Abstract
It is difficult to trace the history of most physical concepts. This is also true for the concepts of work and energy. One line of investigation has been the process of the invention and construction of machines. In different ages, machines and devices invented to save work have always been researched for a variety of aims.
The history of science offers no more surprising case than the phenomenon of simultaneous discovery. We have already named twelve members of the scientific community, each of whom, within a brief period, independently reached the essentials concerning the concepts of energy and its conservation. This list could be extended, in vain, however. This multiplicity already sufficiently suggests that in the two decades prior to 1850 the climate of European scientific thought contained elements capable of guiding receptive scientists to a significant new point of view about nature.
(KUHN, Thomas S. La Tension Esencial. México: Fondo de Cultura Editores, 1996)
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Notes
- 1.
In René Dugas (Dugas 1988), p. 32, we read: “Everything indicates that Heron of Alexandria lived during the second century of our era. His treatise Mechanics discusses certain simple machines like the lever, the block and pulley, and the screw, separately or in various combinations. The treatise is only available in an Arabian version into which it was translated and published by Carra de Vaux”.
- 2.
Aristotle’s works on physics are not contained only in his Physis. We also have the treatise on the heavens, meteorology, and on the heavens and the generation of corruption. The study of motion can be found in books ll and lll, (Aristotle 1999) p. 96 and ff.
- 3.
D’Alembert dedicates Chapter IV of his Dynamic Treatise, Vol. II, to the principle of the conservation of vis viva. He enunciated it and made a demonstration for diverse particular cases, including the case of fluids. Commenting on the application of this principle by other geometers, as he called them, d’Alembert affirms: “Huygens is the first, that I know of to mention these two principles, and Bernoulli the first to make use of them in order to resolve elegantly and easily diverse problems of dynamics. What I intend to present in this chapter, if not a general demonstration for all cases, are at least sufficient principles to find the demonstration in each particular case”, p. 163. And on p. 185: “Daniel Bernoulli, in his excellent work entitled ‘Hydrodynamics’, presents the laws for the movement of fluids in vessels for the conservation of vis viva, but without a demonstration”.
- 4.
Huygens in (Huygens 1973), p. 48, in his proposal X, affirms: If a moving body falls vertically, or descends along some surface, and is considered to be carried up again by the impetus along some other curve, it will always have the same velocity at points with the same height when ascending as descending. In proposition IV, p. 108, we read: If a pendulum composed of several weights and released from rest were to traverse some part of its complete oscillation, and then its individual weights were imagined, under release from constraint to convert their acquired speeds upward and to ascend as far as they can, when this has occurred, the center of gravity composed of all of them will have returned to the same height that it had before the oscillation began.
From the above citations, we can observe that Huygens took the first steps parting from Galileo’s study of falling bodies, in the sense of a balance of potential and kinetic energy, which is not yet an application to machines of the principle of the conservation of the vis viva. He {Huygens} refers his readers to his “Treatise on Equilibrium and the Movement of Fluids”, where the principle is demonstrated in a general way see (d´Alembert 1921).
- 5.
Regarding the influence of Descartes on Newton, Alexandre Koyré sees in the title “Principia” an evident reference to “Principles of Philosophy”, although in opposition. It emerges to the extent that Descartes’ work presents, as the solution for the problem of motion, a mixture of metaphysics and physics. While Newton, when speaking about “Mathematical Principles”, tries to benefit from the Galilean revolution, namely, the mathematicization or geometricization of nature. In short, this means mathematical principles in opposition to principles of physics and natural philosophy in opposition to speculative philosophy.
- 6.
In the next chapter the history of analytical mechanics will be studied in detail.
- 7.
See (Oliveira 2004).
- 8.
Jean-Pierre Séris sums up Parent’s contribution as follows: “While in the machine in equilibrium, the velocity of the fluid (squared) is taken absolutely as a component of the effort on the area, it is the difference in the velocity of the fluid–velocity of the area which, squared, intervenes in the calculation of the current’s effort on the area in motion. This principle, as we shall see, does not introduce any new concept, but adopts an unprecedented procedure”. See (Séris 1987) p. 290.
- 9.
On p. 296, Seris (Séris 1987), affirms: “In reality, Henri Pitot (1695–1771) who in his paper of 1725 entitled ‘New Method of Knowing and Determining the Effort for all Kinds of Machines Moved by a Current or Fall of Water’, would present things in this clearer more coherent manner. Knowing that he must obtain the maximum quantity (V–v), Pitot initially ‘calculated the velocity that the blades of a machine would have to reach in order to produce the maximum possible effect’. This new presentation, more intelligible and more intelligent than Parent’s idea, should not be underestimated. This is what would later popularise (the idea) allowing it to reach a wider informed public. (Euler, Mc Laurin, Daniel Bernoulli), men involved in art (Bélidor) and experimentalists (Deparcieux, Smeaton)”.
- 10.
Daniel Bernoulli, in (Fourier 1789), dedicated all of Chap. 9 to the application of his theory of fluids to machines. The title of this chapter is quite suggestive: Concerning the Movement of Fluids Which are not Impelled by Their Own Weight, but by an External Force, Particularly Hydraulic Machines and their Highest Degree of Perfection Attainable, and How this can be Perfected Later Through the Mechanics of Solids as well as that of Fluids. This chapter is divided into three parts, namely: Part One–Concerning hydraulic machines expelling water upwards without appreciable impetus. Part Two–Concerning hydraulic machines transporting water without appreciable impetus from a lower to higher position. It is precisely in this section, that on p. 202, his famous mechanical principle (known as) Rule 10, explicitly appears as a mechanical principle, which he applies to fluids; and which he later applies to the case of Archimedes’ screw. Part Three - Concerning machines which are moved by the impact of a fluid, in the same way as the force of the wind. This title refers, evidently, to a water wheel, in which the fluid communicates its free-fall motion to the blades of the wheel, causing it to turn. Bernoulli considered that if the fluid had a velocity V, we must consider the relative velocity (v–V) as driving the machine. He also made several considerations on the motion of the blade, placing an algebraic equation between v and V, whose maximum is V = 1/3 v.
- 11.
For a consistent study on the history of the VWP, see (Poinsot 1975). However, this author commits a mistake when he attributes adoption of the term “work” to Poncelet, instead of to Coriolis.
- 12.
Archimedes, in his “Concerning the Equilibrium of Planes” or “The Centres of Gravity of Planes”, Book I at (Poinsot 1975) uses the principle of the lever to study the gravity of flat figures.
- 13.
In the second section of his “Mécanique Analytique”, p. 12, (Lagrange 1989), we read: “The general law of equilibrium in machines is that the forces or potencies are between themselves, reciprocally like the velocity of the points at which they are applied, estimated according to the direction of these potencies. It is this law which contains what we commonly call the “Principle of Virtual Velocities”. This was recognised after a long time as the fundamental Principle of Equilibrium, already shown in the previous section, and which may consequently be considered a kind of axiom of mechanics”.
- 14.
In 1608, Stevin assembled several works which he called “Hypomnemata Mathematica”. They were translated into French in 1634. According to René Dugas, (Dugas 1988), Stevin’s static is developed geometrically in a very similar way to that used by Archimedes. With regard to the Principle of Virtual Veocities, we can find it in Volume IV of his “Hypomnemata”, where he deals with the equilibrium of a system of pulleys.
- 15.
In March of 1751, Koenig, professor at La Haye, and a member of the Berlin Academy, asserted that Leibniz was the first to formulate the principle of least action. This affirmation was based on a letter from Leibniz to Hermann dated 16th October 1707, whose autheticity was questioned by several scholars of the matter. See (Gueroult 1967).
- 16.
Although this correspondence has never been found, Leibniz pronounced several times on the principle of least action, it is not improbable that he himself was the first to formulate this principle. Maupertuis’ defenders, however, argue that he was responsible for the thoroughness and precision of the formulation. See (Gueroult 1967).
- 17.
For a detailed exposition of Maupertuis’ principle, as well as the paper cited, see Suzanne Bachelard at (Actes de La Journée Maupertuis 1975), p. 99.
- 18.
According to Moreira (Moreira 1998), Lanczos in his “The Variational Principles of Mechanics” affirms that Euler discovered the Principle of Least Action independently of Maupertuis.
- 19.
As we know, Lagrange in his “Mécanique Analytique”, postulated a general formulation of the Principle of Least Action for a system of interacting n bodies. See (Lagrange 1989).
- 20.
- 21.
Maxwell, in his introduction to Faraday’s, book reference (Faraday 2003), describes the discovery of the phenomenon of the induction of electric currents by magnetic fields. “In December of 1824, Faraday had tried to obtain an electric current by means of a magnet. On three occasions, he made three fruitless complex attempts to produce a current in a wire by means of a current in another wire, or by means of a magnet. Even so, he persevered. On 12th August 1831 he obtained the first proof that an electric current could induce another current in a different circuit… This was his first successful experiment. During a further nine days of experimenting, he reached the results described in his first series of “Experimental Researches”, read before the Royal Society on 24th December 1831”.
- 22.
In September of 1820, in the Academy of Science session following that in which Oersted’s experiments were announced in France, André-Marie Ampère published his first observations on the magnetic actions of electric currents. He showed the Academy that electric currents mutually attracted and repelled each other and followed those discovered laws which he called electrodynamics and which were fundamentally important for the elimination of magnetic fluids from science. Georg Simeon Ohm, began his experiments with electric currents in 1825. He used Volta’s battery and later replaced it with copper-zinc thermoelectric elements, and could in this way establish the famous law which carries his name. See (Taton 1995), pp. 210∼215.
- 23.
In the next chapter, we approach in more detail, the so-called Laplacian project, with its influences and limitations.
- 24.
Joseph Fourier could be considered the first typical mathematician-physicist. His studies on heat propagation date from 1807, or earlier, and were gathered in a paper presented to the Academy of Science in 1811. His work “Théorie analytique de la chaleur”, was published in 1822. In the solution to his famous equation on partial second-order derivatives he presents the development of Fourier’s series. See (Fourier 1988).
- 25.
Sadi Carnot was fully aware of the importance of the changes that the development of the steam engine and its employment in diverse branches of the economy would bring for society. In the first pages of his celebrated essay, we read: “The study of these engines is of the greatest interest, their importance is enormous, their use is continually increasing, and they seem destined to produce a great revolution in the civilized world. Already the steam-engine works our mines, impels our ships, excavates our ports and our rivers, forges iron, fashions wood, grinds grain, spins and weaves our cloths, transports the heaviest burdens, etc. It appears that it must some day serve as a universal motor, and be substituted for animal power, water-falls, and air currents. Over the first of these engines it has the advantage of economy; over the other two, the inestimable advantage of power which may be employed at any time and in every place, and will never suffer an interruption in its work”. See (Carnot 1990), p. 2.
- 26.
Frensel’s wave theory was a decisive contribution for the abandonment of the imponderable fluids theory. The origin of his work lies in the opposition not only to the scheme of imponderable fluids, but also to Laplace’s corpuscular theory of light and the caloric theory for heat. At the start of these works, around 1814, Frensel wrote that he suspected that light and heat were in some way connected with the vibrations of a fluid. His commitment to the concept of light as a kind of motion of a medium, was basic for his optics theory in terms of the motion of wave propagation in a medium, luminiferous ether. See (Harman 1982), p. 21.
- 27.
Einstein, in one of five articles published in 1905, would study Brownian motion and define a diffusion coefficient for particles in suspension, on the basis of the dimension of the particles, the viscosity of the fluid, its temperature and the Avogadro number. Following the inverse route, that is, having a way to measure this diffusion coeficient, it is possible to experimentally determine the Avogadro number. See (Les Génies de la Science: Einstein and Maio 2002), pp. 26 and 27.
- 28.
Joule’s first works concentrated on the perfection of electromagnets, the manufacture of galvanometers and on the properties of voltaic currents. After 1841 he concerned himself with the heat generated by electrical circuits and by electromagnetic machines. It was this work which led to his famous law.
- 29.
The experimental procedure adopted by Joule consisted in repeating twenty times the process of agitating a liquid by the movement of weights and measuring the final temperature of the agitated liquid. The walls of the recipient containing the liquid were hermetic and made of very thick wood, suitably treated to minimise any heat loss through convection or radiation. His conclusions were as follows: 1) the amount of heat generated by the friction of bodies, whether liquid or solid, is always proportional to the quantity of mechanical work expended; 2) the amount of heat capable of raising the temperature of 1 pound of water (weighed in a vacuum at a temperature between 55° F and 60° F) by 1° F requires for its evolution the expenditure of a mechanical force required by the fall of 772 pounds (350,18 kg) through the space of one foot (30,48 cm). Between 1845 and 1847, Joule repeated these experiments using water, whale oil and mercury, obtaining for these compounds the mechanical equivalents equal to 781.5 lb; 782.1 lb and 786.6 lb, respectively. See (De la Colin 2003), p. 31.
- 30.
It is common to consider the influence of Immanuel Kant (1724-1804) and even that of Leibniz and dynamism on Schelling. For the first two thinkers, the first concept is the inherent force of matter.
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Oliveira, A.R.E. (2014). The Ideas of Work and Energy in Mechanics. 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_3
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