Essay Review: The Concept of Force: Force in Newton's Physics

Domingo de Soto had made this identification and applied the Merton mean-speed theorem to free fall in 1545. Evidently Soto did not see a contradiction between the proportionality of velocity and time, implicit in this identification, and the widespread belief that in free fall, velocity is proportional to distance. On Domingo de Soto, see Duhem P. , Études sur Léonard de Vinci (Paris, reprint 1955), iii, 263–583 and Wallace W. A. , “The enigma of Domingo de Soto”, Isis, lix (1968) 348–401.

See Clagett M. , The science of mechanics in the Middle Ages (Madison, 1959) 409–16.

On the influence of the various traditions in sixteenth-century Italy, see Stillman Drake's introduction to Mechanics in sixteenth-century Italy, translated and annotated by Drake S. Drabkin I. E. (Madison, 1969) 3–60 and Schmitt's C. B. essay review of this work in Studies in history and philosophy of science, i (1970) 161–75. Galileo mentions the doctrine of the latitude of forms in a manuscript dating from his student days, but if he came across the mean-speed theorem at this time, it evidently made little impression, so that he did not remember it in 1604.

Drake S. , Galileo studies (Ann Arbor, 1970) 218–19. As an alternative, Drake suggests that Galileo may have discovered the odd-number rule by rough experiment, to be distinguished from his later carefully controlled experiments on motion along inclined planes. Of special interest in Drake's account of falling bodies is his analysis of Galileo's demonstration that the proportionality of speed and distance is false. Contrary to a widely held view (founded on faulty translations) that this demonstration is based on the Merton mean-speed theorem, Drake shows that Galileo's argument rests on the idea of one-to-one correspondence between two infinite aggregates. Ibid., 229–37. On Galileo's theory of free fall, see also Koyré A. , Études Galiléennes (Paris, 1939) part 2, 75–99, 128–50.

See Koyré A. , Études Galiléennes, part 3, 151–281.

Two of Drake's papers on the subject, published respectively in 1964 and 1967, are cited in the bibliography.

Drake S. , Galileo studies, 257–77. In Drake's view, Galileo had no unifying principle for all cases of inertial motion.

Westfall remarks that Galileo did not face the issue of how impressed force which is accidental lightness can cause any motion apart from vertically upward motion. Galileo did not, however, restrict the idea of impressed force to accidental lightness but envisaged violent downward motion and even violent horizontal motion as well. In De motu he writes, “My opponents express wonder that the same hand has the ability of impressing now lightness, now heaviness, and now even that which seems neither heavy nor light”, On motion and mechanics, trans. Drabkin I. E. Drake S. (Madison, 1960) 81. Cf. Galileo's memorandum on motion in Mechanics in sixteenth-century Italy, 382.

When he wrote De motu, Galileo knew of Philoponus, whose commentaries were repeatedly reprinted in the sixteenth century. See Mechanics in sixteenth-century Italy, 380. On Philoponus's revision, see Clagett M. , The science of mechanics in the Middle Ages, 433–5 and for a German translation of the whole passage see Johannes Philoponus, ed. Böhm W. (Munich, 1967) 144–58.

Benedetti had also attempted to integrate the ideas of Archimedean hydrostatics and the theory of impetus into a single dynamics. Cf. Clavelin M. , La philosophie naturelle de Galilée (Paris, 1968) 128. There is no evidence, however, that Galileo was familiar with Benedetti's work.

See Moody E. A. , “Galileo and his precursors” in Galileo reappraised, ed. Golino C. L. (Berkeley and Los Angeles, 1966) 23–43. Francesco Buonamico, Galileo's teacher in Pisa, taught the doctrine of self-expending impetus.

Anneliese Maier writes: “[Marsilius von Inghen] sieht im impetus, genau so wie Franciscus de Marchia und Oresme, ein qualitätsartiges Moment … das nur kurze Zeit dauert und dann von selbst vergeht. Diese Auffassung ist dann für die ganze Folgezeit—bis Galilei—die übliche geworden. Die einzigen, die im impetus eine Qualität permanenter Natur gesehen haben, waren Buridan und Albert von Sachsen”. Die Vorläufer Galileis im 14 Jahhrundert (Rome, 1949) 139. She writes further: “Die Impetustheorie Alberts ist ein Gemisch aus den Lehren Buridans und Oresmes, die ja, wie wir gesehen haben, keineswegs ubereinstimmen”. Zwei Grundprobleme der scholatischen Naturphilosophie (Rome, 1951) 260.

Although this is a common view, the influence of Copernicanism on the development of Galileo's mechanics is questionable. Defence of the Copernican system needed the concept of inertial motion (at least circular) and the principle of superposition of motions. Now the concept of inertial motion was embodied in the neutral motion of De motu and this idea provided the basis for the superposition of motions. For there was no difficulty in conceiving of the superposition of some motion directed to a goal and a motion to which a body was indifferent. The difficulty had consisted in conceiving a motion simultaneously directed to two goals. The thesis that Galileo's mechanics and astronomy were independent is discussed by Namer E. , “L'astronomie de Galilée. Sa place dans son oevre et dans l'histoire de la pensée”, in Galilée. Aspects de sa vie et de son oeuvre (Paris, 1968) 173–85 and by Hartner W. , “Galileo's contribution to astronomy”, in Galileo, man of science, ed. McMullin E. (New York and London, 1967) 178–94.

It is not necessary to suppose that Galileo abandoned the self-expending impetus for the permanent kind as a result of becoming acquainted with Buridan's theory. For the permanent nature of Galileo's impeto is an immediate corollary of its association with his neutral or inertial motion.

In the Œuvres de Descartes, ed. Adam C. Tannery P. , the presentation of the French translation may be misleading, for the postils are printed in italics in the body of the text. In the Latin version of the Principia philosophiae, they are printed correctly as postils.

Œuvres de Descartes, ed. Adam C. Tannery P. (Paris, 1897–1910) viii, Principia philosophiae, part 2, § 37.

Cohen I. B. , “Quantum in se est: Newton's concept of inertia in relation to Descartes and Lucretius”, Notes and records of the Royal Society of London, xix (1964) 131–55.

Gabbey A. , “Force and inertia in seventeenth-century dynamics”, Studies in history and philosphy of science, ii (1971) 1–67, especially 58–61.

Westfall interprets determination as meaning direction. This is effectively correct, though Gabbey (op. cit., pp. 22–3), in exploring the mediaeval sources of this concept has suggested the more subtle meaning, “directional mode of force”.

Œuvres de Descartes, ix. Principes de la philosophie, part 2, § 40. On Descartes' laws of impact, see Mouy P. , Le développement de la physique cartésienne (Paris, 1934) 21–3, Blackwell R. J. , “Descartes' laws of motion”, Isis, lvii (1966) 220–34 and Taliaferro R. C. , The concept of matter in Descartes and Leibniz (Notre Dame, 1964) 19–22.

Only a little poetic licence is needed to read into Westfall's comment on Huygens the description of a struggle between good and evil. Thus Huygens was drawn away from the good idea of a perfectly uniform gravity by the bad influence of the concept of the subtle matter as the cause of this gravity.

For essays on Galileo's Platonism by Cassirer E. Strong E. W. McTighe T. P. , see Galileo, man of science, ed. McMullin E. (New York, 1967) 338–87: For A. Koyré's essay, see Roots of scientific thought, ed. Wiener P. P. Nolan A. (New York, 1957) 147–75.

For an excellent example of this approach, see Drake S. , Galileo studies (Ann Arbor, 1970).

On Huygens' methodology, see Mouy P. , Le développement de la physique cartésienne (Paris, 1934) 183–7 and A. I. Sabra, Theories of light from Descartes to Newton (London, 1967) 159–84.

See Moscovici S. , L'expérience du mouvement (Paris, 1967).

Westfall quotes and discusses only the text (in translation) of the original printed version of the “Tentamen”, in which Leibniz made a mistake in the calculation of the centrifugal force. Later, as a result of correspondence with Varignon, Leibniz corrected this error. For an account of this correspondence, see Aiton E. J. , “The celestial mechanics of Leibniz”, Annals of science, xvi (1960) 77–82.

The letter was never sent to Huygens.

For a detailed exposition, see Aiton E. J. , “The celestial mechanics of Leibniz”, Annals of science, xvi (1960) 65–82; xviii (1962) 31–41; xx (1964) 111–23. The substance of these articles (in a revised and corrected form) is included in chapter 6 of E. J. Aiton, The vortex theory of the planetary motions (London, 1972).

Westfall supports his thesis by extensive quotations from these papers.

Westfall's choice of words in describing Newton's idea of God as the first cause, “God was an incorporeal aether who could move bodies without offering resistance to them in turn,” contains unfortunate pantheistic overtones that would not have appealed to Newton. It would seem probable that Newton's revision of his description of space as God's sensorium, converting the literal statement into a metaphorical one by the addition of 'tanquam', was intended to avoid the pantheistic identification of God and space. On the relation of Newton's theology and natural philosophy, see Schiffers N. , Fragen der Physik an die Theologie (Düsseldorf, 1968) 58–72.

See Koyré A. , From the closed world to the infinite universe (Baltimore, 1957) 206–20; Hall A.R. Hall M. B. , “Newton and the theory of matter”, Texas quarterly, x (1967) 54–68, and the introduction to part 3 of A. R. and M. B. Hall, Unpublished scientific papers of Isaac Newton (London, 1962) 183–213.

See Rosenfeld L. , “Newton's views on aether and gravitation”, Archive for history of exact sciences, vi (1969) 29–37.

This claim was originally advanced by J. Herivel in 1961 (but later modified) and supported by Westfall in his paper, “A note on Newton's demonstration of motion in ellipses”, Archives internationales d'histoire des sciences, xxii (1969) 51–60.

See Hall A.R. Hall M. B. , “The date of ‘On motion in ellipses’”, Archives internationales d'histoire des sciences, xvi (1963) 23–28 and Whiteside's D. T. review of Westfall's paper in Zentralblatt für Mathematik, cxciv (1970) 2–3.

The translation of I. B. Cohen has been quoted. See Cohen I. B. , “Newton's second law and the concept of force in the Principia”, Texas quarterly, x (1967) 151.

Westfall contrasts force (F) and total force (∫Fdt) where F is accelerative force. The correct comparison is between ‘force’ (Fdt) and ‘total force’ (∫Fdt).

See Whiteside's D. T. essay review of J. Herivel's The background to Newton's Principia in History of science, v (1966) 109–13.

An important key to the understanding of Newton's dynamics has recently been recognised by I. B. Cohen in Newton's idea that force can be impressed altogether and at once or by degrees and successively. See, in addition to the paper cited in note 35, Cohen I. B. , Introduction to Newton's Principia (London, 1971) 163–6.

See Cohen I. B. , Texas quarterly, x (1967) 147–53.

See Aiton E. J. , “The inverse problem of central forces”, Annals of science, xx (1964) 82.