The Measure of All Things Read online

  For the past several years, he had been reading ancient Greek science. To supplement his studies he looked into modern astronomy; this led him to the standard textbook in the field, Astronomy by Jérôme Lalande. While he was at it, Delambre decided to audit Lalande’s lectures at the Collège Royal. One day he heard the teacher comment that the Milky Way had the width of the celestial sphere. After class, Delambre informed the professor that this observation had also been made by the Greeks. From then on, whenever Lalande wanted to check to see whether his students had understood his lecture, he called on Delambre, who always supplied the right answer—not surprising really, since Delambre had gotten all his information out of Lalande’s own textbook. Even two hundred years ago, this was a well-worn student ruse. “You’re wasting your time,” Lalande finally told him one day. “What are you doing here?” For no other reason, Delambre confessed, than to get to know Lalande.

  Everyone knew Lalande. He was France’s foremost scientific publicist, enemy of every human prejudice. He was an outspoken atheist. He ate spiders to prove that arachnophobia was irrational. And he had recently calculated the likelihood that a comet would devastate the earth, causing all Paris to panic. He was a small, ugly man, and impossibly vain. He liked to boast he was as ugly as Socrates. If he was not the world’s greatest astronomer—as he sometimes seemed to think—he was certainly its most famous, having trained many of the world’s leading practitioners, the most recent of whom was Pierre-François-André Méchain. In 1783, looking for a new recruit among the dozens of auditors in his astronomy course, Lalande judged “the abbé de Lambre, already very able.”

  Lalande lent Delambre a three-and-a-half-foot sextant and began to incorporate his student’s observations into the third edition of his Astronomy. Delambre’s eyesight had steadily improved with the years. Despite his late start in science, he had become a superb calculator. When he returned for yet another assignment from his maître, Lalande refused. “Don’t be a fool,” he told him. “Work for yourself, and to get into the Academy.” In short order, Delambre made himself into one of the nation’s leading astronomers. When in 1787 the d’Assy family moved to a new home in the Marais—at 1, rue de Paradis—they built him his own private observatory on the roof.

  For the next twenty years, Delambre lived at the d’Assy residence. The elegant neoclassical structure still stands, renumbered more prosaically as 58 bis, rue des Francs Bourgeois, now the administrative offices of the French National Archives. For Delambre, paradise was on the roof. After climbing the ninety-three steps to his bedroom, he had only one short flight more to enter an observatory built to the most exacting specifications and outfitted with state-of-the-art equipment. In 1789, when the observatory was complete, he had every reason to think he had arrived at astronomer’s heaven.

  The French Revolution, which convulsed Paris that year, overturned the comfortable hierarchies of the Ancien Régime, dragging its unexamined standards of conduct and deference into the harsh light of reason. Among these were the standards which governed the nation’s economic life. The wealth of the d’Assy family, for instance, derived from its marketplace monopoly over the up-and-coming Temple district of Paris. Any butcher or baker who wished to set up shop in the neighborhood near the Marais had had to apply to Geoffroy d’Assy for a license. That monopoly had now vanished, along with the rest of the nobility’s legal privileges. French citizens were henceforth free to trade, independent of the personal control of others. Among the unexamined Ancien Régime standards subject to this searching review were measurement standards—and here it was the savants who led the revolution. In 1790, the newly elected National Assembly authorized the Academy of Sciences to design a system of uniform measures. These savants had the courage to look beyond their immediate historical circumstances and build their standards on a permanent foundation. They vowed to choose a set of measures which would “encompass nothing that was arbitrary, nor to the particular advantage of any people on the planet.” They decided to base their new measures on the size of the earth itself.

  In April 1791, the Academy of Sciences confided this meridian mission to three of its members: Pierre-François-André Méchain, Adrien-Marie Legendre, and Jean-Dominique Cassini. These three eminent savants were the logical choice for a body that prided itself on its logic. Méchain was an astronomical workhorse, the editor of the Connaissance des temps, the annual tables of celestial events that guided French navigators at sea. Legendre was a gifted mathematician who had perfected the calculations for the measurement of the globe. And Cassini—or Cassini IV, as he was known—had every reason to consider the meridian mission his birthright. He had been born in the Royal Observatory, which his father, grandfather, and great-grandfather had each directed in turn. The Cassinis were one of the most illustrious examples of sustained family achievement in the history of science. Each Cassini had surveyed the meridian of France with the most advanced equipment of his day. Since his youth, Cassini IV had worked with his father to create the great Cassini map of France, surveying the stations which would serve as the template for the new meridian mission. No one was more capable of following in the footsteps of Cassini III than Cassini IV.

  If pedigree, seniority, and disciplinary turf mattered in the Academy, it was for such logical reasons as these. Yet Cassini was reluctant to begin the mission. For one thing, his wife’s recent death had left him with five young children to care for. Then there was the problem of his royalist sympathies. On June 19, 1791, Cassini had secured a royal audience for the members of the metric commission. At six in the evening, they presented themselves at the Palais des Tuileries: Cassini, Méchain, Legendre, and a fourth savant, Chevalier Jean-Charles de Borda, the inventor of the repeating circle, the new instrument which would push the expedition to a new level of precision. In the eyes of history, Louis XVI has earned a reputation as a political simpleton. But he had his talents. He was a skilled watchmaker and, like his grandfather Louis XV and his great-great-great-grandfather Louis XIV, a connoisseur of cartography. After all, if the Cassinis owned the map of France, the Bourbons owned the real thing.

  The king also took a surprisingly close interest in the spending of the royal purse. “How’s that, Monsieur Cassini?” he asked the savant. “Will you again measure the meridian your father and grandfather measured before you? Do you think you can do better than they?”

  Cassini managed to preserve filial respect while holding out the promise of progress. “Sire,” he answered, “I would not flatter myself to think I could surpass them had I not a distinct advantage. My father and grandfather’s instruments could but measure to within fifteen seconds; the instrument of Monsieur Borda here can measure to within one second. That is the sum of my merit.”

  The king’s sangfroid was all the more remarkable because that evening the royal family had been secretly preparing to flee the country. The next morning, the king and his immediate circle set out on the infamous “flight to Varennes” which ended when a provincial innkeeper spotted the king, disguised as an English merchant, walking with the notorious Bourbon waddle. Louis was hauled back to an enraged capital and confined to his palace under the city’s watchful eyes. Cassini henceforth considered himself released from all obligations to an “illicit, usurping, seditious government of assassins.” If Louis XVI refused to serve France, how could Cassini IV serve her?

  But while Cassini dithered, the rest of the government grew impatient. Jean-Marie Roland, chief minister of the nation, was an expert on the new economy transforming Britain. He wanted France to enjoy the advantages of a uniform system of measures. Such a reform would aid the free circulation of grain, and so help resolve the food crisis at the heart of the nation’s troubles. A modern nation needed a standard, any standard, and the surest course of action would be to declare the units used in Paris the national units. On April 3, 1792, Roland threatened to do just that.

  Roland’s demand threw the Academy into consternation. Their dream of a universal measure seemed abo
ut to evaporate. At their next meeting, they divided the meridian expedition into manageable sectors—and urged Cassini to set out. One commissioner would take charge of the northern portion, from Dunkerque to Rodez, while the other would take the southern portion, from Rodez to Barcelona. If the northern sector was twice as long as the one in the south, that was because the north had been previously surveyed, most recently by Cassini’s father in 1740, whereas the south was more mountainous and included the uncharted Spanish section. This division of labor was only provisional, of course; the two teams were to work their way toward each other as rapidly as possible and meet up where they would.

  Yet even as he refused to set out, Cassini asserted his right to command any meridian expedition. The Revolution may have upended the kingdom, but the Academy still stood upon certain formalities. He offered to remain in Paris while an adjutant carried out the actual surveying. In the end, the Academy rejected this proposal. A savant needed to have direct contact with nature, to travel and measure for himself, so that he might personally vouch for the reliability of his findings.

  This was where Delambre came in. On February 15, 1792, he had been unanimously elected to the Academy—in part, as Lalande informed him, because the members thought they might need him for the meridian mission. When Cassini refused a final plea to set out, Delambre was elected on May 5 to lead the northern portion of the meridian survey, with Méchain to lead the southern sector. Decades later, Delambre would recall pleading with Cassini to change his mind. The two men had graduated from the same school a year apart. In revolutionary times, Delambre warned his colleague, a citizen must demonstrate his devotion to the national good, if only to shield himself from reproach. But Cassini would not serve a régime he considered illegitimate. For Delambre, it was the sort of career opportunity the Revolution made possible.

  As soon as the king’s authorization arrived on June 24, Delambre began to scout out stations in the vicinity of Paris. His plan was to revisit the stations of the 1740 Cassini survey of the meridian, conduct improved measurements with his new instruments, and wrap up his mission by the end of the year, applying to his geodetic measurements of the earth the same thoroughgoing precision he had so recently brought to his astronomical measurements of the heavens.

  Delambre was a quick learner—a humanist in his mid-thirties who had, in the course of one decade, become one of the nation’s leading astronomers—and the central method of geodesy was in principle quite simple, little more than Euclidean geometry on a curve. The method was known as triangulation and for two hundred years cartographers had been using it to map terrain, and would continue to do so right up to the advent of the satellite. Triangulation relied on an elementary theorem in geometry: if you know all three angles of a triangle, plus the length of any one side, you can calculate the length of the other two sides. Hence, if you know all the angles in a set of triangles connected side by equal side in a chain, plus the length of any single side, you can calculate the lengths of all their sides (since every two connected triangles share at least one side). The geodeser simply took advantage of this. First he identified a series of observation stations that might serve as the nodes (the vertices or “corners”) of his triangles—church steeples, fortress towers, open hilltops, purpose-built platforms—each node visible to at least three other stations, such that they formed a chain of triangles that straddled the meridian. He then traveled from station to station measuring the horizontal angles separating adjacent stations. Next he measured along the ground the actual length of one side of one of the triangles—a “baseline”—typically by placing rulers end to end over the course of several miles, and used this value to calculate the lengths of all the sides of all the interconnected triangles. From this, he could derive the distance along the meridian arc from his northernmost to his southernmost station. Finally, he determined the respective latitudes of the northernmost and southernmost stations using astronomical observations, so that he might extrapolate from the length of that arc to the full quarter meridian. And that gave him the size of the earth.

  This was the principle, anyway. But as in any science where extreme precision is sought, the practical challenges were considerable. First, because the geodeser necessarily measured the angular distances from stations that were somewhat elevated, he had to adjust all his values to a common surface-level triangle. Second, because he could not always place his measuring instrument at the exact vertex of that triangle, another correction had to be included. Third, because atmospheric refraction distorted apparent sightings, all the angles had to be adjusted for the bending of light. And fourth, because the angles of a triangle on a curved surface do not quite add up to 180 degrees, this had to be corrected for as well. All these adjustments complicated the calculations. They did not change the basic principles involved.

  By revisiting the stations used in Cassini’s 1740 survey of the French meridian, Delambre hoped to skip one of the most laborious steps in any triangulation: the identification of workable stations. But first he had to verify that Cassini’s sites could still serve his purpose. For their station in the capital city of Paris, the surveyors of 1740 had chosen the belfry of the church of Saint-Pierre near the summit of Montmartre, a Benedictine abbey which still stands today, a stone’s throw from the current site of the church of Sacré-Coeur. On June 24, Delambre set out with his two assistants to climb the hill of grapevines, quarries, and windmills. Even then, Montmartre offered a famous panorama over Paris. From the hilltop, they could look back on the jumble of low gray buildings which swarmed like angry insects around the city’s massive royal and religious edifices.

  But when they climbed still higher, to set up the instrument on the platform of the bell tower of Saint-Pierre, Delambre met with a disappointment. The view was miserable. None of the surrounding sites used in 1740 was visible. Indeed, the church tower barely cleared the roof. In every direction he looked, the view was blocked by surrounding buildings.

  Back in the capital an old etching cleared up the mystery. Fifty years before, the church had been capped by a tall wooden belfry, since destroyed. A half-century of urban construction and demolition had transformed the Paris cityscape, leveling steeples, raising palaces, filling empty lots. The abbey of Saint-Pierre would no longer serve, and Delambre would have to locate an alternative station elsewhere in the capital. This, he decided, could best be done from the outside looking in. He decided he would travel counterclockwise around the capital, visiting the peripheral stations which ringed the city, scanning for an appropriate landmark in the center.

  The next few weeks of travel showed him just how much the past fifty years had transformed the French countryside as well. To the south of the city, the observers of 1740 had adopted the tower of Montlhéry, an abandoned medieval fortress which guarded the main route into Paris. The tower still stood, as it does today, pigeons fluttering in its broken interior. Delambre discovered that the first ten steps of the staircase had crumbled away, and though he sent a workman up to verify the view, he had no appetite for hoisting himself and his instruments up the ninety-six-foot turret. He settled for an observation point on the overgrown fortification wall below.

  Next, Delambre visited the Malvoisine farmhouse, perched on a low ridge twenty miles to the southeast, which had been used by Cassini III in 1740. The site is still a working farm, its muddy courtyard piled with machinery and patrolled by dogs. But even from the farmhouse roof Delambre could barely make out the adjacent station of Montlhéry. Stands of tall trees had grown up around the property in the intervening fifty years. He secured permission from the owners to add six feet of height to the farmhouse chimney so as to create a workable observation signal there, and continued his travels counterclockwise around the capital.

  The Gothic church tower at Brie-Comte-Robert still suited his requirements. But at Montjai, Delambre encountered new obstacles. Even in 1740, Cassini III had hesitated to climb the medieval tower—the eastern twin of the tower at Montlhéry—not for fea
r of the demons that supposedly haunted its ruins, but because he had been warned that the tower might fall down. Delambre decided the better part of valor was to hire a local carpenter named Petit-Jean to rig a freestanding observation platform alongside the structure. While that work got underway, he continued to Dammartin, a town on top of a steep ridge just outside today’s Charles de Gaulle airport. There he learned that the Collégiale chapel, which had served Cassini III in 1740, was about to be sold off as part of the Revolutionary sale of church lands, and the buyer intended to demolish the church for building materials. On the spot, Delambre decided to make this site his highest priority. But first he had to verify that he could see Dammartin from Saint-Martin-du-Tertre, the next station to the north; there too his preliminary observations did not match those of 1740, suggesting that the position of the church belfry had been shifted by several hundred feet at some point during the past fifty years.

  Geodesy is a natural science. It is the science which measures the size and shape of the earth, a planet formed by the same gravitational forces that had spun the solar system out of a disk of luminous nebular dust (according to Pierre-Simon Laplace’s reigning theory). What is the earth’s shape? Even more: what is meant by shape? Our planet’s surface is not smooth. It is scarred with mountains and valleys, roiled by geological processes. The imaginary shape that our planet would possess if its surface were everywhere at sea level, which scientists today call the “geoid,” was known in the eighteenth century as the “figure of the earth.” A meridian, for these savants, was the surface of an imaginary canal that ran unswervingly from north to south; in this case, from the North Sea to the Mediterranean. Yet to measure the length of this canal, and hence the figure of this imaginary earth, geodesers relied on the very geological processes that have distended the surface of the planet, creating the mountains and hilltops from which they surveyed the terrain.