Antoine Cavalleri (1698–1765) was a Jesuit professor of mathematics at
Cahors
Cahors (; oc, Caors ) is a commune in the western part of Southern France. It is the smallest prefecture among the 13 departments that constitute the Occitanie Region. The main city of the Lot department and the historical center of the Quer ...
during much of the
French Enlightenment in the 18th century, until late in the reign of
Louis XV of France.
Intellectual climate of the age
During the early years of the 18th century
Isaac Newton's work on gravity was still incompletely accepted in France and
Descartes' vortex theory had not yet been conclusively superseded. One result was the difficulty of formulating and establishing a coherent and compelling explanatory theory of tidal action. The French ''Académie Royale des Sciences'' both supported practical research into tidal effects, and offered a prize for the best essay to establish the topic on a sound mathematical and theoretical footing.
Three essays were selected for prizes, all of them by supporters of Newtonian theory. They were
Daniel Bernoulli,
Leonhard Euler
Leonhard Euler ( , ; 15 April 170718 September 1783) was a Swiss mathematician, physicist, astronomer, geographer, logician and engineer who founded the studies of graph theory and topology and made pioneering and influential discoveries in ...
, and
Colin Maclaurin
Colin Maclaurin (; gd, Cailean MacLabhruinn; February 1698 – 14 June 1746) was a Scottish mathematician who made important contributions to geometry and algebra. He is also known for being a child prodigy and holding the record for bei ...
. However, it was rumoured by
Pierre Louis Maupertuis
Pierre Louis Moreau de Maupertuis (; ; 1698 – 27 July 1759) was a French mathematician, philosopher and man of letters. He became the Director of the Académie des Sciences, and the first President of the Prussian Academy of Science, at the ...
that the reason that Cavalleri was added to the list of winners was that one influential judge among those selecting the winning essays was
René Antoine Ferchault de Réaumur
René Antoine Ferchault de Réaumur (; 28 February 1683, La Rochelle – 17 October 1757, Saint-Julien-du-Terroux) was a French entomologist and writer who contributed to many different fields, especially the study of insects. He introduced t ...
, who favoured Decartes' vortex theory, and who insisted that at least one winner should be a supporter of that view, though by that time it was rapidly losing ground and leading workers in the field already were rejecting it. As a sop for Réaumur, his colleagues consented to include an arbitrary choice of essay supporting the vorticist view. Cavalleri not only was fairly prominent in his own right, but had recently won two prizes from the ''Académie de Bordeaux'' for his essays: "''Opacité et diaphanéité des corps''" in 1738 and "''Chaleur et froideur des eaux minérales''" in 1739, so he was a convenient choice.
Cavalleri's obscurity
Though competent, Cavalleri is little remembered. He was perhaps doubly unfortunate; firstly, in an age that produced figures such as the Bernoulli family, Euler,
Lacaille
Abbé Nicolas-Louis de Lacaille (; 15 March 171321 March 1762), formerly sometimes spelled de la Caille, was a French astronomer and geodesist who named 14 out of the 88 constellations. From 1750 to 1754, he studied the sky at the Cape of Good ...
,
D'Alembert
Jean-Baptiste le Rond d'Alembert (; ; 16 November 1717 – 29 October 1783) was a French mathematician, mechanician, physicist, philosopher, and music theorist. Until 1759 he was, together with Denis Diderot, a co-editor of the ''Encyclopédie ...
,
Reaumur, and
Lagrange, even a prominent professor of mathematics is easy to overlook. Secondly, Cavalleri's essay on tides, though penetrating in that he recognised debatable points in both Cartesian and Newtonian theory, amounted to the last substantial support for the Cartesian theory of vortices; in effect a futile rearguard action. It is true that Fontenelle has been referred to as the last defender of the vortices,
[Grégoire François. Le dernier défenseur des tourbillons : Fontenelle.. In: Revue d'histoire des sciences et de leurs applications, tome 7, n°3, 1954. pp. 220–246. doi : 10.3406/rhs.1954.3438 http://www.persee.fr/doc/rhs_0048-7996_1954_num_7_3_343] but unlike Cavalleri he wrote as an interpreter and populariser, rather than as an analyst or formulator of material theory.
On the one hand Cavalleri's objection to Descartes' theory was mainly that it effectively dismissed the obvious tidal influence of the sun. On the other he rejected Newton's theory of remote gravitational attraction. The latter idea might seem naive, but even in 21st century theoretical physics there are echoes of dissatisfaction with the concept of
action at a distance
In physics, action at a distance is the concept that an object can be affected without being physically touched (as in mechanical contact) by another object. That is, it is the non-local interaction of objects that are separated in space.
Non- ...
. He tried to construct a theoretical basis for an inverse square law of gravitational attraction arising from Cartesian vortices. Newton however, had already raised theoretical objections to Descartes' vortex theory, and Cavalleri not only failed to refute the objections, but misinterpreted a modified vortex theory by
Philippe Villemot[Villemot, Philippe. Nouveau systëme, ou, Nouvelle explication du mouvement des planëtes]
/ref> which attempted to reconcile vortices with Newtonian attraction.
Cavalleri's essay, although having received the prize from the Académie, more or less lapsed into obscurity thereafter. Possibly this was because of its being biased towards Cartesian rather than Newtonian gravitational theory; Pope Benedict XIV had ordered two priests to produce a new, annotated edition of Philosophiæ Naturalis Principia Mathematica, Newton's ''Principia''. In the commentary the other three winning essays were included, but Cavalleri's was omitted.
Works
* ''Opacité et diaphanéité des corps'', winning essay for ''Académie de Bordeaux'', 1738
* ''Chaleur et froideur des eaux minérales'', winning essay for ''Académie de Bordeaux'', 1739
* ''Pièces qui ont remporté le prix de l'Académie royale des sciences, en MDCCXL. sur le flux et reflux de la mer'' winning essay for ''Académie Royale des Sciences'', 1740
References
{{DEFAULTSORT:Cavalleri, Antoine
1698 births
1765 deaths
18th-century French Jesuits
18th-century French mathematicians
People from Cahors