Abstract
Lazare-Nicolas-Marguerite Carnot was born on May 13th, 1753 into a bourgeois family from Bourgogne in France, which occupied a remarkable position in local society. Claude Carnot, his father, was a lawyer and public notetaker in Nolay, a small city close to the Côte-d′Or. The place where Lazare Carnot was born has not changed significantly over time and still belongs to Carnot′s family to this day.
If the principle of inertia force, of composed motion, and of equilibrium, are essentially different one of the other, as we cannot prohibit to happen; and if on the other hand these three principles are sufficient to mechanics, one can reduces this science to the least number of principle possible, and assume that it is established on these three principles all bodies' law of motion for any circumstances, as I have accomplished in this work.
(Jean Le Rond d'Alembert—Preliminary Discourse to Dynamics Treatise, G. Villars et Cia., Editors, Paris, 1921.)
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Notes
- 1.
It is also very popular his Essais sur l´histoire génerale des mathematiques, in two volumes.
- 2.
The most known Camus's works are: Élements de géometrie théorique et pratique (1750), Élements de mécanique statique (1751) and Élements d´arithmetique (1753).
- 3.
Coulomb's memoir entitled Théorie de machines simples will be analyzed in depth in the next chapter.
- 4.
This work adopts the Leibnizian approach to investigating differential calculus and tries through the theory of limits to eliminate some conceptual inconsistencies and improve its algorithmical aspects, which was a Leibnizian characteristic.
- 5.
The Brazilian historian Carlos Guilherme Mota analyzes this movement and affirms: It is the radical proposal to a new society which births from the interior of Revolution. He continues: With the takeover of power, it doesn’t make sense to propose a Democratic and Liberal Assembly, but to organize the revolutionary dictatorship for the necessary time to implement the new society. As we know, the movement was defeated after being denounced to Carnot by a militant whose name was Grisel. Carnot, in the position of a strong man of the regime, appointed Cochon de Lapparent on April 3rd of 1796 as the minister of police, a famous enemy of the Jacobins, which commenced the struggle against the “communists”. See (Mota 1989), p. 183.
- 6.
Lazare Carnot and Sophie Dupont had three sons: their first, also named Sadi, was born in 1794 but soon died in 1796. The second Sadi Carnot, born on July 1st, 1796, was a physician and founder of thermodynamics, while his brother Hippolyte was born on April 6th, 1801 and died on March 13th, 1888. He was a deputy, senator and minister of public instruction, as well as a member of the Institute of France.
- 7.
Andrè Fridberg describes Carnot's death: Carnot's death seems has been relatively brief. He suffered of digestive perturbations, and did not take care according with his son, besides the advices received of his family. When he agreed to receive a doctor he spent the time for the interview to discuss scientific and political questions without speaking about the disease. Some days later, Lazare woke up early morning, as usually done in other days, made the toilet and shave himself. Getting fatigued, goes to bed, and during the day expired without apparent suffering. See (Fridberg 1978), p. 221.
- 8.
In the mechanical field, as we mentioned before, the works which we need to note are those of d'Alembert, Euler, Coulomb, Carnot and Lagrange.
- 9.
Obviously, the political process led the great scientist to death and involved more complex reasons than a simple identification of him with the “ancient régime” due the place he occupied within it. Kahane (1974) in Chap. 2, did an analysis of Lavoisier´s social position, his political alignments and contradictions in order to try to explain his condemnation and death. He states: Lavoisier, a bourgeois of origin, tried to become a finance man and therefore associated with the “Ancient Régime”; he also tried to become a big land farmer, being assimilated with the owners of agrarian richness, the rural aristocracy. He belonged then in a double sense to marginal fractions of bourgeoisie, that to be displaced from power by Revolution, and thus it happened with the incidents and the dramas of the process.
- 10.
As we know, Buffon translated Newton´s Calculus of fluxions, to which we had previously referred in Newton (1994) in Chap. 2.
- 11.
This is a panoramic vision of the main scientific developments in the century of the Revolution. For a more detailed study, we recommend the work of the group REHSEIS edited by Rashed (1988).
- 12.
This was already analyzed in detail when the conception of force was discussed in Chap. 2.
- 13.
Indeed, the principle of action and reaction, known as Newton's third law, could represent a conservation principle if we consider the interacting bodies as a system. Thus, visualizing the third law in this manner is much more convenient for any study of the problems of shocks like Carnot's.
- 14.
The concept of geometric motion will be studied in detail in Chap. 6.
- 15.
It is worth remarking that Carnot made a rupture with the essentially rationalist tradition that came from d'Alembert and continued through Lagrange in which mechanics is seen as a branch of pure mathematics and experience as a kind of purely rational legitimation of that principle. Carnot would adopt a kind of empiricism that came from the English school and Newton as he continued to attribute to reason a fundamental role within the system of knowledge in establishing the causal nexus in the formation of laws.
- 16.
In Chap. 7, we will see in Coulomb’s work one of the first and most consistent investigations into mechanical friction, one of the most important forms of resistance to motion. Later on, Coriolis and Poncelet studied one of the general forms of driven force utilization to surpass any resistance and created applied mechanics with other polytechnician engineers.
- 17.
We will study Lazare Carnot’s concept of convertibility at the moment of analyzing the concept of geometric motion in more depth and try to relate this concept to the studies of Sadi Carnot on thermal machines.
- 18.
We are referring to Galileo´s studies about the fall of bodies on an inclined plane which led him to his inertia law.
- 19.
- 20.
In Antonio Drago´s paper entitled: Le lien entre mathematique et physique dans la mécanique de Lazare Carnot, on (Charnay 1990), p. 501, we find several important remarks about Carnot’s notion of geometric motion. The author emphasizes that, to understand this notion well, it is necessary to eliminate certain ambiguities left by Carnot, the obscure points being: (a) Carnot gives two different definitions of geometric motions. (b) He states several times that geometric motions are infinitesimal, and yet, at the same time, he considers them to be finite. (c) Carnot gives local definitions of geometric motions, but later on, he uses this concept from a global viewpoint, i.e., to the whole system. (d) Carnot uses geometric motion in an equation, called the second fundamental equation, where a logical derivation is neither clear nor incorrect. The author only considers geometric motion as a global motion and infinitesimally assumed or accomplished over the system if the opposite motion is possible. In other words, the fundamental characteristic of the geometric motion is its reversibility.
- 21.
It is a living force balance in which the losses due to shocks are transformed into equivalent terms to living forces.
- 22.
It is important to note that the concern with the efficiency of machines is still present in Carnot and will be developed in a wide sense by the polytechnician engineers Navier, Coriolis and Poncelet. However, we should mention the influence of Coulomb´s work about the force of men on the argumentation used by Carnot.
References
Charnay JP (1990) Lazare Carnot ou Le Savant-Citoyen. Presses de l′Université de Paris-Sorbonne, Paris
D’Alembert JL (1921) Traité de Dinamique, vol 2. Gauthier-Villars et Cie Éditions, Paris
Fridberg A (1978) Sadi Carnot, Physician et les “Carnot” dans l′Histoire. La pensée universelle, Paris
Gillispie CC, Youschkevitch AP (1979) Lazare Carnot Savant et sa Contribuition a la Théorie de l′Infini Mathematique. Librairie Philosophique J. Vrin, Paris
Mota CG (1989) The french revolution (in Portuguese). In: Atica SA (ed) Sao Paulo
Oliveira ARE (2004) The contribution of coulomb to applied mechanics, Proceedings HMM 2004 Symposium, Kluwer Academic Publishers, p 217–226
Rashed R (1988) Sciences a l′Epoque de la Revolution Française (Recherches Historiques). Librairie Scientifique et Technique Albert Blanchard, Paris
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Oliveira, A.R.E. (2014). Lazare Carnot’s General Theory of Machines. In: A History of the Work Concept. History of Mechanism and Machine Science, vol 24. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-7705-7_5
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