7 The Measure of Enlightenment

### Pit and Pendulum

The National Assembly approved the Academy's revised proposal on 30 March 1791. The Academy immediately divided its work among five commissions: triangulations and latitude determinations (Cassini IV, Méchain, Legendre), baselines (Meusnier, Monge), pendulum of Paris (Borda, Coulomb), weight of water (Lavoisier, Haüy), and comparison of old and new measures (Tillet, Brisson, Vandermonde).[50] The whole enterprise was to be directed by Borda, Condorcet, Lagrange, and Lavoisier. Soon death and disinclination reduced this extraordinary mobilization of the brains of France. All geodetic work fell to Delambre and Pierre-Francois-André Méchain, an excellent compulsive astronomer; Borda and Cassini took on the pendulum, and Lavoisier the water. The first year went by making instruments. Only one Borda circle, that of 1787, existed in 1791;

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two more, readable to 3 or 4 seconds of arc, were ready in the summer of 1792, when Méchain set out for Spain and Delambre started north. The instrument answered its advertisements: although difficult to use in a cramped church tower, its precision with enough repetitions was, in Delambre's words, "nearly incredible."[51]

Great accuracy was also achieved in the pendulum experiments, which took place during the summer of 1792 in a pit in the Paris observatory. The general technique, by no means original with the metric project, was to observe coincidences between a swing of a simple pendulum of length L and that of a clock that accurately beat seconds. Let t 1 be the clock time when both pendulums move through the midpoint of their swing together, and let t2 be the time of the next coincidence. In the interval Dt = t2 - t 1 , therefore, the number of swings of the two pendulums differs by one and the half period of the simple pendulum is T = Dt / (Dt ± 2). Thence the length of the seconds pendulum Ls can be deduced from the formula T 2 :1 = L:Ls . If Dt is large, Ls can be obtained very accurately.

Borda designed the apparatus, which was made by Etienne Lenoir, who also supplied the repeating circles. The pendulum bob hung from a 12-foot steel cord suspended from a knife-edge mounted on a subterranean wall in the Paris Observatory. Borda and Cassini observed coincidences through a telescope pointed perpendicularly to the wall. The largest departure from the mean of the twenty coincidences they recorded was one part in 100,000. They corrected their computed Ls for the dependence of the period on the amplitude of the swing, on temperature, on air pressure, on the flexure of the support and the steel cord, on the moment of inertia of the bob, and on much else. The result: Ls = 440.5593 lines of the toise used in the expedition to Peru.[52] "Thus," wrote the Commissioners who presided over the metric project in 1794, "the pendulum can be considered the depository of the unit of measure, or even a method of

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measuring the earth; and nothing is more suited to instill admiration of physics and geometry than seeing an undertaking that would appear to require travel from one end of the world to the other with great machines reduced to a very simple experiment done in one place with an instrument of modest dimensions."[53] That would have made an inexpensive as well as a reasonable standard. Lenoir's bill for the circles, the rules, the water apparatus, and the pendulum was just over 34,000 livres. The Academy then estimated—this is from a progress report of 2 May 1792–that the total project would cost 300,000 livres.[54]

### Roughing It

When Méchain and Delambre set out in the summer of 1792, the Revolution had become, in Delambre's words, "truly frightening." Méchain's instruments perplexed the southern peasants, who jailed him as a counter-revolutionary. Officials who understood numbers eventually procured his release. He decided that he would be safer in Spain, and so began his mapping there, with great efficiency until an injury compelled him to break off early in 1793. By the time he had recovered and completed the arc in Spain, with an immaculate determination of the latitude of the southern terminus at Montjouy, the Spanish government had closed the border to Frenchmen. Méchain passed his enforced leisure by observing stars in Barcelona, also with exquisite accuracy; but, to complete his misfortunes, the difference in latitude between Montjouy and Barcelona, as deduced from the stars, came out 3.24 seconds greater than the difference Méchain had calculated from measurements made on the ground.[55] These miserable three seconds tormented Méchain for the rest of his life: he thought that Borda's circle permitted perfection and he blamed himself for blundering. Méchain had measured his angles as exactly as Borda's circle allowed. The discrepancy of 3 seconds—about the angular width of a penny observed at a distance of 450 miles—arose from

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unevenness in the terrain, which dragged Méchain's plumb bobs off the vertical.[56]

While Méchain stagnated in Barcelona, Delambre had one unpleasant adventure after another in the north of France. Anticlerical peasants had knocked down many of the church towers that had served his predecessors; when he hung lanterns as substitute sights, he was suspected of signaling to the enemy. (France had been at war with most of Europe since April 1792.) Once, having been detained by local patriots, he tried to explain his mission in an impromptu lecture on geodesy. To no avail. He was packed off to a higher jurisdiction, in Saint Denis. The square teemed with volunteers waiting to go to the front, who did not have the prerequisites for the crash course in triangulation they forced him to give. "Evening came on. . . . The audience was very large: the front rows heard without understanding; those behind heard less and saw nothing. They grew impatient, and grumbled; some proposed one of those quick means [of dealing with suspect people] then so much in vogue." Were it not for a quick-witted official, who rushed Delambre into protective custody, the arc might have ended in Saint-Denis.

The National Assembly found time while busy transforming France into a Republic, which it declared on 22 September 1792, to issue an order for Delambre's release.[57] That did not signify a regard for academicians. On 8 August 1793 the National Assembly closed the Academy along with other unrepublican corporations. The suppression came only a week after the Assembly had given cause for reassurance to those who expected that the Academy's labors on measures in the national interest would protect it. That first week in August the Assembly had affirmed the decimal system and the meridianal definition of the meter, ordered the continuation of the work, and decreed that the Academy provide for the manufacture,

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distribution, and explanation of provisional meters for general use while it prosecuted its measurements. This provisional meter was defined as a ten-millionth of ninety times the average degree in France as determined by Lacaille, or 443.444 lines of the Peruvian toise. It differed from the definitive meter by about a quarter of a millimeter.

It is not advisable to assign an important job to a specialized government agency one week and to abolish the agency the next. The Assembly therefore immediately accepted the recommendation of the Committee of Public Safety that—because its work would erase the last vestiges of feudal divisions—the Academy's commission on weights and measures should be reestablished, with the same personnel, as an independent temporary commission (Commission temporaire des poids et mesures républicains). It consisted of Borda, Brisson, Cassini, Coulomb, Delambre, Haüy, Lagrange, Laplace, Lavoisier, Méchain, Monge, and Vandermonde.

The Academy's confidence in metrology as an anchor against political storms thus received partial justification. The job of overseeing the making and distribution of the provisional standards brought another large and pressing public responsibility to the academic rump and an important cash flow. The minimum cost of the standards, as estimated by Lenoir and others, would be some 200,000 livres. This minimum provided for copper standards for the geographical departments into which the Revolution had divided the old provinces and for iron standards for the prefectures. The Assembly preferred to avoid this whiff of discrimination and voted an additional 60,000 livres or so to make all the standards of copper except for the platinum prototypes.[58] The temporary commission expected the copper standards to be accurate to around one part in 100,000 for the meter and the grave (kilogram) and one part in 10,000 for the pinte (liter).[59]

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The arrangements of August and September proved provisional in more ways than one. Lavoisier was arrested on 28 November 1793; the temporary commission requested his release as necessary to its work; the Committee on Public Safety of the Convention (into which the Assembly had transformed itself on declaring a republic) refused, and, for good measure, purged the temporary commission of Borda, Brisson, Coulomb, Delambre, and Laplace, who had not, in its opinion, shown a proper hatred for kings. The rejection of the appeal for Lavoisier and the order for the purge were drawn up by Prieur, who thus revenged himself on academicians who had opposed his political views and metrological proposals. When news of the purge, which was made public on 23 December 1793, reached Delambre, he was shivering from cold on the top of a signal tower 64 feet tall that he had erected near Orléans in the service of the people. On his return to Paris, a revolutionary committee studied his manuscripts without making much of them and pounced on a diploma from the Royal Society, which bore the arms of George III. Delambre found it prudent to disappear.[60]

What remained of the temporary commission did little more than print explanations of the new system and revolutionary rhetoric. "Soon [our] vision will no longer be affronted by those old weights and measures that still tell of the odious remains of times and things sullied by tyrants. . . . Every child will know [the system]; and it will help diminish inequality among men."[61] There is no reason to put off enjoyment of the great benefit; the provisional meter will be perfectly satisfactory for commerce; the definitive will only serve to make the whole operation "more worthy of the powerful and enlightened nation that has undertaken it." Neither the rhetoric nor the practical business of furnishing provisional metersticks long protected the pitiful rump commission. In the spring of 1794, it requested 50,000 livres to pay its artisans; Prieur arranged to give 10,000 and to terminate its existence.[62]

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### A Military Connection

Delambre believed, probably correctly, that the Committee on Public Safety and many members of the Convention wished to kill the meridian measurement and declare the provisional meter definitive.[63] At this point a powerful advocate of geodesy came to the rescue: General E.N. de Calon, formerly of the Royal Geographical Engineers (Ingénieurs géographes), which had been suppressed in 1791. Meanwhile Calon had become a deputy and a Jacobin; his rampant republicanism perhaps may be traced to unfulfilled ambition and a sense of injury suffered in the late 1770s, when, though an officer of twenty years' standing, he had been ordered to do survey work usually assigned to his juniors.[64] He was a numerary as well as a passionate man. His few recorded statements in the Convention and the Jacobin Club of Paris were precise and numerical, as in the following complete discourse: "A vehicle drawn by six horses has just been stopped at Neuf-Brisach; it contains a ton of gold and of white and black uniforms."[65]

The suppression of his former corps presented Calon with a vacuum in which to fulfill his ambition. With the corps went the map department of the Dépôt de la Guerre, the headquarters and storehouse of military cartography. The temporary organization put in its place could not handle the flood of maps, and Calon, who became head of the Dépôt in April 1793, managed to recapture most of its archives. He then purged the place of suspect employees installed by his aristocratic predecessor. To repopulate the Dépôt, Calon set up a school there in astronomy, geography, engineering, history, languages, and engraving; and to staff the school and get on with his major mission, providing maps of the front and of captured territories to the Army, he tried to attach to his service all the unoccupied savants he could find. At its height in the autumn of 1796, Calon's

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cartographical program, printing establishment, and school ran at an annual cost of 300,000 livres. His expansiveness caused inefficiencies and inspired jealousies, and by the spring of 1797 he and his empire had fallen.[66]

Among the academicians Calon recalled to government service were Méchain, who had managed to get himself to Genoa in September 1794, after a narrow escape from corsairs, and Delambre. It was agreed, probably early in 1795, that they would triangulate the new departments and that, to prepare as firm a base as possible for the work, they would resume the measurement of the meridian. Then at the zenith of his influence, Calon persuaded the Committee on Public Safety to grant 220,000 livres for map-making, half for extending the Cassinis' Carte de France into the Rhineland and half for finishing the meridian between the Loire and the Pyrenees.[67] This largesse, given on 13 May, fit well with proposals Prieur had made in March for the prompt completion of the metric project.[68] Prieur recommended setting up a temporary agency (Agence temporaire des poids et mesures) to push through the manufacture of provisional standards and to oversee their deployment. He estimated that much could be done for 500,000 livres. He had to request another 500,000 livres the following September. Meanwhile the Army lent a hand by collecting old metal, chiefly church bells and discarded measures, to serve materially and symbolically as raw ingredients for metric measures.[69]

Prieur's program became law on 7 April 1795. It provide for using the "provisional" meter in everyday transactions even after the definitive platinum prototype came into existence; confirmed the basic names, meter, liter, and gram; and ordered resumption of the measurement of the arc. It established a triumvirate under the Commission of Public Instruction to oversee the manufacture, distribution, and explanation of the provisional standards, using machines

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wherever possible, "so as to combine facility and swiftness with precision, and consequently to allow citizens to buy the new measures at a reasonable price"; and it specifically ordered the new agency to provide graphic representations of conversions requiring no calculations by users.[70] Later that month the scientific side of operations was entrusted to academic survivors of earlier commissions: Borda and Brisson were to bring int he exemplar of the copper provisional meter within a "décade" (ten days); Méchain and Delambre, to do their thing; Delambre, Laplace, and Prony, to fix a baseline near Paris; Borda, Haüy, and Prony, to determine the standard of weight; and Berthollet, Monge, and Vandermonde, to oversee the preparation of the platinum to be used in the definitive primary standards.[71]

Matters being thus composed, Delambre left Paris on 28 June 1795 in the capacity of "astronomer of the Dépôt de la Guerre" to resume his observations at Orléans. He had the usual trouble finding intact steeples, and the cost of erecting signals quickly depleted his cash. No one wished to accept the assignats (government IOUs) he carried; and once again Calon tided him over. Three years of republican rule had not made peasants less suspicious and superstitious. They now tore down Delambre's signals on the theory that they attracted storms.

Méchain had his hardships, too, as he crawled north across the mountains toward their rendezvous in Rodez. In one place, on a high outcrop only twelve feet wide, surrounded by precipices, he sat for days waiting for the clouds to lift long enough to work the Borda circle. He arrived within signaling distance of Rodez around 1 September 1797, shortly after Delambre had completed his part of the work. There they stopped. Méchain would not accept Delambre's help and could not go on. "In this cruel situation," he wrote his collaborator, "I prefer to stay in this terrible exile, far from what I most cherish in the world; I will sacrifice everything, give up everything,

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rather than return without finishing my part of the job." Delambre felt that he could not insist and Méchain finished the arc the following September.[72]

After concluding his triangles at Rodez, Delambre joined Laplace at Melun to fix the ends of the baseline near Paris. Borda had devised special rulers for the purpose, which were not ready until the spring of 1798. Their employment was extremely tedious. Delambre could make only about ninety lengths (about 360 m) a day; it took thirty-three days to cover the entire distance of 6075.90 toise. In the summer he redid the Perpignan baseline. That took six or seven weeks. Earlier surveyors had done it in twelve hours. The length of the Perpignan base as calculated from the length of the Melun base and the triangles differed from the measurement on the ground by less than a foot. On 1 brumaire 1798 an VI (22 October 1798), everything required to calculate the length of the arc from Dunkirk to Barcelona was in hand. Méchain and Delambre returned to Paris, where an international committee had assembled to examine, approve, advertise, and propagate their results.[73]

7 The Measure of Enlightenment