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Theorizing the Distinction Between Solids, Liquids and Air: Pressure from Stevin to Pascal

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Part of the Vienna Circle Institute Yearbook book series (VCIY,volume 20)


Seventeenth-century scholars could take for granted distinctions between solids, liquids and air that were by no means novel. In this paper I explore the way in which these distinctions were gradually sharpened up, by way of experimentation and the theorising accompanying it, to the point where important beginnings of a theoretical grasp of the essential distinctions between the three states of matter was achieved.


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  • Modern Concept
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  • Hydrostatic Effect

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  1. 1.

    From a modern point of view it is more natural to speak of gases rather than air, but, of course, the identification of distinct kinds of gases occurred only in the eighteenth century.

  2. 2.

    Boyle’s detailed rejoinder to More is in ‘An Hydrostatical Discourse’ in M. Hunter and E. B. Davis (eds): The Works of Robert Boyle, London: Pickering and Chatto, 1999, Vol. 7, pp. 141–184.

  3. 3.

    The concept of pressure, while obvious to us, was not always so. The history of hydrostatics has hitherto not taken adequate account of the way in which the modern concept gradually emerged from a common sense version in the seventeenth century. There are too revealing studies that I seek to emulate of the emergence of concepts that have since become obvious. One concerns the emergence of the modern concept of motion as the result of the struggles of the likes of Descartes and Galileo to cope with the limitations of earlier concepts in Peter Damerow, Gideon Freudenthal, Peter McLaughlin and Jürgen Renn (Eds.), Exploring the Limits of Preclassical Mechanics: A Study of Conceptual Development in Early Modern Science, New York: Springer, 2004. The other exemplar involves the emergence of the concept of torque in the context of the balance, described in Jürgen Renn and Peter Damerow, The Equilibrium Controversy, Max Planck Research Library for the History and Development of Knowledge. Sources 2, Edition Open Access, 2012,

  4. 4.

    English translations of Stevin’s Art of Weighing and its sequel, The Practice of Weighing, together with the original Dutch versions, are in E. J. Dijksterhuis (ed.): The Principal Works of Simon Stevin, Volume 1, Amsterdam: Swets and Zeitlinger 1955, pp. 97–347.

  5. 5.

    English translations of Stevin’s works on hydrostatics, together with the Dutch originals are in Dijksterhuis, Principal Works of Stevin, op. cit., pp. 393–501. A detailed analysis of Stevin’s hydrostatics is given in Alan Chalmers, “Qualitative Novelty in Seventeenth-century Science: Hydrostatics from Stevin to Pascal” in Studies in History and Philosophy of Science, 51, 2015, pp. 1–10.

  6. 6.

    Stevin’s, admittedly mathematically ingenious, deduction is in Dijksterhuis, Principal Works of Stevin, op. cit., pp. 421–423. The details of my critique are in Chalmers, “Qualitative Novelty” op. cit., pp. 3–9.

  7. 7.

    Stevin explicitly discussed the force exerted on a lock gate. See Dijksterhuis, Principal Works of Stevin, op. cit., p. 497.

  8. 8.

    Robert Boyle: “Hydrostatical Paradoxes Made out by New Experiments” in The Works of Robert Boyle, op. cit., Vol. 5, pp. 207 and 236.

  9. 9.

    A recent English translation of that work is in S. Drake: Cause, Experiment and Science, Chicago: University of Chicago Press 1981.

  10. 10.

    Descartes’ manuscript is in C. P. Tannery (ed.): Oeuvres de Descartes, Vol. 10, 2nd ed., Paris: Vrin 1974–86, pp. 67–74. It is analysed and its significance assessed in S. Gaukroger and J. Schuster: “The Hydrostatic Paradox and the Origins of Cartesian Dynamics” in: Studies in History and Philosophy of Science, 33, 2002, pp. 535–572.

  11. 11.

    Beeckman’s efforts to elucidate Stevin’s hydrostatics in corpuscular terms are discussed in Klaas Van Berkel, Isaac Beeckman on Matter and Motion, Baltimore: The John Hopkins University Press 2013, pp. 134–135.

  12. 12.

    The inadequacies of Descartes’ efforts in this context have been identified and discussed in Alan Shapiro, “Light, Pressure and Rectilinear Propagation: Descartes’ Celestial Optics and Newton’s Hydrostatics” in Studies in History and Philosophy of Science 5, 1974, pp. 239–296, especially pp. 240–241 and 509–514 and in John Schuster, Descartes Agonistes: Physico-Mathematics, Method and Corpuscular Mechanism, Dordrecht: Springer 2013, pp. 117–9 and 509–562.

  13. 13.

    Torricelli’s letter is in G. Loria and G. Vassura (eds.), Opere di Evangelista Torricelli, Faenza: Montanari 1919, Vol. 3, pp. 198–201. An English version is in I. Spiers and A. Spiers: The Physical Treatises of Pascal, New York: Columbia University Press 1937, pp. 167–170. All my references to Torricelli’s letters in what follows are to the English versions.

  14. 14.

    This work is described in C. S. Maffioli, Out of Galileo: The Science of Waters, 1628–1718, Rotterdam: Erasmus Publishing 1994, pp. 71–89.

  15. 15.

    Spiers and Spiers, op.cit., p. 164.

  16. 16.

    Ibid., p. 165.

  17. 17.


  18. 18.

    Ibid., p. 169.

  19. 19.

    Ibid., p. 167.

  20. 20.

    Ibid., p. 169. Note that already Torricelli talks of the pressing and spouting in all directions as resulting from a propensity that liquids possess of ‘their own’, and which is distinct from their natural tendency to gravitate downwards.

  21. 21.

    The quotations are from the English translations of Roberval’s letters in C. Webster, “The Discovery of Boyle’s Law and the Concept of the Elasticity of Air in the Seventeenth Century” in: Archive for the History of Exact Sciences 2, 1965, pp. 497 and 499. This reference gave me an invaluable starting point for the material discussed in this section.

  22. 22.

    See ibid., p. 496.

  23. 23.

    Ibid., p. 497.

  24. 24.

    Ibid., p. 498.

  25. 25.

    See Webster, op. cit., pp. 451–454.

  26. 26.

    Ibid., p. 499.

  27. 27.

    B. Pascal, “Experiences nouvelles touchant le vuide” in L. Brunschvigg and P. Boutroux (eds.): Oeuvres de Blaise Pascal, Volume 2, Paris 1908, pp. 74–76.

  28. 28.

    Pascal’s treatises were published posthumously in 1663. My references are to the English translation in Spiers and Spiers, op. cit. I have discussed Pascal’s theory in more detail in Chalmers, “Qualitative Novelty”, op cit., pp. 6–8, although my critique of Pascal’s Treatise on air is an addition to what is covered in that place.

  29. 29.

    Spiers and Spiers, op. cit., p. xxix.

  30. 30.

    For the clearest formulation by Pascal of this latter, quantitative, point see Spiers and Spiers, op. cit., pp. 7–8.

  31. 31.

    Spiers and Spiers, op. cit., pp. 7–8.

  32. 32.

    Spiers and Spiers, op. cit., pp. 4 and 10.

  33. 33.

    Spiers and Spiers, op. cit., p. 7.

  34. 34.

    Spiers and Spiers, op. cit., p. 29.

  35. 35.

    See Alan Chalmers, “Intermediate Causes and Explanations: The Key to Understanding the Scientific Revolution” in Studies in History and Philosophy of Science 43, 2012, pp. 551–562, especially pp. 555–557, Chalmers, “Qualitative Novelty”, op. cit., pp. 5–8, P. Duhem, “Le Principe de Pascal” in: Revue Gènèral des Sciences Pures et Appliques, Vol. 16, 1905, pp. 599–610 and Dijksterhuis, Simon Stevin, op. cit., p. 69.

  36. 36.

    Boyle’s “Hydrostatical Paradoxes” op. cit., is a commentary on and elaboration of Pascal’s The Equilibrium of Liquids.

  37. 37.

    See Alan Chalmers, “Robert Boyle’s Mechanical Account of Hydrostatics and Pneumatics: Fluidity, the Spring of the Air and their Relationship to the Concept of Pressure” in Archive for History of Exact Sciences 29, 2015, pp. 429–454.

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Chalmers, A.F. (2017). Theorizing the Distinction Between Solids, Liquids and Air: Pressure from Stevin to Pascal. In: Stadler, F. (eds) Integrated History and Philosophy of Science. Vienna Circle Institute Yearbook, vol 20. Springer, Cham.

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