CHAPTER ELEVEN

Méchain’s Mistake, Delambre’s Peace

The fault, dear Brutus, is not in our stars, But in ourselves, that we are underlings.

—WILLIAM SHAKESPEARE, Julius Caesar

The historian owes the dead nothing but the truth.

—J.-B.-J. DELAMBRE, History of Modern Astronomy

What is error? And who decides when it is too great to bear?

Delambre finally grasped what in retrospect appeared obvious. Méchain had deceived him, had deceived them all, and had confessed as much in countless letters, if only they had read between the lines. Throughout their expeditionary years, Delambre had continually reassured his colleague: your measurements are excellent, your measurements are as good as my own. Meanwhile, in his own mind, he had dismissed Méchain’s worries as melancholic self-deprecation, tinged perhaps with jealousy. Then, when Méchain presented his final results to the International Commission, Delambre considered himself vindicated: Méchain’s values for the latitude of the Fontana de Oro beautifully matched his latitude for Mont-Jouy. Everyone had always known that Méchain was a worrier, a pessimist, an obsessive—the very traits which made him a man of unimpeachable integrity. His false alarms had only confirmed their judgment.

Except Méchain had fudged the data.

Delambre had vowed to record every last detail of their expedition “without the least omission, without the least reticence.” When he presented a copy of the Base to Napoleon, the Emperor was magnanimous in his verdict. “Conquests will come and go,” the conqueror said, “but this work will endure.” Delambre was now composing the second volume, to be devoted to latitude measurements. This time, rather than simply transcribe his partner’s summaries, Delambre had decided to pull the data directly from Méchain’s original logbooks.

Except there were no logbooks, only loose scraps of paper.

Méchain’s manuscripts, carted back from Spain, testified to his agony. Time and again he had reworked the data, trying to make them conform to expectations, or what he thought others expected of him. It went far beyond the Barcelona data. He had recorded all of his observations on loose sheets of paper rather than in a bound notebook with numbered pages. He had also recorded them all in pencil. As Delambre wryly remarked, “Loose pieces of paper can be lost; pencil marks fade.” More to the point, loose pieces of paper can be torn up; pencil marks can be erased. In some cases Méchain had recopied observations onto pages dressed up to look like originals, whereas the true originals had vanished. In other instances he had erased values, or rewritten his pencil marks to alter the numbers beneath.

Delambre’s task was to fashion this mess into a permanent record. He retraced each pencil mark in ink, pasted the sheets into a bound volume in chronological order, and appended marginal notes to explain their provenance. He reconstructed Méchain’s journey like a historian, fashioning a logbook where none had existed before. The result was as revelatory as the meridian journey itself.

Méchain had suppressed and altered data. Sometimes, to disguise an anomalous geodetic reading, he had folded a discordant series into a longer series, as if it had been observed on the same day, making the result appear more consistent than was warranted. More often, he had simply discarded those series that did not accord with his prior results, or that prevented his triangles from converging on 180 degrees. In one instance Méchain had dropped a series that appeared to him anomalous, whereas, Delambre discovered, Méchain had simply miscalculated and the data were sound.

MÉCHAIN’S “LOGBOOK” ASSEMBLED WITH NOTES BY DELAMBRE

In the years 1806–10 Delambre reconstructed Méchain’s logbook by pasting into a bound register the loose sheets on which Méchain had recorded his data. Delambre organized the sheets in chronological order, retraced Méchain’s penciled data in ink, and indicated the provenance of each document. On this particular page Delambre has pasted Méchain’s celestial observations from Mont-Jouy for December 15, 1793. In the margin Delambre notes: “Here are some changes that Méchain has made to the angle measurements for which it is difficult to imagine a legitimate rationale.” He goes on to explain that Méchain’s calculations on this page leave no doubt whatsoever that the corrections are not legitimate, but serve only to make the data appear more precise than they actually are. (From the Archives de l’Observatoire de Paris)

As he reconstructed the original values, Delambre also recorded these values in the margins of his personal copy of the Base (now located in the Karpeles Museum in Santa Barbara, California). Page after page of the Karpeles edition documents the data Méchain suppressed or doctored. If anything, the fudging intensified as Méchain approached his encounter with the International Commission. Yet amid the chicanery, Delambre noted a paradoxical integrity at work. In no instance had Méchain’s alterations distorted the final result by more than two seconds, meaning that his adjustments were minor compared to the uncertainties caused by the observer’s inability to correct entirely for the refraction of light in the earth’s atmosphere. He had doctored his results, not to alter the outcome, but to make himself look good—that is to say, to look better than his rival colleague. Beneath the printed text on page 510 of the Karpeles edition of the Base, Delambre wrote in ink:

All the variants I have provided, based on the manuscripts of Méchain, are values for which no observer can answer. Undoubtedly Méchain was wrong not to publish these observations as he found them, and to modify them in such a way as to make them appear more precise and consistent than they were. But he always chose his final values in such a way as to ensure that the average was not altered, so there was no real harm in his action, except for the fact that another observer who published unadulterated numbers would be judged less capable and careful.

In situations where he had nothing else to rely on, Méchain had clung to those who appeared more self-confident. It now appeared that Méchain had also doctored his data for the latitude of the Panthéon, so as to approach Delambre’s value. The stunning convergence had been a sham, the moral theater a mirror show. The irony—which neither Méchain nor Delambre could know—is that Méchain’s suppressed data more closely approximate today’s accepted latitude for the Observatory.

The Barcelona latitude data were something worse. There Méchain had largely been obliged to keep faith with the Mont-Jouy data, having mailed his original results to Paris. (Though even here he had adjusted the observed values after the fact.) But he had left no paper trail for the Fontana de Oro data and was therefore free to rework those results endlessly. The earliest version, which Delambre considered otherwise irreproachable, indicated a residual discrepancy of 3.2 seconds between the latitudes of the Fontana de Oro and Mont-Jouy—the unreported gap that had tortured Méchain for a decade. Yet in later versions Méchain had systematically jacked up his Fontana de Oro observations by three seconds to account, he claimed, for the width of the sight line in his scope. This tweaked the two latitudes back into alignment. But as Delambre noted in the margins of the reconstituted logbook, Méchain had applied this post-hoc adjustment inconsistently: adjusting the values for some stars and not others, and neglecting to “correct” his Mont-Jouy data at all. The inference was clear. Méchain had adopted this “specious” adjustment to convince the Commission to expunge his Fontana de Oro results, not because they were wrong, but because they appeared to be right—and were hence redundant.

Amid the flimflammery, Delambre again saw a paradoxical integrity at work. If Méchain had been disingenuous with the Commission, he had done so in order to keep his doctored data out of the final determination of the meter. He had used subterfuge to spare the Commission an agonizing choice. He had lied (if only by omission) to keep his results honest.

Méchain’s goal had been utopian in its simple-mindedness: he had tried to undo the mess he had made of his mission. He had tried to return to a time before his discrepancy, a time before his accident, a time before the war. No doubt, if he could have found a way to do so, he would have reversed the whole Revolution. It was, in a sense, a perversion of the redemptive promise that science had made since the days of Francis Bacon. Having eaten of the fruit of the Tree of Knowledge (the original error, you might say), human beings were now permitted to use that knowledge to work their way back to Eden. Méchain had sinned to reclaim his innocence. He had tried to erase the past.

Delambre refused to go along with this erasure. Having assured the world’s savants that he would publish all the data of the metric expedition, he (mostly) kept his word. He set out to filter the past through his own scrupulous hands, removing the spurious adjustments, recalculating Méchain’s data, and creating a new set of tables sufficiently trustworthy to publish. In November 1807, in Volume 2 of the Base, he presented the data from Mont-Jouy alongside the data from the Fontana de Oro. As for the remaining discrepancy of 3.2 seconds, Delambre wrote, “it is a fact worthy of astronomers’ full attention.” He even said so in the foreign press. Delambre had decided to treat Méchain’s “error” as a discovery, not a scandal.

Yet there were parts of this story that Delambre did not want the public to know. The lay public did not need to know that Méchain had fudged his data or lied to his colleagues. Too many savants already doubted the meter’s precision. The metric system had enemies enough. Delambre’s solution was to deposit the original manuscripts of the meridian expedition in the archives of the Observatory, and to announce their disposition in the Base. On August 12, 1807, in the octagonal meeting room of the Observatory, where the portraits of Delambre and Méchain now hang, a legal protocol witnessed by three members of the Observatory detailed the inventory. In a note appended to one of Méchain’s reconstructed logbooks Delambre explained his rationale for deciding which materials to publish:

I have carefully silenced anything which might alter in the least the good reputation M. Méchain rightly enjoyed for the care he put into all his observations and calculations. If he dissimulated a few anomalous results which he feared would be blamed on his lack of care or skill, if he succumbed to the temptation to alter several series of observations . . . , at least he did so in such a way that the altered data never entered into the calculation of the meridian.

Then, three years later, after publishing the third and final volume of the Base, Delambre went one step further: he deposited all the private correspondence between himself and Méchain in the Observatory’s archives as well. These letters, however, he thought it “prudent” to place under seal, so that they could not be read unless some serious doubt arose as to the validity of the entire enterprise.

Having called the Barcelona discrepancy a discovery and not a scandal, however, put Delambre under some obligation to explain that discrepancy. There were several possibilities. One might blame the stars or the earth; one might blame the instrument or the methods; or one might blame the observer.

Méchain had blamed the stars—at least at first. His original motive for revisiting Barcelona’s latitude at the Fontana de Oro was an inconsistency within his Mont-Jouy data caused by the star Mizar. He feared that the refraction tables were invalid for towns at lower latitudes, especially for stars that dipped close to the horizon, as Mizar did. Delambre certainly shared this concern and never made use of Mizar. However, even with Méchain’s Mizar data removed, the latitudes of Mont-Jouy and the Fontana de Oro did not agree. As for the suggestion made by later astronomers that Méchain had erred because Mizar is in fact a double star, it turns out that Méchain was well aware of this fact, and always focused on the larger body “in case someone supposes I did not take care.” The fault lay not in the stars.

For his part, Delambre preferred to blame the earth. As he pointed out, the meridian project had confirmed that the shape of the earth was irregular, and that not all meridians were equal. Moreover, by the time he published Volume 2 of the Base, he could cite a new meridian survey in England that confirmed these irregularities. Delambre hypothesized that Méchain’s readings at the two nearby sites had been distorted by local inequalities in the earth’s crust or by nearby mountains. These inequalities, he suspected, had deflected the plumb line the savants had dropped to define the vertical of the star’s transit across the celestial meridian. The plumb line definition of vertical, however, was doubly ambiguous. First, the plumb line pointed to the gravitational center of the earth, and on a nonspherical earth that is not quite the opposite of the perpendicular to the immediate surface of the planet. In other words, astronomical straight up is not the exact opposite of the direction in which gravity tugs down. Indeed, the gap between the two at any point offers a measure of the local difference between the astronomic latitude and the geodetic latitude, reflecting the earth’s eccentricity at that point. Second, the plumb line might be deflected by local gravitational effects (due to mountains and the like) beyond those caused by irregularities in the figure of the earth. This concern was not new. Newton himself had tried to estimate the gravitational pull of mountains. And the French savants had deliberately selected a meridian arc that extended from Dunkerque all the way to Barcelona to avoid any distortion caused by the Pyrénées. Delambre now speculated that Mont-Jouy itself might be to blame for distorting its own measurement.

Today, the science of geodesy consists principally of mapping these gravitational effects. Ballistics engineers estimate the pull of mountains on their rockets. Some of the maps that chart the contours of the geoid are classified as military secrets. Beneath the earth’s surface deep processes have roiled the planet. However, these gravitational differences seem unlikely to explain so wide a divergence in measurements at two sites only a mile apart. The earth’s irregularities are not so finely grained as that.

It is of course possible that Borda’s marvelous instrument was the culprit. Yet Méchain was famous for the excruciating care he took when setting up the apparatus. Nor is there any evidence to support the charming suggestion, made by one Catalan historian, that a patriotic saboteur, posing as an astronomical assistant, queered Méchain’s instrument to prevent him from acquiring data on Barcelona’s defenses. Méchain had always monopolized all the observational work. And while Méchain did use a cumbersome method of calculation that involved much tedious labor, Delambre found that even upon recalculating Méchain’s data, the discrepancy remained.

In the end, Méchain came to blame himself—to his eternal shame and torment. This conclusion was not shared by Delambre. After extensive review, he declared the Fontana de Oro data as credible as the Mont-Jouy data.

There is, however, one other possibility. What if nothing and no one was to blame? Indeed, what if there was no meaningful discrepancy at all? That is: what if the error lay neither in nature nor in Méchain’s manner of observation, but in the way he understood error? Twenty-five years after Méchain’s death, a young astronomer named Jean-Nicolas Nicollet showed how this might be the case.

Nicollet reanalyzed Méchain’s data in a series of steps. First, he threw out Méchain’s data for the inferior transit of the star Mizar, whose passage near the horizon was indeed overly distorted by refraction. Second, he recalculated Méchain’s other stellar heights using accurate tables of stellar declination, tables that had been completed at the very end of Méchain’s life and that circumvented the iterative method by which both Méchain and Delambre had assessed their latitudes. Both these changes were relatively minor, however, compared with the way Nicollet reconceptualized Méchain’s treatment of the data.

Méchain and his contemporaries did not make a principled distinction between precision (the internal consistency of results) and accuracy (the degree to which those results approached the “right answer”). The two are not the same: precise results may appear “reliable” in the sense that they give very nearly the same answer when measured again; yet they may lack “validity” in that they deviate consistently from the “right answer.” Of course, in practice, distinguishing between the two can be extremely difficult because the “right answer” is unknown.

Repetition using the Borda circle was designed to improve precision by reducing those errors that stemmed from the imperfect senses of the observer or the imperfect construction of the instrument’s gauge—the sort of errors we would today characterize as falling into a random distribution. The Borda circle, however, was still subject to errors caused by the basic setup of the instrument as a whole; the sort of errors we would characterize today as those constant (or systematic) errors which made results inaccurate,whatever their level of precision. Constant errors generally go undetected, of course, as long as they stay constant. And in an intuitive way Méchain and Delambre, like all Ancien Régime astronomers, understood this. That is why they were so vigilant about maintaining a consistent setup for their apparatus from one series of observations to the next. What they failed to appreciate was that the same repetition that enhanced precision might reduce accuracy. For instance, constant manipulation of the circle might wear down the instrument’s central axis and, over time, cause the circle to tilt ever so slightly from the perpendicular. It was this unanticipated drift in the constant error, Nicollet suggested, that was the source of Méchain’s discrepancy. This had kept his results for each winter location more or less internally consistent (i.e., precise), while making the results from the two successive winter locations discordant (i.e., inaccurate). Without a concept of error to help him identify the source of this contradiction, Méchain was in torment.

Oddly enough, Nicollet noted, it was Méchain’s own obsessiveness which made it possible to confirm the cause of the discrepancy—and to correct for it. The trick was to compensate for any change in the instrument’s verticality by balancing the data for stars which passed north of the zenith (the highest point of the midnight sky) against those which passed south of it. Because Méchain had measured so many extra stars, such an operation was possible.

To calculate the latitude, Méchain had first calculated the average latitude implied by each star he measured, and then averaged all the averages, giving equal weight to each. Nothing could be simpler—or more naïve. Nicollet, by contrast, first analyzed the data for the stars Méchain had measured that passed north of the zenith (his many observations of Polaris and Kochab, plus those of Thuban and Capricornus), taking the average of the average latitude implied by each. Then Nicollet separately did the same thing for the stars Méchain had measured to the south of the zenith (his sparser observations for Pollux and Elnath). Clustered in this manner, the results seemed to lack precision: at Mont-Jouy the average latitude implied by the north-going stars differed from the average latitude implied by the south-going stars by 1.5 seconds. At the Fontana de Oro they differed by a dismaying 4.2 seconds. But when the northern average and the southern average were themselves combined at each location, they suggested a remarkableaccuracy: the combined latitude for the Fontana de Oro agreed with the combined latitude from Mont-Jouy to within a stunning 0.25 seconds—twelve times as accurate as Méchain’s 3.2-second discrepancy! In sum, Nicollet proved that there was no discrepancy and that Méchain’s reported value for Mont-Jouy was within 0.4 seconds (or forty feet) of the answer indicated by his data, when properly analyzed.

Nicollet was a typical French astronomer of the early nineteenth century: a student of Laplace’s, well versed in error theory. In 1828, when he reviewed Méchain’s results, he was forty-two years old and working part time at the Paris Observatory. Unfortunately, his statistical skills did not stand him in good stead outside astronomy, and he lost his fortune a few years later playing the stock market. He emigrated to America, where his astronomical and mathematical skills earned him the leadership of the first geodetic survey of the upper Missouri and Mississippi valleys. A generation after Lewis and Clark passed through the territory of the Louisiana Purchase, Nicollet compiled the first accurate maps of the Upper Midwest.

The irony was that the very stars Méchain cursed himself for measuring had vindicated his exactitude. By contrast, Delambre had measured only Polaris and Kochab, both of which passed north of the zenith, so his results could not be corrected retrospectively. Between them, Méchain and Delambre had identified most of the sources of error that had produced the discrepancy: the refraction correction, the verticality of the circle, the setup of the instrument. What they lacked was a way to disentangle these errors. Méchain had not so much erred as he had misunderstood what error meant. Yet by his very misunderstanding he had inadvertently contributed to our own understanding of error, forever altering what it means to practice science.

What is error? And who decides when it is too great to bear?

Modern science accepts error as its lot. It does not demand truth from its practitioners, only honesty. It assumes that the truth will emerge eventually from a collective effort—so long as everyone is honest. Certainly scientists care passionately about getting the right answer. But when theory and experiment align too tightly, suspicion is warranted. Thus, the statistician R. A. Fisher concluded that Gregor Johann Mendel’s pea-breeding data could hardly have come as close to the 1:3 genetic ratio as he claimed. The same holds for Robert Millikan, who won a Nobel Prize for an electron experiment in which he suppressed anomalous data. In Mendel and Millikan’s day—from the nineteenth through the early twentieth century—such fudges were common, though frowned on. Today they continue, despite official censure. In Méchain’s day they were not only common, they were considered a savant’s prerogative. It was error that was seen as a moral failing.

Méchain took his science personally. His observations were his to publish or suppress, keep or destroy. He felt no obligation to parade his accomplishments before an anonymous public. Rather, he sought to impress his fellow savants with his ability to approach perfection. Recording his observations in pencil and on loose scraps of paper only facilitated the task of refining the data. Even after he had handed over his scribal report to the Commission, he considered the raw expedition data to be his private property, part of the accumulated experience he carried with him in his trunk wherever he traveled. The data were his legacy and his tombstone; they were all he had. The truth belongs to everyone, but error is ours alone.

Delambre’s scrupulousness was cut of a different cloth. For him, investigators answered to both their colleagues and their sponsors. The Revolutionary government had sponsored their lavish meridian mission, and it deserved a full accounting. That was why Delambre recorded his results like a public official: in ink, in a bound notebook with numbered pages, in order of observation, and with each page signed and dated. He believed that just as the republic operated with transparency—with roll-call votes, public laws, and open trials—so science should open itself to scrutiny. Delambre considered his data public property. All he asked was that he get credit for his labor. Thus, he was forthright about the discrepancies he discovered and the approximations he used. He never pretended that his results were definitive. What mattered was that he had tried to be as exacting as he could, and that the results were sufficiently precise to solve the problem at hand.

Once, on the eve of presenting some astronomical tables to the Academy, Delambre discovered a trivial error in his calculations and spent the next three weeks working day and night to eliminate an error that was “to all intents and purposes imperceptible.” It was the most tedious task in a career of monumental labor, but when it was done, he could hand over the tables with a clear conscience. Then, when a fellow savant detected yet another error—as one colleague soon did—Delambre could freely and publicly acknowledge his mistake and correct it yet again.

As to whether perfection existed “out there,” curled up in nature’s womb awaiting delivery, that was a theological question, and Delambre was a pagan. He had been raised in a devout home, he was schooled by the Jesuits, and he had considered taking holy orders. But he was neither a believer nor an atheist in the manner of his maître Lalande. He was a skeptical Stoic, for whom perfect knowledge lay beyond man’s grasp. Why then should anyone expect him to produce a perfect meter?

This was something he had known all along. He had known it when he stood before the fiery volunteers of Saint-Denis to explain his absurd mission. Even then he had secretly agreed with the volunteers—in part, anyway. His mission was absurd. Why set out to measure the world while the old order was going up in flames, while millions of soldiers were rushing to die in battle? Why measure the world to create a unit of length when a standard “meter” could be created by legal fiat or simple agreement? It was absurd to travel so far to find what lay so near. Yet someone had to do it. Someone had to dedicate himself to the task of reconstructing the world. Otherwise there would be nothing left standing after the soldiers had finished their slaughter and the vandals had leveled the towers to the heights of the “humble cottages” of the sans-culottes. Someone had to construct a new order, a horizontal grid to enable people to keep track of where they stood, and what they made, and how much they bought and sold.

Delambre knew that the International Commission’s boast of perfection was a sham. The Commission had claimed to know the length of the meter to six significant digits, or within 0.0001 percent. Delambre now acknowledged that this was “a precision to which we ought not to presume.” Now that the sanctified platinum bar was safely stored in the National Archives—smug and untouchable in its triple-locked box—he thought it only honest to admit as much. Thus in 1810, in the third and final volume of theBase, he described a range of plausible values for the earth’s eccentricity and a corresponding range of plausible values for one ten-millionth of the quarter meridian. He suggested that the best value for the earth’s eccentricity was probably nearer to 1/309 than the Commission’s 1/334. He took into account both of Méchain’s values for the latitude of Barcelona, thereby shifting the length of the arc by another 0.01 percent. He concluded that a better length for the meter would be 443.325 lignes (rather than the official 443.296 lignes).

It was a trivial adjustment, less than the thickness of a piece of paper. But it was an act of remarkable integrity. Only one decade after the meter had been declared “definitive,” its chief creator, writing in the official account of its creation, acknowledged that scientific progress had undermined its validity. Today we recognize this as a step in the right direction—not because Delambre’s new value closed about a third of the shortfall of the definitive meter (after all, his new value was still less accurate than the provisional meter of 1793), but because it was a calculated homage to the transience of human knowledge.

And Delambre did not stop there. He suggested rounding off the length of the official meter to 443.3 lignes. This may seem another trivial adjustment. But by lopping off two decimal places, Delambre implied that the meter was only accurate to within 0.01 percent. And he noted that the revision had yet another reason to recommend it: the value of 443.3 was easy to remember because it was composed of two 4s followed by two 3s. As for those who still insisted on working with six significant figures, he suggested that they consider the meter to be 443.322 lignes long, because that value too was easy to remember: two 4s, two 3s, two 2s. Nothing illustrates more clearly Delambre’s acceptance of the arbitrariness of conventional standards. As he noted in a private letter to a foreign savant: “Say what you like of the degree of precision we achieved, all I can assure you is that I conveyed every detail of our mission with the greatest possible sincerity and without the least reticence.”

In the end, Delambre took longer to write the history of the meter than to measure France, and in a sense he traveled further in the process. He began writing in 1799 in the wake of the disturbing results of the International Commission. The 1806 volume began as an adventure story; the 1807 volume plunged him into a tale of scandal and discovery; and the 1810 volume concluded with a demonstration of the open-endedness of knowledge. Delambre had come to accept, as Méchain could not, the evanescence of earthly knowledge. So to the extent that he conspired in his colleague’s cover-up he did so for the opposite reason: because he realized that getting the perfect answer did not matter. Which is to say that Delambre understood that Méchain had agonized—and died—for nothing. We live on a fallen planet, and there is no way back to Eden. Delambre had decided to live on the surface of the earth, buckled, bent, and warped though it was.

In coming to terms with the imperfection of earthly knowledge, Delambre had a powerful new intellectual tool at his disposal, one which he and Méchain had inadvertently inspired, but which he alone had lived to take advantage of. For the past century savants had sought to fit imperfect data to a perfect planetary curve. Geodesers had agreed that the earth was an oblate ellipsoid, but they had been unable to agree on its degree of eccentricity, which now seemed, moreover, to vary from place to place. Or were the data faulty? Assume the data then. Assume that the data had been gathered by fallible (but exacting) investigators using fallible (but ingenious) instruments on a (possibly) lumpy irregular earth, and then ask yourself: what was the best curve through the data, and how much did the data deviate from that curve? That was the question Adrien-Marie Legendre asked.

Legendre’s answer, the method of least squares, has since become the workhorse of modern statistical analysis. It was also among the most important breakthroughs in modern science—not because it produced new knowledge of nature, but because it produced new knowledge of error.

Legendre cloaked his personal life in obscurity and invested his clarity in his mathematics. A contemporary of Laplace and Delambre, he was elected to the Academy at the age of thirty for his work on number theory and analysis. In 1788 he showed the geodesers on the Paris–Greenwich expedition how to correct for the curvature of their triangles. Appointed with Cassini and Méchain to the Revolutionary meridian project, he withdrew in favor of Delambre. During the Terror he went briefly into hiding, only to emerge with a bride half his age. Later he codirected the Agency for Weights and Measures and was one of the savants to calculate the length of the meter for the International Commission. He was as baffled by the outcome—an unexpected eccentricity of 1/150—as the rest of them. Five years later—one year after the death of Méchain—progress slipped in sideways yet again.

For centuries savants had felt entitled to use their intuition and experience to publish their single “best” observation as the measure of a phenomenon. During the course of the eighteenth century they had increasingly come to believe that the arithmetic mean of their measurements offered the most “balanced” view of their results. Yet many savants continued to feel, like Méchain, that any measurement that strayed too far from the mean ought to count for less than those near to it, and hence could be suppressed without apology. And even the most rigorous savants were flummoxed when they confronted multivariable phenomena for which they had diverse observations—such as the curvature of a nonspherical earth based on observations at various latitudes, or the elliptical orbit of a planet, especially if that orbit were perturbed. Some mathematicians had tried to find rules to compensate for results that deviated too much. The Jesuit geodeser Boscovich had proposed one method, and several other astronomers had tried their hand. Laplace had introduced a cumbersome method of minimizing the maximum deviation. But these methods remained awkward and unjustified.

Legendre suggested a practical solution. He suggested that the best curve would be the one that minimized the square of the value of the departure of each data point from the curve. This was a general rule, and it was a feasible calculation. It was a practical dictum, and it prompted a radical reconceptualization. Legendre’s least-squares method played off the intuition that the best result should strike a balance among divergent data, much as the center of gravity defines the balance point of an object. As he noted, the least-squares method also justified choosing the arithmetic mean in the simplest cases.

In 1805, just as Delambre was completing the first volume of the Base, Legendre tried out his method on what was now the world’s most famous data set, the one he had puzzled over ever since Delambre and Méchain had handed it to the International Commission. Legendre assumed that the earth’s meridian traced out an ellipse; he then used the least-squares rule to find the eccentricity that would minimize the square of each latitude’s deviation from that curve as it arced—in a kind of high-wire balancing act—along the data Delambre and Méchain had gathered at Dunkerque, Paris, Evaux, Carcassonne, and Barcelona. And when he did, he found that the deviations of the various latitudes from that optimal high-wire curve remained sufficiently large to be ascribed to the figure of the earth and not to the data. And in Volume 3 of the Base, Delambre echoed his analysis: it was the earth that was warped—not the data.

As Legendre presented it, the great advantage of his least-squares rule was that it could be easily and systematically applied. It gave savants a workable method for weighting data. And in a few years, it became something more. It became a method with meaning.

Four years after Legendre’s paper, the mathematical genius Karl Friedrich Gauss claimed that he had been using the least-squares rule—which he called “my method”—for nearly a decade. As often happens, this simultaneous discovery was no coincidence. Both men were working on the same geodetic problem. Indeed, Gauss was working on the same data set, the meridian data gathered by Delambre and Méchain, which had been published in Germany in 1799. They were also reading the same mathematicians, especially Laplace. And, as often happens, this simultaneous discovery prompted a bitter dispute over priority: first, because both parties wanted credit for the discovery and finishing in the rear meant running the risk of being accused of plagiarism; and second, because the two parties differed on the meaning of the discovery. In this instance, there seems little doubt that the two men arrived at the method independently, although it was Legendre who published first. Nor is there any doubt that it was Gauss who suggested the method’s deeper meaning.

Legendre presented his method of least squares as workable and plausible. Gauss justified it by showing that it gave the most probable value in those situations where the errors were distributed along a “bell curve” (known today as a Gaussian curve). This probability-based approach prompted Laplace to show in 1810–11 that the least-squares method had the following advantages: it best reduced the error as the number of observations went up; it indicated how to distinguish between random errors (precision) and constant errors (accuracy); and it suggested how likely it was that the chosen curve was best. This was new. In their search for an illusory perfection, the savants had learned not only how to distinguish between different kinds of error, but also that error could be approached with quantitative confidence. The years between 1805 and 1811 saw the rise of a new scientific theory—not a theory of nature, but a theory of error. It was this theory that would allow Nicollet to redeem Méchain’s honor by distinguishing between those errors that were random and those that were systematic.

Some experiments were inherently erratic; others could be refined. Some investigators took pains with their observations; others were sloppy. The appeal of the new approach was that colleagues could now begin to distinguish between these two forms of uncertainty, and judge one another with the same impersonal techniques by which they judged nature. It was at this time that Delambre, Laplace, and the rest of the French savants started to come to terms with something their British colleagues had just discovered: that even the most fastidious astronomers were subject to idiosyncrasies in their observations (depending on their reaction time and the like), and that these idiosyncrasies introduced a constant bias into their observations, a “personal equation” as it came to be called. This recognition that they themselves were fallible instruments was followed by a program to tame error. Astronomers began to calibrate themselves against one another and to divide their labor to average out personal influences. Over the course of the next few decades astronomy became something of a bureaucratic science, in which a staff of junior observers (career-minded young men) and an office full of calculators (underpaid young women) toiled for a senior astronomer who directed their efforts, analyzed their data, and then published the results under his name.

Approach the world instead through the veil of uncertainty and science would never be the same. And nor would savants. During the course of the next century science learned to manage uncertainty. The field of statistics that would one day emerge from the insights of Legendre, Laplace, and Gauss would transform the physical sciences, inspire the biological sciences, and give birth to the social sciences. In the process, “savants” became “scientists.”

Méchain lived and died a savant. Measurement mattered to him as much as it did to the Ancien Régime peasants, bakers, and families who grew wheat, baked bread, and bought loaves in the marketplace. Whether it was the height of a star or the weight of a loaf, measurement expressedvalue. It was a moral act, an exercise in justice. For the savant, the pattern of the heavens revealed a comprehensive plan. To measure the shape of the earth or the height of a star was to glimpse its place in that pattern, just as the weight of a loaf sustained the just price for bread.

Men like Delambre, Laplace, Legendre, and their generation had a foot in each world. I have called them savants, but the term no longer fits. They were henceforth engaged in a struggle to quantify their uncertainty. They would ask: how confident are we that we know what we think we know? They sought to rid themselves of value judgments about nature and to cordon off meaning from their measurement of the world. They had launched themselves on a very different kind of career. In 1792 Jean-Paul Marat had been the first person to tag savants with the name ofscientifiques (scientists), when he referred sneeringly to the academicians’ self-serving project to measure the earth in order to create uniform weights and measures. For better or worse, the savants were now on their way toward becoming scientists.

As for Lalande, he chafed under the new régime even more than he had under the old. He was the last of the philosophes, now in his seventies: a freethinker who preferred monarchy, an atheist who admired the Jesuits, a feminist who propositioned young women, ugly as ever and still just as vain. The new régime had little patience for these old-time contradictions. Lalande had initially welcomed Napoleon’s rise to power, proud that the general called him “Grandpapa.” Napoleon had studied astronomy under one of Lalande’s students, and had written to Lalande in a manner calculated to flatter the old man. “To divide one’s night between a beautiful woman and a clear sky, and then spend the day matching theory and observation, that is my idea of heaven on earth.”

Lalande’s ego was pure as platinum. When his star chart hit fifty thousand—thanks to the labors of his daughter and his nephew—he published a massive compendium under his own name. Surveying the fifty-four auditors who attended his lectures at the Collège de France, he admitted in his journal that “Lalande is still the one who interests me most.” In the summer of 1798, he handed the lovely Citoyenne Henry, the world’s first woman aeronaut, into a balloon for her maiden voyage, in spite of a ban on female ascension. The next spring, he tried to visit Germany by balloon while observing the stars above the atmosphere’s veil. A wit composed the following verse to accompany him.

Observe the dwarf of academicians

Whose pride could fill a room.

He wanted to hear it straight from the winds

If they talked of him

On the moon, the moon, the moon.

The balloon never made it past the Bois de Boulogne, and he canceled the trip. He was always good copy. When a traveler brought back news of an African people who, like him, ate spiders, the newspapers advised Lalande that he would now have to switch to “insects of distinction.” Yet he was living proof that vanity could serve noble causes. Lalande did not care what people thought. As the editor of the Dictionary of Atheists, he maintained its honor roll of eight hundred adherents: from Socrates to Lalande. In 1799 he signed up several of his colleagues, including“Buonaparte of the Academy of Sciences.”

This was risky. After the vandalism of the Revolution, piety was making a comeback. Wags claimed that Lalande had turned to atheism out of revenge, because God had made him so ugly. “Look at his knock knees and rickety legs, his hunched back and little monkey’s head, his pale wizened features and narrow creased forehead, and under those red eyebrows, his empty glassy eyes.” Lalande answered insults with epigrams:

That men are witless, wicked fools

Proves there’s evil in this house of rot.

A scoundrel’s word can make heads roll;

If God existed, Man would not.

Not all his colleagues appreciated this frankness on their behalf. Lalande’s antics put Delambre in an awkward spot. At first the dilemma was amusing. Delambre had agreed to serve as godfather to Lalande’s granddaughter, Uranie, but her baptism had been postponed until Delambre returned from his mission. By then the child was seven, and able to respond on her own behalf. Asked by the priest if she renounced Satan and all his works, she said “I do renounce.” Asked if she renounced all worldly vanities, she said “I do renounce.” Asked if she swore to live and die in the Catholic Church, she said, in a loud clear voice, “I do renounce.” Everyone in the church laughed, including the priest.

Then Napoleon decided to buy peace among the French by reconciling with the Catholic Church. These delicate negotiations resulted in the Concordat of 1802, and were to culminate in the Pope’s arrival in Paris for the coronation of Napoleon as Emperor. In the midst of these delicate accommodations, Lalande had the temerity to reissue his Dictionary. The Emperor was furious. But was it atheism that enraged him, or something worse? The Dictionary dared to preach peace: “It is up to the philosophes to spread the light of science, so that one day perhaps they may curb those monstrous rulers who bloody the earth; that is to say, the warmongers. As religion has produced so many of them, we may hope to see an end to that as well.”

From the battlefield of Austerlitz—after the finest victory in his career—the Emperor wrote a searing rebuke: Lalande had fallen into dotage, atheism destroyed the moral order, and Delambre, as Permanent Secretary, must convoke the Academy to silence their senior colleague. Delambre tried to make Lalande’s compliance appear voluntary, preserving a semblance of intellectual freedom while bowing to authority, but Lalande refused to be silenced. In 1806, he published another edition of the Dictionary, albeit without Napoleon’s name.

That year Lalande fell ill with a chest ailment. Right to the end, he was insufferable and self-mocking in alternate breaths. In his final moral testament he wrote: “I have sometimes amused myself by saying that I thought I possessed all the human virtues. This phrase of mine has been bitterly cast up against me as if I had claimed ‘to have all the human virtues.’ In fact, what I said was that ‘I thought I had them,’ which is quite a different matter. Nevertheless, I was perhaps wrong to have said as much; but my conscience required it of me.”

In the evening of April 3, 1807, after his daughter had read him the evening papers, he sent her to bed, saying “I don’t need anything else.” At two in the morning he died. Even beyond the grave, he shocked the public. Two days after his death, his family had to deny rumors that Lalande had asked for his dissected body to be put on display in the Museum of Natural History. The eighteenth century was finally over.

This earthly transience—of knowledge, of men, of régimes—was not necessarily a cause for melancholy. On the contrary, in a world of confounding factors, in an age of Revolutionary terror, Delambre felt joy, only joy. Joy had accompanied him through all his travels, through all his labors, through all his life. Not the ecstatic joy of transcendence, but the modest joy of immersion. He had long ago passed the age of illusion. Delambre could accept that we live on a fallen irregular planet, in a world of imperfection and error, because by the collective labor of honest scientists this imperfection could be contained, and error tamed. In 1806 he wrote to a friend who had suffered much during the Revolution:

I have all my life experienced a happiness so gentle, so peaceful, and so untroubled, that if I were truly persuaded that it is man’s lot to discharge a debt of suffering and pain, I would fear for the future. But I like to think that there are exceptions, and I dare to hope that I will be one of them. My good fortune, I think, is due to my character and my temperament. The only passion I have ever known is the one which has never yet caused misfortune; and that is work. My passion for work is not diminished. I continue to give myself to my labors with all my strength.

Delambre’s face had thickened, but his eyes had strengthened with the years. His legs were chancy, but his hand was firm. The traveler who had once traversed much of France could no longer cross a Paris street; in 1803 he had been hobbled by a rheumatic fever. He had seen much in the way of suffering, but his optimism was unabated.

In 1804, after a liaison of several years, he married Elisabeth de Pommard, the mother of his young assistant. He was fifty-five; she was in her forties, a spirited widow with some well situated property to the west of Paris. They made a good match. She read Virgil’s epics in Latin, Addison’s essays in English, and Metastasio’s librettos in Italian. For several years before they exchanged vows, she and Delambre had traded low-interest loans. While the d’Assy family remained in the country, Delambre and his wife could live on the sumptuous rue de Paradis. There they read the classics, followed the Amazon voyages of their young friend Humboldt, and planned a brilliant career for her son, whom Delambre loved as his own.

Young Pommard, who had once planned to be an astronomer like his stepfather, enrolled instead in the Ecole Polytechnique to study the earth: mining and mineralogy. Two years later, he left to join Napoleon’s finance bureaucracy. Pommard was serving in Naples when he died in 1807, at the age of twenty-six, an inconsolable loss to his mother and her new husband. Delambre transcribed this English translation of an Athenian poem for his wife:

Ah! Love how soft and tender

Begins thy happy reign,

But when our heart surrenders

Thou’rt bitterness and pain.

If from the Daylight flying

The shaded woods we rove

Or thro’ the slow night sighing

Of breath but for my love.

Tempt not the soft illusion

DELAMBRE AS PERMANENT SECRETARY OF THE ACADEMY OF SCIENCES

Delambre in his fifties, at the height of his academic influence. (From the Archives de l’Académie des Sciences, Dossier Delambre; photograph by Charmet)

Ye wand’rers free of air

’Tis nothing but delusion

The voice that calls you there

Or tells the heart to languish

The youthful bloom to glow

Then damps that heart with anguish

And fills that heart with woe.

Yet sorrow too is transient. And Delambre would find renewed satisfaction here on earth. He spent the final decades of his life as a power broker of imperial science: dispensing favors, deciding careers, disciplining colleagues. He was simultaneously Permanent Secretary of the Academy, Lalande’s successor at the Collège de France, a member of the Bureau of Longitudes, and Treasurer of the University of Paris. He also became the nation’s premier historian of science. On the title pages of his books his honorary titles took up half the page. He became a star of the cumulsystem, the deplorable French practice of gathering multiple offices into one thick fist. Although the salaries came to a hefty sum, Delambre denied any worldly ambition. “Official positions have come to me unbidden, and I received what I did not covet.”

Generosity during war, honesty under empire, science in an age of puffery: these are the trials of integrity. He conducted fewer astronomical sightings now, and concentrated instead on the inner science of synthesis. For one thing, he had lost easy access to his private observatory. In 1808, he and his wife moved out of the rue de Paradis and into the official residence of the Treasurer of the University. After her son’s death, wife and husband relied on one another more than ever. She learned enough mathematics to help him with calculations. Delambre had an endless appetite for work. In 1806 he published a revised set of solar tables, the most exact to date. In 1813 he published an Abridged Astronomy, and a year later a three-volume Treatise on Astronomy. According to Gauss, these latter works were dull and craftsman-like, mathematically simplistic and lacking conceptual elegance. In other words, they were textbooks.

Delambre made himself useful to the Napoleonic régime, even as he kept his distance from palace intrigue. In 1803, as the Treaty of Amiens faltered, Napoleon ordered detailed maps of landing sites along the south coast of Britain. He also asked which French tower was best situated for his supervision of the planned invasion. No one knew more about the geodesy of the north coast of France than Jean-Baptiste-Joseph Delambre. Within a week, he had supplied a set of tables of optimal viewing sites, based on his own research and that of the 1788 Greenwich–Paris survey. As a servant of the state, he was duty-bound to put peaceful science to bellicose ends. But then, throughout the war, he worked with his opposite number in Britain, Sir Joseph Banks, President of the Royal Society, to save their respective colleagues caught up in the conflict. Banks helped the French geodesers sail home from Egypt; Delambre helped release those trapped on the Continent. Their nations might be at war, but scientists could maintain civility. Delambre shipped multiple copies of the Base du système métrique to Britain—accompanied by hopes for more peaceful times to come.

In 1809 Napoleon directed the Academy to conduct a prize competition for the best scientific publications of the decade. In the category of applied science, the Academy unanimously nominated “the work of Delambre on the meridian.” The work of Delambre? Méchain’s sons wrote to defend their father’s honor and to petition to have his name included. A committee of the Academy, asked to adjudicate, noted that while Delambre and Méchain had split the latitude measurements equally, Delambre had measured 89 out of 115 triangles and both baselines. More to the point, Delambre had refined all the geodesic methods, recalculated all Méchain’s latitudes, and written virtually the entire text of the Base du système métrique. Despite the fact that Méchain’s name came first on the title page, Delambre alone deserved the prize. Deserved perhaps, but would not accept. Delambre withdrew the Base from consideration on the grounds of conflict of interest.

Two years later, the metric system itself was withdrawn. The Revolutionary calendar was the first to go, its own creators delivering the coup de grâce. Rather than knit the world together, the calendar had only isolated France. Even in France, it was universally ignored. Parisians still celebrated January 1, and the ten-day working week had proved curiously unpopular. Napoleon Bonaparte had another objection; he wanted Catholic legitimacy for his new régime, and the Church wanted its Sundays and saint’s days back. Shortly after he was crowned Emperor he asked his Senate to reconsider the reform. Pierre-Simon Laplace, kicked upstairs to become Senator for life, agreed that the calendar should be abolished—for its scientific flaws, he said. At midnight on 10 nivôse of the year XIV, the date in France reverted to January 1, 1806.

The rest of the metric revolution did not last much longer. Since 1801 the metric system (shorn of its classical prefixes) had served as the nation’s official system of measurement—without changing the shopping habits of French men and women. The imperial government exhorted its subjects to do better; it supervised the annual production of 300,000 metric rulers; it commanded its police to punish scofflaws; and it printed detailed instructions on the proper way to dole out wheat, firewood, wine, olive oil, and the countless other commodities that were still being shipped in Ancien Régime containers. Yet Napoleon’s administrators watched helplessly as trading continued in the old units. Again and again they found themselves denying rumors that the government was on the verge of revoking the metric system.

The rumors were true. In 1805 the French savants, led by Senator Laplace and Secretary Delambre, lobbied against further dilution of the metric system as an affront to the rational administration of France. The Minister of the Interior, a chemist, helped his colleagues hold off the day of reckoning. Five years later, when the system came under renewed attack, the academicians took a different tack; now they praised Napoleon’s imperial conquests, arguing that they offered a unique chance to disseminate a universal metrical language. Senator Laplace took this appeal directly to the Emperor himself, pleading with his former examination pupil to retain the decimal division, even bowing so low as to suggest that the measures be renamed the “Napoleonic measures” if it would help. It did not.

With preparations underway for his invasion of Russia, Napoleon decided to minimize economic turmoil at home. On February 12, 1812, France adopted the so-called “ordinary measures.” The empire’s legal standard would still be defined in relation to the platinum Archive Meter, but the workaday measures would approximate those of Ancien Régime Paris. Length, for instance, would be measured in a toise (fathom) two meters long and divided as before into 6 pieds (feet) of 12 pouces (inches) each. In principle the system of decimal weights and measures would still be taught in the nation’s schools and used for public works and wholesale transactions. In practice, however, Napoleon had revoked yet another Revolutionary achievement.

The goal was now imperial uniformity, pure and simple. Napoleon had no patience for the Revolutionary fantasy that a new language for the objects of the material world would create an autonomous and egalitarian citizenry able to calculate its own best interest. Instead, he grasped at central rule. All the other elements of the metric system were discarded to achieve that single goal. Among the few French intellectuals brave enough to decry this act was Benjamin Constant.

The conquerors of our times, peoples or princes, want their empire to possess a unified surface over which the arrogant eye of power can wander without encountering any inequality which hurts or limits its view. The same code of law, the same measures, the same rules, and if we could gradually get there, the same language; that is what is proclaimed as the perfection of the social organization. . . . [T]he great slogan of the day is uniformity.

This was the tragic lesson of the past twenty years. This was the prospective measure of the world. Where absolutist régimes had once been satisfied with the outward show of homogeneity, modern dictators aspired to inner uniformity, leveling any difference that interfered with allegiance to the whole. Condorcet, the dead optimist of liberation, had naïvely imagined a world in which universal law, derived from nature’s truth, could produce equality and freedom without contradiction. Constant, the living pessimist of liberation, had witnessed how uniformity, enforced by mass mobilization, could suppress difference of thought and custom. Both men, of course, were right. Their aspirations and fears remain the two poles of the axis around which the modern world still revolves. And both underestimated just how difficult it would be, for good or ill, to realize that uniformity.

Such a formidable goal lay beyond even Napoleon’s grasp. Across the Empire his “ordinary measures” were rejected, just as the metric system had been. To the people of the annexed territories, the measures were just another attempt to coax them into a unified Continental economic bloc. In Rotterdam, where a prodigious commerce flowed down the Rhine, citizens ignored broadsheets converting Dutch to French measures. The Imperial Prefect there despaired of “the character of the inhabitants, and the notions they have about the new measures.” But back in Paris, the Minister of the Interior was not surprised; he knew firsthand the tenacity with which the common people—French or Dutch—defended their particular ways of doing things.

Failure stirs resentment. Defeat embitters allies. From his exile in remote Saint Helena, Napoleon slandered his former colleagues for foisting the metric system upon him—and upon the French people. “It was not enough for them to make forty million people happy,” he sneered, “they wanted to sign up the whole universe.” The savants had wanted to overturn every custom, rewrite every rule, remake every French citizen into an image of themselves, and all for the sake of a miserable abstraction. They had behaved like foreign conquerors, he said, “demanding, with raised rod, obedience in all things, without regard to the interests of the vanquished.”

Delambre accepted the collapse of Napoleon’s Empire—and the demise of the metric system—with equanimity. He had faith in the long run of history. As the coalition armies entered Paris in the spring of 1814, he was at his desk working.

On the day of the siege, in spite of the cannonade audible in my study, I worked peacefully from eight in the morning until midnight. I was confident that the army would not be so foolhardy as to defend the town long, and would open their gates to the allies, who, piqued with pride, would comport themselves with generosity. Some days afterwards I saw foreign troops crowd onto the quays of Paris, pass under my window, and fill the streets and boulevards. . . . The future does not offer a bright prospect for savants, but they should know how to content themselves with little. My savings will assure my own independence, and my wife’s small fortune offers a still more reliable resource. You know my needs are simple. Work occupies all my time and all my faculties. My happiness does not depend on having a little more comfort; and I do not expect that I will have to change my personal habits.

The fall of the Empire cost Delambre several of his positions and three quarters of his salary. He did not regret their loss, though he had to change residence again, this time to 10, rue du Dragon, convenient to the Academy’s new home in the Collège des Quatre-Nations. Besides, Louis XVIII had reappointed him to the position that mattered most: Permanent Secretary of the renamed Royal Academy of Sciences. And he retained his chair at the Collège de France and his post at the Bureau of Longitudes. As he explained to the new royalist administration, his fellow astronomers had kept their noses out of politics; they ought not to be shunted aside just because the régime had changed. Their political neutrality (some might say their political submissiveness) entitled scientists to keep their posts.

More and more, Delambre concentrated his attention on the past. The obligations of the present had already made him an accomplished historian. In a sense, he had been preparing for this labor all his life. He had spent his youth indoors, hiding his eyes from the sun, studying ancient and modern languages. He had spent his scientific career poring over old texts, combing the work of dead astronomers for data to compare with his own. (In that respect, every astronomer is something of a historian.) Since becoming Permanent Secretary, he had composed eulogies, reports on his colleagues’ accomplishments, plus a Report to the Emperor on the progress made by science during the past two decades. Even his preparation of the Base du système métrique had involved historical reconstruction.

He now dedicated his final years to a comprehensive history of astronomy “from Hipparchus and Ptolemy to us.” One by one, in chronological order, he would pass each astronomer, ancient and modern, through the filter of current knowledge, extricating their genuine contributions from the ephemeral speculations of their age so that, as Delambre put it, his own Treatise on Astronomy would cap the whole. It was a six-volume, 4,000-page scientific-extraction machine, and it was the first great history of science.

His theme was the rise of precision: the relentless drive for exactitude. His method was empirical: a close reading of original works. Delambre sharply criticized those historians who had conjured up an antique people whose comprehensive astronomy had since been lost. There was no evidence of such a people. Nor did he agree with his colleagues who believed that the ancient Egyptians had derived their system of weights and measures from the size of the earth. Delambre had taken great interest in the French geodesers’ trip up the Nile, but he rejected their conclusions. Their pyramid studies had unjustifiably projected current fantasies onto the past.

The historian’s great duty was impartiality, and impartiality began at home. Thus, in his article on Descartes—France’s greatest savant—Delambre adopted a sharply critical tone. “The historian owes the dead nothing but the truth,” he wrote. “It is not our fault ifin astronomy Descartes produced only chimeras.” And he proceeded to document just how often in his physics Descartes had violated his own norms for clear and consistent evidence. By ignoring this evidence Descartes’ many admirers had “cast a kind of ridicule upon the French nation by reviving the memory of the very errors they sought to hide behind the veil of official secrecy.” In the history of science, as in science proper, progress was only possible with the forthright acknowledgment of error.

How fitting, then, that one of Delambre’s last acts as Permanent Secretary was to superintend Descartes’ reburial—and to determine whether they had buried the right man. One hundred fifty years earlier the great philosopher had died in self-imposed exile in Sweden, but his body had been exhumed and returned to France soon after. Since that time his remains had been buried in a church, exhumed again, and then transferred to an Egyptian-style sarcophagus for storage in a national museum during the Revolution (alongside the royal statuary from the basilica of Saint-Denis) while politicians debated whether he was worthy of being panthéonized. By 1819 the Panthéon had been reconsecrated as a Catholic church, Voltaire and Rousseau’s tombs had been shunted aside, and the motto “AUX GRANDS HOMMES, LA PATRIE RECONNAISSANTE” had been covered over by scaffolding. Descartes, it was decided, would be better off re-reburied in the church of Saint-Germain-des-Prés. Delambre watched as they opened the sarcophagus and removed the small interior case engraved “René Descartes, 1596–1650.” Inside, there was not much to see. “Only the femur was recognizable; the rest had been reduced more or less to dust.”

Imagine everyone’s horror then, when two years later, Sweden sent France a precious gift: the skull of its greatest genius, Descartes. Had a horrible error been committed? Had the wrong man been buried? It was another discrepancy to resolve. The Permanent Secretary was seventy-two years old by then, and in failing health. Yet he marshaled the documentary and forensic evidence, and adjudicated the matter with the same rigor he had brought to science and history. The gift skull, he concluded, was fake; the authentic skull of Descartes was presumably dust. After the physical evidence was gone, only inference remained. That would have to be enough.

That year Delambre made careful preparations for his own death. He knew all too well what historians are capable of. He destroyed the bulk of his personal papers. He also set aside his correspondents’ letters so that his wife might inquire after his death whether they wished to have them returned, lest their confidences fall into indelicate hands. He also composed a short manuscript autobiography, which later became the basis for the biography published by his student and scientific executor Claude-Louis Mathieu, and thus (as he knew it would be) the basis for all subsequent biographies.

All this was part of a conscious strategy. He was acutely aware that he would one day become the subject of historical investigation. And he did what he could—within the bounds of honesty—to shape that story. Thus, he planted the clues to the true story of the metric system in plain sight, publicly announcing that the logbooks of the meridian expedition were on file in the archives of the Observatory. He did not destroy Méchain’s letters, but placed them under seal in the archives. He made it possible for historians to tell a story that he could not tell in his own lifetime.

Jean-Baptiste-Joseph Delambre died at home, at 10, rue du Dragon, at ten o’clock in the evening on August 19, 1822. The Permanent Secretary was buried in the Père-Lachaise cemetery so that a new Permanent Secretary might live. Jean-Baptiste-Joseph Fourier’s first eulogy paid homage to his predecessor. This was not a eulogy by an Ancien Régime savant but a speech by a modern scientist intent on glorifying science. Fourier puffed up the meridian project with exclamation marks: he called it the greatest application of science in living memory—yet he gave all his data in the old units of measurement, the law of the land in Restoration France.

History is made by the dead as well as the living. Their obsessions perch like fetishes upon our mantels and upon our consciences. Science likes to think of itself as the one human endeavor free of idolatry. It imagines that it erases the past each time new knowledge sweeps the mantel clean. But the errors of the past can shape the direction of science as much as its truths.

Delambre left the sixth and final volume of his comprehensive history of astronomy unpublished at the time of his death. He warned his friends that The History of Astronomy in the Eighteenth Century would tell “the whole truth.” If they found some of its judgments severe, they should remember that history was no eulogy. He had written the book, he said, to “discharge my conscience.” Perhaps for that reason he profiled only dead astronomers and delayed publication until his own death. Mathieu, Delambre’s student, shepherded those pages into print five years later.

Among the final astronomers to be discussed was Pierre-François-André Méchain. This was no eulogy. Delambre had learned a great deal about his former colleague since his funeral oration seventeen years before. So he began at the beginning: there was no evidence for the story that Méchain had made his start in astronomy by selling his telescope to Lalande to pay off his father’s debts. He reassessed his colleague’s career: Méchain had never been a scientific innovator and had borrowed all Delambre’s formulas for his calculation of the meridian. He hedged on the exact date when Méchain departed for Barcelona: delays in the making of the instruments, Delambre now said, meant that the operation “could not commence” until June 25, 1792—which is not the same thing as saying that Méchain actually left Paris on June 25. He reapportioned credit for the grand mission: Tranchot deserved full recognition for his work. (The engineer had died in 1815 while triangulating at Montlhéry, the station just south of Paris where Delambre had begun his survey thirty years earlier.) He revisited the discrepancy at Barcelona: Méchain’s “fatal decision” to conceal the 3.24-second gap in the latitudes had made a mystery of what any other astronomer would have frankly acknowledged. And he supplied further revelations: Madame Méchain had been obliged to coax the astronomer to finish the mission; Méchain had refused to return to Paris until promised the directorship of the Observatory; Méchain had hidden his data from the Commission and obstinately clung to the notion of returning to Spain; Méchain had kept his secret intact until his papers were brought back to Paris.

Yet, after all this, Delambre still considered Méchain a man “admirable in every way,” and assured his readers that they could have confidence in the meridian the two men had jointly measured.

No one can claim to have known Méchain in his capacity as an astronomer better than I. For ten years we maintained an intensive correspondence. I long had his papers in my hands, and made a careful study of them, going so far as to revisit every calculation which bore upon our mission. In this way, I assured myself that Méchain, enamored above all by exactitude, but also very jealous of his reputation, had the misfortune to believe that the repeating circle could produce a degree of agreement and precision which was, in truth, impossible. When his observations presented unexpected anomalies, instead of reconsidering this view, he began to doubt his own abilities. Indeed, he feared that his own (unjust) opinion of himself would come to be shared by others, and would eventually overshadow his reputation. But this was not to be, and he remains an astronomer forever worthy of our admiration.

Delambre had left one more manuscript unpublished. In The Size and Shape of the Earth, he carried the history of geodesy up to his own day. In it, he rectified Méchain’s suppressed observations so as to “release ourselves from the obligation to disclose the falsehoods to which we had, in some sense, been made complicit.” Yet he also recorded them to console those geodesers who would follow in the path that he and his partner had marked out, and thereby “disabuse them of the chimera of perfection, which mankind has yet to achieve and will probably never achieve.” These revelations were considered impolitic by Mathieu, then campaigning to revive the metric system. Not until 1912 did an edition of this work find its way into print. It was at that time that the sealed letters between Delambre and Méchain were opened in the archives of the Observatory, where they lay unread for the rest of the twentieth century.