## Base du système métrique décimal, ou mesure de l'arc du méridien compris entre les parallèles de Dunkerque et Barcelone, executée en 1792 et années suivantes.

Paris: Baudouin & Garnery, 1806-1810.

First edition, uncut in contemporary boards, of the foundation work of the metric system. “For many centuries there were no general standards for measurement: every trade and craft had its own peculiar units and they differed even in various regions of the same country. Since the development of international trade in the Middle Ages this chaotic situation had become more and more tiresome, but all efforts towards standardization were strongly resisted by vested interest … We owe the introduction of an international metric system to the French Revolution. In 1790 the Académie des Sciences, at the request of Talleyrand, set up a commission to consider the question: among its members were J. C. Borda, Lagrange, Laplace, G. Monge and Condorcet. In 1791 they reported that the fundamental unit of length should be derived from a dimension of the earth: it should be the ten-millionth part of a quadrant of the earth’s meridian extending between Dunkirk and Barcelona. As the distance was already approximately known, a provisional meter was at once adopted. The new unit of weight was to be the gram: the weight of one cubic centimeter of water at 4° C. The Constituent Assembly set up a general commission of weights and measures to carry these proposals into effect and in 1795 a law was passed introducing the metric system into France with provisional standards. The astronomers Jean Baptiste Joseph Delambre and Pierre Francois André Mechain were charged with the task of measuring accurately the newly adopted length along the meridian arc between Dunkirk and Barcelona. Owing to the disturbances of the revolutionary period their work was much impeded, but in 1799 their measurement was completed. The above work, Base du système métrique decimal, embodies their report. The length of a meter (equaling 39.37 English inches) was marked on a platinum bar, and the unit of weight was also constructed of platinum, being the weight of a cubic decimeter, or liter, of pure water at its maximum density. These original bars remained the basic standards until 1875 and are still preserved in Paris. The metric system was gradually accepted by most nations – with the notable exceptions of England and (for weights and measures) the United States; but optional use was legalized in 1864 (England) and 1866 (U.S.A.) and its general adoption in England was proposed in 1965. After meetings of an international commission in 1872 the International Bureau of Weights and Measures was set up in 1875. It is now situated near Sèvres and has since remained the international center for all questions of standards. New units made from a bar of platinum alloyed with 10 per cent iridium were constructed, copies of which were distributed to the various participating countries” (PMM).

“Measures in the eighteenth century not only differed from nation to nation, but within nations as well. This diversity obstructed communication and commerce, and hindered the rational administration of the state. It also made it difficult for the savants to compare their results with those of their colleagues. One Englishman, traveling through France on the eve of the Revolution, found the diversity there a torment. "[I]n France," he complained, "the infinite perplexity of the measures exceeds all comprehension. They differ not only in every province, but in every district and almost every town...." Contemporaries estimated that under the cover of some eight hundred names, the Ancien Régime of France employed a staggering 250,000 different units of weights and measures.

“In place of this Babel of measurement, the savants imagined a universal language of measures that would bring order and reason to the exchange of both goods and information. It would be a rational and coherent system that would induce its users to think about the world in a rational and coherent way. But all the savants' grand plans would have remained fantasy had not the French Revolution -- history's great utopian rupture -- provided them with an unexpected chance to throw off the shackles of custom and build a new world upon principled foundations. Just as the French Revolution had proclaimed universal rights for all people, the savants argued, so too should it proclaim universal measures” (Alder).

“In 1788 the Académie des Sciences decided to establish a “uniform system of measures” founded on some “natural and invariable base.” The plan for the new system of measures was formally approved by a decree of the Assembly of 8 May 1790, proposed by Talleyrand; it was approved by Louis XVI on the following 22 August. A commission on the metric system, consisting of Borda, Lagrange, Laplace, Monge, and Condorcet, was thereupon appointed by the Academy. In a report submitted on 19 March 1791, the commissioners rejected two proposed bases for the fundamental unit of measure: the length of a seconds pendulum (at 45° latitude), and one-quarter of the terrestrial equator. Instead they chose one-quarter of a terrestrial meridian, the common practical unit to be a ten-millionth part of this quantity. Accordingly, it was proposed to make a careful and accurate measure along an arc of the meridian through Dunkerque (which had in part been measured by the Cassinis in 1718 and in 1740), extending as far south as Barcelona.

“Three fundamental tasks were envisaged. First, to determine the exact difference in longitude between Dunkerque and Barcelona (and to make any needed latitude determinations in between); second, to check by new observations and calculations the triangulations used earlier to find the distance between Dunkerque and Perpignan; third, to make new measurements that could serve for successive triangulations. Clearly a major part of this assignment would be to compute carefully the difference in actual lengths (in *toises*) corresponding to the same difference in latitude at various points along the meridian, so as to be able to determine the actual shape of the earth. While these operations were being performed, other scientists would be engaged in establishing a standard of mass. The instruments, chiefly made by Lenoir according to the plans of Borda, were ready by June 1792, and the work was started shortly afterward.

“Originally, the geodetic survey was to be entrusted to Méchain, Cassini, and Legendre. The latter two begged off, and Delambre—just made a member of the Academy—was appointed. It was decided that Delambre would be in charge of the survey from Dunkerque to Rodez, leaving the survey from Rodez to Barcelona in the hands of Méchain. An account of the labors and adventures of Méchain and Delambre is available in their joint publication, *Basedu système métrique décimal* (3 vols., Paris, 1806, 1807, 1810) …

“Delambre explains the inequality of the assigned distances (Méchain—170,000 *toises* from Rodez to Barcelona; Delambre—380,000 *toises* from Rodez to Dunkerque) as follows: “The reason for this unequal division was that the Spanish part was entirely new, whereas the remainder had already been measured twice; we were agreed that the former would provide many more difficulties.” Then he remarks, “We did not know that the greatest difficulties of all would be found at the very gates of Paris.” Méchain, the first to set out, on 25 June 1792, was arrested at his third observational site, at Essonne, by uneasy citizens who were convinced that his activities had some counterrevolutionary aspects. Only by constant explanation and good fortune was Méchain able to continue, and eventually to carry his survey into Spain. Delambre encountered similar difficulties; and, in addition, when he returned to Paris and had to leave again, he had to seek new passports as the government changed. It seems almost incredible that in time of revolution Delambre was able to continue his work as much as he did. In eight months of 1792, however, he had established only four points of triangulation; but in 1793, despite delays in getting his passport, he made better progress. Then, in January 1794, he received an order from the Committee of Public Safety to stop all observations at once. On his return to Paris he learned that as of 23 December 1793 he had been removed from membership in the commission of weights and measures, along with Borda, Lavoisier, Laplace, Coulomb, and Bresson.

“Happily, the enterprise was revivified by the law of 18 Germinal *an* III (7 April 1795), and Delambre and Méchain were able to take up their old assignments, now under the title of *Astronomes du Dépôt de la Guerre*, serving under the head of that establishment, General Calon, a member of the Convention. Delambre thereupon set out for Orléans on 28 June 1795 and completed his assignment within four years.

“Delambre’s task was not merely to make a series of correlated astronomical observations and terrestrial measurements; he had also to carry out extremely laborious calculations. The latter were made especially tedious by the need to convert the observations from the new centesimal units of angle-measure (used in Delambre’s instruments) to the older units of degrees, on which all tables of logarithms and of trigonometric functions were then based …

“Méchain died in 1804, and it became Delambre’s sole responsibility to complete the computations and to write up the final report. This constituted three volumes containing the history of the enterprise, the observations, and the calculations. The third volume was completed in 1810, some twenty years after the project was begun. When Delambre presented a copy of this work to Napoleon, the emperor responded, “Conquests pass and such works remain.”^{7}

“Delambre’s results were put into the hands of a commission of French and foreign scientists, who then determined the unit of length which became the standard meter. Jean Joseph Fourier said that “no other application of science is to be compared with this as regards its character of exactness, utility, and magnitude.” The newly constituted Institut de France designated this survey “the most important application of mathematical or physical science which had occurred within ten years” and in 1810 gave Delambre a prize for his share in the great work. The accuracy with which Delambre carried out his task may be seen in a comparison of two base lines: Perpignan and Mélun. Delambre measured both by direct methods. Then, making use of a network of triangulation, he used one to compute the other. According to Fourier, although the distance between the two bases is some 220 leagues, the results of calculation differed from the results of direct measurement by less than threetenths of a meter, less than one part in 36,000” (DSB, under Delambre).

PMM 260; Norman 1481 (lacking half-titles); *En Français dans le Texte* 212. Alder, *The Measure of All Things*, 2002.

Three vols., 4to, pp. [iv] [ii] 180, 551 and 8 plates; xxiv 844 and 11 plates; [iv] 4, 704, 62 (index) and 9 plates. Contemporary boards, uncut.

Item #4789

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Price:
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