The Measure of All Things

by Ken Alder

  As for Napoleon, he refused to learn the metric system. Inspecting a gunpowder factory in Essonnes, he quizzed the plant’s manager about the chemical processes in considerable detail. But every time the manager supplied him with a weight in kilograms, Napoleon insisted that he restate the formula in poids de marc (old-style pounds). He said he could not think in the new units.

  Faced with this obstinacy, the government temporized even as it persisted. One year after the meter was made definitive, the first compromise was made. On November 4, 1800, the metric system was at last declared to be the sole measurement system for the entire nation, and the use of the nomenclature of compound words—decimeter, kilometer—was abolished. The meter was still the meter, and its use would be obligatory throughout the nation as of September 1801. But the Greek and Latin prefixes “which frightened the people” were replaced with “ordinary names.” After consultation with Laplace and Delambre, the decimeter was renamed the palme (the hand-breadth), the centimeter the doigt (the finger-breadth), the millimeter the trait (the trace), and so on.

  The instigator of this compromise was none other than Napoleon Bonaparte, back from Egypt. To honor their colleague’s return, the Academy had struck a commemorative medal from the residual platinum left over from the making of the meter. That way, they said, the medal would last “almost as long as your glory.” Thirteen days after accepting the medal, Napoleon seized absolute power in the coup d’état of 18 brumaire—and held it for the next sixteen years. One of his first acts was to make his old mathematics examiner, Pierre-Simon Laplace, Minister of the Interior, with responsibility for enforcing the nation’s laws and the metric system. The savants, it appeared, had bet on the right general. Imagine their dismay, then, when they learned of his compromise. Laplace tried to reassure his colleagues: a retreat on the nomenclature did not imply that the entire system would fail. Lalande smirked, “Monsieur Laplace is not in his place.” After only forty days in office he was turned out in favor of Napoleon’s brother. Other retreats were to follow.

  The French were not only the first nation to invent the metric system; they were also the first to reject it.

  CHAPTER TEN

  The Broken Arc

  The fact is that nowhere, these days, is anyone genuinely happy, and that of the countless faces assumed by the Ideal—or, if you dislike the word, the concept of something better—travel is one of the most engaging and most deceitful. All is rotten in public affairs: those who deny this truth feel it even more deeply and bitterly than those who assert it. Nevertheless, divine Hope still pursues her way, assuaging our tormented hearts with the constant whisper “There is something better—namely, your ideal!”

  —GEORGE SAND, Winter in Majorca

  Redeemed from his suicidal melancholy in the remote Montagnes Noires, Méchain had been elevated to the celestial post of the nation’s chief astronomer. Honored by the nation’s leaders for his scientific integrity, he had been welcomed into the arms of his loving family and respectful colleagues. No wonder his conscience troubled him.

  To expiate his sins, Méchain threw himself into his new administrative role. He complained that the Observatory had been neglected during his absence, and he vowed to transform it into the world’s premier astronomical facility. He bought superior telescopes and decided on their placement in the building. He resumed his own celestial observations, discovering two comets in 1799 and another in 1801, and joining in the exciting hunt for the newest members of the heavens, the minor planets known as asteroids. Yet he was miserable.

  Friends and colleagues were baffled. He enjoyed every reward a savant could desire: a capable wife, a warm family, the most eminent position in his field, the respect of his peers, and last but not least—this was Paris, after all—the sumptuous Cassini apartments and full use of the Observatory gardens. Some colleagues found him reserved, severe, even caustic. Some, behind his back, took great pleasure in reviling his character. Yet everyone agreed he was a savant of unimpeachable integrity.

  These public accolades only made his secret more unbearable. The more honors that were showered on him, the more unworthy he felt. He was a hollow impostor, a scientific fraud—and in a matter of such terrible consequence. He had introduced an error into the fundamental scientific value, the measure that would forevermore serve as the foundation for all scientific and commercial exchange. He avoided his colleagues, retreating to his apartment whenever one of them came by the Observatory.

  Meanwhile, his one-time partner had been given the honor of composing the official account of their expedition. The choice was understandable. Although Delambre was the junior colleague (five years younger in age, with ten years less tenure in the Academy), he combined a background in the humanities with the necessary technical know-how—plus he had actually performed the bulk of the work. Delambre planned to publish everything: the tale of their adventures, the full roster of their data, all their formulas and technical apparatus. The work would be entitled the Base du système métrique décimal (The Foundation of the Metric System) and would run to two thousand pages in three thick volumes. It would show the world the exactitude of their labors. To complete the first volume by the end of the year, he needed Méchain’s data.

  No wonder they resented each other. Their mission was done, yet they remained tethered together. Delambre needed the complete data of a man who had decided—out of spite, it must have seemed—to supply the absolute minimum, and in his own good time, too. As for Méchain, everyone knew he had only completed his mission with Delambre’s help: reason enough for him to begrudge Delambre’s success. On top of all this, Delambre was one of the First Consul’s favorites—Napoleon had taken a liking to him on his first day at the Academy—whereas the First Consul hardly knew who Méchain was. Méchain resented Delambre’s facile way with words and pretentious classical learning. He despised the ease with which the cloth-seller’s son moved in the highest circles of the new France.

  The fall from camaraderie was hard. For seven years the two savants had trekked the high geodetic plateau, first in opposite directions and then on convergent paths, but always in a spirit of collegial rivalry. But a year in the capital had turned them into petty quarrelers. Paris can do that to you. There is something about the proximity of money and power that makes people peevish. Late in 1800 Delambre was elected president by rotation of the Bureau of Longitudes, making him Méchain’s nominal superior. A squabble ensued over who controlled the account books. A question was raised as to whether Méchain could officially claim the title of director of the Observatory. Méchain wrote bilious letters denouncing his “hyperpedantic and outrageously ambitious” colleague who had overstayed his term as president of the Bureau of Longitudes. Méchain complained that he had been reduced to begging his colleague for firewood and candlelight. Privately, he referred sneeringly to Delambre as his “absolute master.” Publicly, he threatened to resign unless he was formally installed as Observatory Director.

  Deeper grievances festered. As Méchain now saw it, Delambre had deliberately deprived him of his rightful honors by relegating him to a secondary role on the meridian mission: grabbing two thirds of the triangles, muscling in on the latitude of Paris, and seizing both baseline measurements—including the one at Perpignan, which clearly lay within Méchain’s sector. And Méchain had proof of this. Late in 1799 he had become Borda’s scientific executor and had thereby gained access to all the commander’s papers. Among them he discovered the series of letters between Delambre, Borda, and his own wife. One can imagine the reaction of Méchain—a man given readily to paranoia—as he read of the conspiracy unfolding against him: their plan to lure him down from the Montagnes Noires, his wife’s secret mission to Rodez, their exchanges of confidences, their vows of silence. They had manipulated him, treated him like an underling, and tricked him across the finish line.

  By the time Méchain had reclaimed full recognition as director of the Observatory, Delambre had risen higher still. In 1801 Napoleon adde
d the presidency of the Academy of Sciences to his other titles, making him ruler of both the nation and the sum of its knowledge. Napoleon’s first act as President was to reorganize the Academy, appointing Delambre to the post of Permanent Secretary. This made the cloth-seller’s son the most powerful figure in French science: successor to Condorcet, liaison to the highest political authorities, author of its eulogies, and hence guardian of his colleagues’ reputations.

  These circumstances go some way toward explaining why, on September 6, 1801, a member of the Bureau of Longitudes (Méchain, presumably) proposed extending the meridian measure south of Barcelona, as far as the Balearic Islands. The extension had long been one of Méchain’s fondest ambitions, and he insisted on his right to report on its feasibility. Such an extension would improve knowledge of the shape of the earth by anchoring the arc’s southern latitude on an island, where nearby mountains could not distort the readings. The new arc would straddle the 45th parallel of latitude, making any extrapolation from the partial arc to the quarter meridian less sensitive to the earth’s eccentricity. These were excellent scientific rationales for the expedition, and Méchain agreed to report on them—if, and only if, he was allowed to lead it.

  Why would a fifty-seven-year-old man, reunited with his family after seven years of backbreaking travels, wish to undertake such a mission? Delambre and the rest of his colleagues argued that the task be given to someone younger. Méchain was needed in Paris, where he had begun to accomplish wonderful things at the Observatory. Moreover, he had just recovered from a severe illness which had nearly cost him his life, and which he himself blamed on the “long travails and thousand vexations of my mission, as well as those which followed upon my return.” But the more his colleagues protested, the more adamant he became. As Observatory Director and the nation’s senior astronomer, Méchain had the right to send whom he chose. And he chose to send himself.

  Méchain had something to prove. He would prove he did not need Tranchot to lay out geodetic triangles. He would prove he could traverse an arc as great as Delambre’s. He would prove he did not need his wife’s help to complete a mission. Above all else, he would prove he could be trusted. Beneath their accolades Méchain could sense his colleagues’ skepticism. (They were professional skeptics.) He still had yet to release all his data for the latitude of Barcelona. He had not handed his logbooks over to Delambre. Only a new expedition could redeem his reputation, the thing he held most dear.

  He had a secret motive as well. By extending the arc to the Balearic Islands, he would leapfrog the contradictory latitudes of Barcelona and fix a new secure southern anchor for the meridian. This was not a task he could hand over to someone else. Another savant, triangulating from Barcelona, might discover that its latitude did not match the published results. Already Alexander von Humboldt, on his way to South America, had stopped in Barcelona, checked himself into the Fontana de Oro, and set up his own repeating circle on the hotel terrace. He had taken latitude measurements there, he said, to follow in the footsteps of the illustrious Méchain. Was no place on earth safe from these prying savants? Was no fact of nature secure from their meddling? Mercifully, the young German had devoted only one night to observation, and his results did not contradict Méchain’s findings. But he had posted his data privately to Delambre, and Delambre had noted some minor discrepancies.

  In the end, however, all these rationales pale before the only motive that ever really justifies scientific labor. To triangulate across the Mediterranean to the Balearic Islands would require measuring a geodetic triangle with sides 120 miles long, whereas ordinary triangles had sides of forty miles at most. It was a stupendous challenge: an expedition across uncharted terrain. Méchain had long held the extension to the Balearic Islands “close to his heart.” It was a challenge he could not resist.

  That is not to say that the mission served no practical purpose. As Méchain himself astutely noted in his proposal to Napoleon, the expedition would cement the “intimate union” between France and Spain. The Balearic Islands occupied a strategic position in the western Mediterranean. Indeed, the British navy had occupied the island of Menorca in 1798 to intercept Napoleon’s invasion of Egypt, and Spain had only recovered the island in March 1802 when Britain and France signed the Treaty of Amiens. That treaty had ended a decade of warfare and opened the world’s sea lanes to France. Yet the peace was precarious, with Britain and France already probing for advantage. In September 1802 Napoleon—on Delambre and Laplace’s say-so—approved this scientific thrust into the western Mediterranean.

  So scientific history repeated itself: the first time as epic, the second time as quixotic farce. The expedition began, appropriately enough, with Méchain on one of his periodic upswings. He spent 1802 assembling a team. This time, he intended to do things right. To maintain the repeating circle, he recruited a young naval engineer named Dezauche. For diplomatic cover he invited a former student of his, Jean-Baptiste Le Chevalier, who had just returned from a year spent in Madrid, ostensibly as an apostle for the metric system, but more probably as a spy. And for moral support, Méchain took along his younger son, Augustin, now a strapping lad of eighteen, born on the grounds of the Observatory and home schooled in astronomy.

  Méchain also adapted his equipment for the mission. He refitted his Borda circle with more powerful lenses to triangulate far across the Mediterranean. And he procured outsized parabolic reflectors—some of them specially ordered from London—to take accurate nighttime readings. By early 1803 all the human and material elements were ready. He reminded his team to bear in mind that “never before and never again will anyone undertake so vast and important an operation under the watchful eyes of all the savants of Europe, subject to their criticism and to those of the centuries to come.”

  As before, Méchain’s final act before leaving for Spain was to hand over a document: not a power of attorney this time—Madame Méchain had already been authorized to administer the mission’s 20,000-franc budget and run the Observatory in his absence—but rather the data Delambre had waited three years to publish. This consisted of his geodetic results, described in indifferent prose, and the same summary data he had already supplied to the International Commission.

  Méchain expected to complete his mission in six months, and be back in Paris in ten. He planned to leave in early February, measure the triangles before the summer haze set in, observe the new southernmost latitude on the island of Ibiza during the winter, and resume the directorship of the Observatory by spring. He planned to do everything right this time. But the usual delays—as inevitable as they were unanticipated—prevented him from leaving Paris until April 26. After passing through Perpignan, he and his team sailed into Barcelona harbor on May 5, 1803—at which point everything fell to pieces.

  Nothing in Spain was ready. Everywhere he turned he found obstruction, incompetence, conspiracy. On his first day in Barcelona the governor-general informed him that Madrid had yet to supply the passports he would need to travel to the islands. Next he learned that Captain Enrile of the frigate Prueba (Test), who had agreed to transport him across the straits and assist in the measurements, had been held up in the port of Cartagena, apparently on orders from Madrid.

  These obstacles—or so his Spanish friends informed him—were no accident. Father Salvador Ximenez Coronado, director of the Royal Observatory of Madrid, hated France, hated the French Revolution, and considered the metric system a “fantastical lie” to pervert Spanish virtue. José Chaix, the Observatory’s vice-director, who had come to assist Méchain, warned the Frenchman that Ximenez Coronado was “ignorant, malevolent, and a mortal enemy of the sciences and all who cultivate them.” From Madrid he was blocking any assistance for the expedition. At last Méchain had a real conspiracy to contend with.

  Behind these petty intrigues loomed the prospect of renewed war between France and Britain. Spain hoped to stay neutral, but seemed likely to be drawn into the conflict over the Mediterranean sea lanes. Méchain’s
Paris colleagues asked their British counterparts to intercede with the British navy and grant safe conduct to the peaceable scientific mission. In the meantime, Méchain deferred his sea voyage. Instead, he set off with his team down the Catalan coast, scouting out new stations in the mountains south of Barcelona.

  By attaching a new chain of triangles to his old chain via the stations of Montserrat and Matas, Méchain intended to bypass his old measurements at Mont-Jouy and the Fontana de Oro. During July and August, through the all-consuming Catalan summer, he sized up stations as far south as Montsia, an isolated 2,200-foot peak that marked the border where Catalonia ended and the Spanish province of Valencia began. There, on the dusty mountain above the pink flamingo marshes of the Ebro river delta, he was joined by Enrile, and they began triangulating their way back north toward Barcelona. All that autumn they worked, through torrential rains and gale-force winds. It was just Méchain’s bad luck that the mild Catalan autumn had suddenly turned ferocious. By late October he found himself back up at the Montserrat monastery, enjoying its thousand-year-old tradition of hospitality, and climbing once again to the Notre Dame chapel to take his measurements on top of the organ-pipe stone pinnacle. (Five years later, the monastery would go up in flames during Napoleon’s invasion.) Then in early November he went back down to Barcelona to prepare again for his sea trip across the straits.

  A REFLECTOR SIGNAL ABOVE MONTSERRAT