Hegel and Newtonianism pp 383-397 | Cite as

# The Concept of Force in Eighteenth-Century Mechanics

## Abstract

If one wanted to characterize the general scientific approach of the eighteenth-century by means of a single concept, there would be much to be said for selecting the notion of *force*. Newton’s *Principia* (1687) had unified the laws of terrestrial mechanics and planetary motion by propounding a mathematical conception of force applicable in principle within every field of natural philosophy. Discussion of the universal principles and characteristic quantities of motion had entered a new stage as a result of the publication of this book. The plan to extend the application of the conception of mechanical force to the fields of optics and chemistry was explicitly formulated by Newton in his *Opticks* (1704), and developed into what was to become the general paradigm of Newtonian physics.

## Keywords

Centrifugal Force Eighteenth Century Circular Motion Uniform Motion Universal Principle## Preview

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## Notes

- 1.Freind and Keill were the most important Newtonians in Britain at that time. See Cassirer, 1974, II, pp. 401ff., 421ff.; cf. Rosenberger, 1895, pp. 342ff., 359ff., Guerlac, 1981, pp. 41-74.Google Scholar
- 2.For the first reactions to Newton’s physics in France, see Rosenberger, 1895, pp. 354ff.Google Scholar
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- 8.Cohen, 1978, p. 166.Google Scholar
- 9.For example: Newton
*Principia*bk. 3, prop. 4, theor. 4, scholium; bk. 3, prop. 5, theor. 5, scholium.Google Scholar - 10.Cohen, 1978, p. 48.Google Scholar
- 11.See Newton’s use of the term
*centrifugal*in the*Principia*bk. 1, prop. 4, theor. 4, scholium, the interpretation of this provided by Westfall, 1977, pp. 145-148, and the correct description of the force in Baumgartner, 1829, § 252, p. 193. Böhme, 1988, brings out the importance of the concept of the centrifugal force in Newton’s development of hydrodynamics: see the*Principia*bk. 2, sect. 5, prop. 23, theor. 18; sect. 7, prop. 33; sect. 7, prop. 33, cor. 3; sect. 7, prop. 33, cor. 6: bk. 3, prop. 4, theor. 4, scholium; prop. 19, prob. 3. In all these cases, Newton treats the centrifugal force as having a component opposed to the centripetal force. Elsewhere, he maintains that the centripetal becomes a centrifugal force when the path changes from a parabola to a hyperbola: bk. 1, prop. 10, prob. 5, scholium; prop. 12, prob. 7.Google Scholar - 12.f = ma.Google Scholar
- 13.The new co-ordinates may be
*x*;*w*is the rotating velocity:*f*_{eff}=*f-2m*(*w*· d*x*/d*t*)-*mw*(*w*·*x*). Cf. Goldstein, 1963, p. 149.Google Scholar - 14.Newton
*Principia*, law 2.Google Scholar - 15.Newton
*Principia*, bk. 3, rule 3.Google Scholar - 16.Newton
*Principia*, def. 3.Google Scholar - 17.Wolff, 1978, pp. 16ff., 320ff. — but Wolff did not always succeed in describing centrifugal force in a correct way (pp. 321, 328).Google Scholar
- 18.Newton seems to adopt the main features of Descartes’ principle of inertia from the second law stated in Descartes, 1644, II. Part, § 39.Google Scholar
- 19.Cardwell, 1966, pp. 209-224.Google Scholar
- 20.Kant, 1746, discusses the notion of force in the Leibnizian tradition.Google Scholar
- 21.Cf. Freudenthal, 1982, pp. 46ff., 61ff.Google Scholar
- 22.See also Bernoulli, Joh. 1742, chap. V, §§ 2, 3,
*Opera omnia*III, p. 35f.Google Scholar - 23.Leibniz, 1982, p. 13 (1695);’ s Gravesande tried to confirm this by experiments:’ s Gravesande, 1748, pp. xii, xx, xxvf., 229ff., 245ff., and Musschenbroek, 1741
^{2}. Musschenbroek argued that even a body which is at rest can transfer motion to another body (§ 196, p. 78).Google Scholar - 24.Here Leibniz, 1982, refers to Newton’s
*Principia*(1687), from which it can be inferred that the various notions of force are being respected.Google Scholar - 25.Leibniz, 1982, p. 15.Google Scholar
- 26.The dicussion concerning the impenetrability of matter deserves to be dealt with in more detail. The problem was discussed by Euler, 1773, vol. 1 and, for example, by Hamberger, 1741, §§ 35ff., who says that the impenetrability of matter, as well as its resistence, are induced by the
*vis insita*, which enables the body to move in any direction; § 28 of this work is concerned with the*vis inertiae*.Google Scholar - 27.Cf. Kleinert, 1974.Google Scholar
- 28.In
*France*: Voltaire, 1738; Algarotti, 1745; Fontenelle, 1780; Pluche, 1753ff.; Regnault, 1729-1750; Clairaut, 1747, were important. In*Britain*: Pemberton, 1728, described planetary motion in an orthodox Newtonian manner, without mentioning*centrifugal force*; another common description derived from Martin, 1778; Martin’s book was used by Hegel: cf. Neuser, W. 1990b; Hegel DOP; cf.*Encyclopedia*§§ 245-271; tr. Petry I, 1970. In*Germany*: Erxleben, 1787^{4}— the main source of the physical knowledge of the late Kant; Euler, 1773 ff., vol. 1. Algarotti’s, Pluche’s and Fontenelle’s books were written in Italian or French and then translated into German, and do not give a very precise account of Newton’s theory of planetary motion. Erxleben sometimes conceives of centrifugal force in the right way (§§ 56, 659), sometimes not (§ 660). Martin confused centrifugal force with the force of inertia. Euler, 1773 ff., 1, provides a clear and instructive discussion of the different aspects of Newtonian and Leibnizian physics.Google Scholar - 29.Borzeszkowski and Wahsner, 1978, pp. 19-57.Google Scholar
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*Principia*that she was aware that Newton’s centrifugal force is perpendicular to the tangent of the circle; cf. Châtellet, 1756, I, p. 57; II, p. 15; II, p. 35.Google Scholar - 34.Châtellet, 1740, § 357.Google Scholar
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- 36.Gehler, 1787, vol. 1, pp. 487ff; 494; cf. 1787, vol. 5, p. 194 below. In modern textbooks of experimental physics one still finds this interpretation: Gerthsen and Kneser, 1969, p. 16; Westphal, 1970, p. 68. Bergmann and Schäfer, 1970, vol. 1, pp. 115ff.Google Scholar
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- 42.Zedler, 1737, unwittingly provides an instructive example of the confusion of Newtonian and Leibnizian physics in the article on force; he describes all types of forces as dead or living, but refers only to Newton’s force of
*inertia*(pp. 1681, 1691ff., 1691ff.), not to that of Leibniz; cf. Iltis, 1971, pp. 21-35; Laudan, 1968, pp. 131-143.Google Scholar - 43.Mach, 1933, pp. 39ff.Google Scholar
- 44.Cf. Goldstein, 1963, eh. IX.Google Scholar
- 45.D’Alembert, 1743, p. 14.Google Scholar
- 46.D’Alembert, 1743, pp. 33-34.Google Scholar
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- 52.Philosophische Gesellschaft an der Universität zu Wien 1899, p. 115.Google Scholar
- 53.Boscovich, 1758, pp. xii, xiv, xvi, 35.Google Scholar
- 54.Gren, 1788, provides an excellent discussion of these problems, cf. Adickes, 1924, vol. 1, p. 171.Google Scholar
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