4. THE ÉCOLE NORMALE DE L’AN III

It would be difficult to overestimate the significance for the future of higher professional education, and not only in France, of the École Normale de l’an III (1795), the École Polytechnique (called École Centrale des Travaux Publiques [Public Works] for its first year), and the Écoles de Santé (Health), the euphemism for medical schools. The Comité d’Instruction Publique drafted measures providing for all three in 1794 with their eyes fixed both on the future and the immediate past. In point of recruitment, pedagogy, and school spirit, or élan, the inspiration for the entire trio was the “revolutionary method” in the crash program of courses on saltpeter, gunpowder, and weaponry of the preceding months. Nevertheless, the eventual adoption not only in Europe but America of the term normal school (which to be sure was already used in Austria and Italy) for the formation of teachers, of the term polytechnic for the formation of engineers, and of the centrality of clinical experience for the formation of physicians and surgeons, all this suggests that the educational purpose of these institutions, however clothed in revolutionary rhetoric, answered to fundamental opportunities in the domains they served.¹²⁴

First, the École Normale: the viability of a national system of education would clearly depend on training a corps of teachers, and forthwith.¹²⁵ After failing to adopt the Condorcet plan or any other, the Convention did accept a low-keyed measure framed by one Gabriel Bouquier, a hitherto obscure member of the Comité d’Instruction Publique, requiring the establishment of primary schools to which parents would be obligated to send their children. That law passed on 19 December 1793. In May 1794, near the height of the Terror, the Committee further drafted a plan to bring four young men from each district to Paris to be given a revolutionary, which is to say accelerated, training in pedagogy by specialists. They would then return to their districts where they would set up “normal schools” to standardize the training of elementary school teachers in order that the Bouquier Law might be implemented generally.¹²⁶

Primarily responsible for magnifying that modest prospect into a grandiose educational experiment involving the foremost scientists of France was the intervention of Dominique-Joseph Garat. A minor man of letters in the 1780s, Garat had frequented the salon of Madame Helvétius in Auteuil, and become a leading figure among those of the idéologue circle who were pulling legislative strings in the Thermidorean Convention. He had been Minister of Justice in 1792 and Minister of the Interior prior to August 1793. His fence straddling in office aroused the distrust of both Girondists and Montagnards, and he lowered his profile to the level of invisibility during the Terror. In October 1794 Garat was named to direct the Commission d’Instruction Publique, the executive arm of the Comite d’Instruction Publique and, in effect, a proto-Ministry of Education. A fellow literary bureaucrat, Pierre-Louis Ginguene, who edited the ideological journal Décade philosophique, headed the office concerned with “sciences et arts.” Garat drafted the proposal that Lakanal, again on the parent Committee, presented to the Convention on 24 October 1704. It was the intention of his fellow deputies, or so Lakanal informed them, to develop a vast plan for public education. To that end, “you have wished to create in advance a large number of teachers capable of carrying into effect a plan . . . the purpose of which is regeneration of the human understanding in a Republic of twenty-five million men all of whom democracy makes equal. In these schools it will not be the sciences that are taught, but the art of teaching them. The disciples will not only be educated men; they will be men capable of educating.”¹²⁷

Regeneration of the human understanding, the telos of the idéologues, went far beyond the scope of the Bouquier law. Not only had the anticipated level of preparation for teachers risen from reading, writing, and arithmetic to an undefined height, but in a planning document of 28 November the notion of regional normal schools had given way to a single École Normale concentrated in the capital.¹²⁸ Accordingly, on 1 pluviôse an III (20 January 1795) some 1,400 aspirants overflowed the amphitheater of the Muséum d’Histoire Naturelle, which had seats for 750, and spilled out into the garden. Like the munitions workers who had warmed the same benches, they had been selected by district authorities throughout France in numbers proportional to the local population, in many cases on recommendation of local patriotic societies. These were not youths. There was no question of exemption from military service, and they ranged in age from twenty-five to the sixty-six years of the navigator and explorer Bougainville, included by some quirk of the selection process. Their preparation varied from none to the sophistication of a significant number of former teachers in the colleges and schools of the old regime.¹²⁹ Foremost among the latter was the twenty-seven-year-old Fourier, who had been teaching mathematics in a Benedictine school in Auxerre, where he had been imprisoned momentarily during the Terror.

Also like their predecessors, would-be teachers were paid a stipend to sit at the feet of leading scientists, and now of scholars, too. Theirs was intended to be a short day but a full week, or rather décade. By the original schedule, classes were to run from 11 A.M. to 1:15 P.M. On the first and sixth days, mathematics was to be taught by Lagrange and Laplace, physics by Haüy, and descriptive geometry by Monge; on the second and seventh, natural history by Daubenton, chemistry by Berthollet, and agriculture by Thouin; on the third and eighth, geography by Buache and Mentelle, history by Volney, and moral philosophy by Bernardin de Saint-Pierre; on the fourth and ninth, grammar by Sicard, literature by LaHarpe, and analysis of the understanding (i.e., psychology) by Garat himself. In the second meeting of each décade students were expected to ask questions and to raise subjects for discussion, while the fifth day was to be reserved for conferences open to the general public as well. Lectures were to be pedagogical, exemplifications of how to teach the subject, and not learned discourses. Still, that could be accomplished only by exposing students to the subjects them-selves. On the day of rest pupils were to visit museums, botanical gardens, libraries, observatories, and the Conservatoire des Arts et Métiers.

Monge was much the most accomplished teacher. He and Berthollet were the only two who had given courses in the revolutionary program on arms and munitions. Daubenton and Haüy had taught in the Jardin du Roi, while in the 1780s Garat and LaHarpe had given fashionable adult education in literary topics at the Lycée, and Mentelle was a geography teacher at the secondary level. Laplace had held classes in a small roomful of cadets in the École militaire for several years when he first came to Paris, and Lagrange had taught for a short time at the Royal Artillery School in Turin some forty years previously. As for the others, Bernardin de Saint-Pierrre, Thouin, Vandermonde, and Volney had had no teaching experience, and Berthollet only his brief stint in the revolutionary munitions courses. Instructions to the faculty on the necessity of thorough preparation and improvised delivery are no less pertinent today than at the time. Professors at the École Normale were enjoined not to read their lectures. Instead regulations called for stenographers to take down every word. The professors were to have the opportunity to revise their texts, which would then be printed and circulated to faculty and students of the École Normale in time for the discussions, and thereafter to deputies in the Convention, to district administrators throughout the country, to ministers of state, and to diplomats abroad.

At the opening session on 20 January 1795, a frigid winter’s day, Lakanal and Deleyre, clad in the regalia of representatives of the people on mission, presided on the dais festooned with revolutionary banners while looking over the shoulders of the professors who delivered the first three lectures, Laplace, Haüy, and Monge. The original schedule could not be met in what followed, however. For some reason no classes were held on the second day. On other days there might be one or two lectures, often running overtime, instead of the three intended. The number delivered by members of the faculty varied greatly. Sicard actually completed the course he planned. Famous for the sign language that enabled deaf-mutes to communicate, he let himself go before an audience that could hear and delivered twenty-eight wordy discourses on the art of speaking (not grammar as announced). Dau-benton, Nestor of the faculty at age seventy-nine, managed seventeen and urged the merit of systematics in natural history over the stylishness of a Buffon, to whom he had played second fiddle for most of his career. Laplace came close to fulfilling his program in ten lectures but had to skip the discussion of celestial mechanics he had intended. Monge delivered thirteen lectures on descriptive geometry while Lagrange gave five on fine points of analysis supplementing the more elementary and comprehensive presentations by Laplace. Haüy’s course on physics came to fifteen lectures, Buache’s and Mentelle’s on geography to fourteen, Berthollet’s on chemistry to twelve, and Volney’s on history to five.

In general the softer and less articulated the subject, the more fragmentary its coverage. LaHarpe’s course on literature met five times, Garat’s on analysis of the understanding only twice, and Bernardin de St.-Pierre’s on moral philosophy once, and then a month late. Thouin, scheduled for agriculture, was with the army in Belgium and Holland and never appeared on the podium at all. Instead, Creuzé-Latouche, he who had been the legislative protagonist for transforming the Jardin du Roi into the Muséun d’Histoire Naturelle, and who was now a member of the Comité d’Instruction Publique, proposed substituting political economy.¹³⁰ The move was significant in two respects. First, the course was the first ever offered in that subject in France, and one of the earliest anywhere. Second, in an indication that the idéologues did not have everything their own way, the person chosen to teach political economy was not a would-be social scientist or reformer of the human mind, but Alexandre Vandermonde, mathematician and technologist.

Students who wished to pose a question of the professor were required to register it the day before a discussion session. In the courses on political economy, geography, history, and language, the material lent itself naturally to these “debates,” though even there the number of participants was a small minority of the student body. That physics was still largely a qualitative science is evident in the number of objections Haüy had to meet in eight discussions concerning its scope and its definitions of the properties of bodies—weight, density, liquidity, elasticity, porosity, and so on. Not much was said of experiment until the last three discussion periods when Hauy stilled his sometimes impertinent interlocutors by enlisting Lefévre-Gineau to demonstrate the use of a hygrometer, the law of falling bodies, and the existence of atmospheric pressure.

Mathematics was less susceptible to objections. In the single discussion held during Laplace’s course three students, all clearly knowledgeable, asked questions, one about the convergence of series, a second about incompatibility between the notion of infinitesimals and logarithmic calculation, a third about the effect of the oblate figure of the earth on determination of the meter. Lagrange too held only one discussion, in which he took the precaution of including Laplace at his side. His discourse on number systems occupied most of the time, after which he and his colleague answered three questions on that and on the relative advantages of decimal and duo-decimal bases. Monge on descriptive geometry was more accessible both personally and substantively. He alone addressed his interlocuters as “tu” and “toi,” a politically correct affectation whose time had passed in the views of some, and his subject matter was notably less abstract. Fourier took the occasion of the first debate to show his mettle by proposing definitions of the straight line, plane, and circle that he deemed more rigorous than accepted Archimedean formulations. Monge gently responded that he had begged the question, to which soft rebuff another student agreed. Six or seven others engaged in exchanges at a comparable level in two remaining discussions.

Pedagogically, the brave, or perhaps foolhardy, experiment could only be a spectacle, not a success. Relatively few of the auditors were adequately prepared even for elementary lectures. Unable to find seats or to follow when they did, many of the others took to drifting about town.¹³¹ Inevitably, in a city as critical as Paris, what a journalist called the “tower of Babel in the Jardin des Plantes” became an object of ridicule in the press, while its expense, lack of focus, and general disorganization came to seem a scandal in the eyes of deputies to the Convention. Four months was to have been its term. Among other uncertainties, the legislation had never specified what its future was to be. Garat, Ginguené, Sicard, and others wished to continue it as a permanent institution for the training of secondary, not elementary, school teachers. Instead, the Convention closed it down. Sicard gave the last lecture in the last session, the sixty-first, on 16 May (26 floréal). His subject was punctuation. Gilbert Romme, who (it will be recalled) had tried to save the essential principle of the Condorcet Plan, had administered the coup de grace in a speech to the Convention:

I think that the École Normale has completely failed to fulfill its mission. The students consist of two sorts. The first are well informed in certain respects and very little in others; the second in none. The latter expected to find elementary ideas in the lectures of their professors. All they got were academic notions. One of the greatest vices of the teaching is that the professors presume that their students already have superior knowledge. Besides that, it was assumed that the attention of young people could be sustained long enough to follow three very different subjects presented very rapidly in a single sesssion. The professors themselves would be incapable of paying such attention. This school could be very useful for people who already have extensive knowledge. It is useless for those who do not. . . . Since all I see in the institution is organized charlatinism, I ask for its suppression.¹³²

That was Romme’s last success. The Convention ordered abolition of the École Normale as of 19 May (30 floréal). As we have seen, his intervention on behalf of the insurgents of the following day, 1 prairial, landed him in the prison where he committed suicide.¹³³

The short-lived École Normale thus had nothing but the name in common with the Napoleonic École Normale of 1810, which was subject to the Imperial University, much less with the famous École Normale Supérieure of the rue d’Ulm, which has been the principal nursery of the French academic elite since the middle of the nineteenth century. Nevertheless, its influence on the actual practice and content of secondary education under the Directory, though minimal, was not negligible. On 16 December 1794, Lakanal, still spokesman for the Comité d’Instruction Publique, followed up on the summons to create the École Normale with a proposal to establish a system of Écoles Centrales, one in every department. They would combine what in Condorcet’s plan would have been secondary and higher education (lycées and instituts).¹³⁴ A measure to that effect passed the Convention with little discussion on 3 ventôse an III (21 February 1795), even as the presumed cadre of teachers entered on their second month of preparation in the École Normale. Little happened after its demise until 23 October (3 brumaire an IV) when, in one of its last acts, the expiring Convention finally codified an educational system in legislation drafted by François Daunou. The legislative expert among the idéologues, Daunou was principal author also of the Constitution of the year III, which established the Directory and embedded the Institut de France in the foundations of the Republic. From a modern point of view, the Écoles Centrales that opened under the Daunou law were curious institutions, as indeed they seemed at the time to those accustomed to the rigid stratification year by year in the clerical colleges of the old regime. There were no prerequisites, no requirements, no curriculum, no promotion from one grade to the next, and no diplomas. Examinations were at the option of each professor. In the arrangement of courses, the Écoles Centrales resembled a set of junior-grade Collèges de France. Inscribed students, and others for that matter, might attend as many or as few of the offerings as they pleased, in any order, and for as long as they liked. Most courses occupied one year, a few two or even three years, again as the professor chose. The enabling legislation prescribed what the courses should be, but administrative oversight, financing, and staffing were left to local departmental authorities. The courses were to be nine in number, grouped loosely into three divisions. In the first were drawing, ancient languages (i.e., Latin), and natural history; in the second, mathematics and physics-chemistry; in the third, general grammar (i.e., idéologie ), belles-lettres, history, and legislation. If observed, provisions of the Daunou law would have entailed a rough sequence. In principle the minimum age for taking courses in the first group was to have been twelve, for the second fourteen, and for the third sixteen. In practice that stipulation was widely ignored, and students of any age were to be found in any course. Recent quantitative studies estimate that approximately 70 percent of 629 known professors had been teachers in the old clerical colleges. Most of the rest were artists teaching drawing, doctors teaching natural history, and lawyers teaching legislation. Over 10 percent of the sample professoriate, 78 in all, had enrolled in the École Normale.

By 1799 about 10,000 boys were attending the Écoles Centrales. The number was far short of the 50,000 enrolled toward the end of the old regime in the clerical colleges, whose premises in many cases had been taken over. The social mixture was more heterogeneous, however. There were three schools in Paris, the Prytanée (the once and future Louis-le-Grand), the Panthéon, and the Quatre-Nations. Among the fathers of 885 students among the 979 enrolled, 30 percent were of the prosperous bourgeoisie, another 30 percent were of the artisanal, shopkeeping, and even working classes, 25 percent were civil servants, and 12 percent were lawyers or doctors. The figure 10,000, however, was not the sum total of those receiving some sort of secondary education in France under the Directory. A large number of private schools, some of them former colleges that had survived the Terror, had sprung up to serve families who could pay the fees.¹³⁵ For the most part, theirs continued to be a classical curriculum based on Latin with little room for modern subjects.

No matter how inchoate the teaching program, the Écoles Centrales were far from an unqualified failure educationally. Distinguished people were on the faculties of the three schools in Paris: among them Georges Cuvier in natural history, Sylvestre Lacroix in mathematics, M. J. Brisson in physics and chemistry, F. U. Domergue in general grammar, J. P. L. Fontanes in belles-lettres, and P. C. L. Guérolt in ancient languages. All but Gueroult were members of the Institute, and he became director of the 1808 École Normale. The course in drawing attracted the largest enrollment by far throughout the country. Many boys studying the subject did become artists, illustrators, or mechanics, and might enroll further in the Conservatoire National des Arts et Métiers. Boys studying natural history did go into agriculture, pharmacology, or medicine, the last after going on to one of the Écoles de Santé. Some boys studying legislation did become lawyers. A few boys taking mathematics and physics-chemistry did present themselves for admission to the École Polytechnique.¹³⁶ In the judgment of a historian of French scientific education, provision for chairs of natural history, mathematics, and physics-chemistry was “the birth certificate of an autonomous teaching of natural science at the secondary level.”¹³⁷ In brief, the short life of the Écoles Centrales, immediate forerunners of the very different Napoleonic Lycées, might be taken as an illustration of a dictum attributed to Otto Neugebauer to the effect that no one has ever devised an educational system that could spoil a really good mind.

However that may be, the experience of the École Normale, like many another pedagogical experiment before and since, accomplished more for the education of its professors than of its students. Except for Mentelle, a school teacher, not one of them had ever been called on to address the whole range of his subject in public. Contributing greatly to their doing so in the École Normale was the obligation to review and revise stenographic copies of the lectures for publication. The contemporary editions are a bibliographical hodge-podge, not to say a nightmare—inevitably so, given the urgency of getting them into print somehow, anyhow, first in order to be circulated for discussion, and in two later revisions in order to mitigate the dearth of school books.¹³⁸ The ensemble of those texts, taken as a window into the mindset of the late 1790s, furnished the subject for systematic study in a seminar at the École Normale Superieure in the late 1980s, the fruits of which are a critical annotated edition currently in course of publication.¹³⁹ Although the test of time is by no means the sole, or perhaps the most important, criterion of historical importance, the courses that have stood it best in the eyes of one reader in the early twenty-first century are those of Laplace, Monge, and Volney.

It is hard to imagine what portions of his published text Laplace could have squeezed into the forty-five minutes allotted for each lecture. In the first eight he led his auditors along the classical sequence of topics from arithmetic through operations of algebra and formulations of geometry and trigonometry to analytic geometry and the theory of curves and surfaces. The subject matter was elementary, although the treatment was novel in that Laplace conveyed the sense of mathematics as a living investigative enterprise rather than an inert body of Euclidean proofs and Cartesian rules. His intention was not simply to teach the elements, but to show how they should be taught. In that respect, as Sylvestre Lacroix testified, his course served as model for a generation of textbooks. Laplace’s immediate purpose, however, was to prepare the mathematical ground for exhibiting the cosmic basis of his principal civic commitment, the metric system, and also the civic dimensions of the principal areas of research in his own career, celestial mechanics and probability. Those dimensions had not, it may be noted in passing, been much mentioned in his earliest memoirs, nor were they fully evident to him prior to the circumstances of the Revolution.

Laplace devoted his ninth lecture to the rationale for the survey of the meridian discussed above in chapter 4 on the metric system.¹⁴⁰ Had he been able to carry out the program as announced, he would have treated the calculus of difference and differential equations, rational mechanics, astronomy, and the theory of probability. Forced to cut his course short, he elected to skip to the last topic, the one that was least understood and most important for civil society. He promised to repair the omission in a forthcoming book on mechanics and astronomy designed for readers unversed in mathematical analysis. As good as his word, Laplace published Exposition du système du monde the next year, in 1796. That book is one of the most successful verbal accounts of mathematical science ever composed. He there exhibits for the educated public the results of a century of research into the motion of planets, much of it his own, and all of it confirming the stability of the solar system in service to the Newtonian law of gravity. The first edition closes with a panegyric of astronomy—and a political statement. The merit of the science is that it

dissipates errors born of ignorance about our true relation with nature, errors all the more damaging in that the social order should rest only on those relations. TRUTH! JUSTICE! Those are the immutable laws. Let us banish the dangerous maxim that it is sometimes necessary to depart from them and to deceive or enslave mankind to assure its happiness.¹⁴¹

Laplace published Exposition du système du monde three years before the first two volumes of Traité de mécanique céleste (1799), the mathematical magnum opus from which he extracted it. By contrast its counterpart for a general public, the Essai philosophique sur les probabilités (1814), appeared a year and a half after Théorie analytique des probabilités (1811), the mathematical master work it epitomized verbally. The Essai philosophique has lasted. Its most recent edition appeared in 1986.142 The nucleus was Laplace’s tenth lecture at the École Normale.

That concluding lecture was an extraordinary performance. His early memoirs on probability had done more than the writings of any other to develop the old theory of chances (hasards), which bore mainly on games and other genuine or imagined binary models, into a branch of analysis that was of fundamental philosophical significance and applicable to real problems of science and social science alike. The main themes Laplace distilled out to put before his class at the École Normale were as follows: what are taken for irregularities in the natural world are evidence neither of miracles nor of indeterminacy, but are simply events of whose causes we are ignorant; probability is relative in part to our ignorance and in part to our knowledge; multiplication of instances permits prediction of future events with a probability amounting to certainty when carried to infinity; the credibility of testimony diminishes with the number of times it is relayed; tables of mortality permit reliable estimates of the size and distribution of a given population; the size of the sample in demographic studies has a precise relation to the margin of error; probabilistic demonstration of the overall life-saving effect of inoculation against smallpox cannot ease the anxiety of parents who decide to expose a child to its danger; inverse probabilities permit estimating the reliability of decision making by judicial panels and electoral bodies; putting money into lotteries is folly, whereas soundly based life-income schemes, tontines, and insurance policies are wise investments. Laplace con cludes with a remark on the prospective value of probabilistic analysis in political economy:

Let us treat economics as physics has been treated, in the light of experience and analysis. Simply consider, on the one hand, the large number of truths to discovery of which that method has led in the study of nature, and on the other hand, the mass of error that the mania of systems has produced; and you will feel the need of consulting experience in all things. It is a slow guide, but always sure, and abandoning it leads to the most dangerous errors (écarts).¹⁴³

Laplace may have included that closing remark in deference to Vander-monde’s course in political economy. He never recurred to the subject. The point about which he evidently felt most strongly was the one he considered in the middle of his lecture, for he had taken those paragraphs almost verbatim from the manuscript of Exposition du système du monde , where they appeared the next year in the concluding passages. Laplace there exemplifies the probabilistic argument for the determinacy of nature in the case of the structure of the planetary system. So far as then known it consists of seven planets, fourteen satellites, and the rings of Saturn. All observable motions together, both of revolution and rotation, some thirty in all, are in the same direction; all orbits are almost circular and almost in the same plane. The probability that so coherent an arrangement could be the result of chance is effectively null. There must be a unitary cause, and here Laplace invokes what in later times has been called his nebular hypothesis. Misleadingly so, for the question does not concern nebulae in outer space. The accurate term would be atmospheric hypothesis, since what Laplace had in mind was condensation of the matter in an atmosphere surrounding the sun, rotating with it, and now shrunken to the dimensions observable in a telescope. It is a further mistake to suppose that Laplace was anticipating the nineteenth-century shift of attention from the structure of nature to its development over time. Again not so, his problem was with the probability of cause. There is no better illustration of the reciprocity, rather than what might at first glance seem the incompatibility, of his lifelong preoccupations with probability and determinism.¹⁴⁴ It is worth noting, finally, that Laplace did not recur to the formation of the solar system in Essai philosophique des probabilités, addressed like Exposition du systéme du monde to an educated public to whom the mathematics in the Traité de mécanique céleste and Traité analytique des probabilités was inaccessible.¹⁴⁵

Reading Laplace, one feels that he cared about what he could do with mathematics in respect to philosophical determinism, cosmic order, and ultimately civic order. Reading Lagrange, one feels that he simply loved the mathematics. There was a poetic quality to his mathematical sensibility. Lagrange, thirteen years Laplace’s senior, had also given instruction only briefly as a very young man, in his case at the Royal Artillery School in Turin. After having distinguished himself in Turin, his birthplace, Lagrange was called to Berlin in 1766 and there made his reputation by inventing the calculus of variations and composing elegant memoirs on planetary perturbations, number theory, and theory of equations. His election to the Academy of Science and move to Paris in 1787 preceded by a year publication of his masterpiece, Mécanique analytique (1788). A person of gentle disposition, Lagrange entered on a state of mild depression after that effort. He withdrew from active analysis and instead interested himself in Lavoisier’s reform of chemistry, which in his opinion introduced into that science a coherence previously characteristic of mathematics and astronomy. As we have seen, he also served a bit passively on successive commissions overseeing the metric system. Now at the age of fifty-nine, a return to the classroom had the immediate effect of drawing him back to mathematics. Or rather, his return to classrooms, for Lagrange was also on the faculty of the École Centrale des Travaux Publics (the future Polytechnique), which opened on 21 December 1794, a month before the École Normale.

Fourier tells of the impression he made on students in the latter:

Lagrange, the foremost savant in Europe . . . has delicate features and a dignified appearance. His complexion is slightly pitted, and he looks pale. His voice is very feeble unless he warms to his subject. He has a marked Italian accent and pronounces s’s like z’s. He dresses plainly in black and brown. He speaks in a familiar manner, with some difficulty. His speech is halting and simple, like a child’s. Everyone recognizes that he is an extraordinary man, but one has to have seen him to appreciate that he is a great man. He talks only when he is lecturing, and sometimes uses phrases that excite laughter. The other day he said, “There are still many important things to say on this subject, but I shall not say them.” The pupils, most of whom are incapable of appreciating him, don’t give him much of a welcome, but the professors make up for that.146

The poetic strain in Lagrange’s mathematical sensibility led him to try to convey the charm of his subject by historical asides. “Citizens, in the words of an ancient Greek, arithmetic and geometry are the wings of mathematics. ” So opened the second lecture. Not to speak metaphorically, Lagrange continued, these two sciences are the foundation and the essence of all sciences that treat magnitudes. Not only are they fundamental, they are complementary. When you find a result, in order to use it you must translate it either into numbers or into lines. For the one you need arithmetic, for the other geometry.¹⁴⁷

Virtually nothing in Lagrange’s expositions would have shown his students how to solve such problems. The two lectures on arithmetic deal not with its operations, but with properties of numbers and propositions of number theory in general. Only if geometry be thought completely reducible to analysis, and Lagrange did think that, might the remaining three be thought to treat the second wing of mathematics. They concern in fact the theory of equations. The third, on resolution of third and fourth degree equations, is particularly abstract. The fourth and fifth are a shade more accessible. The former contains the interpolation for the solution of numerical equations since known as the theorem of Lagrange. In the latter he shows, among other things, how to solve higher order equations by plotting the curves.

Whatever the pedagogical failure, preparation of these lectures was important mathematically to Lagrange. After editing the texts for publication in the first edition of Séances de l’École Normale (1796), he went on to develop their central theme of algebraicization in his second general treatise, Théorie des fonctions analytiques (1797). A famous passage in the preface to its predecessor, Mécanique analytique (1788), states the purpose of that work:

We already have several treatises of mechanics, but the plan of this one is entirely new. I propose to reduce the theory of that science and the art of solving problems relating to it to general formulas, the simple manipulation of which gives all the equations necessaary for the solution of any problem. . . . No diagrams will be found in this work. The methods I set out require neither constructions, nor geometric or mechanistic reasoning, but only algebraic operations, in conformity with a regular and uniform procedure. Those who love analysis will be pleased to see Mechanics become a new branch and will be grateful to me for having thus extended its dominion.¹⁴⁸

The full title of his final treatise announces the extension of this programmatic algebraicization to the calculus itself: Theory of analytic functions, containing the principles of the differential calculus free from all considerations of infinitesimals, vanishing quantities, limits, and fluxions, and reduced to the algebraic analysis of finite quantities. In the former work, Lagrange thought to base mechanics on the principle of least error; in the latter to base the differential calculus on the expansion of power series, which is to say on the algebra of polynomials.¹⁴⁹ By now teaching and publishing were complementary for Lagrange. He further explicated and developed that theme in his courses at the École Polytechnique from 1795 through 1798, which he then published as Nouvelles Leçons sur le calcul des fonctions.¹⁵⁰ Owing in large part to the work of a protégé of later years, and onetime student at the École Polytechnique, Augustin Cauchy, his program for founding the calculus on algebraic operations did not fi

Unlike Lagrange, who gave only an inaugural lecture at the École des Travaux Publics, Monge taught there in the mornings and in the afternoons at the École Normale. His subject matter, descriptive geometry, was the same at both, but the latter course was more elementary. In the preliminary lecture at the École Normale, Monge defines descriptive geometry as an “art” with two purposes: “The first is to represent with exactness in designs that have only two dimensions objects that have three and that are capable of rigorous definition. . . . The second purpose . . . is to deduce from the exact description of bodies everything that follows necessarily from their forms and respective positions.”¹⁵¹ The term “descriptive geometry” was new with Monge. The subject and the topics treated, on the other hand, were anything but new. Desargues, as Monge acknowledged, had anticipated much of it in the early seventeenth century, after which his work was lost to view amid the brilliant triumph of Cartesian analysis.¹⁵² Monge developed what he still called the art into a unified science by discerning the geometry implicit in techniques long since employed in artistic perspective, stereotomy (shaping stones for construction of vaults and arches), architectural and mechanical drawing (blueprints in later usage), delineation of shadows, design of sundials, cartographical profiling, grading of highways, the art of fortification, and so on.¹⁵³

Monge began his course in an elementary manner with the conventional methods of projection. The first lecture considers determining the position of a point in any body by its projection, first onto three other points, next onto three right lines, then, and this was the most convenient, onto three planes of known location. In the second lecture Monge moved on to orthogonal projection of a line onto two nonparallel planes, the intersection of which determines its position. Those techniques suffice for the representation of any polyhedral surface since they permit plotting the location of its edges and vertices. Not so for curved surfaces, and Monge develops in the third lecture the procedure for generating such surfaces by the motion of curved lines. He here alludes to but does not develop the possibility of expressing the same construction analytically by formulating the equation of the curve in question. In the fourth and fifth lectures Monge turns to constructions. The problems are to find the tangents and normals to curved surfaces at any point. Single cylinders and cones offer the simplest cases. Other figures and combinations of figures are more complicated. Further lectures on descriptive geometry proper deal with the intersections of surfaces of various sorts. Let us take a sample problem at random: in the case of two planes each tangent to a different surface, find the line, tangent to both surfaces, along which the planes intersect. Throughout Monge gives examples of the applicability of geometric construction to practical tasks such as shaping stones to support a vault, shading of colors in a painting, and adjusting for differences of altitude in triangulation of a territory. In all this he thought to show how geometric construction could often reach solutions to practical problems more readily and directly than analysis. At the same time, he sought to exhibit the complementarity of the two major mathematical modes by devoting two lectures to an elementary presentation of the differential geometry with which he had made the reputation that had won him election to the Academy of Science in 1780.

At the opening of his course Monge evoked the need to liberate France from its dependence on foreign (i.e., British) industry. That would require in the first place focusing education on subjects that require exactness. Artisans must learn to make things with precision. Consumers must learn to require it. The public must be informed concerning the natural resources of the country, fortunately ample. Manufacturers must learn the use of labor-saving machines and standardized methods of production. For all those reasons a national system of education must be given a new direction. The readiest instrument for that purpose would be familiarization with the use of descriptive geometry. A command of it would benefit intelligent young men of all classes. Those with inherited means would learn to invest them more productively. Those with no fortune other than their education would learn to earn higher returns from their work.

It must be said, however, that the interest of Monge’s lectures lies in the geometry of the examples he adduced from the practice of many trades rather than in its capacity to fulfill those civic purposes. He implied, but cannot realistically have supposed, that determination of the normals to the curved surface of a vault would lead bridge builders to construct more symmetrical arches or that constructing a plane tangent to the curved surface that was determined by the position of the beholder’s eye and the location of light sources would lead artists to paint better pictures.¹⁵⁴ Indeed, among the multitude of examples Monge cites, the only one that clearly changed a given practice was the method he himself had invented when a youth at Mézières for determining the defilade (the protection from artillery fire afforded by terrain) at any point in a fortified position. The influence, in short, of descriptive geometry was less on specific technologies than it was, first, on the immediate exemplification of rational procedures it afforded to students of engineering at the École Polytechnique, and, second, on the future of mathematics. Laplace, who was of an ungenerous disposition, could not have considered Monge’s descriptive geometry to be a branch of mathematics, analytically speaking. Lagrange, who was generous, may have privately agreed.

Geometry did nevertheless regain importance in the nineteenth century. In the opinion of Michel Chasles, and no scholar has been better placed to judge, that it did so was largely owing to Monge’s teaching and example. Poncelet’s projective geometry and principle of continuity, Lazare Carnot’s Géometrie de position (1803) and theory of transversals, Charles Dupin’s Développements de la géometrie (1813), Etienne Malus’s Traité d’optique (1813), Chasles’s own contributions to pure geometry, the many geometrical memoirs by graduates of the École Polytechnique in Gergonne’s Annales de math-ématique pure et appliquée—in Chasles’s account all this and current rational geometry in general derived directly or indirectly from descriptive geometry.¹⁵⁵ The new geometry dealt with problems of extension in a different manner from that of its classical predecessor. Operational might have been a better adjective than rational. Its procedures were constructive rather than deductive. Instead of being a given body of proofs and theorems, it arrived at theorems by transforming the properties of three-dimensional figures into properties of two-dimensional figures that could be represented on paper as the former could not. The resulting diagrams then permitted discovery of otherwise undetected relations among the elements of the original forms. In other words, plane geometry became an instrument of research into spatial relations.

Monge loved teaching and disliked writing. Had it not been for the stenographers who took down his course at the École Normale, we would have only the testimony of students and not Traité de géométrie descriptive, the most widely read and influential of his two treatises. His assistant and disciple, Nicolas Hachette, who had seconded him at Mézières, gathered it together from the Séances des Écoles Normales, and saw the book through the press in 1799 while Monge was absent with Bonaparte in Egypt. It is thanks to Monge’s course at the École Polytechnique that we also have the other of his completed treatises, again through the good offices of Hachette, Analyse appliquée à la géométrie (1805). Of Monge’s mathematical work, there would have otherwise remained in print only the series of specialized and largely inaccessible memoirs of infinitesimal and differential geometry presented to the Academy of Science in the 1770s.

By contrast with the mathematical courses, there was little innovative about the presentations of Haüy on physics or of Berthollet on chemistry. It was the first time either had addressed himself in public to the whole range of the science he was called upon to teach. Haüy indeed had begun as a naturalist. His scientific reputation rested on his crystallogaphy. As it happened, his determination of the geometry of crystalline forms proved to be less influential in physics than in chemistry, where it introduced the notion of a “molécule intégrante” at the basis of atomic structures.¹⁵⁶ Haüy had reached a wide scientific public in 1787 with a nonmathematical explanation of Aepinus’s theory of electricity and magnetism, to which he added an account of Coulomb’s early experiments.¹⁵⁷ Like Aepinus and Franklin, he there adhered to the one-fluid theory of electricity and also of magnetism, although in his course and later writings he shifted to the two-fluid model.¹⁵⁸ No doubt Haüy’s availability was the main factor in his being chosen to teach at the École Normale. Students complained in one of the discussions that he was giving too much prominence to crystallography. Unlike most of his colleagues, Haüy intended to present his subject in a manner suited to instruction in primary schools. In his account physics is still a largely qualitative, descriptive, and experimental science without a hint of the mathematicization that would shortly overtake and transform it. The same is true of his textbook, Traité élémentaire de physique (1803), which he developed from the stenographic copy of his lectures. A highly successful textbook, it won him election to the Légion d’Honneur.

Unlike Haüy, Berthollet was known as a major figure in the science he was teaching. Indeed, following the loss of Lavoisier, he was the leading chemist in France. So far, however, his reputation rested, not on any novel views about the subject as a whole, but on particular discoveries such as the chemistry of chlorine compounds, on his service to the dyeing industry as consultant to the Gobelins in the 1780s, and on his recent contribution to munitions-making in the 1790s. A valuable treatise on the art of dyeing, Élémens de l’art de la teinture (1791), was his only book so far. For all his eminence, his course was no less conventional than Haüy’s, if pitched at a higher level. He in common with almost all his colleagues placed great hopes on an eventual unification of the science of chemistry around the notion of affinities, which he developed at the outset, but which was not then, nor would it ever become, capable of organizing the established heads of chemical information that Berhollet presented in the body of his course. He elaborated on the stenographic copy of his introductory remarks in Recherches sur les lois de l’affinité (1801), a synthetic work reporting on the state of an unresolved question. His lectures contain no hint of the reorientation in the direction of physical chemistry that Berthollet did give the science in the Essai de statique chimique of 1802, written in consequence of the discoveries he made in 1799 Egypt, to be discussed in the next chapter.

Of the two remaining courses touching on science, geography was a boring failure, political economy an interesting failure, and neither left a mark on the immediate or distant future. The former was split between two professors of geography whose differing views of the subject, the one theoretical, the other pedagogical, induced confusion instead of complementing each other. Jean-Nicolas Buache de Neuville, Buache during the Revolution, was a hereditary geographer in a family long attached to the court. His uncle, Philippe Buache, Geographer Royal, constructed theories of physical topograpy according to which the surface of the earth is arranged in systems of mountains, river valleys, plains, and seas organized hierarchically. Buache de Neuville continued that program, to which he added ethnographic considerations concerning the peoples inhabiting the various terrains. Detailed descriptions of surface features in France province by province and in neighboring countries served the larger purpose of formulating geopolitical recommendations to government. Edme Mentelle, by contrast, considered that geography was an affair of territories, boundaries, cities, routes, rivers, mountains, distances, populations, and so on. All the data existed needing only to be compiled and imparted. He spent his career imparting it in tandem with the facts of history at the École Militaire. He and Buache attempted to unify their course by situating the description of the earth in its astronomical setting. They did have two things in common. Both considered geography to be a necessary adjunct of historical knowledge and a guide to power politics, and both practised it as a sedentary pursuit to be cultivated from books and maps. The travels of an Alexander von Humboldt lay some distance in the future of the science, and nothing in their course pointed the way.¹⁵⁹

According to contemporaries, Alexandre Vandermonde had an unprepossessing personality and an important mind. He now turned the inquiring spirit he had long since brought to mathematics and technology to problems of economics. In March 1794, soon after he closed his interchangeable-parts workshop, the Atelier de Perfectionnement, the Committee of Public Safety sent Vandermonde to Lyons to oversee adaptation of the silk industry to production of the taffeta required for fabrication of military balloons. On his return to Paris he wrote a report, not simply on that, but on the state of industry and commerce in Lyons generally.¹⁶⁰ In all likelihood that was what led to his appointment to the belated chair of political economy in the École Normale. It is unclear who else could have been at all qualified. Dupont de Nemours was in exile in New York. Jean-Baptiste Say had yet to make a reputation. The course as such was not a success. Vandermonde apologized frequently for his lack of preparedness. He agreed when students complained of its incoherence. Let us all study together, he appealed to them. In retrospect certain of his positions seem preposterous, particularly his enthusiasm for assignats. The lecture on money praises them to the skies. They are the most rational form of currency ever invented. They do not conflate, as do precious metals, the properties of possessing value and representing value. The value they do reflect, land, is the main source of real wealth. What is to blame for inflation is insufficient production of goods, not oversupply of paper money.

In other respects Vandermonde is shrewd. He knew his Wealth of Nations thoroughly, and agreed with Adam Smith on the advantages of division of labor and substitution of machines for human labor where feasible. He disagreed on free trade, however, and preferred the protectionist recommendations of James Steuart when it was a question of shielding real and human value, say the skills of the silk workers of Lyons, against ruinous competition. He shared the position, virtually axiomatic at the time, that the right to property is the foundation of social order, but he disagreed with the prevailing view that its basis is natural law. In Vandermonde’s analysis, it originated in a convention and its justification is social utility, not natural right.

Perhaps the most interesting feature of Vandermonde’s treatment of political economy is his standpoint. Unlike Condorcet and his followers, the ideologues, who thought to quantify a social science by calculating the probability of desirable outcomes, Vandermonde was no moralist. In his view political economy should not be studied as a normative subject. It was descriptive and analytical. His instinct agreed with Laplace’s injunction to treat political economy on the model of physics, “by way of experiment and analysis.”¹⁶¹ He would make of economics an exact science, at least in its theoretical formulations, even if it could not be so in its application to the complications of commercial reality. He was much attracted to Adam Smith’s model of the invisible hand holding a balance between supply and demand. The concept of a natural equilibrium in a market economy would permit eventual mathematization of the factors in terms, not of probabilities, but of the functional analysis of differential calculus.

There are no equations in Vandermonde’s text, however. His mathematical sense only led him to prefer such a direction. On 22 April he ended his eighth lecture, which was on pricing mechanisms, with the promise that he would develop their consequences in the next meeting and, if time permitted, take up the question of the effect on prices of the money supply. That did not happen. In failing health, Vandermonde was unable to complete his course. He died on 1 January 1796.¹⁶²

It could be argued that the course on history given by Volney broke fresher ground in its field than did any other offered in the Ecole Normale. In all likelihood, Constantin-François Chasseboeuf chose the pen name Volney in token of his admiration for Voltaire at Ferney. Born in 1757 into the prosperous provincial bourgeoisie, even like Voltaire half a century earlier, Volney completed his secondary education, a classical education, at the college of Angers, where he began the study of law and also of Hebrew. He came to Paris in 1775, at first to qualify himself in medicine. Among his fellow students was Cabanis, who became and remained an intimate friend and companion, and who introduced him to the salon of Madame Helvétius in Auteuil and the circle of future idéologues. There he met baron d’Holbach, whose salon he also frequented and whose empirical standpoint in political and moral philosophy he admired and later emulated. Medicine proving little to his taste, Volney had the wit and also the means to explore the resources of the capital. He threw himself into the study of oriental languages, perfected his Hebrew, and learned Arabic with Leroux des Haut-erayes at the Collège Royal.

In December 1782 the twenty-five-year old Volney set forth on a journey of exploration to Egypt, Libya, Palestine, Lebanon, and Syria. Whether he was on his own or on a secret mission for the ministry of foreign affairs is unclear. He lived and traveled in the near East for over two years, perfecting his Arabic and spending time in Alexandria, Tripoli, Cairo, Damascus, Aleppo, Haifa, St.-Jean d’Acre, Jerusalem, and various monastaries and retreats along the way. Returning to France in March 1785, he settled down at home in Anjou to write an account of all he had seen and learned. Voyage en Égypte et en Syrie appeared in two volumes 1787. An immediate success, it made his reputation.¹⁶³

Late twentieth-century critics of European and American attitudes to the Near East might find in Volney’s book an early instance of the “Orientalism” they deplore. Its thesis is that despotic polity, religiosity, oppression, and slavery were responsible for arrested social, economic, and intellectual development in the Ottoman Empire. However that may be, many good books are more than their thesis. Volney penetrated the life and atmosphere of the countries he visited and conveyed their inwardness as no European had done in modern times. Its tone is sympathetic in a human sense and in no way condescending. Consistent in his antipathy to oppression, he joined Condorcet, Grégoire, and other opponents of slavery in the Société des Amis des Noirs in 1788.

Coming from such a background, Volney naturally welcomed the Revolution. He represented Anjou in the Constituent Assembly and took an active part in company with Mirabeau, Sieyès, and Bailly in the political maneuvers that assured the dominance of the Third Estate. A liberal of 1789 and nothing radical, Volney was of the view that his agenda for the Revolution was complete with the work of the Constituent Assembly. After its dissolution in September 1791, he left Paris for Corsica, where he thought to cultivate oranges while occupying his mind with study. He had just completed a second major work in a vein not unlike Gibbon’s on Rome, the very successful, much translated, and frequently reprinted Ruines, ou Méditations sur les révolutions des empires (1791).

In Corsica Volney met and was much impressed with a young artillery officer, Napoleon Bonaparte. The agricultural experiment a failure, he returned to Paris in 1793. His La loi naturelle, ou le Catéchisme du citoyen français, appearing that September, is a timely pamphlet designed to base personal morality and civic duty on a rigorously empiricist, or sensationalist, psychology.¹⁶⁴ It in no way satisfied the emerging Robespierrist equation of virtue and terror. Volney was then planning a trip to America in order to complement his study of the Near East with a scrutiny of still farther parts. He was arrested in November 1793, on the eve of his intended departure and spent the Terror in confinement. On release he resumed association with the circle of idéologues now engaged in forming the polity of a stabilized revolution.

Such were the circumstances in which Garat tapped Volney to give the course on History at the École Normale. Soon after it was finished, in September 1795, he did depart for the United States, where he traveled and observed the new republic and its Indian neighbors for three years, returning to Paris in June 1798. The fruit, Tableau du sol et du climat des États-Unis (1803), delivers more than its title promises and is too little known in the land it describes. It will be clear from this summary that there were historical dimensions to Volney’s thinking, but that he was not a historian.

His Leçons d’Histoire are no less worth the attention of historians and others for that.¹⁶⁵ Volney was at one with fellow heirs to the Enlightenment in considering the physical and natural sciences to be the cynosure of exact knowledge. History has no such claims. Historical facts are known, not through the senses, but through testimony and memory, both fallible. Their certitude is at best probable. The historian’s job is to estimate the degree of probability, which subject Volney takes to be the most important taught at the École Normale. Historians cannot think to command agreement. They must needs respect the opinions of those who differ even as they expect others to tolerate theirs. History is, in effect, simply an investigation of facts that can be known only through intermediaries. They need to be interrogated, like witnesses. “The historian conscious of his duties should regard himself as a judge who calls narrators and witnesses before him, confronts them, questions them, and seeks to arrive at the truth, that is to say the existence of the fact, such as it was (tel qu’il était).”¹⁶⁶ The emphasis can only call to mind Ranke’s famous injunction to tell it as it really was, “wie es eigentlich gewesen.”

With respect to purview, Volney, the student of other cultures, has no patience with limiting history to accounts of three privileged peoples, Jews, Greeks, and Romans, let alone to the story of any single nation in early or modern times. On the contrary, its proper scope is all humanity taken as a single society composed of peoples considered as its individual actors. The facts to be searched for are not the dramatic episodes about which myth, legend, tradition, and patriotism cluster, but rather such common and ordinary experiences as occur frequently enough to constitute patterns and to reveal principles: “for principles are not abstract things, existing independently of humanity; principles are general and summary facts resulting from the addition of particular facts and thereby constituting, not tyrannical rules of conduct, but the basis of approximate calculations of likelihoods and probabilities.”¹⁶⁷ Volney clearly shared not only Condorcet’s confidence in probabilistic analysis, and also the sense that history embraces all humanity. Even if he had read Sketch for a Historical Picture of the Progress of the Human Mind, however, he cannot have had time to consider his late friend’s testament, for it issued from the press only while the École Normale was in session. What Volney did not share was Condorcet’s fixation on the idea of progress or his confidence in it.

In point of method, Volney prefigures Tocqueville, who must have read his account of America before departing for his famous investigation of the workings of equality there. Whether or not Tocqueville consciously modeled his treatment on Volney’s, they both eschewed narrative of events in favor of analysis and comparison: analysis of the structure and workings of the societies they studied and comparison with relevant evidence elsewhere. In Tocqueville’s work the terms of comparison were America and France. Volney’s brief course afforded less opportunity to deploy his method, but he does suggest that comparison of the state of contemporary Asian society with that of classical antiquity would be revealing. As just noted, he also intended to scrutinize America with similar ends in view.

Analysis and comparison, then, constitute the mode of writing and teaching history, not narrative. That had been understood in antiquity, when the word had the connotations of inquiry and description, as it had done in the writings of Thucydides and Herodotus, and for that matter (though Volney does not mention this) in Francis Bacon, and as it still does in the phrase “natural history.” In modern usage, so he thought, it too often means telling edifying stories. People who want that would do better to read novels, or on occasion biographies. History understood as the scrutiny of societies through “an array of fully positive well determined facts” is not well suited for schoolchildren.¹⁶⁸ In a modern plan of education, study of elementary mathematics, science, natural history, and geography should precede history, which would better be reserved for those furnished with the knowledge enabling them to be critical. Of all persons who may profitably study history, it most directly behooves the public interest that those charged with affairs of government should have done so.

Ths scope is as follows. Historical scrutiny of the most renowned peoples will comprise the course and progress

1. Of such artisanal and skilled activities as agriculture, commerce, navigation.

2. Of various sciences such as astronomy, geography, physics.

3. Of private and public morality, and the examination of ideas formed thereof in different epochs.

4. Finally, we will follow the course and progress of legislation; we will consider the origin of the most remarkable civil and religious codes; we will investigate what the mode of transmission of these codes from one people and one generation to another has been; what effects they have produced in the habits, customs, and character of nations;what relation is to be found between the customs and character of nations and the climate and physical state of the land they inhabit; what changes are produced in their customs by migrations and the mixtures of races. . . .¹⁶⁹

Clearly Volney would not have approved of a work like the present one, even though it concerns science and the working of institutions, since it also seeks to recreate as well as interpret past events. He would, on the other hand, have felt completely at home in the company of Fernand Braudel, Marc Bloch, Lucien Febvre, and contributors to the journal Annales.

At the conclusion of the fifth lecture Volney acknowledged that the course so far had concerned historiography (though he did not put it that way) rather than history itself. He would have to leave it there, however. He had been given only two weeks to prepare his thoughts and was exhausted. He needed to rest, draw breath, and assemble the materials to be presented in treating examples of history proper.¹⁷⁰

Instead, the École Normale closed. However abortive educationally, the failed experiment brought into the open a set of relations between science and its public that was latent in the structures reciprocally of science and society (for example in Condorcet’s plan for education) but not yet expressed institutionally at the turn of the nineteenth century. For the first time anywhere, science and higher learning were enlisted in the service of public education. For the first time, students were to be formed by new knowledge imparted firsthand by its makers and not old knowledge retailed by clergymen seeking to mold their morals and characters on models from the past, classical and religious. In the future scientists would typically be professors at the highest level and not just researchers. Reciprocally professors at institutions of higher learning would ideally be researchers and not just teachers, as they had been in the eighteenth century and earlier. Nor did the failure of the École Normale diminish those expectations, which continued in force in the regimes of the École Polytechnique, the medical schools,

The École Normale instantiated a related feature of the change. Even at the highest level a professor must address himself to the whole range of his subject, and not merely to his specialty. In doing so he thinks to form students in the practice of a discipline. Reciprocally, however, doing so may lead the more innovative to consider forming, or rather reforming, an entire discipline in line with the thinking that guides their own research. The less innovative then follow suit in line with the research they admire. The effect reached beyond the lecture hall. A change in the mode of scientific publication accompanied the transformation of scientists into professors. It was not merely, or mainly, a matter of textbooks, though a considerable literature of scientific textbooks did issue from the press to meet the demand poorly served by publication of three successive editions of the Séances of the École Normale. More important, in the early decades of the new century scientists published in two ways. On the one hand, immediate results of particular pieces of research came out in the new monthly or quarterly journals, and this was by far the greater part of a large volume of scientific literature. On the other hand, whole sciences form the subject of a number of treatises intended, not to resolve particular problems, but to reform (not necessarily revolutionize) entire disciplines.

There were precedents, of course, antedating whatever impetus participation in the École Normale may have given. The most notable were Lagrange, Mécanique analytique (1788), and Lavoisier, Traité élémentaire de la chimie (1789). We will reserve a discussion of discipline formation for the conclusion, but a glance at the most important titles appearing over a thirty-year period will suggest the amplitude of a return to the mode of publication of treatises, which had been the instruments through which Copernicus, Vesalius, Kepler, Galileo, Harvey, Descartes, and Newton, to mention only the foremost, had wrought a more conceptual, if less institutional, transformation of thought about nature.

Here is the list.

MATHEMATICS

Lagrange, Théorie des fonctions analytiques (1797).

Lazare Carnot, Réflexions sur la métaphysique du calcul infinitésimal (1797); Géometrie de position (1803).

Monge, Géometrie descriptive (1799 and later editions).

Legendre, Essai sur la théorie des nombres (1808).

Laplace, Théorie analytique des probabilites (1812); Essai philosophique sur les probabilités (1814).

Dupin, Développements de géométrie . . . (1813).

Poncelet, Traité des propriétés projectives des figures (1822).

ASTRONOMY

Laplace, Traité de mécanique céleste (5 vols., 1799–1825); Exposition du système du monde (2 vols., 1796 and later edition.).

PHYSICS AND MECHANICS

Lazare Carnot, Principes fondamentaux de l’équilibre et du mouvement (1803).

Malus, Traité de l’optique (1810); Memoire de la double réfraction de la lumière dans les substances cristallisées (1810).

Hachette, Traité élémentaire des machines (1811).

Poisson, Traité de mécanique (2 vols., 1811).

Fourier, Théorie analytique de la chaleur (1822).

Ampère, Recueil d’observations electro-dynamiques (1823).

Sadi Carnot, Réflexions sur la puissance motrice du feu (1824).

Coriolis, Du calcul des effets des machines. . . . (1829).

CHEMISTRY

Fourcroy, Philosophie chimique, ou vérités fondamentales de la chimie moderne (1792, and many later editions).

Berthollet, Essai de statique chimique (2 vols., 1803).

Chaptal, Chimie appliquée aux arts (4 vols., 1807).

Gay-Lussac and Thenard, Recherches physico-chimiques . . . (2 vols.,1811).

Dumas, Traité de chimie appliquée aux arts (8 vols., 1828).

COMPARATIVE ANATOMY, ZOOLOGY, AND PALEONTOLOGY

Cuvier, Leçons d’anatomie comparée (5 vols., 1800–1805); Recherches sur les ossemens fossiles de quadrupèdes (4 vols., 1812); Le règne animal, distribué d’après son organisation (vols. 1, 2, 4, vol. 3 by Latreillle, 1817).

Lamarck, Philosophie zoologique (2 vols., 1809); Histoire naturelle des animaux sans vertèbres (7 vols. 1815–22).

Geoffroy Saint-Hilaire, Philosophie zoologique (2 vols., 1818–22).

Savigny, Mémoires sur les animaux sans vertèbres (1816).

Blainville, De l’organisation des animaux, ou principes d’anatomie comparée (1822).

PHYSIOLOGY AND MEDICINE

Cabanis, Du degré de certitude de la médecine (1798); Rapports du physique et du morale de l’homme (2 vols., 1802).

Bichat, Recherches physiologiques sur la vie et la mort (1800); Anatomie générale (4 vols., 1801); Traité d’anatomie descriptive (5 vols., 1801– 03).

Magendie, Précis élémentaire de physiologie (2 vols., 1816–17).

5. THE ÉCOLE POLYTECHNIQUE

The École Polytechnique has been and remains the most glamorous of the foundations of the year III. Its history is a puzzle of paradoxes. Founded in the spirit of Monge, it was soon dominated by the mathematics of Lagrange and Laplace. Intended to form civil and military engineers, it also educated the founders of mathematical physics and, a little later, protagonists among the Saint-Simonians. Once the first, creative generation had graduated, a school conceived at the height of the Terror became the nursery, not of scientists or reformers, nor of industrialists, but of the technocratic elite of nineteenth and twentieth-century France. Throughout Europe and America, however, it served at the outset as the very model of a modern engineering school—witness West Point, Boston Tech (later M.I.T.), the English polytechnics, and the Technisches Hochschulen of Germanic countries.

Situated throughout most of its history on the Montagne Sainte-Geneviève in the heart of the Latin Quarter, it was a colorful thread woven into the civic and cultural fabric of Paris, but has flourished for the last quarter-century in an American-style campus in the suburbs. From the beginning, the École Polytechnique has marked its graduates personally with the experience of their education in a way more characteristic of elite American and British undergraduate institutions than of other French counter-parts. Their identification with alma mater and sense of privileged solidarity sustains an alumni association in Paris. Mathematics and exact science have been more or less emphatically the basis of the curriculum throughout. The school is known familiarly to its intimates as “X” (from the ubiquity of that letter in mathematical analysis). Graduates identify their class by the year of entry, X-1826, X-1934, and so on.¹⁷¹

None of this was intended. Far from being created ex nihilo, the École Polytechnique emerged from a synthesis of elements drawn from the two engineering schools of the old regime. It combined an educational legacy from the military engineering school at Mézières, where Monge had started his career, with an institutional carryover of the École des Ponts et Chaussées in Paris. Mézières foundered in the Revolution. Beset by contradictions between the revolutionary sympathies of the teaching staff and the royalist loyalties of the military command, drained of personnel by needs of the army at war, and unable to attract cadets untainted by aristocratic lineage who could also pass the entrance examinations, the school had all but ceased to function in the final months of 1792. In the wake of many conflicts and frustrations throughout the ensuing year, including the suicide of a commandant, it was officially closed by order of the Committee of Public Safety on 12 February 1794. Its facilities were transferred to Metz, where they served for training in siegecraft. Carnot, who framed that measure, expected that basic training for both military and civil engineers would henceforth be conducted in the École des Ponts and Chaussées in Paris. A month later, on 11 March (21 ventôse), the Convention adopted a further measure calling for establishment of an École Centrale des Travaux Publics.

That law simply recognized what already existed, for in the meantime the École des Ponts et Chaussées had expanded, though not without difficulty, and had been redesignated École Nationale des Travaux Publics in January 1793. Even before its mission was broadened to encompass elementary preparation for military engineering, other exigencies of the Revolution required the services of more technically trained people than its cramped facilities and outdated reliance on self-help pedagogy could ever have produced. Prony, the leading member of the Corps des Ponts et Chaussées, developed a proposal for a full-fledged school with a proper faculty offering instruction on the theory as well as practice of construction in general.¹⁷² This and other suggested reforms went nowhere until the death in February 1794 of the eighty-six-year old Perronet, who had founded the school in 1747 and directed

Perronet was succeeded by a leading engineer in the Corps, Jacques-Élie Lamblardie, who proceeded to modify the regime. Enrollment had mean-while expanded to 167 students. He received authorization to appoint seven professors to conduct an in-house program of teaching, instead of farming it out to private courses on specialized subjects throughout Paris while relying on advanced students to tutor their juniors in the basics of geometry, trigonometry, surveying, and stereotomy. Lamblardie further succeeded in housing the school in adequate quarters. The Hôtel de Lassay, adjoining the Palais Bourbon (the modern Chamber of Deputies), afforded space for lecture halls, classrooms, and study rooms, and eventually for chemistry laboratories, a library of books and maps, a natural history gallery, a collection of machines, and workshops fitted with a forge, an anvil, and tools for stone-cutting, carpentry, and construction.¹⁷³

That much, and it was quite a lot, was in prospect by May 1794, when Monge stepped into the picture and proceeded to redesign it in keeping with his program for basing a technical general education on descriptive geometry, one might almost say messianic geometry in the light of his belief in its transcendent economic, social, and cultural value. Monge had given considerable thought to questions of education in its relation with science. He had consulted with Condorcet in 1792, when the latter was designing his master plan, and had drafted but never communicated a scheme for secondary school education of artisans and workers in September 1793, after quitting the Ministry of Marine Affairs.¹⁷⁴ He is certain to have collaborated with Carnot, Prieur, and scientific veterans of the Arms Commission in framing provisions for the new school of public works. Fourcroy, a member of the thermidorean Committee of Public Safety, presented the legislation to the Convention on 24 September 1794. Four days later the founding law, known by its date of 7 vendémiaire, was adopted without ado. The measure affects to implement the decree of 11 March (21 ventôse) calling in the midst of the Terror for establishment of an École Centrale des Travaux Publics.¹⁷⁵ Now, however, Fourcroy’s report dresses the proposal out in rhetorical flourishes celebrating the overthrow of the latter-day tyrants and the emergence of true republican values.

The new school would be quite different from its predecessors. Instead of limiting itself to elementary preparation of a handful of military and civil engineers for specialized service in the respective corps, it would be entirely independent of both the military and the Ponts et Chaussées. The purpose was a higher education for engineers in general. The country, so runs Fourcroy’s report, required five species of engineer: 1° military engineers, 2° civil engineers, 3° cartographers (ingénieurs géographes), 4° mining engineers, and 5° naval engineers. Separate schools, and those inadequate, had existed for the first, second, and third. The sector of mining, of great importance, had been particularly ill served by a recent, small, and merely theoretical school. For mapmaking and naval construction, aspirants had learned by the equivalent of apprenticeship after picking up what elementary mathematical instruction they could find in private courses. The École Centrale des Travaux Publics, by contrast, would provide a three-year curriculum of higher technical education, the purpose of which went beyond improvement of public works to increasing scientific literacy in general, in the first instance among its graduates and more largely by setting an example for a national educational system. As at the École Normale, where the inspiration was comparable, the faculty would consist of leading scientists. Theory would inform practice, practice would exemplify theory, and professors would combine teaching with research. They would advance pedagogy and knowledge reciprocally by publishing their courses and communicating their findings in a journal, the Journal de l’École Polytechnique. Like the Muséum (though Fourcroy does not mention the analogy) the institution would be governed by its faculty sitting in council.¹⁷⁶

Enrollment was to be four hundred students. That would be over twice the size of the recently expanded École des Ponts et Chaussées and orders of magnitude larger than Mézières, which had normally numbered twenty students at the end of the old regime. They would be paid a stipend of 1,200 livres and would lodge with reliable families in loco parentis, for the Committee of Public Safety worried about their moral welfare in the capital. Unlike their counterparts in the École Normale, and their predecessors in the revolutionary courses of the year II, who were nominated by local authorities in numbers proportional to the population of the region, candidates for the École Centrale des Travaux Publics, sixteen to twenty years old, would undergo a national competitive examination on arithmetic, algebra, and geometry. It would be given in Paris and twenty-one provincial cities. A distinctive aspect of the initial organization was not mentioned in the Fourcroy report. The detailed prospectus that followed, anonymous but certainly drafted by Monge, emphasized that study halls, recitations, problem sets, drawing lessons, and laboratory work would occupy the greater part of a student’s day. Those exercises would be conducted in groups or “brigades” of twenty students each. They would be supervised by “chefs de brigade,” selected from among the best students in their final year. Their role would be similar to that of prefects in a modern boarding school, except that they would be chosen for academic rather than personal merit and leadership.¹⁷⁷

Like the student professors in the former École des Ponts et Chaussées, a chef de brigade would help his juniors with their lessons and lead them in recitations, draftsmanship, and laboratory exercises. Among the early chefs de brigade were Biot and Malus. The positive effect of a tight internal articulation on morale and school spirit contributed fundamentally to the distinctiveness of an education at the École Polytechnique in its early years. Instead of being a set of young people connected only when attending disparate classes, students were members of a body academic headed by their professors, themselves holding the equivalent of regular faculty meetings to regulate the whole.

The curriculum was Monge’s dream child. He laid out the design of the teaching program in the shape of a tree of knowledge growing horizontally.¹⁷⁸ The form was encyclopedic. The spirit was positivist. The two main branches consist of mathematical science and physics. The former divides into analysis and the description of objects. Analysis applies to geometry on the one hand and mechanics on the other. Objects that may be described are of two sorts, those that can be defined rigorously and those that cannot. The former are to be studied in courses on stereotomy, architecture, and fortification. (Architecture then comprised both theory and practice of constructions of all sorts, not merely buildings but roads, bridges, canals, ports, and ships.) The latter, undefinable objects are to be captured by drawing—one might say the science of drawing since “dessin” had a connotation both wider and more precise than its modern translation. Physics, the second main branch, divides less neatly. Its upper stem, general physics, is simply that, the properties of bodies, extension, heat, light, sound, electricity, and magnetism. The lower, particular physics or chemistry, has three parts according to the chemical nature of the substances to be analyzed.

The course of study was to take three years, though students who failed to complete it might be allowed a fourth. The guide throughout would be descriptive geometry. Monge gives the reason:

Descriptive geometry is a language necessary for and common to the ingenious person [homme du génie] who conceives a project, the skilled persons [artistes] who must direct its execution, and the workers who must carry it out. This language, which is capable of precision, has the further advantage of being a means for seeking the truth and for reaching desired or unknown results. Like all other languages, habitual use is the only way to become familiar with it. Thus, students at the École Centrale des Travaux Publics will practice it continually throughout the three years that the course of instruction lasts.179

Monge would not have expressed it this way, but for him descriptive geometry had a transcendent quality in that it put human faculties in contact with the mathematical structure of external reality. Its proper scope in his mind was far wider than anything he claimed for it at the École Normale, where it was one course among many. At the school of public works, where the initial design was his doing, it was the core of the curriculum. He devotes half his prospectus, twenty pages, to that one subject.

That plan provides three instructors for geometry, three for chemistry, one each for analysis and general physics, and an unspecified number of drawing masters. Mathematics occupies six days in every décade. For all three classes, the respective courses in descriptive geometry begin with an hour’s lecture at eight in the morning, after which the brigades repair to their respective study rooms where students work individually on problems and constructions until two in the afternoon. On two of the six days alloted to mathematics, each of the three classes spends the hours from five to eight in the evening in different courses on analysis. The first-year men do analytical geometry, the second analytical mechanics, and the third analytical hydrodynamics. Those courses consist of an hour’s lecture followed by a two-hour problem session. In the other four afternoons of the six devoted to mathematics, the two classes not doing analysis take drawing lessons. Chemistry has two days a décade, beginning with an hour in lecture and the rest of the morning and afternoon in laboratory instruction and experimentation. General physics gets short shrift. One two-hour lecture on the fifth day of the décade suffices for what was a merely descriptive science. There being no laboratory work, students take the same course every year for three years in order to fix the definitions in their minds. The rest of the day was free for study or relaxation. The tenth day of every décade is open for exercise and recreation. Thus, of the seventy-four hours of schooling every décade, a student would spend thirty-six on descriptive geometry, twelve in drawing lessons, twelve doing analysis (applied to descriptive geometry in the first year), eighteen learning and practicing chemistry, and two listening to physics. Theory would occupy the twelve hours spent in lecture halls by all members of each course. Application would occupy the sixty-two spent by the brigades in practical work and drawing. After three years a well-rounded polytechnician would be a fully educated man ready for any career involving technical talent and virtuosity.¹⁸⁰

That ideal was an enlarged projection of Monge’s experience at Mézières upon the tabula rasa of a new educational system. It was never completely fulfilled. Exigencies of the moment and political expediency required that an initial class of engineers be produced within a year. To that end the proponents of the new school drew upon the example of the revolutionary courses of the year II, as did the organizers of the École Normale and the École de Sante. The École Centrale des Travaux Publics opened with three months of revolutionary courses before initiating its regular teaching schedule. They had in common with the putative model only the political appeal of the name, the eminence of the teachers, and an accelerated pace. The revolutionary courses at the École Centrale ran the whole body of the accepted students through the subjects of the three-year curriculum in three months, the first-year courses in the first month, the second-year in the second, and the third-year in the third. The compression was accomplished by offering only the lectures and postponing the classroom and laboratory work. Examinations followed, the purpose of which was to sort the student body into the three classes that would then begin a normal school year. The most accomplished would follow the regular third-year courses and graduate in one year, the middling group would take the second-and third-year classes and graduate in two, and the least prepared would follow the entire three-year curriculum. The word “polytechnic” appears for the first time in the printed announcement: “Programmes de l’enseignement polytechnique de l’École Centrale des Travaux Publics.”¹⁸¹

Many notables attended the ceremonial opening on 21 December 1794. It featured chemical oratory by Fourcroy and a lecture by Lagrange, who did not appear again until the revolutionary courses terminated three months later, almost concurrently with the demise of the École Normale. Present at the creation were 272 students and some twenty-five provisional chefs de brigade, who had been chosen in advance from among the applicants. These latter had arrived in Paris six weeks earlier to be put through an intensive course in preparation for their responsibilities as teaching assistants.¹⁸² They and their successors selected from each graduating class would supplement a distinguished faculty. Fourier, a student in the École Normale, was appointed an instructor in May 1795. Besides Monge, Lagrange, and Fourcroy, others who served on the teaching staff of the École Polytechnique more or less regularly under the Directory were Hachette, Guyton de Morveau, Vauquelin, Berthollet, Chaptal, Pelletier, Prony, and Baltard, among a number of less remembered names.

The revolutionary courses and the remainder of the first academic year were anything but a flying start. Monge fell gravely ill and had to be replaced in the descriptive geometry course for some weeks. A further round of entrance examinations brought the number of students almost to the 400 allowed, but the latecomers straggled in irregularly. The winter of 1794–95 was bitter cold. Bakeries were often empty of bread. The Committee of Public Safety authorized military rations for the students, which excited the resentment of workers at the school and in the neighborhood. Tardiness was chronic. The starting hour had to be put back to 8:30, and even then the first classes in the morning were ill attended. Often only twenty or thirty students would show up for a lecture. The worst was physics. The subject was a bore and Hassenfratz a deadly teacher whose students would some-times hiss instead of applaud him, as they did Monge and Fourcroy. Discipline was lax. During the many hours spent in study halls, students would often talk, gossip, and horse play instead of ordering their notes, working their problems, and constructing their geometric figures. Many had colds and coughed and sneezed all day. The chemistry laboratories were not ready at the outset. In those with minimal equipment, ovens sometimes roasted potatoes instead of heating reagents.

Temptations of the big city were irresistible for many a student. Roaming the streets when they should have been doing descriptive geometry, a number took part in the quasi-gang wars between gilded-youth muscadins and plebeian jacobins. Coming for the most part from fairly well-to-do families, they tended to side with the former, to the dismay of their teachers. Other political involvements were involuntary. Like all able-bodied men, students were liable for service in the national guard, which took them out of school at regular intervals. Most of them were mobilized to serve in putting down the last popular rising of the Revolution on 1 prairial (20 May 1795). Politics also took its toll upon the faculty. In the aftermath of prairial, Monge, having missed the early weeks of his course, perforce went into seclusion for some months, as did Hachette, lest their well-known jacobin sympathies expose them to the imprisonment that Gilbert Romme had terminated by suicide. A warrant did issue for Hassenfratz but was never executed, while Fourier was arrested a few days after joining the staff and held in custody for several months.

Upon completion of three months of revolutionary courses, what had been intended as the regular curriculum began on 24 May 1795, five days after the risings of prairial. Lagrange gave his first lecture at the ceremonial opening. Neither then nor later was his course comprehensible to more than a handful of his auditors. With only five months left of a normal academic year, it was impossible to complete the original plan. Beset by difficulties and criticism, the École des Travaux Publics soldiered on as best might be throughout the summer of 1795 in imminent danger of going the way of the Ecole Normale. Acting for the Committee of Public Safety, Prieur initiated the reform that turned it into the École Polytechnique as of 1 September and saved the day at the expense of Monge’s original, perhaps unrealistic conception.

Abandoned was any notion of a general technical education. Abandoned was any idea of independence from the special interests of the existing civil and military engineering services. Instead, the École Polytechnique would recruit their students and give them basic training. The several service schools—the revived Ecole des Ponts et Chaussées, the Ecole du Génie and Ecole de l’Artillerie (combined at Metz in 1802), the small École des Géographes (attached by Prony to the cadastre), and the three naval schools (École des ingenieerus de vaisseaux, École de navigation, and École de marine)—all these, now to be called écoles d’application, would be upgraded and admit only graduates of the École Polytechnique.¹⁸³ The relation, in a word, would be comparable to that of a modern American undergraduate education to graduate professional training.

Abandoned too, therefore, was the ideal of educating technically competent generalists in courses that married theory with application. Application would henceforth be the affair of the higher schools of that name while the curriculum of the École Polytechnique, with which they were now associated, would become increasingly abstract and theoretical. Abandoned also was the wider thought of centering a school of general technical education in a national system built on similar principles. Abandoned, finally, was any aspiration to model education nationally upon what was available to the brightest and the best. The modern separation of the grandes écoles, top schools, from an eventual system of universities open to all secondary-school graduates dates from the reform that turned the generalist École Centrale des Travaux Publics into the analytical École Polytechnique.

Despite the distractions and confusions of the first year, the fledgling École Centrale des Travaux Publics had given direction to a minority of committed students, among them Jean-Baptiste Biot, Etienne Malus, Louis Poinsot, Edme Jomard, Jacques Chabrol de Volvic, Prosper Jollois, and Michel-Ange Lancret. The first three are famous in the annals of physics and mathematics; the last four (as will appear) were crucial participants in Bonaparte’s Egyptian expedition.¹⁸⁴ Many years later Jomard remembered vividly the impression Monge made on them and their fellow students. Without the benefit of a blackboard, his elocution exhibited the properties of three-dimensional geometrical objects

with their forms, their magnitudes, their inflections, their diverse intersections. Monge did not make us see them simply by word and gesture. He made his auditors feel as if they were touching them, so to say, with their fingers, such was the harmony between word, gestures, and even posture at each moment. And then, what a light in his eyes! What power in his voice! What variety in his intonations! His features, a little irregular, lit up so as to transform his face. . . . When he described a surface of revolution verbally and designed it manually, you saw it; a developable surface, you developed it with him; a gauche surface or any other of double curvature, he engendered it with an eloquent gesture in such a way that it became palpable. Abstractions took on body with him. He had the art of making the most complicated things simple and the most obscure things clear.¹⁸⁵

Such was the teaching that now reached beyond the few and important people Monge had trained or worked with at Mézières—Carnot, Meusnier, Lacroix, Hachette—and inspired the first generation of students formed at the École Polytechnique, who elevated him to the status of patron mentor, if not saint.

Historians have contrasted the school as Monge imagined and started it, “Monge’s School,” to “Laplace’s School,” the forcing house of mathematical analysis that it soon became.¹⁸⁶ There is no doubt that Monge and Laplace were very different in personality, temperament, political attitude, and mathematical taste. The one was generous, outgoing, and enthusiastic; the other haughty, reserved, and severe. There is reason to think that feelings of innate hostility occasionally found overt expression. Apart from personal factors, their respective relations with the institution were not fully comparable. Monge was less committed to mathematics than Laplace. His teaching systematized descriptive geometry and brought it into the open but invented little. His interests had spread also to other things, to chemistry, to physics, to technology, to warfare, to politics, to education. Before long he would gravitate into an orbit around Napoleon’s rising star.

Monge inspired the École Polytechnique. He did not administer it. He did not even stay with it. Absent by reason of illness or political prudence for much of the first academic year, neither did he complete the second, 1795–96. Instead he departed with Bonaparte on the first Italian campaign in May 1796, returned briefly to Paris in October 1798, and was away again until October 1799, first in Rome, then in Egypt. On his return he resumed teaching, but concentrated mainly on analytic geometry, leaving descriptive geometry largely to Hachette. The course was already diminished by 1800. Monge retired in 1809. The next year descriptive geometry, now paired with theory of machines, had only 85 hours and analysis 137.¹⁸⁷

In contrast to Monge, Laplace came into the affairs of the École Polytechnique almost as a deus ex machina, and not at first of his own volition. He had remained in semi-seclusion near Melun during the months of its gestation, had nothing to do with its foundation or original curriculum, and never taught there. His initial involvement was peripheral. He served briefly on the ad hoc panel headed by Vandermonde that examined candidates to fill up the ranks of the École Centrale des Travaux Publics in the supplementary competition of November 1794. Laplace had been dismissed from his post as examiner of artillery cadets (an important source of income) shortly after suppression of the Academy of Science in August 1793. On 23 July 1795 the thermidorean Committee of Public Safety reinstated him in that post, observing that he should never have lost it. So it happened that, beginning in 1795–96, when the écoles d’application were subordinated to the École Polytechnique, Laplace was ipso facto examiner for its graduates applying for admission to the artillery school. Not only so, he and Bossut, who had been reinstated as examiner of cadets for the Corps of Engineers, were to select candidates for admissision to the École Polytechnique itself. Setting entrance examinations and final examinations, Laplace assisted by Bossut was thus in the position of watchdog over the entire course of study.

At the end of the first year Laplace was dissatisfied with procedures and results. A letter to the Director in December 1796 makes recommendations regarding both admissions and the course of study.¹⁸⁸ Instead of relying on regional examiners employing individual criteria, the selection process needed to be centralized. Only a single panel sitting in the precincts of the school would be in a position to rank candidates from the entire nation according to uniform standards. Prior to that teachers everywhere should no longer rely on preparing pupils out of the classic textbooks of Bézout and Bossut. They should be supplied with the syllabus of a specific course of instruction. Instead of attempting to judge of a youngster’s general knowledge, the examiners could then be very demanding with respect to the required materials.

Examining the polytechnicians who had in principle completed the course, Laplace found very few to be qualified for the respective services. His judgment accorded with the experience of Prony, whose students in the course on analytical mechanics were so ill prepared that he taught them elementary calculus instead. Accordingly Laplace considered it indispensable that the time devoted to calculus and analytical mechanics be increased. The spirit of his recommendations was not perfectionist, however. He recognized that in a school of public service it was more important to train the majority of students reasonably well than it was to pitch everything at the level of the few strongest, though neither should the latter lack opportunity to sharpen their talent. The future development of their subjects depended on them.

Laplace’s criticisms and recommendations were ill received by all concerned. Most students disliked advanced and abstract mathematics and resented being held to higher standards. Members of the staff, personally sympathetic to the absent Monge and in tune with his ideas, considered Laplace a threat to the École Polytechnique at a time when its very existence was still precarious. Officials of the écoles d’application, and especially the artillery, which needed young officers fast, denounced the requirement that they pass first through the École Polytechnique. Calculus was no help to a battery commander laying his guns in combat. Politicians, other than Carnot and perhaps Prieur, could scarcely understand the issues. Nevertheless, such was the leverage afforded by the post of examiner that Laplace prevailed. In two years’ time, uniform entrance examinations took place in Paris. In 1796–97, students willy-nilly spent almost a third of their class hours on calculus and analytical mechanics, more than three times the fraction Monge had allocated to analysis at the outset.

Beginning in 1799–1800, Laplace disposed not merely of leverage, but of direct authority. Among graduates of the École militaire whose qualifications for the artillery he had examined in the old regime was a sixteen-year-old Corsican, Napoleone Buonaparte. Immediately after the coup d'état of 18 brumaire (9 November 1799), Bonaparte in power as First Consul named his onetime examiner, whose fellow member of the Institute he now was, to serve as Minister of the Interior. Laplace’s time in government was far briefer than Monge’s had been, six weeks instead of eight months. Napoleon at Saint Helena famously said of him that he brought the spirit of infinitesimals to administration. There is no reason to think that Napoleon favored Laplace over Monge personally or with respect to their mathematical programs. He admired them both in their different ways. Nevertheless, Laplace’s brief tenure of the ministry allowed him to modify the regime of the École Polytechnique in a signal manner. Governed academically by the Council composed of the teaching staff, it had been administered incoherently by a sequence of directors, none holding office for more than a year. Lamblardie returned to the modified École des Ponts et Chaussées in 1795, to be succeeded there in 1798 by Prony for a tenure of forty years. Monge served as director for a few weeks in 1797–98 and few months in 1799–1800, and Guyton de Morveau for a few months in 1798.

There being no legislative body to debate and delay proposed reforms, as had regularly happened under the Directory, Laplace was able to impose a thorough reorganization in December 1799. The Conseil d’Instruction composed of the teaching staff would still conduct the week-to-week academic business. Exercising ultimate authority, and reporting to the ministry, a newly constituted body would function as the equivalent of a modern Board of Trustees. This Conseil de Perfectionnement consisted at the outset of the two mathematics examiners (i.e., analysis); two examiners all told for descriptive geometry, chemistry, and physics; three members of the Institute; four commissioners elected by the teaching staff; and the representatives delegated by the various service schools to participate in the final examinations of applicants graduating from the École Polytechnique.¹⁸⁹ At the same time, enrollment, which had been lowered to 250 under the Directory, was fixed at 300. The normal course of study was now reduced to two years of preparation for the écoles d’application. Students who then felt unready to take the examinations qualifying them for admission were to be dropped. Those who tried and failed might have a third year. Though not yet militarized, polytechnicians were to wear a uniform and be paid the stipend of a sergeant in the artillery.¹⁹⁰

A few weeks previously Lagrange had retired from teaching, recognizing that a broad range of students needed a more accessible road to analysis than a course on its frontiers could afford. Lacroix, who succeeded him, was a superb teacher. Laplace, of course, resigned as examiner on becoming Minister of the Interior. Appointed in his place was Legendre. If mathematicians were to be graded like students, the top three at the time would have been Lagrange, Laplace, and Legendre, in that order. On leaving the Ministry in favor of Lucien Bonaparte, Laplace exerted strong influence on the regime of the École Polytechnique from the vantage of the Conseil de Perfectionnement. Descriptive geometry, grouped with “machines” and no longer included under the rubric of mathematics, continued to suffer ineluctable reduction in the curriculum at the expense of analysis.¹⁹¹ Chemistry under-went a concurrent decline despite the prestige and influence of Fourcroy, Guyton de Morveau, and Berthollet, all three members of the faculty, and the last named close to Napoleon and to Monge and closer to Laplace personally than was any other colleague.¹⁹²

The proximate cause was the examination system, the effects of which went beyond its motivation. The purpose was straightforward and meritocratic. It was to select the students best qualified on grounds of ability alone, first for admission to the École Polytechnique, and on finishing their course, for admission to professional training in the service schools. What exceeded, and perhaps distorted, that objective were the means chosen to achieve it. Laplace’s purpose, and that of his colleagues, was not to aggrandize analysis to the detriment of other studies or to favor young people from fortunate backgrounds over others. Quite the contrary. It was simply that mathematical ability, unlike general intelligence, literacy, and culture, could be measured comparatively and exactly. That might once have been true of Latin, but schooling in the classics had so deteriorated in the revolutionary years that it was dropped from the entrance examinations in 1800.193 The same argument eliminated chemistry and physics from the final examinations in 1810.

In consequence students preparing both for entrance and final examinations concentrated their efforts on mathematics and neglected other subjects. The examinations came to seem more important to them than the courses. Their attitudes reflected the very structure of the institution, in which teachers and examiners were distinct from each other in order to ensure objectivity and of equivalent importance in the educational scheme of things. They received the same salaries and had equal representation on the Conseil de Perfectionnement. A further provision assured the privileged position of mathematics. Its two examiners had permanent tenure while their colleagues examining lesser subjects were appointed annually.

Educational experience in the United States and elsewhere has shown that insistence on strictly objective testing may have unintended consequences. It was never the purpose of Laplace and his colleagues to provide a means for recruiting a technocratic elite from well-placed families that would dominate much of French polity in the next two centuries. Neither, to suggest more or less remote historical comparisons, did Confucius concoct his philosophy in order to furnish material for the examiners who chose the administrators of the Chinese empire. The dons did not teach classical letters at Oxford, nor mathematics at Cambridge, in order to select officials from the governing class—“Send forth the best ye breed”—who would rule in India and else-where. Such, however, among other things, was what followed out of the Classical Honours School at Oxford and the Mathematical Tripos at Cambridge, neither of which had the slightest relation to the future duties of honours men and wranglers. What mattered functionally was the role and conduct of the examinations, not its content. It was essential, however, that the subject matter be so precise that the legitimacy of the ranking not be questioned and that the fairness and objectivity of the competition be recognized both by the candidates and the general public.

Mathematics met the case in France. But why analysis instead of descriptive geometry? Its expansion in the curriculum of the École Polytechnique, gradual prior to 1802, then became an express policy. The report of the Conseil de Perfectionnement for 1806 notes that the teaching of statics, until then based on synthesis, must henceforth be analytic in form. Without mentioning Monge’s original design, the report for 1808–9 contradicts it in stating that “mathematical analysis applied to geometry, mechanics, and several branches of physics forms the basis of the teaching program.”¹⁹⁴

Any search for a satisfactory explanation of the change will need to go deeper than incidental personal rivalries or mere academic politics. For the transition to analysis in the curriculum answered to negative demand. Except in Lacroix’s course from 1799 to 1808 and Prony’s courses throughout on analytical mechanics, analysis was badly taught. Lagrange was way over most students’ heads at the outset. Ampère and Cauchy were brilliant minds. The former was a poor teacher from 1816 until 1828, when he realized it and resigned, and the latter a pedagogical disaster from 1816 until 1830, when he went into a royalist exile.¹⁹⁵ A majority of students disliked the subject and resented the time spent on it and the pressure it put upon them. Their future employers were no more enthusiastic. Already in 1809 the commandant of the École de l’Artillerie et du Génie in Metz complained that students coming out of the École Polytechnique were ill prepared for practical exercises and quickly forgot the abstract courses they had endured. The Conseil de Perfectionnement appointed a commission headed by Malus to examine the criticisms. It found them to be justified in large part, and recommended changes, none of which were ever made.¹⁹⁶ But it was in the 1820s, at the height of Cauchy’s creativity in mathematics and Ampère’s in electrodynamics, that complaints from all sides about their teaching reached a maximum, again to no avail.

What skills, in point of fact, did a young engineer use in the early nine-teenth century? One may think in the first place of the striking achievement of the contingent of twenty-odd early graduates of the École Polytechnique who accompanied Bonaparte to Egypt, namely the superb plates of their magnificent Description de l’Égypte, of which more in the next chapter. The treatment of light and shadow, of the floor plans and elevations of temples, of sculpture and monuments, of land and sky, of mapping—all of it was accomplished, not by artists, but by engineers. The preparation of that magnificent work bears witness to the value of their training in drawing, stereotomy, and perspective, which is to say descriptive geometry.

More generally, in order to apply the laws of statics and dynamics, of hydrostatics and hydrodynamics, of friction and the strength of materials, to the construction of roads, bridges, canals, buildings, fortifications, and ports, the original program of the École Centrale des Travaux Publics was precisely what was needed. Practicing engineers had no use for the analytical parts of Prony’s Mécanique philosophique of 1799. In 1817, when C.-L. Navier, X-1803, a foremost engineer in the Corps des Ponts et Chaussees, published a new edition of Bélidor’s century-old manual of construction, the classic La science de l’ingénieur, he relegated the analytical apparatus he supplied to the foot-notes.197 It is further worth recalling that the suspension bridge across the Rhone at Tournon, the first in the world hung from iron cables, was constructed in 1824–25 by a self-made engineer, Marc Seguin, who was totally ignorant of analytical mathematics. When he submitted the design to the General Council of the Ponts et Chaussées for approval and authorization, Navier recommended its rejection. Ironically enough, the Pont des Invalides that Navier himself designed shortly afterward collapsed when a ruptured sewer main poured a flood into the Seine.¹⁹⁸ There is no reason to think that public works in France constructed by polytechnicians in the early nine-teenth century exhibited improvements upon those built in Britain by graduates of Woolwich or by self-taught engineers who learned their trade by apprenticeship. Contemporary observers, among them Charles Dupin, X-1801, on the whole thought not.¹⁹⁹

What, then, in the absence of practical applicability or demand, did drive the displacement of descriptive geometry and related subjects by analysis in the curriculum of the École Polytechnique? One such factor it shared with the École Normale and the École de Santé. It was the proposition that leading scientists should do the teaching. Leading scientists in any milieu prefer to be on the cutting edge. Fourcy cites the author of a memoir in 1797 who reminds the reader that the École Polytechnique, founded at a time when all scientific and educational institutions had been suppressed, was intended not only to supply engineers, but also to be a “repository destined to conserve the teaching of the arts and sciences.”²⁰⁰ That was never forgotten. The 1816 report of the Conseil de Perfectionnement states that, besides preparation for the public services, which remains the primary mission, the method of instruction also serves “to develop the faculties of those rare individuals whose tastes and inclinations call them to a profound study of the sciences.”²⁰¹ To that end, the professors are urged to keep their courses up to date and drop the obsolete manuals of Bézout and Bossut. The Journal de l’École Polytechnique had by then become the most prestigious of journals for mathematics and pure science. Students and former students, not to be left out, were encouraged to circulate their research and memoirs in the less formal Correspondance de l’École Polytechnique, started by Hachette.

Finally, and this is perhaps the essential matter, the issue was not one of rivalry between fields of mathematics of equal weight. The roles of analysis and descriptive geometry in the evolution of mathematics were not symmetrical. Descriptive geometry pertained to synthesis, the time of which was largely past. Its revival was owed to the particular genius of Monge and not to some strong undercurrent of mathematical development emerging from the depths. That “géomètre” meant mathematician well into the nineteenth century was a lexicological anachronism. Even Chasles draws his contemporary developments from the classics in his Développements des méthodes en géométrie (1837). The case Monge makes for the educational value of his favorite subject, and for its utility in stonecutting, construction, and theory of machines, is more convincing than are his afterthoughts about its access to discovery of truth.

The very career patterns and personalities of geometers and analysts were different. Of Monge’s successors at École Polytechnique, Hachette was a faithful wheelhorse, and Leroy, who taught the subject after 1815, when Hachette was exiled as a jacobin, was a nonentity. Like Monge himself, his scientific heirs, although they did work in geometry, also spread their interest and efforts across a range of subjects. Meusnier did experimental chemistry, contributed to aerostatics, and died a soldier. Carnot organized victories. Lancret directed the Description de l’Égypte. Poncelet had a military career, became a general, and contributed to the theory of machines. Dupin went into politics, as did Arago. These were worldly men, “positive spirits” in the parlance of the times. Not only did they apply geometry, they applied them-selves to wider enterprises.

Those drawn rather to analysis sat at desks in a focused manner. Lagrange, Laplace, Legendre, Sophie Germain, Ampère, Cauchy, Poisson—they were persons of active thought, not action. Rather than apply their mathematics to construction and technology, they drew their mathematics out of analysis of the behavior of physical objects and forces. Thus Fourier—who to be sure was an active administrator as prefect of the Isère Department—invented the branch of analysis that immortalized his name for a study of heat conduction. When analysis is justified at all, the claims are different from those for geometry. “The cultivation of mathematics,” writes Lacroix in the preface to his textbook, “may be considered from two points of view. . . . Generally it is only a means for exercising the mind, developing the intellectual faculties, and offering matter for meditation and discussion; Sometimes also, but unfortunately much more rarely, it furnishes precepts and results applicable to daily use and to the needs of society.”²⁰² In like manner, observes the Director of Studies in the École Polytechnique, “Advanced theories, although they are rarely applicable in the public services, are nevertheless a subject for study of the highest importance in that they exercise the students’ intelligence and in some sense give the measure of their ability.”²⁰³

Not only did pure analysis come to dominate the curriculum, the courses in analytical geometry and analytical mechanics became more and more abstract. Except for theory of machines, developed by Cauchy, Coriolis, and Poncelet, the other topics initially treated as applications of descriptive geometry, to wit draftsmanship, stereotomy, theory of shadows, and perspective, diminished with it and eventually vanished. We have to do here, so it would seem, with an instance of what may well be the most general tendency in the history of science, which is the ineluctable progress of mathematicization. Chemistry in the eyes of Lavoisier, physics in the eyes of Laplace, economics and even historiography in our own day, the entire world picture in the seventeenth and eighteenth centuries—all have sought to find expression so far as possible in the language of mathematics, or at least to assume the guise of quantification. The displacement of descriptive geometry by analysis in the École Polytechnique was nothing other than a special case of the working of this process within mathematics itself. Its movement over the long term is toward abstraction, rigor, and generality. That occurs, not in response to outside pressures, whether sociological or political, but by “la force des choses,” a more powerful dynamic than the pallid “force of things” suggests.

In the École Polytechnique mathematics served to inculcate intellectual discipline as well as skill in calculation. That was the reason for which Dupin opposed introducing literature and fine arts into the curriculum. He was second to none, he explained, in his admiration for high culture in itself. But he feared lest such courses prove seductive and sap the intellectual vigor of the students.²⁰⁴ Whatever their intellectual vigor, an unintended psychological side effect did occur. Passing such a test, clearing so high a hurdle, reinforced the feeling of initiation into a highly select elite. Like many a shy American freshman subjected to hazing in a fraternity, and many a timid Prussian Burschenschaftler sporting the scars of a duel, a basically unmathematical polytechnician who nevertheless survived the ordeal of analysis would rally to the “X” tradition once he had proved his mettle.

A second element of discipline complemented mathematics in the ritualization of the polytechnic experience. In 1804 Napoleon regimented the École Polytechnique. What with his positive sense of the contribution of young graduates to the Egyptian expedition, and his admiration for Monge on the one hand and Laplace on the other, he had long taken a close interest in the school. Its discipline left much to be desired, and not only in his eyes. Attendance at class was spotty. The behavior of students in public, particularly at the theater, was often rowdy.²⁰⁵ Scattered about the city in lodgings, they were under no control when out of class. Youthful political instincts led them to gird against authority, whatever the complexion of the government. A number had taken part in the royalist rising against the Convention that Bonaparte came to the fore by dispErsing on 13 vendémiaire (5 October 1795). With all these things and prospective needs of the army in Napoleon’s mind, the decree of 16 July 1804, among the earliest he promulgated as EmperoR, placed the École Polytechnique under military authority, where with many modifications it remains to the rresent day.²⁰⁶

A general, Gérard Lacuée, took command as governor, seconded academically by a field-grade officer, S. Gayvernon, who taught the course on fortification, as Director of Studies.²⁰⁷ The student body henceforth consisted of a battalion composed of four companies. A battalion commander, two captains, four lieutenants, and a quartermaster were to enforce discipline and oversee military training, which however must not occupy the hours devoted to class work. Students would henceforth live in dormitories and eat in dining halls. They had worn uniforms since the early days, but would now be outfitted in the style of line infantry. From that decree derive the sword and jaunty bicorne cap that came to bespeak the esprit de corps born of living, learning, marching, and maturing together at a formative time of life. No more unexcused absences, no more straggling in late—students would march back and forth to class, and from one class to another, each company under the command of an officer and preceded by a drummer.

Readying the former Collège de Navarre to receive the school required a year. Only in 1805 did the École Polytechnique move from the Hôtel de Lassay adjoining the Palais Bourbon, seat of the lower house of the legislature, to the quarters it occupied until 1976. The separation came as a relief both to students who resented the censorious eyes of legislators and to legislators who had had enough of noisy students. No change was envisaged in the curriculum. A momentous change in the regime, however, did follow in 1805. No longer to be paid modest stipends, students would henceforth be charged fees of 800 francs a year. Instead of a school selecting its students on the basis of merit alone, it became a school selecting the most meritorious students whose parents could pay tuition. War was expensive, Napoleon wrote the governor in explanation of the forthcoming decree, and he wished to keep costs down. Considerations of another sort further justified the change in the Emperor’s eyes: “For people who are not well off, it is dangerous to give them too great a knowledge of mathematics.”²⁰⁸ Hence the social complexion of graduates of the École Polytechnique in the nineteenth century. Provision for twenty-five scholarship students did little to modify the picture despite Monge’s generosity in donating his salary to swell the fund. “The cradle of the sciences,” commented Charles Dupin, “was suddenly transformed into a mercenary barracks of apprentice pretorians.”²⁰⁹

Militarization did not exclude or much affect the tiny minority of first-generation graduates who brought about mathematicization of physics. Our section on the École Normale closed with a list of titles. A short list of those avant-la-lettre mathematical physicists follows: Fourier on the theory of heat; Sadi Carnot and Clapeyron on the foundation of thermodynamics; Biot on chromatic polarization of light; Malus on reflective polarization and double refraction of light; Fresnel on interference and the wave theory of light; Cauchy on foundations of the calculus and properties of an elastic ether; Poisson on the potential function in electrostatics and magnetism; Ampère on electrodynamics; Coriolis on work and energy—in only one area, acoustics, did the cardinal contribution, which was the theory of elastic surfaces, come from other than a teacher, graduate, or both of the École Polytechnique, and that other was Sophie Germain.

Nowhere else in the history of science is the wellspring of so momentous a set of developments to be located in a single institution.

6. THE ÉCOLE DE SANTÉ AND CLINICAL MEDICINE

In 1865 Claude Bernard entitled the classic of nineteenth-century French physiology Introduction à l’étude de la médecine expérimentale. In his view, the strategy of basing medicine on the science of which he was past master stemmed from the reform of the healing arts two generations earlier. Experimental physiology became a sustained specialty in Paris in consequence of a modernized medical education and conversion of the Hôtel-Dieu into a teaching hospital. Such was the discredit of faculties in general early in the Revolution, and of the Faculty of Medicine in particular, that the schools opening in January 1795 were euphemistically called Écoles de Santé.

The thermidorean Convention thus made provision for professional education of physicians as well as engineers and teachers. In this instance too the revolutionary courses on saltpeter and gunpowder were the putative model to be emulated in recruitment and, initially, for pedagogy. On 23 August 1794 the Committee of Public Safety jointly with the Comité d’Instruction Publique appointed a commission, Fourcroy in the chair, with instructions to frame a measure for the training of doctors, most urgently for the Army. He brought in a report on 27 November (7 frimaire). The draft proposed a medical clone of the École des Travaux Publics, to be called École Centrale de Santé and situated in the former College of Surgery, now known as the ancienne Faculte in the rue de l’École de Médecine. Local officials were to choose one student from each district. On arrival in Paris they were to be assigned to classes at the level of first-, second-, or third-year instruction according to the degree of their preparation and to be taught in the accelerated manner of revolutionary courses as their contemporaries were to be at the future Polytechnique.²¹⁰ There was no mention of schools out-side Paris.

It was not, evidently, Fourcroy’s doing that the eventual design derived rather from Vicq d’Azyr’s New Plan for Medicine. Amendments moved during debate and incorporated in the legislation of 14 frimaire an III (4 December 1794) brought the model closer to the reform that Fourcroy’s one-time mentor had designed, albeit with modifications in the interest of economizing time and cost. Duration of study was to be three years instead of four, and instead of the five schools Vicq d’Azyr had recommended, there were to be three. Three hundred students were to enroll in Paris, one hundred and fifty in Montpellier, and one hundred in Strasbourg. Courses were to begin on 1 pluviôse (21 January 1795). In one respect the provisions were more generous than those of the New Plan. Students would receive a stipend, as at the Ecole Polytechnique, instead of paying tuition.²¹¹

The central feature of Vicq d’Azyr’s reform was not then put in doubt. Henceforth, training of doctors and surgeons was to be unified. Not merely would the inferior status of surgery be eliminated. The very distinction must disappear. Graduates would be neither doctors nor surgeons. All would be Officers of Health. The staff would consist of twelve professors and twelve assistants in Paris, eight such pairs in Montpellier, and six in Strasbourg. Each school would be associated with local hospitals and would be furnished with a library, laboratories, anatomical and natural history collections, surgical instruments and apparatus, and a garden of medicinal plants. As to the curriculum, provisions of the legislation were an abbreviated summary of the scheme for courses of instruction that Vicq d’Azyr had elaborated in 1991. Students in the second and third years would accompany their professors or other doctors in their hospital rounds, assist in surgical operations, and observe or even perform autopsies.

The teaching, in a word, was to be clinical, as it had long been in surgery, instead of bookish as it had reputedly been in medicine. With respect to this, the fundamental reform, students both medical and surgical had already voted with their feet. The legislation in effect legitimated their response after 1789 when Pierre-Joseph Desault, chief surgeon of the Hôtel-Dieu since 1786, invited students in general to attend his public lessons and operations in the new surgical amphitheater of the huge hospital. Prior to construction of that facility, built in 1788 to accommodate 300 spectators, students at the College of Surgery had accompanied Desault in his rounds as an extracurricular part of their training. Desault himself described how they were obliged to cluster about a bed, often containing several patients. Those in the back would climb on the edge of other beds in order to see the invalids and hear the diagnosis and prognosis. All would then crowd around operating tables located right in the wards. So closely did they press in that his elbow would often be jostled while cutting, excising, and suturing.

Throughout his career, beginning with private courses in the 1760s, Desault committed himself equally to the improvement, systematization, and teaching of surgery. Appointed professor at the College of Surgery in 1776, he was later named surgeon at the Charité hospital, second in size to the Hôtel-Dieu. Throughout, students followed him in his rounds, but only in the small hospice of the college was clinical experience an integral part of its own training program. Hospitals, after all, were not and are not primarily educational institutions. Desault’s admission of students to the Hôtel-Dieu met with fierce resistance from the nursing staff, consisting of Augustinian sisters. In their view patients, for the most part indigent, were properly objects of charity, there to be cared for. Their suffering was not a matter for public display. Installation of an amphitheater, where operations became drama, gave even greater offense than violation of the corpse by autopsy.

The administrators of the hospital overrode the objections and supported Desault in his determination to impart the highest possible degree of skill to future physicians and surgeons alike. He met with other chagrins, however. In the heady egalitarian climate of 1791, students who were not among the select 300 admitted gratis to his course rebelled against his authority. Claiming to be 2,000 strong, they presented a petition to the National Assembly objecting to his charging fees, which effectively excluded them, and which indeed were dropped thereafter.

His reputation on the left did not recover. On 28 May 1793 Desault was arrested by order of the radical Revolutionary Committee of the Luxem-bourg. 212 Intervention by Fourcroy, who put in hand a petition signed by fifty doctors, won his release three days later, and Desault continued his course throughout the Terror. On 14 December 1794 the Comite d’Instruction Publique named him to be professor of clinical surgery, one of the twelve chairs instituted at the École de Santé, even while he continued in his post at the Hôtel-Dieu (renamed Hospice d’Humanité).²¹³ Courses began in January 1795. In early May the Committee of General Security called on Desault to attend the infant son of Louis XVI, who had fallen ill in prison in the Temple. Desault became violently sick on 1 June after dining with certain representatives of the people and died that night. Though never confirmed, poison was suspected, the more so that the colleague who had been with him in the Temple and another named to take their place died soon afterward in the same manner.²¹⁴

Desault published nothing on his own. The main source for knowledge of his methods and techniques is the edition of his Oeuvres chirurgicales, compiled by the most noted of his disciples, Xavier Bichat.²¹⁵ Beginning in 1792 the value of Desault’s teaching was proven on the field of battle, where realities of combat forced physicians to join surgeons in handson treatment of casualties. The eminence of many of his students constitutes longer-range evidence of his place in medical history (although he himself, ironically enough, opposed the unification of surgery with medicine). Among them, besides Bichat, were five members of the staff at the École de Santé: J.-N. Corvisart, Philippe Pelletan, Marie Lallemand, François Chaussier, and Antoine Dubois, and countless physicians and surgeons both military and civilian. Bichat in turn inspired the careers of Jean-Louis Alibert, Gaspard-Laurent Bayle, François Magendie, and above all Théophile Laënnec, inventor of the stethoscope. Such was the surgical component that in considerable part formed the practice of the Paris School of Clinical Medicine, drawing students from all over Europe and America in the early nineteenth century.

The view has been long and widely held in medical circles, and among historians of medicine, that in general the teaching hospital, newly associated with a university faculty, became the seat of medical education and research at the hands of the Paris School of Clinical Medicine. Pathological anatomy there and then, it has been said, displaced nosology as the basis for the understanding of disease. Classification gave way to analysis. The explanation of a malady henceforth lay in the lesions it produced in certain body parts, not in some interaction between its nature and the nature of the invalid. No longer content with external observation and mere symptoms, doctors sought to penetrate inside the body so far as possible—by auscultation, by palpation, by thoracic and abdominal percussion, by peering down throats, by thumping and listening to chests front and back, if need be by surgery. The stethoscope worn around the neck became the doctor’s signet.

They treated diseases, not patients. Physicians observed the facts and abjured theories, with the exception in some instances of vitalism. The classic Hippocratic consideration of environment, individual temperament, humors, diet, climate, seasons, symptoms, and appearance was a practice of the past. Alleviation of suffering was to be achieved by intervention, not by aiding nature to effect a cure. Detailed case histories were to be kept for selected patients with interesting conditions, not only or mainly in order to follow their individual progress or decline, but with the larger purpose of establishing records of the course of every identifiable disease in statistically significant numbers. Their availability drew the interest of Laplace to medicine as a field ripe for the application of probabilistic analysis to human concerns. Indefatigable dissection broadened the data base—Bichat was said to have opened 600 cadavers. With respect to this, the canonical picture, scholars of very different persuasions, most influentially Erwin Ackerknecht and Michel Foucault, have agreed that all of the above were main features of the revolutionary transformation that modernized the profession and practice of medicine, first in France, then throughout Europe.²¹⁶ In no art or discipline was the transition from an encyclopedic to a positivistic frame-work of knowledge and action more categorical and complete.

Recent scholarship has qualified and tempered this viewpoint in several respects, and in one important instance rejected it altogether.²¹⁷ Certain reservations turn on the immediate realities in Paris. Laurence Brockliss has complemented his reevaluation of the curriculum of French colleges in the old regime with a collaboration exhibiting that medical education and practice, also far from null, were more solid and effective than revolutionary rhetoric allowed.²¹⁸ Furthermore, the promise of an egalitarian, vitalized, hands-on medical training in the 1790s was far better than the performance until well into the nineteenth century. Legislation could not erase the prejudice that relegated surgeons to a lower status than doctors in point of professional prestige. There was still no formal institutional connection between faculty and hospital. Lectures in the classroom remained quite separate from clinical instruction. Too many students with too little discipline crowded into Paris. The number exceeded 1,000 by 1800, and the official courses in clinical medicine failed to be effective for more than a favored handful. Few of those trooping along in a professor’s wake could push close enough to the bed to see the patient, about whose case the discourse was often hurried and perfunctory. For most students, real access to sustained bedside experience required paying the fee to enroll in one of the private courses given by physicians with privileges at one or another of the many hospitals in Paris. Final oral examinations in the École de Médicine were little more than a formality. There was no provision for licensing. Quacks abounded through-out the city and the country, and the vast majority of the population still depended on folk medicine.²¹⁹

Attempts to meet realistic expectations began with creation of an École Pratique de Dissection in October 1797. It marked the first formal retreat from the principle of equal access. Chosen through competition, 150 select students, scalpel in hand, could there learn anatomy by opening cadavers.²²⁰ It was left for the Consulate, however, to systematize what the Revolution had begun while restricting liberty and equality, though not fraternity, in the interest of practicality. In the field of medicine, as throughout the polity at large, the initiative came from Chaptal in the Ministry of the Interior. A directive adopted by the Conseil général des Hospices on 23 February 1802 opened the posts of extern and intern in the Paris hospitals to medical students who succeeded in the competition for appointment. They might apply for an externship in their second year of studies. Those accepted would take an active part alongside the doctors in examining and treating patients. Others, the majority, could be no more than spectators in the clinical offerings of the École de Médecine and would have to pick up what training they could get in private courses. On completion of their medical studies externs might apply for an internship. Interns were in effect residents at the beginning of their careers who, while reporting to the responsible physician, would themselves treat patients and be available in emergencies. Such a post, obviously, has become a universal stage in medical education throughout the world.²²¹

Finally on 11 March 1803 (19 ventôse an XI) the Corps Législatif adopted the measure that is the historical point of departure for the body of regulations governing both medical education and medical practice in France ever since. Fourcroy framed the legislation as he had done the 1794 law (14 frimaire) that it replaced. The Écoles de Santé were now renamed Écoles de Médecine (to become Facultés in 1808). Not to go into detail, medical practitioners, including midwives and pharmacists, had now to be licensed by the state. The degree and diploma of doctor were restored and extended to surgeons. As in the old regime, it required successful completion and defense of a thesis, though no longer in Latin. Physicians and surgeons were still to be trained together, but the distinction of the specialties was recognized. The term “officers of health” henceforth designated, not the whole profession, but a lower tier, the equivalent of country doctors. Without taking a degree they might qualify themselves through three years of medical education, five years of hospital training, or six years of apprenticeship to a licensed practitioner. Clearly it was bound to require a generation or more before the transformation of the medical profession in its higher reaches in Paris, Strasbourg, and Montpellier had appreciable effects in the delivery of health care in town and country throughout France.²²²

More generally, indeed very generally, Othmar Keel has recently drawn together the findings of meticulous studies published over the last twenty-five years and extended them in an impressive work.²²³ He there disputes the primacy of the Paris School of Clinical Medicine with respect to any and all of the factors that, he agrees, did modernize the European practice of medicine in the period between, roughly, 1750 and 1830. His main findings follow.

Item: Clinical teaching and research, though not called that in the late eighteenth century, had already begun then under the leadership of Auen-brugger in Vienna, of Morgagni in Pavia, of William and John Hunter in London, and of James Carmichael Smyth, Alexander Munro primus, and Alexander Munro secundus in Edinburgh. So also had hospital reform under the impetus of enlightened despotism in Austria and Germany and of philanthropy in England and Scotland. In Paris too, not only Desault but also his successor at La Charité, Corvisart, neither of whom had any connection with the Faculty of Medicine, were conducting students on their rounds in the years before the Revolution.

Item: The importance of surgery in the study and teaching of anatomy for medical purposes was not peculiar to France. Even like Desault and Corvisart at the Charité, and indeed before them, leading teachers and practitioners in Britain, the Hunters in London and the Munros in Edinburgh, had had their formation in surgery before turning to medical teaching. They trained their many students accordingly, among them Matthew Baillie and Benjamin Rush.

Item: In the wars of the eighteenth century, military medicine throughout Europe amounted to a dress rehearsal for reform of public health later in the century. Physicians, surgeons, and pharmacists perforce worked together in service to hygiene, sanitation, treatment of wounds, and controlling epidemics. Military hospitals could not in effect fail to be clinical.

Item: In Vienna, Pavia, London, Edinburgh, and elsewhere, hospitals had begun evolving into institutions for the professional study and treatment of disease at the hands of doctors and surgeons and were no longer merely charitable foundations for nursing the poor and sick and sheltering the outcasts of society—the orphans, the aged, the mad, the homeless, the syphilitic—although those needs had still to be met.

Item: The modern conception that disease is the manifestation of pathological lesions in specific parts of the body did not originate with the French school. It may be traced back at the very least to the anatomical work of Giovanni-Battista Morgagni in Pavia, who indeed was much cited by Vicq-d’Azyr in the Dictionnaire de Médicine. True, Morgagni largely limited his scrutiny to the pathology of particular organs in this, that, or the other location in the body and did not analyze the nature of the tissues that compose them.

Item: With respect to diagnosis, the notion is quite wrong that percussion and auscultation as developed by Auenbrugger in Vienna fell out of use until Corvisart’s translation of his treatise in 1808. In fact (in Keel’s view) Corvisart failed to understand the technique fully. In any case, variants were part of the regular procedures practiced and taught by others in Austria and Germany and by the Hunters and Alexander Munro secundus in Britain. In all those centers regular autopsies served to confirm or disconfirm diagnoses.

Item: Finally, appreciation of the pathology of tissues, though it did not figure in Morgagni’s work, did antedate Bichat and the French Clinical School to whom it is normally attributed. Knowledge that lesions characteristic of a certain disease affect the same tissue—synovial, muscular, serous, nervous, and so forth—in the same way, whatever the organ in which they are constituents, is the crux of pathological anatomy. In Keel’s account, Bichat had it from Pinel who in turn had taken the point without acknowledgment from Smyth. Haller also carried analysis beyond organs to the level of membranes and tissues, as did the Hunters. The approach later called histological and the discipline of general anatomy that flowed from it were thus not, Keel insists persuasively, the fruit of Pinel’s application of Condillacian ideology to pathological problems.

This summary oversimplifies a work rich in convincing detail. Keel does not deny that the Paris School of Clinical Medicine did exist, and that it did dispense a medical training and promote a medical practice transformed in France during the Revolutionary and Napoleonic period. Nor does he deny that it made important contributions to the development of medicine elsewhere, though what they were he does not specify. Instead, the central purpose of his book is to reduce the role of the French School to politicizing, rhetoricizing, and in signal instances plagiarizing innovations that had been underway elsewhere in Europe since the middle of the eighteenth century.

In a historiographical sense Keel’s deconstruction of the Paris School of Clinical Medicine may be read as the case in medicine of revisionism concerning the French Revolution itself. Of those events in general, it may similarly be said that no essential aspect of modernity was original with the revolutionary generation. Natural rights, consent of the governed, sovereignty of the people, representative and constitutional government, republican polity, citizenship, the dignity of labor, democratic principle, public safety as the supreme law—these assertions and practices and others like them are to be found in one or several of the following: Athenian governance, the Roman Republic, the Glorious Revolution of 1688, the American Revolution, the writings of the philosophes, particularly of Voltaire, Montesquieu, Rousseau, the physiocrats, and the Encyclopedists. Reforms attempted in France itself during the reign of Louis XVI are a further instance. It may further be argued, and in a restricted sense Tocqueville hinted as much, that the French Revolution was unnecessary, that the elements of modernity would have come together in the normal course of historical evolution without being fired in the crucible of idealism, passion, violence, terror, war, and imperialism. Perhaps. Who can know? But the fact is they did not, and counterfactual history can never be more than hypothetical. The fact is that the French Revolution fused those elements into a concerted, messianic movement to remake the world and to shape a democratic future. The political dynamics of the nineteenth century and much of the twentieth stem from that seminal fact.

But the French Revolution was more than politics. The tsunami it launched into the future stirred deeper waters. As will appear, the leading spirits in sectors comparable to medicine partook of the general determination to remake their professional worlds in keeping with the positivist orientation that defined the historical moment. The makings of a modern exact physics existed before the foundation of the École Polytechnique. But only its early graduates, no longer either géomètres or natural philosophers, founded modern mathematical physics on purpose by expressly practicing it. The makings of comparative anatomy were there before transformation of the Jardin du Roi into the Muséum National d’Histoire Naturelle. But only the members of its staff turned themselves from naturalists into practitioners of a new science of life, a rigorous biology. These developments, as seminal in their sectors as the political impetus in the larger society, did not unfold out of some logic inherent in the respective sciences any more than democracy followed from the logic of enlightenment. They came about in consequence of programs, programs of research.

Our concern is not with medicine itself, but with the scientific roots (there were also other roots) and with the by-products of Paris Medicine, of which the autonomy of experimental physiology was the most important. Nevertheless, a word needs to be said, if only in passing, about the modernization of medicine. For in France that process was if anything more programmatic than was the concurrent formation of the modern scientific disciplines. Vicq d’Azyr’s New Plan for Medicine was a far more express and comprehensive blueprint than any course laid out in advance for physics or biology. Vicq d’Azyr was well aware that its prescriptions were nothing new in detail. They simply reflected the best and most effective practices, both technical and institutional, that were already under way, in France and abroad. Paris Clinical Medicine went to school, so to say, to that plan, however modified in practical reality. Its novelty was in the whole and in the revolutionary spirit animating members of the generation who answered to the summons.

Nothing of the sort emanated from the entourages of Morgagni, Haller, Smyth, Munro primus and secundus, nor even the Hunters. Their discoveries in pathology (Keel leaves no doubt that these were real), their practices in diagnosis (he leaves no doubt that these were penetrating), their teaching (he leaves no doubt it happened at the bedside)—in none of all this did they envision a reform of the whole system of health care, including the profession of medicine, in a manner consonant with the reform of society at large. Connotations of the word rhetoric have become pejorative in recent usage. None of the above physicians was guilty of it in their writings, whether in Latin or in the vernacular. Their case histories and pathological reports are severely and properly technical, written for the trade in the sense that mathematics is said to be written for mathematicians. If language is to have effects outside such boundaries, however, it had better partake of rhetorical qualities.

That was clearly not the only reason for the appeal Paris held for foreign students. After the close of the Napoleonic wars and until mid-century, thousands of American, British, German, Dutch, and other medical students flocked to Paris. They did not normally take degrees at the Faculté de Médecine. Their purpose was to experience a year or two of practical training in what was widely considered the world center of medical sophistication. The excitement of living in Paris certainly had a lot to do with it. But the main attraction was the wealth of opportunity for observing and helping to treat patients in the Hôtel-Dieu, the Charité, the Saint-Louis, and other of the many hospitals, for observing operations in surgical amphitheaters, and for performing autopsies and dissecting cadavers in the attached facilities. Foreign students were astounded that no tuition fees were charged. Still, the official courses at the École de Médecine and the Collège de France were crowded.

Up to 200 French students or more might follow the professors in morning rounds during which their expositions would often be hurried and inaudible. Many Americans were unable to follow lectures in French in any case. They got their hands-on training from their contemporaries. Interns gave private courses for modest fees to small groups of pre-doctoral French and foreign students, usually four or five at a time. They were allowed to circulate in the wards in the late afternoons or evenings and to pick out the most interesting and instructive cases for discussion and treatment. That is how the neophytes learned the diagnostic techniques of percussion, auscultation, and stethoscopic analysis. American students would typically attend a few lectures of Laënnec, Alibert, Dupuytren, Magendie, Broussais, or Corvisart just to say they had seen and heard the great men. It was, however, through time at the bedside, and general exposure to the ambience of Paris medicine, rather than through the express tutelage of its leaders, that they came home imbued with the conviction that observation and experience were alone reliable, that theories were a sham, and that the practice of medicine was a positive, newly professional undertaking based upon science.²²⁴

1 Gillispie (1971).

2 Crosland (1969b) is a modern edition.

3 Perhaps the author may be permitted an anecdote to illustrate that the prestige of the Institute remains high. During a time when he and his wife were residing in Paris, the person who helped with household chores was impressed to hear that he was working at the Institute. “Ce ne sont pas des imbéciles sous la Coupe,” she said.

4 Below, chapter 8, section 3.

5 For the list, see Crosland (1992), p. 54. This is an excellent, detailed, and thoughtful history of the Academy of Science from 1795 to 1914 with many informative asides on the Institute in general. For the statutes governing the latter and also the old academies, see Aucoc (1889).

6 Journal des mines de la République 1 (vendémiaire an III), p. 3.

7 Crosland (1994), a highly original history of the Annales de chimie, also gives an informative census of nineteenth-century French scientific periodicals in general.

8 Mémoires de la Société d’Histoire Naturelle de Paris (an V, 1797).

9 “Quelques idéées générales sur les phénomènes particuliers aux corps vivants,” Bulletin des sciences médicales 4 (1809), pp. 145–170.

10 Mémoires de physique et de chimie de la Société d’Arcueil (1807–1807, 1809, and 1817). Crosland (1967b) is a facsimile reprinting with illuminating editorial commentary. For the society itself, see Crosland (1967a).

11 PVIF, 11 vols., 1910–1922.

12 Above, chapter 6, section 6.

13 The literature on Cuvier is large. See the bibliography in Bourdier, “Cuvier,” DSB 3, pp. 527–528. Appel (1987) is excellent on his relations with Geoffroy. Laurent (1987) discusses the relations of Cuvier and Lamarck in a manner favorable to the latter. Dehérain (1908) is a catalogue of Cuvier manuscripts at the Institute. Outram (1980) is a calendar of his correspondence, and Outram (1984) treats Cuvier’s career as a public figure rather than his science. Coleman (1964) presents an illuminating analysis of his theoretical standpoint. Daudin (1926) is an indispensable account of the development of the taxonomy supplemented with an ex-haustive chronology of relevant publications.

14 Georges Cuvier’s Briefe an C. H. Pfaff aus dem Jahren 1788 bis 1792 (Kiel, 1845). A French translation by Louis Marchant appeared in 1858.

15 For bibliographical detail of these and other papers, see Daudin (1926), pp. 286–287.

16 “Mémoire sur la structure interne et externe, et sur les affinites des animaux auxquels on a donné le nom de Vers,” Décade philosophique 5 (1795), pp. 385–396; “Second mémoire sur l’organisation et sur les rapports des animaux à sang blanc,” Magasin encyclopédique 2 (1795), pp. 433–448.

17 Leçons d’anatomie comparée (5 vols., 1800–1805). The first two volumes were edited by A. C. Duméril, the last three by G. L. Duvernoy.

18 PVIF 1, p. 1n.

19 Laplace to Lakanal, 2 nivôse an III (22 December 1794), PVCd’IP 5, p. 309.

20 PVCd’IP, 21 germinal an III (10 April 1795), 6, p. 67.

21 PVCd’IP 6, pp. 125, 223, and for the complete text, pp. 321–328.

22 The Procès-Verbaux from the first meeting on 6 July 1795 through 27 December 1810 are contained in three registers. Bigourdan (1928–1933) is a history of the Bureau des Longitudes organized topically in installments.

23 PVCd’IP 6, pp. 207, 459–460, 488, 501.

24 Procès-Verbaux, 2^e registre, 9 prairial, 4 fructidor, 19 fructidor, an VI (1798).

25 Bigourdan (1930), pp. A.18–A.26.

26 Bigourdan (1928), p. A.17.

27 Gillispie (1997), p. 278. On Bouvard’s career, see A.F.O’D Alexander, DSB 2, pp. 359– 360.

28 PVCd’IP, Bigourdan (1928), pp. A.17, 25–27; and for detail of the involvement of the Bureau des Longitudes with metrology, (1930), C.1–92.

29 Extrait du registre du Comité de Salut Public, 8 nivôse an II (28 December 1793); Prony’s commission from the Minister of the Interior, Bibliothèque de l’Ecole des Ponts et Chaussées, MS. 724.

30 Above, chapter 4, section 5.

31 For these and other measures, see Bibliothèque de l’École des Ponts et Chaussées, MS 2630, 31; 2922.

32 PVCd’IP 5, pp. 551–563.

33 Delambre, Base du système métrique 1, p. 60.

34 A.-G. Belmar, “L’Agence temporaire des poids et mesures et la diffusion du système métrique en France,” in Débarbat and Ten (1993), pp. 67–77. Cf. Champagne (1979), pp. 217–224. Records of the the Agence temporaire are in AN, F¹².1288, F¹².1298, F^12*.210, F^12*.215–218, and F^12*.220.

35 PVCd’ IP 6, pp. 91–92. Séance du 28 germinal an III (17 April 1795).

36 Letter over the signature of Fourcroy, 22 pluviôse an III (12 February 1795), AN, ADVIII, 37.

37 Élements du nouveau système métrique (1801); Tables de réduction des anciens poids en nou-veaux et réciproquement à l’usage des pharmaciens (1801); Explication . . . de l’arithmographe (1806), etc. See Dictionnaire de Biographie Française, article by St. Le Tourneau. Among a number of competing manuals were M.-J. Brisson, Réduction des mesures et poids anciens en mesures et poids nouveaux (an VII, 1799); Étienne Bonneau, Arithmétique décimale (an VII, 1799); S.-A. Tarbe, Manuel pratique et élémentaire des poids et mesures et du calcul décimal (an VII, 1799).

38 “Analyse des triangles tracés sur la surface d’un sphéroïde,” MIF 7, Pt. I (1806), pp. 130– 161. On Legendre’s participation, see Hellman (1936).

39 The names and salaries are contained in a folder of administrative documents in AN, F¹².1288. For the payroll following transfer to the ministry, see AN, F¹².1289.

40 Ministre de l’Intérieur aux Administrations Centrales des Départements, undated letter, AN, AF¹²*.215, 6.

41 Receipts consisted of 1,755,469.45 francs, of which 11,138.40 came from the proceeds of sales of new measures, and the rest from the Treasury, leaving a balance of 80 centimes. The accounts down through 1813 are in AN, F¹²*.220. Cf. A.-G. Belmar, op. cit., n. 34, above.

42 AN, F¹²*.217, #999.

43 Aisne, Aube, Eure, Eure-et-Loire, Loiret, Oise, Seine-Inférieure, Seine-et-Marne, Seine-et-Oise, Somme, Yonne. AN, F¹²*.217, #1074. Efforts to bring the metric system into use are abundantly documented in AN, F^12*.215–218.

44 Article 10 of the law of 18 germinal an III calls for completing the determination of the basic units of the metric system. On 17 April 1795 the Comité d’Instruction Publique named as commissioners those who had been involved from the beginning: Berthollet, Borda, Brisson, Coulomb, Delambre, Haüy, Lagrange, Laplace, Méchain, Monge, Prony, and Vandermonde (PVCd’IP, 6, p. 92, Séance du 28 germinal an III). Formally, their authority ended with the dissolution of the Convention and its committees on 26 October 1795. The First Class of the Institute thereupon named the same commissioners, with the exception of Van-dermonde and the addition of Legendre, to exercise the responsibility vested in it by Article 25 of the law (Aucoc, 1899, p. 25) founding the Institute (PVIF, Séance du 6 floréal an IV [27 December 1795], 1, p. 30).

45 PVCd’IP 6, pp. 321–328; Delambre, Grandeur et figure de la terre , p. 216. It is an exaggeration to suggest, as does Heilbron (1990), pp. 230–232, that Delambre resumed operations in service to Calon. Calon, formerly an officer of the Corps des Ingénieurs-Géographes and currently a deputy to the Convention, had been director of the Dépôt de la Guerre since April 1793. He was engaged in a complicated game of bureaucratic empire building and named noted scientists, among them Laplace, Delambre, and Méchain, to his roster in the role, essentially, of consultants. He also obtained funds from the Committee of Public Safety with a view to mapping the newly annexed departments and to completing the survey of the meridian. The sum promised the latter was rather small—110,000 francs. A letter from Méchain makes it doubtful that he or Delambre ever received the money (Méchain to Calon, 13 fructidor an III [30 August 1795], copy in dossier Méchain, Archives de l’Académie des Sciences).Calon’s attempt to centralize all cartography in the Dépôt de la Guerre miscarried. On this complicated affair, see Bret (1991b); Berthaut (1902), 1, pp. 135–146.

46 Laplace to Delambre, 10 pluviôse an VI (29 January 1798), in Laissus (1961). Cf. PVIF 1 (1795–99), p. 335, séance du 1^er pluviôse, an VI. Talleyrand’s letter of invitation is reported in Le Moniteur, no. 261, 21 prairial an VI (9 June 1798).

47 Above, chapter 4, section 3. Delambre’s account of his measurement of the Perpignan base is contained in a letter to Prony, 4^e jour complémentaire de l’an VI (20 September 1798), Bibliothèque de l’École des Ponts et Chaussées, MS. 724.

48 This account of the last phase of the survey is drawn from Base 1, pp. 65–97.

49 Delambre, Histoire de l’astronomie 6, pp. 761–762.

50 Crosland (1969a); Jean Dhombres, “Le regard étranger sur la vie scientifique française vers 1800,” in Debarbat and Ten (1993), pp. 41–64.

51 John L. Heilbron, “The Measure of Enlightenment,” in Frängsmyr, Heilbron, and Rider (1990), pp. 233–235; Dhombres, op. cit., n. 50 above.

52 “Discours prononcé à la barre des Conseils du Corps législatif, au nom de l’Institut National des Sciences et des Arts, lors de la prèsentation des étalons prototypes du mètre et du kilogramme.” Séance du 4 messidor an VII, Base 3, pp. 584–591.

53 Above, chapter 7, section 2.

54 For Fabbroni’s career in general, see Pasta (1989), and for his participation in the Congress on the Metric System, chapter 6, section 1, pp. 435–455.

55 On Mascheroni, see A. Seidenberg, DSB 9 (1974), pp. 156–158. For his relations with Bonaparte, and the so-called Mascheroni-Napoleon problem, see Fischer (1988), app. 6.3, pp.318–323.

56 “Rapport fait par M. d’Arcet . . . sur les ouvrages en Platine exécutés par M. Janety fils,” Bulletin de la Société d’Encouragement pour l’Industrie Nationale 11 (1812), pp. 207–208.

57 The note printed in Lavoisier OL (cited chapter 4, n. 78) is very cursory. There is a much fuller account in “Rapport fait à L’Académie des Sciences le 19 janvier 1793 sur l’unité des poids et mesures,” printed in “Recueil de pièeces relatives à l’uniformité des poids et mesures,” Annales de chimie 16 ( January 1793), pp. 272–277.

58 “Notes communiquees par M. van Swinden,” Base 3, pp. 434–446.

59 Van Swinden, “Rapport fait à l’Institut national . . . le 29 priarial an 7 . . . sur la mesure de la méridienne de France,” ibid., p. 619.

60 Ibid., p. 421, note; cf. vol. 2, p. 704.

61 Ibid., pp. 135, 432, n. 1.

62 Ibid., p. 193.

63 Bureau des Longitudes, Procès-Verbaux, 13 fructidor an X; A. E. Ten and J. Castro, “La jonction géodésique des Iles Baléares au Continent et le système métrique décimal,” in Débar-bat and Ten (1993), pp. 148–154.

64 Méchain to Jaubert, 13 messidor an XII (2 July 1804), Dossier Méchain, Archives del’Académie des Sciences.

65 An error, no doubt typographical, in Base 1, p. 96, has “troisième jour complémentaire an 13” (instead of an 12); many reference works follow that and give the date as 20 September 1805. See Louis Marquet, “A propos de la mort de l’astronome Méchain en Espagne,” in Débarbat and Ten (1993), pp. 163–176.

66 Laplace to Minister of the Interior, 11 June 1806 (AN, F¹⁷.1065A, dossier 16); Bureau des Longitudes, Procès-Verbaux, séance du 2 mai 1805.

67 Biot’s full account of the extension of the meridian occupies the first part of Recueil d’observations géodesiques, astronomiques, et physiques, exécutées . . . en Espagne, en France, en Angleterre, et en Écosse, pour determiner la variation de la pesanteur et les dégrés terrestres sur le prolongement du méridien de Paris, faisant suite au troisième volume de la Base du système métrique (1821). Although the title continues “rédigées par MM. Biot et Arago,” the introduction and all the text were composed by Biot. The work is always catalogued under his name. A note explains that Arago proposed to write up his observations on the longitudinal arc between Formentera and Majorca in a companion volume (p. xxx). He never did. See also Ten and Castro, op. cit. n. 63 above.

68 Documentation in AN, F¹⁷.1065A, dossier 16. Arago recalled (and certainly embroidered) his adventures many years later in Histoire de ma jeunesse (Brussels and Leipzig, 1854). Cf. Daumas (1987), Sarda (2002).

69 “Expériences sur la longueur du pendule à secondes faites à différentes parties du méridien depuis l’île de Formentera . . . jusqu’à Unst,” op. cit. n. 67 above, pp. 439–520. For the Borda determination, see above, chapter 4, section 3.

70 “Recherches sur les réfractions extraordinaires qui s’observent trèsprès de l’horizon.” Lu le 8 août 1808. MIF 10 (1809/10), pp. 1–266. Biot seldom included the names of collaborators as co-authors of his memoirs.

71 “Mémoire sur le phénomène connu sous le nom de mirage,” Décade égyptienne 1 (an VII, 1799), pp. 37–46; reprinted in Mémoires sur l’Égypte 1 (1800), pp. 64–78.

72 “Mesures du pendule en Angleterre, en Écosse, et aux Iles Shetland,” op. cit. n. 67 above, pp. 521–572.

73 “Exposé des résultats des grandes opérations géodésiques faites en France et en Espagne par MM. Biot et Arago, pour la mesure d’un arc du méridien et la détermination du mètre,” MIF 9 (1808–09), Histoire, pp. 16–21. Clerks at the Bureau des Longitudes calculated the difference to be even smaller, less than 0.0001 lignes. Biot, op. cit. n. 67 above, introduction, p. xvii.

74 Op. cit. n. 67 above.

75 Base 3, p. 546.

76 On the cadastre, see Konvitz (1987), pp. 41–62.

77 “Situation du travail des Bureaux du Cadastre et des Transports le 30 frimaire de l’an deuxième,” Bibliothèque de l’École des Ponts et Chaussées, MSS. 2402. The occasion was a decree of the Convention uniting the Bureau du Cadastre with the Commission des Subsistances et Approvisionnements.

78 See Gillispie (1980), p. 47, and, for a full discussion, Brian (1994), pp. 256–286.

79 “Résultats du travail fait au Bureau du Cadastre pour connaître la superficie et la population du territoire français,” Bibliothèque de l’Ecole des Ponts et Chaussées, MSS 2149.

80 Document cited in n. 77 above.

81 Aulard, Recueil des Actes du Comité de Salut Public 13, pp. 312–313. Séance du 17 floréal an II.

82 Prony, Notice sur les grandes tables logarithmiques et trigonométriques, calculées au Bureau du cadastre sous la direction du citoyen Prony. Prony read the notice before the First Class of the Institute on 1 germinal an IX (22 March 1801). A report by Delambre on behalf of Lagrange, Laplace, and himself is appended, as is an essay by Prony on the history of logarithms. The three pieces were printed together as a brochure (1801) and also in MIF 5 (An 9 [1801]/1804), “Histoire,” pp. 49–93.

83 Prony, Notice sur les grandes tables logarithmiques et trigonométriques (1824), p. 5.

84 Sheets of calculations, some in manuscript, others printed, are in AN, F¹⁷.1244b. See also Bibliothèque de l’École des Ponts et Chaussées, MS 1745. For a summary of the mathematical details, see Grattan-Guinness (1990), 1, pp. 177–183. Prony treated the formal aspects of constructing the tables in his “Cours d’analyse appliquee à la mécanique” at the École Polytechnique, Journal de l’École Polytechnique, cahier 1 (1795), pp. 92–119; cahier 2 (1796), pp. 1–23; cahier 3 (1796), pp. 209–273; cahier 4 (1796), pp. 459–569.

85 Op. cit. n. 83 above, pp. 7–8.

86 Aulard, Recueil des Actes du Comité de Salut Public (13, p. 433), séance du 22 floréal an II. 87 See the 1801 report by Delambre, cited in n. 82 above.

88 Johann Philipp Hobert and Ludewig Ideler, Neu trigonometrische Tafeln fur die Deci-maleintheilung des Quadranten (Berlin, 1799). Published also in a French edition.

89 Tables trigonométriques décimales . . . calculées par Ch. Borda, revues, augmentées, et publiées par J. B. J. Delambre (an IX, 1801), 114. The volume also contains a set of log tables for numbers from 10,000 to 100,000 carried to ten decimals.

90 Two manuscript minutes in Prony’s hand concerning the negotiations, dated 2 March and 8 March 1819, are in his dossier in the Archives de l’Académie des Sciences. Also in the dossier are a separate printing of the memoir Prony read at the Séance publique of the Académie des Sciences on 7 June 1824, Notice sur les grandes tables logarithmiques et trigonométriques, adaptées au nouveau système métrique décimal (1824), together with a printed “Note sur la publication, proposée par le gouvernement anglais, des grandes tables logarithmiques et trigonométriques de M. de Prony. ”

91 Bibliothèque de l’Institut de France, MSS.1496–1514.

92 For administration and financial accounts, 1796–98, see AN, F¹⁷.1393. Dossiers 3 and 4 contain documents on the École des géographes. For the relations between the École des Géographes, the Dépôt-Général de la Guerre, and the militarized École des Ingénieurs-Géographes founded in 1809, see Bret (1990).

93 Prony to the Minister of the Interior, le 14 ventôse an VII (4 March 1798), AN, F¹⁷. 1393, dossier 4. On the difficulty of securing agreement among various agencies on cartographical scales, see AN, F¹⁷.1135, dossier 17; and on the general paralysis in 1799–1800, the memoirs “État de la situation du Cadastre” and “Projet d’organisation,” dated 1 messidor an VIII (20 June 1800) AN, F⁴ . 1246.

94 Bureau des Longitudes, Procès-Verbaux, le 4 et le 20 floréal an X (24 April and 10 May 1801).

95 A new cadastre was organized in 1807 with the mission of piecing together local surveys into a national system of land registry. For its further history, see Dreux (1933), and Recueil de documents législatifs, projets, et lois, réglements, rapports, etc., concernant le cadastre (Imprimerie nationale, 1891), BN, Lf158. 236.

96 Mécanique céleste by the Marquis de La Place (4 vols.: Boston, 1829–1839).

97 Op. cit. n. 90 above.

98 Op. cit. n. 67 above, pp. 183–185.

99 J.-A. Chaptal, “Observations sur le savon de laine et sur ses usages dans les arts,” MIF 1 (an IV/an VI [1798]), lu le 1^er prairial, an IV (20 May 1796), pp. 93–101; J.-R. Tenon, “Recherches sur le cran humain,” MIF, lu le 16 messidor an IV (5 July 1796), pp. 250–279.

100 Honoré Flaugergues, “Mémoire sur lieu du noeud de l’anneau de Saturne en 1790,” MIF, lu le 16 floréal an IV (4–5 May 1796), pp. 75–88.; H.-A. Tessier, “État de l’agriculture des Iles Canaries,” MIF, lu le 6 brumaire an V (27 October 1796), pp. 250–279.

101 “Mémoire sur les mouvements des corps célestes autour de leurs centres de gravité,” op.cit., lu le 1^er pluviôse an IV (21 January 1796), pp. 301–376.

102 “Rapport sur la mesure de la méridienne de France,” MIF 2 (An VII [1799]/1800), lu le 29 prairial an 7, pp. 23–80. Also printed in Base, this is the report cited in n. 60 above.

103 “Mémoire sur la décomposition des sels marins calcaires par le moyen de la chaux, de l’alcali fixe, et de l’alcali volatil,” MIF 5 (an IX [1801/1804]), pp. 89–104.

104 Above, this section.

105 “Sur le nouveau système de mesures,” Journal des mines 3, no. 14 (brumaire an III), pp. 73–85. An English translation appeared in Nicolson’s Journal, no. 5 ( July–August 1797).

106 “Description d’une machine simple et peu coûteuse, propre à épuiser les eaux, dans les recherches des mines et les exploitations naissantes,” Journal des Mines 1, no. 3 (frimaire an III), pp. 15–28.

107 A list of those named by the Committee of Public Safety as of 15 vendémiaire an III (6 October 1794) consists of three agents, seven inspectors, twelve engineers, and two of the forty students authorized, with the remaining thirty-eight places to be filled by a competition ( Journal des Mines 1, no. 1 (vendémiaire an III), pp. 125–126.

108 R.-J. Haüy, “Observations sur les pierres appelées . . . Hyacinthe et Jargon du Ceylan,” Journal des Mines 5, no. 26 (brumaire an V [September–October 1796]), p. 99.

109 Instruction sur les Poids et Mesures de la République Française, suivie d’un Vocabulaire de ces mesures, et de tables exprimant leurs rapports avec les mesures anciennes,” Annales de chimie 20 (an V ou 1797), pp. 191–252. For the first two years, Annales was one of the very few publications to give the old-style along with the republican dates. That ceased with the year VIII.

110 Above, n. 100; Annales de chimie 21 (pluviose an V, January 1797), 27–71.

111 Gaspard Monge, “Notice sur la fabrication du fromage de Lodézan connu sous le nom de Parmézan,” Annales de chimie 32 (vendémiaire an VIII [September 1799]), pp. 287–295; J. A. Chaptal, “Suite du traité sur les vins,” ibid., 36 (an IX [1801]), pp. 3–49.

112 On the Société d’Encouragement, see below, chapter 8, section 4.

113 For the proceedings at the foundation, see the Recueil des Procès-Verbaux for the early months, 1 November 1801 to 22 September 1802, Bulletin de la Société d’Encouragement pour l’Industrie Nationale 49 (1850).

114 Gillispie and Dewachter (1988).

115 Bigourdan (1901), chapter on “Atteintes portees à la pureté du système métrique,” pp.

190–199. Cf. Morin (1873), pp. 35–40.

Above, chapter 4, section 5. Lucien had had a conference with Laplace, Berthollet, and Monge before framing the measure. See “Rapport présenté aux Consuls de la République par le Ministre de l’Intériéur,” 9 brumaire an IX (31 October 1800). AN, ADVIII, 38.

117 Circular letter from Chaptal to Prefects, 2 frimaire an XI (23 November 1802), Circu-laires, instructions et autres actes émanés du ministère de l’intérieur de 1797 à 1821, 4, pp. 359–381. For further items of correspondence between the Ministry of the Interior and prefects in many departments, particularly Haut-Rhin, Bas-Rhin, Vosges, Meurthe, and Ille-et-Vilaine, see AN, F¹².1295, F¹² .1298.

118 Bigourdan (1901), pp. 194–199. For the background and consequences of this law, see documentation in AN, ADVIII, 38; F¹².1292; F¹².1298; correspondence of Montalivet (Minister of the Interior) with prefects, op. cit., n. 117, 12 (1812), pp. 56–69.

119 “Opinion de B. M. Decomberousse (de l’Isère) sur la résolution relative aux poids et mesures,” 9 fructidor an VI (26 August 1798). AN, ADVIII, 37.

120 Base 3, p. 651. Baudin cites the Dictionnaire de musique.

121 “Observations sur le nouveau système des Poids et Mesures,” Bulletin de la Société d’En-couragement pour l’Industrie Nationale 3 (1804), pp. 103–105.

122 Cited in Bigourdan (1901), pp. 202–211.

123 French domination was not what implanted the metric system in Europe except, perhaps, at a bureaucratic level. Ample documentation shows Napoleon’s prefects in Germany failing to bring metric units into use in occupied territories as signally as did their colleagues in France. AN, F¹².1290; F¹² .1295.

124 The term “normal school” was not novel. That the French were well aware of the precedents is evident from the lengthy appendix, in Italian, to volume 6 of the collection Séances des Écoles Normales (1800), detailing provisions for the “Sistema normale” developed in the Prussia of Frederick II and adopted in Austria and much of Italy.

125 On the École normale, see Dupuy (1884), reprinted in Le Centenaire de l’École Normale, 1795–1895 (1895), pp. 21–209; Julia (1981), pp. 154–171; Palmer (1985), pp. 213–220.

126 On the Bouquier plan, see Palmer (1985), pp. 179–183, 200–201; and for the documentation, PVCd’IP 3, pp. xxiv–xlviii, 56–62, 191–196; 4, pp. xl–xlix, 451–452, n. 4; pp. 461–462.

127 PVCd’IP 5, pp. 151–158, p. 157.

128 Ibid. pp. 263–265; Palmer (1985), pp. 211–212.

129 Of the 250 whom Dupuy could identify, some 60 had been professors in clerical colleges, and another 75 had taught primary school. See Centenaire de l’École Normale, pp. 116–135.

130 Above, chapter 3, section 2.

131 An amusing and irreverent student’s eye view of the proceedings is the letter that Mat-thew Bonace wrote to his cousin and published in Journal de Paris. Excerpts are in PVCd’IP 6, pp. 98–105.

132 27 germinal an III (27 April 1995) PVCd’IP 6, p. 96.

133 Above, pp. 297–298.

134 PV Cd’IP 5, pp. 299–309.

135 For these and further generalizations, see Palmer (1985), pp. 247–251, and for the quantitative studies on which they are based, p. 243, n. 27.

136 Palmer (1985), pp. 246, 252–257, and notes.

137 Belhoste (1995), p. 26.

138 Seances des écoles normales, recueillies par des stenographes, et revues par les professeurs. The first edition was gathered and published in 7 volumes in 1796, and a third in 1806. Available to me has been the second edition (1800–1801) in ten volumes plus three of débats. Volumes 1–5 and the first part of volume 6 contain the enabling legislation and regulations and the revised lectures in the order of their delivery. Reading straight through brings home what it must have been for students listening to one topic after another. The second part of volume 6 is a 450page appendix in Italian of the “sisteme normale” normalizing the preparation of teachers in Prussia, Austria, and much of Italy. Volume 7 has a 142-page abstract of Laplace’s Mécaniquecéleste composed by Biot in 1800, followed by the historical part of the course Thouin could not give on agriculture and his tabulation of European plants. Volume 8 has the continuation of Daubenton on natural history and Lacepède’s first course on natural history (1798) at the Muséum, followed by his éloge of Daubenton. Volume 9 contains the completion and corrections of Berthollet’s interrupted course on chemistry, followed by the rest of Thouin’s undelivered course on agriculture. Vol. 10 consists of Lagrange’s Leçons sur le Calcul des fonctions on a level immeasurably above anything in the preceding volumes.

139 Two volumes have appeared, Dhombres (1992) on mathematics (Laplace, Lagrange, and Monge) and Nordman (1994) on forerunners of political science (Volney, Buache and Mentelle, and Vandermonde). A communication from Jean Dhombres brings word that the third on literature, moral philosophy, and general grammar is in press, and that what is intended to be the conclusion, a critical overview, is a year away from publication. The volume with Haüy’s course on physics, Berthollet’s on chemistry, and Daubenton’s on natural history has been further delayed, in part because of the untimely death of the initial editor, Michelle Goupil. Also informative are the remarks on the content of the courses by Garat, LaHarpe, and Bernardin de Saint-Pierre (with which we will not be concerned) in Moravia (1968), pp.387–405.

140 Above, p. 241.

141 Exposition du système du monde (1796), 2, p. 312. For fuller discussions of the work, see Dhombres (1992), pp. 30–37; Gillispie (1997), pp. 166–175.

142 Editions Christian Bourgeois, with an illuminating preface by René Thom and an exel-lent historical postface by Bernard Bru.

143 In Dhombres (1992), p. 140.

144 For further discussion of Laplace’s standpoint, see Dhombres (1992), pp. 11–47, and Gillispie (1997).

145 On Essai philosophique, see Dhombres (1992), pp. 37–41; Gillispie (1997), pp. 224–242; and the preface and postface to the edition cited in n. 142.

146 Quoted by Amy Dahan Dalmédico, “Leéons de Lagrange,” in Dhombres (1992), p. 184.

147 Ibid., p. 211.

148 Quoted in ibid., p. 186.

149 I owe this summation to Amy Dahan Dalmédico in ibid., pp. 185–186. Cf. Jean Itard, “Lagrange,” DSB 7 (1973), p. 570.

150 The 1801 edition of Séances de l’École Normale, vol. 10. Above, n. 138.

151 Dhombres (1992), pp. 305–306.

152 Taton, “Desargues,” DSB 4 (1971), pp. 46–51.

153 The standard and indispensable work on Monge is Taton (1951). See also his “Monge,” DSB 9 (1974), pp. 469–478. Belhoste and Taton, “L’invention d’une langue des figures,” is a fine analysis of the lectures at the École Normale and the École Polytechnique in Dhombres (1992), pp. 269–303. There is an account of Monge’s career prior to 1789 in Gillispie (1980), pp. 519–529.

154 Dhombres (1992), quatrième leçon, pp. 340–341.

155 Chasles (1889), pp. 189–253; cf. Dupin (1819).

156 Mauskopf (1976).

157 Exposition raisonnée de la théorie de l’électricité et du magnetisme, d’après les principes d’Aepinus (1787). Aepinus’s main work appeared in 1751, Testamen theoriae electricitatis et magne-tismi. That Aepinus had begun with what would now be called the piezo-electricity of crystal-line tourmaline may well be what had attracted Haüy’s attention.

158 Séances des Écoles Normales 5 (1800), p. 330.

159 Nordman gives an account of the background and content of the course in Nordman (1994), pp. 137–166.

160 “Rapport sur les fabriques et le commerce de Lyon,” Journal des arts et manufactures 1 (1794), pp. 1–48. Cited by Jorland in Nordman (1994), pp. 342–343.

161 Above, this section.

162 For a detailed analysis and evaluation of Vandermonde’s course, see the collaborative introduction to his lectures by D. Woronoff, A. Alcouffe, G. Israel, G. Jorland, and J. C. Perrot in Nordman (1994), 340–358. See also the analysis by Moravia (1974), pp. 729–734.

163 Gaulmier (1951).

164 Reprinted with Leçons d’histoire in Gaulmier (1980).

165 Barthélémy Jobert provides an excellent introduction and notes to Volney’s Leçons in Nordman (1994).

166 “Leçons d’histoire,” in Dhombres (1992), p. 62.

167 Ibid., p. 61.

168 Dhombres (1992), pp. 82, 105.

169 In Nordman (1994), p. 60.

170 On returning from America, Volney revised the stenographic copy printed in his absence into the form published in 1800 and reprinted many times, most recently in Gaulmier (1980).

171 The history of the early years of the École Polytechnique has been very thoroughly studied, beginning with the nearly contemporary Fourcy (1828), republished in 1987 with critical apparatus and an excellent introduction by Jean Dhombres. Leverrier (1850) gives a broad and illuminating survey. École Polytechnique, Livre du centennaire (3 vols., 1894), con-tains histories of the teaching and biographies of graduates. Shinn (1980) is a social history of polytechnicians. Belhoste, Masson, and Picon, eds. (1994), is a lavishly illustrated portrayal of polytechnicians in Paris. Belhoste, Dahan Dalmedico, and Picon, eds. (1994), contains proceedings of the bicentennial symposium. A number of articles, cited by author, appear in Bulletin de la Société des amis de la Bibliothèque de l’École polytechnique, cited in the notes that follow and in the bibliography by its acronym SABIX. The archives of the school are now well organized and admirably maintained in the library of the school at Palaiseau.

172 Picon (1992), pp. 259–261.

173 Belhoste (1989) supersedes earlier accounts of the conversion of the École des Ponts et Chaussées into the École Nationale des Travaux Publics. In SABIX No. 11 (February 1994) he publishes extensive documentation concerning the founding of the École Centrale des Travaux Publics.

174 Published by Taton in Dhombres (1992), pp. 574–582.

175 For the legislative history, see Langins (1980).

176 Extracts from the two registers recording the minutes of meetings of the Conseil de École Polytechnique, an III–an VII (1795–99) have been transcribed by E. L. Dooley and l’published in SABIX N°12 (November 1994).

177 Développemens sur l’enseignement adopté pour l’École Centrale des Travaux Publics, pub-lished by order of the Committee of Public Safety. Reproduced by facsimile in Langins (1987a), pp. 227–269.

178 Reproduced by facsimile in Langins (1987a), pp. 128–129.

179 Op. cit., n. 177, p. 230.

180 Developpemens sur l’enseignement adopté pour l’École Centrale des Travaux Publics is repro-duced by facsimile in Langins (1987a), pp. 227–269.

181 Facsimile in Langins (1987a), pp 126–198.

182 Monge gave an account of their training in the first number of the Journal de l’École Polytechnique 1 (1795), p. 6; see Langins (1987a), pp. 24n., 270–271.

183 On the École des Ponts et Chaussées, see Picon (1992), pp. 272–288; on the École du Génie et de l’artillerie, see Belhoste and Picon (1996); on the École et Corps des Ingénieurs Géographes, see Berthaut (1902), Bret (1991b); on the École des mines, see Aguillon (1889).

184 Fourcy (1828) lists the names of all entering students in the classes from 1794 through 1827.

185 Jomard (1853), pp. 13–14.

186 The contrast began with the recriminations against the influence of Laplace by the geometer Théodore Olivier, X-1811, a champion of descriptive geometry, advocate of applied science as the basis of an engineering education, and moving spirit in the founding of the practically oriented École Centrale des Arts et Métiers in 1829. Mémoires de géometrie descriptive, théorique, et appliquée (1851).

187 For discussions of the displacement of descriptive geometry by analysis, see Belhoste (1994), Gillispie (1994), Sakarovich (1994), and Paul (1980). In a broader sense the transition is a central theme of the magisterial study by Grattan-Guinness (1990).

188 Laplace to the Director of the École Polytechnique, 19 frimaire an V (5 December 1796), published in Langins (1987b), pp. 176–177, to whose discussion I am much indebted.

189 The minutes of the meetings of the two councils, Registre des procès-verbaux du Conseil d’Instruction and Registre du Conseil de Perfectionnement, and also the printed Rapports du Conseil de perfectionnement depuis l’an X jusqu’à l’année 1839 addressed to the Minister of the Interior, may be consulted in the Bibliothèque de l’École Polytechnique at Palaiseau. Extensive photocopies will be deposited under my name in the library of Princeton University.

190 Fourcy (1828), pp. 192–200.

191 On the course on rational mechanics and “machines,” see Chatzis (1994), and on the teaching of mechanics down to 1850, see Dupont (2000).

192 Smeaton (1954); Langins (1981); Tron (1996).

193 Rapport sur la situation de l’École polytechnique . . . par le Conseil de perfectionnement établi en exécution de la loi du 25 frimaire an 8 (n. 189), p. 4.

194 Registre du Conseil de Perfectionnmenmt, 1808–1809, fol. 1.

195 On Cauchy’s course, see Gilain (1989).

196 Fourcy (1828), pp. 300–303.

197 Bernard Forest de Bélidor, La science de l’ingénieur (1727). In 1819 Navier edited Bélidor’s companion work, Architecture hydraulique (2 vols., 1737–39) in similar fashion.

198 Gillispie (1983), chapter 5.

199 Dupin, Force commerciale de la Grande-Bretagne (1824).

200 Fourcy (1828), pp. 122–123.

201 Registre des procès-verbaux du Conseil de Perfectionnement, 4, 82v.

202 Traité élémentaire du calcul differentiel et du calcul intégral (1802), p. iii.

203 Registre du Conseil d’Instruction, 25 September 1812.

204 Dupin (1819), pp. 62–63.

205 On 1 thermdor an XII (20 July 1804), Fourcroy, then Councillor of State in charge of Public Education, apologized to Napoleon for the “bagarre au Théatre français.” AN, AFIV, 1050.

206 Fourcy (1828), pp. 246–249; Bradley (1975, 1976).

207 Bradley (1975).

Napoleon to Lacuée, 23 March 1805, quoted in Bradley (1975), p. 440. The decree was promulgated on 22 fructidor an XIII (9 September 1805).

209 Dupin (1819), p. 70.

210 PVCd’IP 4, pp. 979–980. The full report was printed separately, “Rapport et projet de décret sur l’établissement d’une École centrale de santé à Paris” (1794/an III).

211 Above, chapter 1, section 4; PVCd’IP 5, pp. 281–283.

212 Gelfand (1973) publishes the petition and Desault’s outraged response, in which he gives a full account of his practice.

213 PVCd’IP 5, p. 316.

214 PVCd’IP 6, p. 380, n. 1.

215 Oeuvres chirurgicales de P.-J. Desault (3 vols., 1798). Bichat’s Éloge appears in volume 1. Translated into many languages, the work was a trusted manual in the early nineteenth cen-tury. The four volumes of the ephemeral Journal de chirurgerie (1791–1796) mostly consist of notes taken by students.

216 The principal works are Ackerknecht (1967), Foucault (1963), and Sournia (1989). important for particular aspects are Gelfand on surgery (1980), Maulitz on pathological anatomy (1987), Nicolson on diagnosis (1992, 1993), and Pickstone on physiology (1981).

217 Essays and a valuable introduction discussing the state of the question are in Hannaway and La Berge (1998).

218 Brockliss and Jones (1997).

219 Ramsey (1988); Brockliss and Jones (1997), pp. 818–834; Brockliss (1998).

220 Imbault-Huard (1973); see Keel (2001), chapter 4.

221 On the externat and internat, see Keel (2001), chapter 4.

222 Ramsay (1988), pp. 77–82; Brockliss (1989).

223 Keel (2001).

224 Warner (1998a, 1998b).