The Measure of All Things

by Ken Alder

  Among the sixteen savants who scratched their name below was the young MÉCHAIN.

  Geodesy would not only colonize the globe, it would colonize time. Built into the embankment of the nearby island of Elephantine, the expedition discovered the “Nilometer,” an ancient standard of length that gauged the great river’s height. Comparing this ancient measure with the new meter seemed to suggest that Eratosthenes’ estimate for the size of the earth had come within 0.4 percent of the modern value. And when they looked even further back in time, to the origins of Egyptian civilization a full three millennia earlier, the French discovered something more remarkable still: evidence that the ancient Egyptians had also derived their standard measures from geodesy, building them into the design of the Great Pyramid at Giza. There really is nothing new under the sun. Already some Ancien Régime astronomers had speculated that the Egyptians had derived their standard unit of length from the base of the pyramid, itself said to be 1/500 of one degree of the circumference of the earth. Now the expeditionary savants had discovered evidence that the perimeter of the Great Pyramid measured 1,842 meters, which came to within a miniscule 0.5 percent of the value of one minute of the earth’s meridian. Peering into antiquity, the savants saw their own origins reflected back at them. Whether this was a coincidence or not, no one was prepared to say.

  The invasion was an imperial fiasco. Nelson destroyed the French fleet at the Bay of Abukir, Napoleon slouched back to Paris, and his geodesers were left up the Nile. But the invasion proved a scientific success. The expedition mapped a possible canal through the isthmus of Suez. French archeologists unearthed the Rosetta stone. And by agreement with the British, the remnants of the expedition, young Méchain among them, sailed back to France in October 1801, with their invaluable logbooks.

  Other Frenchmen, meanwhile, were extending their metric rule even further afield. Where the diversity of measures had once hampered colonial trade, the metric system would coordinate a new overseas empire. During the Ancien Régime, the residents of then-French New Orleans had complained that ship captains often shorted their deliveries of flour, beef, lard, and wine. The captains had always responded that these were not short measures, merely different measures. Not to be outdone, the colonists ran the deceit in reverse. Merchandise often arrived short-weighted from the Americas “where they say trickery and bad faith are contagious.” The Crown ordered all parties to use standard barrels, filled to within one sixteenth of true weight. But the official measurement bureaus—established to levy taxes and stop smuggling—never monitored more than a tiny portion of the colonial traffic. The metric system now promised to integrate the Caribbean colonies with the mother country, rationalizing transatlantic trade, just as the meter would tame the world.

  Already the French state had dispatched circumnavigators armed with Borda’s repeating circles to chart the globe. Between 1785 and 1788, the Crown sent La Pérouse to explore the Pacific coast from Alaska to California, and then across to Asia and Australia. He sent back reams of precision data before ultimately vanishing in the Indian Ocean. Between 1791 and 1794, the Republic sent Entrecasteaux on a mission to learn the fate of La Pérouse. He charted the Indian Ocean and some of the South Pacific archipelagoes before succumbing to disease. In the short run the French metric empire failed, but it would return.

  This project of global coordination depended on making the meter “definitive.” Making the meter definitive meant that the International Commission had to guarantee its precision. So the Commission focused its attention on the exactitude of Delambre and Méchain’s seven-year mission.

  But as yet Delambre and Méchain were not ready to present their data—or at least Méchain was not. In the meantime, then, as a pledge of their exactitude, the French offered to stage a “theater of precision” under the Commission’s supervision, pitting Delambre against Méchain in a friendly competition to determine the latitude of Paris. Paris was one of those “superfluous” latitudes chosen to exhibit the curvature of the earth as it arced from Dunkerque to Barcelona. Each astronomer would measure the capital’s latitude from his respective site: Delambre from the rooftop of 1, rue de Paradis, and Méchain from the rooftop of the National Observatory, which he now directed. Both men would then adjust their measurements to converge on the Panthéon: offering “authentic proof” of the excellence of the repeating circle and the skills of the savants who wielded it.

  The great dome remained essentially unchanged, a testament to the royal state’s engineering prowess and magnificent investment. But the meaning of the building had been altered—again—along with slight changes in the decor. Delambre’s old crow’s-nest observatory had been torn down. The 52,000-pound statue of Fame had been declared too burdensome for the dome to support. Mirabeau, the first man to be panthéonized—and the first to be de-panthéonized—was now supposed to be re-panthéonized—except that no one could find his body. Descartes, France’s greatest savant, was also being reconsidered for the honor.

  Delambre and Méchain both began observing on December 7, although they did not embrace their roles with equal enthusiasm. In addition to the faithful Bellet, Delambre was also assisted by Charles de Pommard, the son of Elisabeth-Aglaée Leblanc de Pommard, a longtime intimate of Delambre and a gifted scholar of Latin in her own right, “learned . . . , but not pedantic.” She and her son now resided on the rue de Paradis with Delambre, who doted on the boy. He was already six feet tall, with gray eyes and chestnut hair, and Delambre thought he combined “much intelligence with a great love of work.” The young man hoped to become an astronomer—or at least that was Delambre’s fond hope. Each night that winter, they climbed to the rooftop above the Marais to observe the stars. Each morning, Delambre handed down their nighttime observations to the International Commission.

  Méchain did no such thing. He held fast to his data, as he always did—and in return the data tortured him, as they always did. After twenty nights and five hundred sightings, he announced that he would have to start from scratch. His data were inconsistent. This time it was the wintry cold of northern France that was apparently to blame, rather than the heat of Catalonia. His assistant seemed incapable of maintaining the level of the instrument. Or perhaps the refraction correction was askew. In any case, it was all too much. He was despondent, distressed, desperate. To Delambre, he complained that if he did not get acceptable results soon, he would “renounce it all.” To Borda, he admitted that his results were unacceptable, while “Delambre obtains results that are as consistent as one could wish.”

  The self-doubt that had stalked Méchain through the mountains of southern France had followed him to Paris. Melancholic comparisons sapped his confidence. Every morning he learned that Delambre’s results had arrived on the Commission’s desk. And every evening he searched for “the hidden defect” within his data and within himself. He began to avoid his colleagues. He skipped meetings of the Academy of Sciences and the Bureau of Longitudes, over which he nominally presided. He even stopped attending sessions of the International Commission. He announced he was too busy gathering new data to discuss old results.

  The Commission began to schedule its meetings at the Observatory so that Méchain could not avoid them. Delambre had to stall to protect his colleague. In an attempt to drag out the process, he revisited observations long after the results had stabilized. Méchain, meanwhile, refused to hand his data over for others to sort out. No matter how great his anguish, he insisted on bearing the burden of precision himself. Anything else was an abdication of his responsibility. He was not some lackey who had been sent to gather chestnuts, but a savant entrusted to make delicate judgments. He was not a menial technician, but an emissary of the Academy, whose integrity underwrote his observations. He knew better than anyone which values were valid and which were not. It was his duty to choose. . . . But which would he choose: Mont-Jouy or the Fontana de Oro? A full confession or an admission of failure?

  As the delays piled up, rumors began to circulate. Th
e foreign delegates were not as docile as Laplace supposed. The Danish Royal Astronomer, Thomas Bugge, had been the first foreign savant to arrive in Paris. For three months, while he waited for Delambre and Méchain, he had been forbidden to begin his own calculations. The Academy expressly forbade all savants to publicly release their own estimates of the meter in advance of the official report. Bugge had begun to feel he was being used. He heard Lalande privately dismiss the whole operation as “a charlatanism of Borda.” Now, three months after Delambre and Méchain had returned, the Frenchmen had yet to present their geodetic data. Whisperers made slanderous accusations: the data were wretched, the mission had been botched. If the conference was not concluded by January, Bugge declared, he would return to his duties back home.

  When rumors circulate through the world of cosmopolitan science, they circulate far and fast. A German astronomer wrote to Lalande with evident schadenfreude of “the scandal of the new measurements.” He had heard from Bugge that the expedition’s value for the curvature of the earth was apparently implausible and its geodesic measurements were “worthless, poorly executed, inconclusive, and untrustworthy—which pains me greatly.” “These shameful aspects of astronomy are best kept hidden,” he purred with thinly disguised glee. Nearer to home, an obscure amateur astronomer from the French provinces wrote to Delambre to express condolences that his “zeal and skill had not produced satisfactory results.” Although he did not know the astronomer personally, he offered him this consolation: “You have been poorly seconded.”

  When January ended without Delambre or Méchain presenting their data, Bugge acted on his threat. No sooner had he left for Copenhagen than he was attacked in the Paris press for “ridiculing” the metric project. Yet his departure provoked the French into action. Delambre stopped covering for his colleague and formally presented his own data to the International Commission on February 2, 1799. It was an all-day ordeal. The Commissioners went through each page of his logbook, querying each station, vetting each observation. In the end, they accepted almost all his data, including some results Delambre himself doubted. But as he himself noted, once data were recorded they became a sacred thing. At this remove from the time and place of observation, it was no mean feat to distinguish a flawed from a valid result. The commissioners had no choice but to trust the logbook and accept its inky assertions, no matter what the author himself now said. By the day’s end, Delambre’s triangles from Dunkerque to Rodez had been officially endorsed, as had his latitude data for the northern anchor at Dunkerque. Méchain was next.

  A few days later, Laplace himself paid a private visit to the Observatory. He had come to deliver an ultimatum. Méchain had ten days to hand over all his data. No further delay could be tolerated.

  It is easy to picture Méchain’s reaction: his eyebrows hitched high in supplication, his eyes searching for some sign of sympathy from a man who could see right down to the whirling nebula of dust that had formed the solar system. There was nowhere left to hide. Every excuse was worn out, every academic courtesy exhausted. Méchain’s moment of trial had come. So he agreed to present his data “without fail” in ten days, under one condition. Rather than supply his original logbooks—which he admitted were in a state of disarray—he would present the summary results for each station as corrected by the usual formulas. To this, Laplace secretly agreed. That was how badly the Commission needed Méchain’s data.

  In the intervening ten days, Méchain discovered that a loose screw on his lower scope had been responsible for his erratic data, or so he informed the Commission. His results had now begun to converge, and he promised to make his presentation ten days hence. Indeed, they were approaching within 0.13 seconds of Delambre’s. It was a stunning display of observational prowess. By locating his position on the surface of the earth to within thirteen feet, Méchain had demonstrated that, in the right hands, the precision of the repeating circle was limited only by the observer’s patience. Naturally, the Commission agreed to wait.

  Ten days later he was still not ready to present his data. And ten days after that, he postponed the meeting again. Then, finally, on March 22, Méchain presented the results of the southern expedition.

  He arrived for the all-day session with his results copied out in a beautiful scribal hand. The commissioners subjected his results to the same ordeal that Delambre had faced. The angles for each station from Mont-Jouy to Rodez were vetted individually before being officially accepted. At times, Méchain considered the review “a bit severe.” But in the end the Commission was compelled to congratulate Méchain for the remarkable consistency of his triangles. As for his latitude data from Mont-Jouy and the Fontana de Oro, they too were found to be in superb order, and in remarkable conformity with one another. Indeed, their conformity was so great that, at Méchain’s request, the International Commission agreed to set the Fontana de Oro data aside as redundant, and use only the data from Mont-Jouy.

  Just like that, the nightmare lifted. His anxieties, his fears, and his sense of inadequacy, all evaporated like phantasms. The International Commission had recognized his work as a masterpiece of astronomical precision. Indeed, one of the foreign commissioners privately approached Delambre to ask him why his results were not as precise as Méchain’s. The tables had turned. Méchain had triumphed.

  All that remained was to boil down those concatenated results into a single number: the meter. For the next few weeks, each commissioner calculated independently, using his own preferred method. The mathematician Legendre deployed refined calculations using ellipsoid geometry. The Dutch astronomer Jan Hendrik Van Swinden made use of traditional geodetic techniques. Delambre employed improved methods that he had recently published.

  Borda was not present for these final calculations. The inventor of the repeating circle and the guiding force behind the meridian project did not live to see the meter become definitive. During Méchain’s final procrastination the old commander, after a long illness, died. In a pounding rain, a cortège of international savants bore his body up a muddy road for burial below Montmartre. His legacy was a conundrum.

  As each savant completed his geodetic calculations, it became increasingly clear that the rumors were justified: something was wrong. The meridian results were shocking, unexpected, inexplicable. Against all odds, the meridian expedition had produced something unanticipated: genuine scientific novelty.

  This had never been their intention. Delambre and Méchain had not been sent out to unearth new knowledge. They had been sent out to refine to a nicer degree of exactitude what was already known. But the world, they had now discovered, was more eccentric than anyone supposed. Was it a scandal, or a discovery?

  According to the data gathered fifty years earlier in Peru and Lapland, and confirmed by Cassini III in France, the eccentricity of the earth was approximately 1/300—which is to say that the earth’s radius at the poles was 1/300 (or 0.3 percent) shorter than its radius at the equator. By contrast, Delambre and Méchain’s data for the arc from Dunkerque to Barcelona suggested that the eccentricity was 1/150, or twice as great. Even more startling, when the Commission plotted the curve tracked by the intervening “superfluous” latitude measures at Dunkerque, Paris, Evaux, Carcassonne, and Barcelona, they discovered that the surface of the earth did not even follow a regular arc, but shifted with every segment. It was a stunning discovery. But what did it mean?

  The reversal clearly delighted Méchain. It was a vindication of sorts. His colleagues would now regret their refusal to let him triangulate as far as the Balearic Islands or take additional latitude measures. He took the experimentalist’s perverse joy in baffling his theoretical colleagues—Laplace most of all. He gloated that “the earth has refused to conform to the formulas of my mathematical colleagues, who have insisted until now, with absolute certainty, that it is a perfectly regular spheroid of revolution.” It was perhaps Méchain’s one true moment of joy in the entire expedition. It was also a moment of great discovery, as he wrote to his Carcass
onne friends.

  Our observations show that the earth’s curve is nearly circular from Dunkerque to Paris, more elliptical from Paris to Evaux, even more elliptical from Evaux to Carcassonne, then returns to the prior ellipticity from Carcassonne to Barcelona. So why did He who molded our globe with his hands not take more care . . . ? That is what they cannot comprehend. How did it happen that by the laws of motion, weight, and attraction, which the Creator presumably decreed before He set to work, He allowed this ill-formed earth to take this irregular shape for which there is no remedy, unless He were to begin anew?

  Progress, as so often happens, had slipped in sideways where least anticipated. Unexpectedly, the meridian project had produced new and baffling knowledge. Instead of a spherical orange of an earth, or even an oblate tomato of an earth, the geodesers now discovered that they lived on a lumpy squash of an earth.

  Everyone knew that the earth was not a perfectly smooth surface, everywhere becalmed at sea level. For a hundred years, savants had known that the figure of the earth was not a perfect sphere but was flattened at the poles. For the past few decades, they had begun to suspect that its figure was not even an ellipsoid but rather some more complex form of ovoid. Now they had discovered that its shape was not even that of a curve of rotation, a well-defined figure turned symmetrically on an axial lathe. They had discovered that we live on a fallen planet, a world buckled, bent, and warped. And they had discovered this only because they were seeking perfection. Examined from a great enough distance the earth appeared to be a sphere. Move in closer and it appeared flattened at the poles. Closer still—at the stunning level of precision achieved by Delambre and Méchain—and the earth was not even symmetrical enough to be approximated by a curve rotated through space. Delambre and Méchain had discovered that not all meridians were equal. The meridian that ran through Paris was not the same length as the meridians that ran through Greenwich or Monticello or Rome.