Theorizing the Distinction Between Solids, Liquids and Air: Pressure from Stevin to Pascal
Alan F. Chalmers
Common Distinctions Between Solids, Liquids and Air
Seventeenth-century scholars could take for granted distinctions between solids, liquids and air that were by no means novel.1 In this paper I explore the way in which these distinctions were gradually sharpened up, by way of experimentation and the theorizing accompanying it, to the point where important beginnings of a theoretical grasp of the essential distinctions between the three states of matter was achieved.
Distinctions between solids, liquids and air apparent in everyday phenomena presumably lay behind the Aristotelian theory of the four elements, air, earth, water and fire. Linked as they were to the notions of natural places and natural motions, the Aristotelian distinctions were to prove increasingly inadequate to cope with a range of phenomena revealed by experiment in the seventeenth century. As we shall see, an adequate theoretical response to such developments involved moves towards a technical notion of the concept of pressure. However, it is worth noting that as late as 1672 it was necessary for Robert Boyle to counter is some detail Henry More’s resistance to his own introduction of pressure, which resistance was based on the Aristotelian presumption that water does not weigh in water. 
As a background to the ensuing discussion I note some knowledge of solids, liquids and air that was implicit in everyday knowledge or in technologies familiar by the dawn of the seventeenth century, although they were not singled out and listed in this way at the time.
Solids have a definitive shape and size, up to a point. The qualification ‘up to a point’ is necessary because the shape and size of solids can be modified by distorting forces. A solid normally returns to its original size and shape on the removal of a distorting force. That is, solids are more or less elastic, a phenomenon familiar from the behaviour of bows, lute strings and the expansion and contraction of the bladders of animals, for instance.
A sample of a liquid also has a natural size, but, unlike a sample of a solid, it does not have a natural shape. It adopts the shape of any container into which it is poured. Liquids flow in a way that solids do not, and solids can float in liquids but not in other solids. Unlike solids, liquids are virtually incompressible; they are inelastic. Other distinctions can be brought out by attending to differences in the behaviour of water and sand. Both can be transferred from a high to a low level via a pipe, but the water can climb a subsidiary hill in a way that sand cannot and when ejected from the bottom of the pipe it will not form a heap in the way that sand does.
A sample of air has neither a definite shape nor a definite size. It expands to fill any container into which it is put. Like solids, but unlike liquids, air is elastic. When a sample of air is compressed it resists the force of compression to a degree, as evident from resistance felt when a plunger is thrust into a closed syringe or gun barrel. The difference between the behaviour of a syringe filled with water and one filled with air exemplifies the compressibility of the latter as opposed to the former.
Phenomena suggesting that fluids press in directions other than the downwards direction of their weight were familiar by the seventeenth century. The fact that wine will be forced horizontally our of a leaking barrel and that water pushes horizontally against a lock gate, in spite of the fact that the weight of the liquids involved acts downwards, provide examples, as does the uniform expansion of a bladder when inflated which contrasts with the behaviour of a wire when stretched. However, as we shall see, a precise and quantitative grasp of the isotropy of the transmission of forces in liquids and air was only achieved as a result of seventeenth century advances. What proved to be a necessary condition for the achievement was a precise grasp of the concept of pressure.
With respect to the aim of making precise technical sense of, that is, of adequately theorizing, distinctions of the kind discussed above, there was one significant achievement that could be taken for granted in the seventeenth century. I refer to the science of weight. The latter was a mathematised theory consisting of a body of theorems derived from seemingly unproblematic axioms in the style of Euclid and Archimedes. It had been developed rigorously and in detail and applied to a wide range of mechanical systems involving balances, levers, pulleys and so on. Simon Stevin’s The Art of Weighing, published in 1586, which included an original treatment of equilibrium on inclined planes, bears witness to the degree of sophistication reached in the science of weight of which seventeenth-century scholars were able to take advantage. Another technical achievement that could be drawn on in the seventeenth century was Archimedes’ theorization of the phenomenon of floating.
I conclude this introductory section by making an observation that sets the scene for my discussion. Solids and liquids alike possess weight, and a few decades into the seventeenth century it was generally appreciated that air does too. Consequently, if sciences concerning the behaviour of liquids and air were to be developed, it was necessary to grasp theoretically the distinctive features of them other than their weight. Those are the developments that I now trace.
-  From a modern point of view it is more natural to speak of gases rather than air, but, of course, theidentification of distinct kinds of gases occurred only in the eighteenth century.
-  The concept of pressure, while obvious to us, was not always so. The history of hydrostatics hashitherto not taken adequate account of the way in which the modern concept gradually emergedfrom a common sense version in the seventeenth century. There are too revealing studies that I seekto 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 andGalileo to cope with the limitations of earlier concepts in Peter Damerow, Gideon Freudenthal,Peter McLaughlin and Jurgen Renn (Eds.), Exploring the Limits of Preclassical Mechanics: AStudy of Conceptual Development in Early Modern Science, New York: Springer, 2004. The otherexemplar involves the emergence of the concept of torque in the context of the balance, describedin Jurgen Renn and Peter Damerow, The Equilibrium Controversy, Max Planck Research Libraryfor the History and Development of Knowledge. Sources 2, Edition Open Access, 2012, http://www.edition-open-access.de.
-  English translations of Stevin’s Art of Weighing and its sequel, The Practice of Weighing, togetherwith the original Dutch versions, are in E. J. Dijksterhuis (ed.): The Principal Works of SimonStevin, Volume 1, Amsterdam: Swets and Zeitlinger 1955, pp. 97-347.