Beyond Pascal to Boyle’s Concept of Pressure in Liquids

In recent articles I have followed Pierre Duhem and Dijksterhuis and credited Pascal with having formulated the modern concept of pressure.[1] [2] I now consider that claim to be in need of serious qualification. According to its modern usage, ‘pressure’ specifies the state of a fluid throughout its volume. A fluid presses equally on either side of any plane within a body of fluid in equilibrium. Within the body of a fluid the net force due to this uniform pressing in all directions is zero. It is only on solid surfaces bounding a fluid that the pressure is no longer balanced and a net force results that is equal to the product of the pressure and the area of the surface. Pascal identified the forces on solid surfaces, but as far as the transmission of forces through the body of liquids is concerned he attributed it to their ‘fluidity and continuity’ without further elaboration. In his Treatise Pascal talked freely of liquids pressing on surfaces using the verb ‘presser’ but he did not use the noun ‘la pression’. A full account of how hydrostatic effects are caused must include the details of how forces are transmitted through liquids by way of elements of liquid pushing against and being pushed by their neighbours. Insofar as Pascal fell short of doing that, he fell short of capturing the notion of pressure that is necessary to specify the state of a liquid and that is distinct from weight.

It was left to Robert Boyle to modify and extend Pascal’s account in order to supply what was needed in these respects.[3] Boyle introduced the theoretical device, now taken for granted, of considering the forces acting on either side of imaginary planes in the body of a liquid. He thereby specified the way in which forces are transmitted through liquids and so provided a full mechanical account of how hydrostatic effects are brought about. Boyle did employ a concept of pressure that was an anticipation of the modern one and made full use of the term ‘pressure’ to describe it. It was also left to Boyle to capture the distinctive feature of air by way of the ‘spring of the air’, his elaboration of Roberval’s ‘power of rarefaction’ and Pecquet’s ‘elater’. I have recently analysed these contributions of Boyle in detail and will not reproduce them here.[4]

  • [1] Spiers and Spiers, op. cit., p. 29.
  • [2] See Alan Chalmers, “Intermediate Causes and Explanations: The Key to Understanding theScientific 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 Principede Pascal” in: Revue General des Sciences Pures et Appliques, Vol. 16, 1905, pp. 599-610 andDijksterhuis, Simon Stevin, op. cit., p. 69.
  • [3] Boyle’s “Hydrostatical Paradoxes” op. cit., is a commentary on and elaboration of Pascal’s TheEquilibrium of Liquids.
  • [4] 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 forHistory of Exact Sciences 29, 2015, pp. 429-454.
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