Abstract
Following an early version in an unpublished manuscript, Newton included a concise version of his hydrostatics in the Principia. It was based on his identification of the property of liquids that distinguishes them from solids, namely, the inability of the former to resist distorting forces. Any portion of a liquid, however small, is presumed to possess this property. In this way Newton made precise theoretical sense of the continuity and fluidity of liquids that had been presupposed in a more common sense by Stevin, Pascal and Boyle before him. Newton began his treatment of hydrostatics by considering a sphere of non-gravitating liquid. In doing so, he clearly distinguished pressure from weight. He freely adopted the technique, introduced by Boyle, of considering the pressures acting on either side of planes within the body of a liquid. The strict continuity of liquids enabled Newton to construct proofs that relied in spherical surfaces touching planes or other spherical surfaces at points. Newton was able to show how his definition of a liquid has the consequence that, within a body of liquid in equilibrium a pressure exerted on its bounding surface is transmitted as the same force per unit area normal to any surface within the body of liquid, whatever its orientation. Having achieved that result, Newton then introduced gravity and showed how the pressure in a liquid is proportional to the depth below its surface. Newton construed the unpublished version of his theory as a mathematical one following from grantable assumptions. It is better seen as an empirical theory, with its capacity to explain a range of observable and experimental phenomena providing the evidence justifying his definition of the liquid state.
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Notes
- 1.
I have referred to the version of the Waste Book in Herivel (1965, pp. 128–182). The same work (pp. 1–34) contains a discussion of Newton’s early moves in dynamics.
- 2.
The incompatibility of the construal of light as a pressure and its linear transmission is explored in great detail in Shapiro (1974).
- 3.
I have used the English translation of De gravitatione in Hall and Hall (1962, pp. 121–156). The opening paragraph discussed here is on p. 121.
- 4.
- 5.
Newton’s discussion of comets and pendulums is in the final paragraph of Newton’s digression on space, time and motion in De gravitatione.
- 6.
All of my quotations from the Principia are from the translation by I.B. Cohen and A. Whitman in Newton (1999). Newton’s concise version of hydrostatics is on pp. 687–692.
- 7.
As Shapiro spells out in detail, Descartes’ view that light is a pressing transmitted through a fluid medium (the second element or ether presumed to fill the space between Sun and earth) clashes with the rectilinear transmission of light once the isotropy of pressure is appreciated.
- 8.
Newton’s characterization of the mathematical structure of his theory, with its propositions derived from definitions and unproblematic postulates, bears a strong resemblance to the position advanced by Stevin on the status of his hydrostatics. This fact adds to the circumstantial case that Shapiro has made for the claim that Newton had read and was influenced by Stevin.
- 9.
Newton pointed out that the assumption of continuity in play here is akin to that involved in the assumption that materials have a density. The mathematics presumes continuity, but ‘in physics things seem otherwise’ (p. 150) insofar as matter is made up of atoms.
- 10.
In their translation of Definition 18 Hall and Hall write ‘overwhelming pressure’ which I have replaced with ‘impressed pressure’. (The Latin is ‘praepollenti pressioni’.) In the text that follows the definition Newton made it clear that adjacent parts of a liquid can be ‘moved separately by any impressed force’. Even a solid will yield to a force that is sufficiently ‘overwhelming’.
- 11.
The move by Newton from the corpuscular or atomic level to a macroscopic level that assumed continuity may well have been influenced by Boyle’s ‘New experiments physico-mechanical touching the spring of the air’ of 1661. Newton’s familiarity with that work is manifest by a number of references to it in his early notebooks. Near the beginning of The Spring of the Air Boyle referred to speculations concerning the properties of air that invoked the motion of its particles, citing Descartes in this connection. But he was at pains to emphasize that his notion of the ‘spring of the air’ that he invoked to explain the behavior of air, especially as revealed by experiments with his air pump, could be developed and supported in a way that was quite independent of assumptions about underlying corpuscles. ‘Wherefore I shall decline meddling with a subject, which is much more hard to be explicated than necessary to be so, by him, whose business it is not, in this Letter, to assign the adequate cause of the spring of the air, but only to manifest, only that air has a spring, and to relate some of its effects’. Elsewhere , in Chalmers (2012), I have documented Boyle’s articulation of a distinction between intermediate causes , such as weight and the spring of the air, and underlying atomic or corpuscular explanations of them, and the extent to which knowledge of the latter is not necessary for the pursuit of experimental science. Boyle’s stand here matches the stand that Newton took on gravitational attraction which he invoked but could not explain at a deeper level. I have no direct evidence that Newton explicitly drew on this aspect of Boyle’s work.
- 12.
As was noted in Chapter 5, Damerow et al. (2004, pp. 81–94) have given a detailed exposition of Descartes’ adoption of a logic of opposites or contraries.
- 13.
Shapiro (1974, p. 281) has noted that Newton’s brief proof lacks validity and suggests that it can be rendered valid by adding the assumption that the forces on PSQ act normal to the surface. Since, as Shapiro acknowledges, Newton nowhere states such an assumption I have preferred to render his argument valid by drawing on the definition of a liquid that Newton did state.
- 14.
Shapiro (1974, p. 280) refers to this assumption as ‘Newton’s principle of liquefaction’ and likens it to the ‘principle of solidification’ that some have read into Stevin’s Elements of Hydrostatics’. I avoid talk of such principles because I believe it is misleading from a historical and logical point of view. Neither principle is explicitly formulated, either by Stevin or Newton. The principles of solidification is presumed by Stevin in the sense that adding it to his postulates renders some of his proofs valid which are otherwise invalid. But that move would have been problematic for Stevin insofar as he required his postulates to be sufficiently unproblematic to be granted at the outset of his deliberations. A principle of solidification could no more be taken as an evident starting point for Stevin than a principle of liquefaction could be taken as a starting point for Newton. The replacement of solid confining surfaces by liquid ones was sanctioned by Newton as a consequence of the fact that equilibrium requires forces to be balanced, together with some features of solids and liquids that did form the basis of his hydrostatics. It is therefore misleading to talk of that assumption as a ‘principle’. The first explicit formulation of a general principle in this context was the principle of solidification formulated by the French mathematician Alexis Clairaut in 1743, long after Stevin and Newton had made their respective contributions to hydrostatics. On this latter point see Truesdell (1954, pp. xi and xix–xx). An engineer’s perspective on the history of this issue can be found in Casey (1992). I owe this latter reference to Alan Shapiro .
- 15.
See Boyle (1999, pp. 161–164).
- 16.
Euler’s ‘General principles of the state of equilibrium of liquids’ was published in 1757 (Euler 1954, pp. 2–53). A partial English translation of and commentary on it is included in Truesdell (1954, pp. lxxv–lxxxiii). Euler identified the ‘essential property of fluids’ by specifying that ‘a fluid mass cannot be in equilibrium unless it is subject at all points of is surface to forces equal and perpendicular to the surface’ (Truesdell 1954, p. lxxvi).
- 17.
Euler (1954) developed a general theory of hydrostatics applying to both compressible and incompressible fluids. His derivations were facilitated by his ability to argue algebraically using partial differential equations rather than being restricted to geometrical arguments aided by diagrams, as Newton had been.
- 18.
A translation of Newton’s Preface is in Newton (1999, pp. 381–383).
- 19.
Shapiro assumed a publication date of around 1668 for De Gravitations, a position that was totally reasonable in 1974, a decade before the case for a later date had begun to gain credence.
- 20.
Letter to Oldenburg in Turnbull (1959, p. 175).
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Chalmers, A.F. (2017). Newton’s Hydrostatics: Liquids as Continua. In: One Hundred Years of Pressure. Archimedes, vol 51. Springer, Cham. https://doi.org/10.1007/978-3-319-56529-3_9
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