Abstract
This article in an attempt to identify the precise way in which Robert Boyle provided a mechanical account of the features that distinguish liquids and air from solids and from each other. In his pneumatics, Boyle articulated his notion of the ‘spring’ of the air for that purpose. Pressure appeared there only in a common, rather than in a technical, sense. It was when he turned to hydrostatics that Boyle found the need to introduce a technical sense of pressure to capture the fluidity of water which, unlike air, lacked a significant spring. Pressure, understood as representing the state of a liquid within the body of it rather than at its surface, enabled Boyle to trace the transmission of hydrostatic forces through liquids and thereby give a mechanical account of that transmission according to his understanding of the term. This was a major step towards the technical sense of pressure that was to be adopted in Newton’s hydrostatics and in fluid mechanics thereafter.
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Notes
See Duhem (1905).
I have analysed Stevin’s hydrostatics from this point of view in Chalmers (2015).
Boyle used the term ‘intermediate’ causes in ‘A Proemial Essay’ (1661) which was an introduction to Certain Physiological Essays which reported on some of Boyle’s early experimentation other than that in pneumatics. It is reproduced in The Works of Boyle (1999), Ed. Hunter and Davis, Volume II, pp. 9–34. (Hereafter, I identify sources in this collection simply as Works followed by a roman numeral representing the volume and the page number, e.g., Works II, p. 23.) Boyle characterised intermediate causes more fully in a manuscript fragment dealing with final causes and the uses of experiment, dating from around 1688 and reproduced in Boyle (1990), Vol. IX, f40-41, reel 5, frame 250. ‘Of the subordinate or intermediate causes or theories of natural things, there may be many: some more and some less remote from the First Principles and yet each of them capable to afford a just delight and useful instruction to the mind. And these we may call the cosmographical, the hydrostatical, the anatomical, the magnetical, the chemical and other causes or reasons of phenomena as those which are more immediate (in our way of estimating things) than the general and primordial causes of natural effects’. See also Boyle (1990), Vol. VIII, f184, reel 5, frame 189.
Works VII, p. 148.
For an appreciation of the degree of sophistication reached by developments in the science of weight prior to the seventeenth century, see Renn and Peter (2012).
As I have stressed elsewhere, this use of mechanical ‘in the usual sense of the word’ differs from the sense involved in ‘the mechanical philosophy’ characterised by the insistence that phenomena be traced back to the interaction of corpuscles of universal matter characterised solely in terms of their shape, size and motion. The distinction between mechanism in the strict, philosophical, sense and in a more common sense is spelt out in Chalmers (1993, 2002, 2009, 2012).
Works II, p. 24.
Works I, p. 166.
Works V, p. 194.
The Elements of Hydrostatics in Stevin (1955), pp. 393–483.
As is argued in Chalmers (2015), the mechanics of simple machines on which Stevin modelled his hydrostatics could be presented in Euclidean guise only to the extent that common sense and familiar technologies could yield propositions about weight that could be regarded as evident. The move to pneumatics, and to a lesser extent hydrostatics, involved a move beyond that familiar world to one revealed by way of experiment. As a consequence, novel notions other than weight needed to be fashioned and the adequacy of various claims made with their aid needed to be established, not by appeal to their unproblematic character but by appeal to their explanatory power and the extent to which their use was illustrated and supported by experiment. Hence, Boyle’s reference in the passage in the main text to ‘surprising’ discoveries, and ‘unobvious truths’ revealed by ‘diligent examination of particular bodies’ and requiring for their comprehension novel concepts that are ‘handsome productions of reason’.
Works II, pp. 207 and 236.
Works II, p. 195.
In the full title of Spring of the Air and elsewhere, Boyle referred to his pneumatics as ‘physico-mechanical’. I suspect that by doing so he was drawing a contrast between his mechanical exposition and works with a more mathematical emphasis which were being referred to as ‘physico-mathematical’, as exemplified in the title of Mersenne (1644).
Works I, p. 66.
My account of the background to Boyle’s introduction of ‘spring’ owes a debt to Webster (1965).
Pascal (1937), p. 169.
Ibid. Torricelli had investigated the horizontal, and also vertical, efflux of liquids early in the 1840s. For details, see Maffioli (1994), pp. 71–89.
The quotations are from the English translation of Roberval’s letters in Webster (1965), pp. 497 and 499.
Pascal (1937), p. 497.
The debt that Boyle, and other English researchers such as Henry Power, owed to Pecquet is stressed by Webster (1965), pp. 451–458.
Works V, p. 205.
Works I, p. 245.
Works III, pp. 22–23.
About a decade later, Boyle devoted a whole tract to the differences between pressure in solids and in fluids. See Works VII, pp. 215–225.
Works I, p. 171.
Works I, p. 174.
Works I, p. 238.
Works I, p. 210.
Webster (1965), pp. 467–470.
Alan Shapiro noted the importance of the distinction between the common and technical senses of the term ‘pressure’ in his discussion of the hydrostatics implicit in Descartes’ cosmological theory of light which, as Shapiro stresses, lacked a technical sense of ‘pressure’. See Shapiro (1974), especially p. 251, note 29.
The confusions occur in Shapin and Schaffer (1985), especially Chapter 2. They are discussed in footnote 42.
Works I, p. 165
Boyle frequently used the term ‘notion’ to describe the concepts involved in his science and stressed the fact that novel experimental advances make necessary the fashioning of novel notions or the modification of old ones. See, for example, his remarks to this effect in Proemial Essay, Works II, p. 20.
Works I, p. 245.
As noted above, this kind of point had already been made by Torricelli in his response to Ricci’s queries.
Works VI, p. 62.
On a number of occasions Boyle pointed to the phenomenon of capillary rise as an additional cause, significant when liquids in narrow tubes are involved.
In Leviathan and the Air Pump, a book that, as noted in Wootton (2015), Chapter 11, has been referred to as ‘the most influential book in the history of science since Kuhn’s The Structure of Scientific Revolutions’, Shapin and Schaffer find ambiguities in Boyle’s use of ‘pressure’ that can be seen as of their own making once the relationship between spring and weight on the one hand, and a common sense of ‘pressure’ on the other, is appreciated. According to our authors, Boyle used the term ‘pressure’ generically to refer to spring and weight. ‘So “pressure” is to be read as an embracing term, and its ambiguities and variation of meaning were themselves a resource that Boyle used in debating the air-pump trials’ (Shapin and Schaffer (1985), p. 55). By grouping together weight, spring and pressure as Boyle’s ‘principal ontological concern’, Shapin and Schaffer interpret passages in Boyle as ambiguous and merely rhetorical which, on the account I offer, can be interpreted literally and not merely rhetorical as making clear and explicit claims about the relationship between pressure, in the common sense of the term employed at the time, and its causes, the spring, weight and fluidity of air.
Works I, p. 168.
Works V, p. 206.
Works V, pp. 206 and 255.
Works V, p. 194.
Works V, p. 207.
See Pascal (1937), pp. 7–8 for a clear and explicit expression of this point.
Works V, p. 207.
Works V, p. 239. This much was entailed by Stevin’s Elements of Hydrostatics, but, to use Boyle’s words, Stevin had asserted that it was true without showing why it was true. The inadequacies of Stevin’s proofs are discussed in Chalmers (2015).
Works V, p. 248, emphasis in original.
Stevin introduced two technical terms in his Elements of Hydrostatics that to some degree resemble Boyle’s imaginary planes. According to Stevin’s Definitions VII and VIII a ‘surface vessel’ is ‘the complete geometrical surface of a body, conceived as separable therefrom’ and ‘bottom’ [bodem] is ‘any plane against which rests any water’. Stevin explicitly likened the former to the planes of geometry, describing them as ‘vessels without any corporeal magnitude and without any weight’ (Dijksteerhuis 195, p. 385). Although they do not have ‘corporeal magnitude’, Stevin’s ‘surface vessels’ are solid insofar as they can contain water, in accordance with the nature of solids as specified in Definition VI which reads ‘Solid body is one whose matter does not flow, and though which penetrates neither water nor air’. The surface vessels need to be solid surfaces in order for him to put to work his Postulate III, the only postulate that introduces significant hydrostatic content into his theory. ‘The weight causing a vessel to sink less deep to be lighter, but the weight causing it to sink deeper to be heavier, and that causing it to sink to the same depth, equally heavy’. This postulate is one that can be ‘granted’ insofar as it is an abstraction from common experience of the effect of adding or subtracting weights to floating vessels, which need to be solid to hold or support them. It is also clear from the context in which Stevin uses the term ‘bottom’ that these, although lacking thickness and weight, are solid surfaces against which water can press. The solid nature of ‘bottoms’ is made quite explicit when Stevin describes each of those bordering a rectangular prism of water as ‘a corporeal rectangle’ (Dijksterhuis (1955), p. 415). So, in spite of the degree to which Stevin’s surface vessels and bottoms abstract from weight and corporeal magnitude they do not abstract from solidity as possessed by solids and so cannot perform the function played by Boyle’s imaginary planes against which liquids press in a way not involving pressure against a solid surface.
Works VII, p. 159.
An English translation of the relevant passages from More’s Enchiridion Metphysicum of 1671 is given by Boyle, Works VII, p. 160.
The details of the interchange can be followed in Works VII, pp. 158–164.
Works VII, pp. 162–163.
Works VII, p. 161.
Proposition 5 of Book 1 of Archimedes’ On Floating Bodies reads, ‘Any solid lighter than a fluid, if placed in the fluid, be so far immersed that the weight of the solid will be equal to the fluid displaced’ (Heath 1950, p. 257). This is not the case in Boyle’s experiment with the wax.
There is no direct evidence that Boyle was drawing on Galileo’s work here. He did, in Works V, p. 194, cite Galileo amongst those of his predecessors who made considerable contributions to hydrostatics. However, Boyle included him amongst those who handled hydrostatics ‘rather as geometricians than as philosophers’, a judgement that makes sense in the light of the contrast between the treatment of floating by Boyle and Galileo that I am highlighting here.
See Drake (1981), p. 31.
Drake (1981), p. 41.
Stevin’s critique of the appeal to imaginary displacements as causes can be found in Dijksterhuis (1955), p. 509. However, he did not respond to the problem by supplying mechanical causes as Boyle was able to do.
Works VII, p. 164.
This comparison is developed in some detail in Chalmers (2015).
Works V, p. 207.
See the recent discussion of this issue in Malet (2013) and the references cited there.
Pascal (1937), p. 6.
Pascal (1937), p. 8. Pascal introduced this point by announcing it as a ‘proof which will be understood only by geometers and may be disregarded by others’, thereby reinforcing my rejection of the characterisation of Pascal’s approach as mathematical as opposed to experimental. I have modified the translation by Spiers and Spiers in Pascal (1937) to make it conform better to the French original.
See Pascal (1937), pp. 7–8 for a clear and explicit expression of this point.
See Mersenne (1644), pp. 215–233. As noted in Duhem (1905), Mersenne’s somewhat disorganised survey of the hydrostatics available to him contains some original observations. They include an anticipation of the hydraulic press (p. 228) and the recognition that hydrostatic effects are destroyed if the water is frozen ( pp. 228 and 229). The latter page is wrongly numbered as 239 in the copy of Mersenne (1644) available on http://books.google.com.
This position is argued in Chalmers (2015).
Newton (1954), p. 290.
Shapiro (1974), p. 274.
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Chalmers, A. Robert Boyle’s mechanical account of hydrostatics and pneumatics: fluidity, the spring of the air and their relationship to the concept of pressure. Arch. Hist. Exact Sci. 69, 429–454 (2015). https://doi.org/10.1007/s00407-015-0159-7
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DOI: https://doi.org/10.1007/s00407-015-0159-7