Pascal’s Moves Towards a Technical Concept of Pressure

Pascal was fully aware and able to take advantage of the developments we have discussed and participated in them himself, performing experiments of his own. In 1647 he published an account of his early experiments that included a version of Torricelli’s experiment using water in place of mercury.[1] He orchestrated a repetition of Torricelli’s experiment at the top of the Puy de Dome, conducted in 1648. My focus in this Section is on the drawing together of all of these considerations in the two Treatises that Pascal wrote in 1654, The Equilibrium of Liquids and The Weight of the Mass of the Air. In the first of them in particular, we find an advance in the characterization of the distinguishing features of liquids which was to be a significant move towards the modern concept of pressure.


In the subtitle of his Treatises Pascal promised to provide ‘the explanation of the causes of various effects of nature which had not been known hitherto’.[2] As far as liquids are concerned, he provided explanations of a range of hydrostatics effects, some of them novel and some of them long known, by describing how forces applied to a liquid, whether they originate from weights or humans pushing on a piston or from the weight of the liquid itself, are transmitted through the body of the liquid. Pascal specified that the force per unit area at the point of application of a force to a liquid in a container appears at any other surface of the liquid, whatever its orientation, as the same force per unit area.[3] This behavior was attributed by Pascal to features characteristic of liquids as such, namely, their ‘continuity and fluidity’.[4] This is borne out by the fact that hydrostatic effects are destroyed if the liquid responsible for them is frozen.[5] Pascal articulated his account of hydrostatics by reference to a set up that was to become known as the hydraulic press. He stressed the point that the multiplication of force achieved by such a press comes about because the water ‘is equally pressed upon under the two pistons’, the force being greater on the larger one in proportion to the degree to which its cross sectional area exceeds that of the smaller one.[6] This constituted a significant move towards the modern concept of pressure but fell short of it in ways that I identify in Sect. 5.6.

We have seen that the path of the previous decade that led to Pascal’s hydrostatics involved interplay between the exploration of liquids and air and analogies between them both and the behavior of solids, with novel conceptualizations as well as novel experimental findings emerging. Pascal did not take maximum advantage of those developments when it came to his second treatise, The Weight and Mass of the Air. The title itself hints at what was indeed the case, namely, that Pascal was intent on explaining pneumatic phenomena by appealing to the weight of the air and, as a consequence, failed to match the progress he made with the distinction between solids and liquids with a theorization of the way in which air differs from both of them. As I have stressed above, air does not differ from solids and liquids by virtue of possessing weight.

In the first chapter of The Weight and Mass of the Air Pascal spells out consequences of the recognition that air has weight and sets out his pneumatics in subsequent chapters by appeal to those consequences. In particular, he is intent on showing that phenomena thought to require appeal to the force of a vacuum for their explanation can all be explained better by appeal to the weight of the air. He notes that atmospheric air presses on the earth by virtue of its weight just as the oceans do and he observes that the degree of this pressing is proportional to the height of air, just as is the case with water. He also observes that ‘bodies in the air are pressed on all sides by the weight [lepoids} of the air above them’, drawing a comparison with what he had shown in The Equilibrium of Liquids?4 The reference to ‘pressing on all sides’ alludes to the isotropic character of the pressing but the centrality of that notion is obscured by the use of the term ‘weight’, a feature that is characteristic of the whole of Pascal’s treatise on air.

By developing his pneumatics by emphasizing the weight of air, and also exploiting isotropy of the forces exerted by liquids on solid surfaces only covertly, Pascal had sidestepped the issue of just what it is that distinguishes air from liquids and solids. He failed to exploit to full advantage experimental findings and their attempted theorization by the likes of Torricelli, Roberval and Pecquet. Air shares with liquids and solids the property weight, and it shares with liquids, but not with solids, the isotropy of the distribution of forces within it. It also shares with solids a certain kind of elasticity insofar as it responds to contractions with a resisting force, although there are differences insofar as the elasticity of air is isotropic and air has a spontaneous propensity to expand and so does not offer a resistance to expansion in the way that solids do. These differences were already illustrated, by experiments performed by Roberval for example, as we have noted. Key ones involved the effects of introducing a small volume of air into the Torricellian space, as compared to introducing an equal volume of water, and the effect of placing an airtight bladder largely free of air into that same space. Such experiments are simply not mentioned in Pascal’s treatise on air. Pascal contributed significantly to the task of identifying the distinguishing features of solids and liquids but he did not succeed in capturing the distinctive feature of air with equal clarity. Pascal did not make significant progress in that respect because he failed to capitalize on the grasp of the character of air that Roberval had alluded to by his ‘power of rarefaction’ and Pesquet had with his concept of elator.

  • [1] 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.
  • [2] Spiers and Spiers, op. cit., p. xxix.
  • [3] For the clearest formulation by Pascal of this latter, quantitative, point see Spiers and Spiers, op.cit., pp. 7-8.
  • [4] Spiers and Spiers, op. cit., pp. 7-8.
  • [5] Spiers and Spiers, op. cit., pp. 4 and 10.
  • [6] Spiers and Spiers, op. cit., p. 7.
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