The Measure of All Things

by Ken Alder

  —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 ma
king of new knowledge: Bugge of Copenhagen, Zach of Gotha, Maskelyne of Greenwich, and now his compatriot, Delambre of Paris.

  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.”

  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.”