured seven stations south from Bourges toward Evaux, each station posing its own particular problem, and each requiring its own solution. For instance, at Morlac, the first station south of Bourges, the belfry, which had once risen forty feet above the twelfth-century church, had been dismantled by the “hammer of the Revolutionaries.” Delambre offered to split the cost of a replacement tower with the villagers (population 748), but they refused. So Delambre offered instead to cap the church with a cheaper eighteen-foot wooden pyramid, the cost of which he would split with them and which would also keep the congregation dry when the rains came. They spurned this offer too. So, somewhat peeved, he cut a deal with a timber merchant, who helped him build the tower at a reduced fee in exchange for the right to reclaim the wood once the readings were done. When the merchant arrived to remove the church roof a month later, however, the villagers balked. A trial ensued, and five years later, the church tower was still in need of repairs. Then at Arpheuille, the last station in this sector, Delambre’s measurements were skewed by a large oak tree that cast a distracting shadow against the church belfry; even so, he refrained from pruning it because it also shaded the peasants’ Sunday dances.

Delambre arrived in Evaux—the halfway point of the arc—on November 24, 1796, and took lodgings at the Auberge du Cheval Blanc. The inn also rented him space in an attic granary by the main town gate. There he pierced a hole in the roof to fashion an observatory, much as he had at Dunkerque. After a run of clear skies and 210 observations of Polaris, the weather turned dreary. Snow fell overnight. During the next two months only two nights were suitable for astronomy.

His initial results disagreed sharply with those obtained by Cassini in 1740. This discrepancy, which would have sent Méchain into paroxysms of anxiety, led Delambre to recheck Cassini’s work. He discovered an error in Cassini’s methods. He spent his days updating his calculations, refining his formulas, and triple-checking his results. All of these he supplied regularly to Méchain, at Méchain’s request. No doubt he sampled the thermal baths as well.

Evaux lies at the northern edge of the Massif Central where a hot spring emerges from the hillside at 60 degrees Celsius, flush with minerals. The town’s Roman bathhouse was destroyed by fire in the third century C.E. During the Middle Ages, the baths served as a pilgrimage site, the waters being said to heal injured limbs and chronic diseases. By the eighteenth century there were three bathhouses, superintended by a consulting doctor. After months of hard travel, Delambre would have found Evaux a welcome respite.

Evaux is a fine place to rest, but not to get stranded. Delambre was determined to finish the expedition in the coming season. “No sacrifice is too great for me to finish this summer.” He hinted at some “additional reasons” for returning to Paris, though he did not specify what they were. We may speculate, however, that he wished to resume his scientific career, interrupted so soon after it had begun. And he presumably wanted to spend more time with a charming Paris widow he had recently come to know.

In December he began soliciting an advance from Calon for the next campaign season, yet another round in a scientist’s endless scramble for grant renewals. Calon promised to do what he could, but the government had shifted strategies on inflation. Whileassignats and mandats were being phased out, hard currency was still difficult to come by. Delambre might supplement his pay with army rations; as a cavalry captain, he was entitled to 9 livres a day, plus double rations for himself and his horse. The problem was that these rations could only be redeemed near the war front, and as the paymaster kept reminding him, there was no place in France further from the front than Evaux. Worse, Calon himself was beginning to lose influence. He no longer sat in the legislature, and he had been accused of mismanaging his budget. He requested detailed accounts from Méchain and Delambre so that he might in turn justify their expenditures to his superiors. “Some of the employees I’ve had to fire are vile worms who seek to blacken even the most honorable conduct.” By the middle of spring, Calon himself had lost his post. To make up for the loss of their military patron, the Paris savants called in their political chits. Lalande lobbied Lazare Carnot, a former engineer, now one of the nation’s executive directors. Lalande also offered to chat up Lavoisier’s widow, “who they say is very rich.”

The truth, Delambre wrote Méchain, was that he had salted away a backup fund of 2,000 francs in hard currency, money he had saved out of his salary and his small annuity. He also hoped to divert his honorarium as an Academy member. It would only be enough to fund one signal, but that was one less signal that had to be covered out of the budget. This slush fund had to be kept secret, of course. “It is best if they think us more beggarly than we are.” But if the only way to start his expedition in the spring was to finance it out of his own pocket, he would do so. And in the end, that is what he had to do.

On April 1, 1797, after four months in the bathhouse town, Delambre began his final push toward Rodez. He had thirteen more signals to plant across the high Auvergne plateau, eleven triangles left to close. As he advanced south, each station posed a greater challenge, like the Stations of the Cross. In his eagerness, he may have set out prematurely. The early spring weather was horrendous; almost every day it rained. Some days he sheltered in an inn. On other days he was caught in the downpour. To the east, through the gloom, he could see a row of brooding beehive volcanoes, their black humps flecked with snow. The greatest of these was the Puy de Dôme. Over a century earlier, the great Blaise Pascal had sent his brother-in-law to the summit with a crude barometer to prove that the atmosphere was finite. Over a thousand years ago, the Romans had worshiped Mercury in a magnificent temple by the crater. Over ten thousand years ago, this entire plateau had been born in a volcanic surge—although it had only been ten years since savants had first suggested as much, and their theory was still controversial.

Years, decades, centuries, millennia . . . day by day men crawled like ants across the corrugated arc of the world, peering ahead to the next ridge, seeking to uncover the processes that had shaped the earth. Where they had once expected perfection, they were beginning to learn how eccentric our planet is, suspended as it is between accident and necessity. And in the interstices between geological time and their daily labor, human history unfurled, likewise poised between accident and necessity. The planting season had begun. The earth was damp, the rivers flush, the air heavy with rain. The rich black soil fed lush green pastures. Cattle, sheep, and horses grazed by the road. Everywhere, nature had been shaped for human ends, in turn shaping human choice. Even the Gothic churches had been constructed of the black lava stone.

From a distance, through the gloom, Delambre had difficulty picking out the clock tower of Herment, a walled medieval town of 527 souls perched on top of the steep summit of a conical hill. Each of the triple towers of Herment’s church had been demolished and rebuilt: destroyed by Huguenots, rebuilt by the Catholics, destroyed by Revolutionaries, and now rebuilt by science. When Delambre arrived, the fifty-three-foot clock tower was a dark skeleton. He filled the interior of the tower with bales of hay to make the tower solid and so visible from afar. But when he tried to drape the tower’s frame with a white signal cloth, the locals balked. White was the color of the royalist flag—and the region’s administrators were battling a reactionary resurgence. The townspeople did not want to be mistaken for counterrevolutionaries. Only a few weeks before, a crowd of hooligans had absconded with a baptismal font that they considered sacrilegious and heckled the curé for having sworn allegiance to the Republic. To appease the patriots, Delambre sewed a red strip of cloth to one edge of the white sheet and a blue strip to the other, transforming his signal into a makeshift Revolutionary tricolor flag. This satisfied the townsfolk long enough for him to conduct his measurements and get out of town. The day after he left, a rowdy royalist crowd circled the church and forced the curé to take part in their procession. “The enemies of law, government, and order have not surrendered their foolish hope of sowing chaos here,” complained one local administrator.

At his next station Delambre needed to call on administrative help. No sooner had he set his signal on the strange gray organ-pipe cliffs above the town of Bort-les-Orgues, than a torrential storm brought a mudslide down from the hills, filling the streets with a three-foot-deep sludge of earth and stones. Residents blamed the flood on the bizarre signal on the mountaintop and demanded that it be torn down. This self-important town along the Dordogne had long suffered from inundations, despite its annual sacrifice to the river. Early each spring, on the eve of Ash Wednesday, a procession of boys in white robes marched through town, bearing torches and singing a dirge-like chant as they carted an effigy of an old man on a tumbrel: “Farewell, old man, you must go, I remain! Farewell, farewell, farewell!” When they reached the river, the oldest living man present set the effigy on fire and tossed it, still burning, into the river. The rite dated back to the Celts, who sacrificed their eldest travelers at rivers too wide for them to cross. By the eighteenth century, the ceremony had been supplemented by official demands for flood mitigation. Municipal leaders dissuaded the towns-people from destroying Delambre’s signal; it helped, too, that the signal was well out of reach, beyond the high cliffs.

His next station, the peak of Puy Violent, was the highest point along the entire meridian arc: six thousand feet above sea level. There Delambre had the choice of lodging either in the nearby Renaissance town of Salers—an onyx outpost of judicial palaces, slate-roofed inns, and black-stone battlements, but an arduous three-hour climb to the mountaintop—or in a cowshed an hour from the peak. As it was mid-August, Delambre thought it would be safe to save himself the daily hike, and he decided to lodge in the cowshed.

For the ten days of my labor, I slept in my clothes on bales of hay, living on milk and cheese. I could almost never sight two stations simultaneously because a thick fog obscured the horizon. In the long intervals while I waited ten or twelve hours for a view from the summit, I was scorched by the sun, chilled by the wind, and drenched by the rain, all in succession. But nothing irritated me more than the inaction.

Though Puy Violent was not named for its weather, it might as well have been. It rose beside its sister peak like the cusp of a molar. To the east—to Delambre’s back—a range of higher mountains, scarred by barren cirques, hemmed in the view. To the west, the panorama opened out over a green skirt of lava that plunged toward convergent river valleys draining into an invisible Atlantic two hundred miles away. Geologists had recently come to suspect that this entire region had once been the site of a single vast volcano. When the clouds cleared, Delambre could look out over its well-worn shards. Through the scope of his circle, he could see the black battlements of Salers on its basalt prominence across the valley, plus all his surrounding stations: his signal above the organ-pipe cliffs of Bort, the church tower at La Bastide, and his next destination, the signal upon the ruined castle wall at Montsalvy. It was a silent perch under a long low sky, without a human being in sight, only hawks angling on the wind and cattle grazing on the slopes. Today’s red-coated Salers cattle are the result of late-nineteenth-century breeding, but their eighteenth-century forebears were already famous for their cheese, the region’s chief export. On summer days they grazed on the high slopes; every evening, to protect them from wolves, the shepherds drove them down to the shed where Delambre joined them for the night.

The up-country people were handsome, with blue eyes and dark brown hair. They mistook Delambre for a sorcerer. Who else would have paid a team of men to cart four twenty-two-foot timbers to the peak of Puy Violent and assemble them in a pyramid? When a cow refused to give milk, when a plow broke in the field, when a journey proved unlucky, the sorcerer’s evil eye was to blame.

As part of his mission, the government had asked Delambre to assess the common people’s view of the metric system as he traveled through the countryside. Delambre found that the vast majority of the common people had never heard of the new measures. The workmen who built his signals were illiterate, innumerate, and did not speak French. This did not mean that they were inarticulate or unskilled; Delambre found them quite adept at constructing his bizarre pyramids. For a sympathetic hearing, however, he addressed himself to the region’s “enlightened citizens”: its magistrates, state officials, and educated men. These citizens looked forward to the new era. During the Ancien Régime, the province of Auvergne had been ruled by a jumble of legal codes; half a village might owe allegiance to Roman law and the other half to the common law. This legal tangle nourished the region’s multiplicity of measures, turning every marketplace into an arena of “frauds, deceptions, cons, and thefts.” Or so the region’s enlightened citizens believed.

In the past two hundred years, customs have changed, people have changed, animals have changed, even the terrain and weather have changed—all, paradoxically, while seeming to have stayed essentially unchanged. The population of these central regions has been stable for two hundred years, although there has been a steady emigration toward the towns and no one under the age of sixty habitually speaks Occitan anymore. The Salers cattle have multiplied, bred to a glossy muscularity, but the wolves are gone. Cantal cheese is still the mainstay of the region’s economy (after tourism), and is now exported around the world—except to America because the U.S. health inspectors ban the cheese, prompting bitter complaints from the French that the market for cheese is not global enough. The winters are less bitter than they were in the eighteenth century, though the great storm of 1999 leveled 300 million trees. Even the modern highway still follows the route laid by the Ancien Régime engineers, though it is now paved in asphalt. On the road out of Salers on his way to Montsalvy—known today as the D920, then as the Route de l’Intendant—Delambre was caught in a powerful rainstorm. It felt, he said, like traveling inside a cloud accompanied by continual thunder and lightning.

At Montsalvy on August 12 Delambre sighted Rodez through his repeating circle for the first time. The horizon was hazy, and he had trouble distinguishing the target. But the next day he saw it sharply outlined against the blue: the serene red-stone head of the Virgin Mary rising from her pedestal on top of the cathedral. The statue would link his chain of stations and Méchain’s. Delambre’s observations from the hilltop just north of Montsalvy are commemorated today by a finely wrought orientation table, which points out features as near as Rodez and as far as the Pic de Nore, Méchain’s station north of Carcassonne.

Delambre’s final goal lay just ahead. Rodez sat on a hillock in the warm basin of Rouergue, and as he descended, the temperature rose to meet him. The soil lightened to a crumbly orange, the yellow houses turned their open windows toward the sun. Suddenly, he could no longer sense the Atlantic behind him, but instead smell the Mediterranean ahead: the fruit trees, the corn husks, the olive trees, the dry dust of the south. Lizards, some a foot long, skittered behind rocks. Delambre had entered the Midi. Half the Massif Central was yet to come, with pine-blue ranges and deep gorges that carried cool air down from the mountains. But it was the south nonetheless. Delambre had only two stations left, two stations to link his triangles with those of Méchain.

He expected to hear from his colleague any day now, either at Rodez or at neighboring Rieupeyroux. The two savants had been out of contact since spring, presumably because Méchain was also converging on Rodez, traveling from town to town and out of reach of the mails. On August 23, while observing at Rieupeyroux, Delambre sighted one of Méchain’s signals to the immediate south. It was a good sign. It meant that he and Méchain were closing in simultaneously on Rodez. What a glorious finish that would be, the perfect resolution to their six-year mission of competition and cooperation. Hurrying to complete his measurements, he and Bellet set out the next day to drive the last twenty-five miles to Rodez. On the road, they met a traveler journeying alone in the opposite direction. It was Tranchot, on his way to look for them. His mission was complete, he said. Méchain had given him meticulous instructions to build a chain of signals from Carcassonne to Rodez, so that Méchain might follow behind, taking the geodetic measures with his repeating circle. It was Tranchot’s signal at La Gaste that Delambre had sighted a few days earlier. Yet Méchain was nowhere in sight.

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.

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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)

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