Abstract
As we have already commented, d’Alembert presents the general principle of dynamics in a somewhat different way from the Traité de Dynamique [§.1].
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Notes
- 1.
We note that this paragraph was not in the Mss.7.
- 2.
D’Alembert uses the sign minus, probably expressing that the velocity is decreasing.
- 3.
This paragraph does not have an antecedent in the Manuscript.
- 4.
A classic text such as the Hydrodynamics of Horace Lamb states: “The fundamental property of a fluid is that it cannot be in equilibrium in a state of stress such that the mutual action between two adjacent parts is oblique to the common surface”. The first edition was published in 1879. We quote the reprinting of the sixth edition in the Cambridge University press, 1945. Cf. p. 1.
- 5.
The question was either the Earth was flattened or elongated at the poles. Newton opted for the first solution as a result of his theory of gravitation. As he stated in the Principia, assuming our planet as a fluid in rotation, if two channels were driven to the center, one from one pole and the other from the equator, both must be in equilibrium but the latter will be alleviated due to the centrifugal force, therefore equator channel must be longer than the pole one. As a consequence he estimated the flattening in 230/231.On the other hand was the Cartesian theory of gravitation, in which external vortices were responsible for the attraction of the bodies. These vortices dragged the bodies towards the center of the earth, an action which Descartes denominated “conatus”. With this theory the magnitude of the flattening should be less than the Newtonian one, in a value of 576/577.
In counterpoint to these values stood the geodesic measurements of the meridian arcs made in France at the end of the eighteenth century by such distinguished geometricians as Picard and Cassini. From those it was concluded that the Earth had an oblong shape, stretched towards the poles, with a difference in diameters of 1/262. This opposition between the theoretical derivations and experimental measurements, together with the difficulty of accepting the theses of Newtonian mechanics, radicalized the scientists’ positions, and divided the Academy of Sciences of Paris, and even came to have national and theological implications. In words of Lafuente “Theory vs. experiment, Newtonianism vs. Cartesianism, laicism vs. scholasticism, savant vs. Academic, England vs. France, all were, in the end, powerful alternatives to stir up controversy and kindle all the passions” (p. 48).
The controversies caused rivers of ink to run, but their positive side was that the Academy of Sciences of Paris sponsored two important scientific expeditions: one to Lapland and the other to the Spanish Viceroyalty of Peru, in present-day Ecuador. The aim of both was to measure the meridian arcs in two very separate latitudes. With these measurements, together with those made in France, the intention was to obtain the longitude of a meridian degree at various points of the Earth, and thus to clarify the value of the Earth’s flattening. It was a crucial experiment about whose was the true theory: whether it was that of Newton or that of Descartes.
- 6.
In the Manuscript, it is only quoted the second work as Paris 1740, p. 210, prop. 1, art. 3.
- 7.
Cf. Traité, §XVI–XVII.
- 8.
Truesdell wrote that this chapter contained many propositions and corollaries which were incomprehensible for him [p. LII]. We will try to solve some of these incomprehensibilities and uncertainness scrutinizing the Manuscript in order to untangle what d’Alembert’s original thoughts could have been.
- 9.
“Nam siquidem particulæ fluidi extra spatium [Σ] positæ, multis (hyp.) viribus agitantur” Mss.25. “Because the fluid particles placed outside Σ are impelled by many forces [hyp.].
- 10.
In the Essay says “the variable force ψ” which we think is a lapse for “the force ψ”, as expressed in the Manuscript [Mss.27].
- 11.
The narrative description given in the Essay for this figure does not correspond at all with the depicted as Fig. 3.6 in the Essay [§.30]. The one we show here is similar to that given in the Manuscript as Fig. 12.
- 12.
See Annex I.
- 13.
As we have mention previously, Guilbaud analyzes the antecedents of this formula in the Traité de l’équilibre.
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Simón Calero, J. (2018). The Preliminaries. In: Calero, J. (eds) Jean Le Rond D'Alembert: A New Theory of the Resistance of Fluids. Studies in History and Philosophy of Science, vol 47. Springer, Cham. https://doi.org/10.1007/978-3-319-68000-2_16
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