Abstract
The rational mechanics of Galileo, Descartes and Newton was not, then, directly applied to machines and is not surprising that parallelly it was maintained a “corpus” of experimental knowledge, more or less formalized, addressed to practical constructors… It will be necessary to wait until the end of the eighteenth century to that Lazare Carnot’s sciences of machines could be formally integrated to rational mechanics.
The rational mechanics of Galileo, Descartes and Newton was not, then, directly applied to machines and is not surprising that parallelly it was maintained a “corpus” of experimental knowledge, more or less formalized, addressed to practical constructors… It will be necessary to wait until the end of the eighteenth century to that Lazare Carnot’s sciences of machines could be formally integrated to rational mechanics.
(François Vatin—The Work: economy and physics, 1780–1830, PUF, Paris, 1993)
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Notes
- 1.
Again, the relationship between Carnot’s mechanics and Newtonian mechanics appears in the context of Cartesian thought where mechanics was a pure rational science.
- 2.
In Locke’s work (Locke 1973), we can find a discussion of this question in book II entitled: The Ideas, Chap. I, page 165. In the subtitle All the ideas come from sensation or reflection, one reads: “Suppose, then, that a mind is a blank paper, without characters, without ideas; how does it can be provided? From where come this vast stock, which activates the boundless man´s fantasy with a variety almost infinite? From where he apprehend all the reason materials and knowledge? I answer, in one word from the experience. All knowledge is founded in it, and from it derives fundamentally our knowledge itself. Employed in the sensible external objects as well as in the internal operations of our minds, that are realized by us and reflected, our observation provides our understanding with all thought’s materials. From these two sources of knowledge arise all our ideas, or that we have”.
- 3.
Carnot refers to the dispute between Descartes and Leibniz about the quantity that is conserved in the universe, owing to the quantity of motion (according to Descartes) or the living force (according to Leibniz). If the main concern is what better represents the forces of bodies in motion, that would seem to be a semantic question, because each one can be representative, depending on the context.
- 4.
Work appears here as a form of living force.
- 5.
As we have seen, Poinsot (1975) in Chap. 3 makes the critique of the virtual velocities principle as a fundamental principle of mechanics.
- 6.
The decomposition of velocities using the d’Alembert principle transforms cosine law into a conservation principle of mechanics (principle of living forces).
- 7.
Indeed Carnot is trying to generalize the principle of virtual velocities to systems in motion, in spite of being restricted to what he defines as geometric motion.
- 8.
See Oliveira (2004) in Chap. 3.
- 9.
It is possible to find the principles of conservation enunciated by Carnot using the definition of geometric motion.
- 10.
Before Carnot, machines were studied case by case as a succession of particular cases. Carnot had the objective of a general theory of machines.
- 11.
A machine study, even one such as that conducted by Carnot with the purpose of knowing their motions and finding a physical approach to the problem related to forces, cannot be dissociated from the problem of replacing human labour. In other words, economic questions are automatically underlined.
- 12.
This discussion is at the center of the question of energy conservation and can be used in different forms, but is limited to a certain quantity establishing a limit to its capacity to undertake certain work.
- 13.
The fundamental differences between the mechanics of Lagrange and Carnot are that the first studies motion through continuous variations of position and the second through sudden variations, but the quantity known as work plays a fundamental role for both. Another difference between them is related to the methods of analysis. Lagrange uses variational calculus while Carnot applies geometry and trigonometry, which is a revalorization of the physical theories. Thus, geometry, as an ancient form of mathematics, found new possibilities with Carnot.
Reference
Locke J (1973) Ensaio Acerca do Entendimento Humano, Coleção Os Pensadores, Abril Cultural, S. Paulo
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Oliveira, A.R.E. (2014). The “Fundamental Principles of Equilibrium and Motion” of Lazare Carnot. 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_6
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