The Measure of All Things

by Ken Alder

  From this day forth, my most cherished occupation will be to extract from this archive everything that may contribute to the glory of a colleague with whom I was honorably bound in a long common labor. And if I have not succeeded today in painting a picture of the departed astronomer worthy of his merits and the feelings I have for him, I am at least certain that whatever I publish of his work will do far more for his memory than even the most eloquent oration.

  It was a sincere and moving eulogy. While it glossed over certain embarrassing details, it was true to the dead man’s spirit. It read Méchain’s character as the source of both his triumphs and his limitations. The family expressed their gratitude, and at their request Delambre had his eulogy published so that they could distribute it to their friends. No one, however, reclaimed Méchain’s body and it remained in the cemetery of Castellón de la Plana.

  In January 1806, the same month the eulogy appeared in print, the first volume of the Base du système métrique was also published. There Delambre paid even greater homage to his deceased partner by listing Méchain first as the expedition leader. The volume offered a lengthy preface laying out the history of the meridian expedition, followed by the record of all the triangulation data from Dunkerque to Mont-Jouy. It deferred the latitude measurements to the second volume.

  But between his delivery of the eulogy and its appearance in print, in the gap between the writing of the first volume of the Base and its publication, Delambre made a discovery—a scandalous discovery. The publisher had been pressing Delambre to deliver the first volume of his book manuscript, and so he had postponed his examination of Méchain’s papers. Now, as he worked his way through them, he discovered the discrepancy between the latitude results for Barcelona and those for Mont-Jouy, and worse—far worse—a systematic effort to cover up that discrepancy, suppress observations, and rewrite scientific results. It was a discovery and it was a scandal, for while it clarified many of the mysteries that Delambre had delicately glossed over in his eulogy and in his preface to the Base, it also presented him with an acute dilemma. The platinum meter had been constructed; the metric system had been published and made law. The metal bar sat contentedly in its triple-locked box in the National Archives. The bar did not equal the meter; it was the meter. What did it now matter that the data that had gone into its making had been erroneous? What should Delambre reveal?

  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, s
o 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 mil
e 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.