Essai sur la théorie des comètes is a mathematical and astronomical memoir by the French mathematician and philosopher Jean-Antoine-Nicolas de Caritat, marquis de Condorcet (1743–1794). It was written for a prize competition of the Royal Academy of Sciences and Belles-Lettres of Prussia in Berlin and was awarded a share of the prize in 1778. It was printed at Utrecht in 1780, together with the other competing essays, in a collective volume. It belongs to the scientific phase of Condorcet’s career, before his reputation rested chiefly on his work in philosophy, social mathematics and politics.
Author and context
Condorcet was born at Ribemont in Picardy. Biographical accounts treat the years from 1765 to 1774 as the purely scientific period of his life. During that period, on 25 February 1769, supported by d’Alembert, he was elected to the Royal Academy of Sciences. His early reputation rested on works in integral calculus and celestial mechanics, including Du calcul intégral (1765), Du problème des trois corps (1767) and Essais d’analyse (1768). In 1776 he was elected perpetual secretary of the Academy of Sciences, and in 1782 to the Académie française.
The historian Pierre Crépel notes that the leading science of the day, after Newton and Leibniz, was differential and integral calculus, applied in particular to the motion of the heavenly bodies, the Earth, machines and fluids. Condorcet’s work on comets belongs to this tradition of applying analysis to gravitational astronomy. French reference listings of his physical works place it alongside the three-body memoir of 1767 and the 1778 Nouvelles expériences sur la résistance des fluides, written with d’Alembert and Bossut.
The Berlin prize competition
The essay was composed in response to a question set by the Berlin Academy. In 1772 the Academy proposed a prize, to be awarded in 1774, for an easy method of calculating the parabolic orbit of a comet from three observations, with a demonstration of its use in solving the problem as simply and exactly as possible. The problem of determining a cometary orbit from a small number of observations had long occupied mathematicians. In his biography of Condorcet, François Arago observed that the problem was not satisfactorily resolved even after Newton, Fontaine, Euler and others had made it the subject of their most assiduous research, and that when the Berlin Academy proposed it as a prize subject, astronomers were still using graphical methods involving cardboard parabolas of various parameters.
The competition was slow to attract entries. For lack of competitors, the Academy extended the deadline to 1778, and the prize was awarded to Condorcet and Tempelhoff. A reference summary of the Academy’s prize questions records that the 1778 prize on calculating the orbit of comets went to the Marquis de Condorcet of Paris and Tempelhoff, described as a Prussian artillery sergeant. The same summary adds that the question was repeated several times, the prize was doubled, it was divided between the two winners, and two other essays received the accessit.
Arago preserved a remark of Joseph-Louis Lagrange, then a leading figure at the Berlin Academy, in a letter to Condorcet dated 8 June 1778. Lagrange wrote that the piece would have won the entire prize had it applied the theory to a particular comet, a condition that was in the programme. Arago explained that Condorcet had an extreme aversion, in his own words, to calculations that demand much attention without engaging it, which accounts for the division of the award. Lagrange himself contributed further work on the same problem to the Berlin Academy’s memoirs in 1778 and 1783.
Publication
The essay was published in the volume Dissertations sur la théorie des comètes qui ont concouru au prix proposé par l’Académie royale des sciences et belles-lettres de Prusse pour l’année 1777 et adjugé en 1778. The volume was printed in French at Utrecht by Barthélémy Wild in 1780. Catalogue records describe the book as a quarto of roughly 239 pages (the pagination has an error, 239 for 237), including 3 engraved plates and 7 folding tables. The title page notes that the dissertations were published with the permission of the Academy.
The volume brings together the following contributions:
- Condorcet’s Essai sur la théorie des comètes, which opens the collection.
- Georg Friedrich von Tempelhoff’s Essai sur la solution du problème: déterminer l’orbite de la comète par trois observations, the other prizewinning piece.
- Johann Friedrich Hennert’s Dissertation sur le problème où il s’agit de déterminer l’orbite parabolique d’une comète.
- A second contribution by Hennert, Mémoire sur la théorie des comètes.
Hennert (1733–1813), a mathematician at Utrecht, was also a contestant in the competition. Because the volume collected the competing essays, it served as a reference work on contemporary approaches to the cometary-orbit problem. It reached scholars across Europe, and the Portuguese mathematician José Monteiro da Rocha, who was working independently on parabolic comet orbits, is documented as having received the Utrecht volume containing the Berlin dissertations by Condorcet, Tempelhoff and Hennert.
Manuscript and reception
A manuscript copy of the essay survives in Paris. The Condorcet Inventory, a database of the academician’s manuscripts and printed works, lists a corrected fair copy of the Essai sur la Théorie des Comètes, held at the Bibliothèque de l’Observatoire in Paris (Z 43).
The essay is generally treated as one of the last major pieces of Condorcet’s purely mathematical-astronomical work. A biographical note from his modern publisher states simply that he won a prize at Berlin for a Théorie des comètes. His interests turned increasingly towards probability, the analysis of collective decisions and political reform. His most celebrated mathematical work after this period was the 1785 Essai sur l’application de l’analyse à la probabilité des décisions rendues à la pluralité des voix, which contains the results now known as Condorcet’s jury theorem and Condorcet’s paradox. The theory of comets had meanwhile advanced through the contributions of Lagrange and Laplace, and the Berlin competition remains a documented episode in the history of the cometary-orbit problem.
Editions
The work first appeared in the 1780 Utrecht volume. It was later listed among Condorcet’s physical works in the nineteenth-century Œuvres and in French bibliographies, and the text is catalogued among his writings on Wikisource. Original copies are held by research libraries, including the Austrian National Library, whose digitised example is available online.
