John Smeaton and the vis viva controversy - SAGE Journals

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HOS0010.1177/0073275317745455History of ScienceMorris

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John Smeaton and the vis viva controversy: Measuring waterwheel efficiency and the influence of industry on practical mechanics in Britain 1759–1808

HOS History of Science 2018, Vol. 56(2) 196­–223 © The Author(s) 2017 Reprints and permissions: sagepub.co.uk/journalsPermissions.nav https://doi.org/10.1177/0073275317745455 DOI: 10.1177/0073275317745455 journals.sagepub.com/home/hos

Andrew M. A. Morris

Université libre de Bruxelles, Belgium

Abstract In this paper, I will examine John Smeaton’s contribution to the vis viva controversy in Britain, focusing on how the hybridization of science, technology, and industry helped to establish vis viva, or mechanic power, as a measure of motive force. Smeaton, embodying the ‘hybrid expert’ who combined theoretical knowledge and practical knowhow, demonstrated that the notion of vis viva possessed a greater explanatory power than momentum, because it could be used to explain the difference in efficiency between overshot and undershot waterwheels. Smeaton’s conclusions were correct since waterwheel efficiency was already measured in terms that were proportional to vis viva, not momentum, as a result of the industrial applications of waterwheel technology, which favored measuring efficiency by the product of mass and vertical displacement. Toward the end of the eighteenth century, the loss of motive force in the inelastic collision driving the undershot wheel began to be seen as equivalent to the expenditure of labor in the manufacture of commodities, further underlining how strictly scientific conclusions about motive force could have their origin in industrial practices. Keywords John Smeaton, vis viva controversy, hybrid expert, waterwheel efficiency, practical mechanics, industrial applications, eighteenth-century natural philosophy, British Newtonians

Corresponding author: Andrew M. A. Morris, Philosophie, Université libre de Bruxelles, ULB – Campus du Solbosch, CP133/02, Avenue F.D. Roosevelt, 50, Brussels 1050, Belgium. Email: [email protected]

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Introduction and historical background By the middle of the eighteenth century the vis viva controversy had all but ended, with most participants holding either that the controversy was a dispute over the definition of force or that the Cartesian/Newtonian position favoring momentum had won. Yet from 1807 vis viva was to be known as energy, taking a central place in the emerging discipline of thermodynamics as a counterpart to the notion of work. At the same time, these concepts began to be put to use in the service of industry as part of the nascent Industrial Revolution. This paper will explore how John Smeaton’s study of waterwheels contributed to the adoption of vis viva by British scientists at the beginning of the nineteenth century, and how this was a consequence of the blurring of the boundaries between science, technology, and industry.1 The vis viva controversy began in 1686 when Gottfried Leibniz took issue with René Descartes’ understanding of the conservation of motive force. Descartes proposed, in his Principles of Philosophy, that God always conserved the same quantity of motion – what we know of as momentum – and that this quantity was a composition of body and motion, the two most basic constituents of a mechanistic world.2 Thus, for Descartes, quantity of motion was measured by the product of mass and velocity.3 Leibniz devised a thought experiment involving falling bodies which showed that quantity of motion was not the correct measure of motive force, but that vis viva, or the product of mass and velocity squared, was.4 Leibniz’s article drew responses from French Cartesians, but it was the Dutch natural philosopher, Willem ’s Gravesande, who attempted to resolve the controversy with an experiment in favor of vis viva, which realized, in slightly altered form, Leibniz’s thought experiment. ’s Gravesande discovered that the impressions left by copper balls falling into clay was proportional to mv2 not mv, and therefore the motive force that the balls possessed could be measured by mv2.5 His results, however, were disputed by partisans of momentum. The interpretation of ’s Gravesande’s experiment brought to the fore two key points of contention which had already marked the start of the controversy. The first was the question of whether motive force was proportional to time or

  1. Vis viva was given many different names, such as ‘mechanical power’, during this period. For terminological clarity in this article, the term ‘vis viva’ is used to refer to the quantity mv2.    2. René Descartes, “Principia Philosophiæ,” in Charles Adam and Paul Tannery (eds.) Œuvres de Descartes 8 (Paris: Léopold Cerf, 1905), pp.1–329, 61.    3. I will use the terms ‘mass’ and ‘weight’ interchangeably in this article, since a consensus had not yet emerged during this period concerning the distinction between these two terms.    4. Many commentators on the controversy focus on these early papers. cf. Gregory Brown, “‘Quod ostendendum susceperamus’. What did Leibniz Undertake to Show in the Brevis Demonstratio?” in Roger Woolhouse (ed.) Gottfried Wilhelm Leibniz Critical Assessments, Vol. III (London: Routledge, 1994), pp.177–97; Carolyn Iltis, “Leibniz and the Vis Viva Controversy,” Isis 62 (1971): 21–35; and David Papineau, “The Vis Viva Controversy: Do Meanings Matter?” in Roger Woolhouse (ed.) Gottfried Wilhelm Leibniz Critical Assessments Vol. III (London: Routledge, 1984), pp.198–216.    5. See ’s Gravesande, “Essai d’une nouvelle théorie sur le choc des corps,” Journal littéraire de la Haye 12 (1722): 1–53.

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distance, and the second concerned whether motive force was conserved in inelastic collisions.6 Following the debate surrounding this experiment, a number of natural philosophers began to suggest that, although there were differences between the partisans of vis viva and the partisans of momentum, neither position was strictly false.7 Instead, the dispute hinged on what was meant by the word ‘force’, since the time taken for a body to fall was proportional to the final velocity of the fall, while the distance fallen was proportional to the final velocity squared. Choosing between momentum and vis viva had become a simple question of deciding to measure motive force in terms of time or distance.8 In spite of this uncertainty, by the early to mid eighteenth century, momentum had gained the upper hand among natural philosophers, because momentum was better suited to measuring the forces exerted in collisions between bodies. In addition to this, momentum was conserved in inelastic collisions while vis viva was not. There were some areas of research which required the use of mv2, such as the study of springs, but momentum sufficed for most applications. During this period, natural philosophers in Europe began to focus more attention on the behavior of fluids, with important works appearing by influential continental mathematicians Daniel and Johann Bernoulli, as well as Jean le Rond d’Alembert.9 This focus on fluid mechanics also led natural philosophers to understand how to better harness the power of water, since waterwheels were widely used in Europe at the turn of the eighteenth century, but not well understood.10 Before the invention of the steam engine, the    6. Carolyn Iltis, “The Controversy over Living Force: Leibniz to d’Alembert” (unpublished doctoral thesis, University of Wisconsin, 1967), provides the most comprehensive survey of the controversy from Leibniz’s first article on the subject, up to d’Alembert’s famous claim that the controversy was a dispute over words. The issues of time vs displacement and inelastic collisions are discussed by Thomas Hankins, “Eighteenth-Century Attempts to Resolve the Vis viva Controversy,” Isis 56 (1965): 281–97, with a focus on the work of ’s Gravesande and Roger Joseph Boscovich.   7. This compromise was reached by a number of participants in the debate, including ’s Gravesande, d’Alembert, Desaguliers, and many other later writers on the subject.    8. Larry Laudan, “The Vis viva Controversy, a Post-Mortem,” Isis 59 (1968): 130–43, disputes the claim that d’Alembert ended the controversy with his famous diagnosis, according to which the controversy was a dispute over words. Mary Terrall, “Vis Viva Revisited,” History of Science 42 (2004): 189–209, shows how personal and institutional alliances played a role in the continuation of the controversy.    9. For an account of the development of fluid mechanics from the eighteenth century until the present day, see Olivier Darrigol, Worlds of Flow: A History of Hydrodynamics from the Bernoullis to Prandtl (Oxford: Oxford University Press, 2005).   10. Terry S. Reynolds, in his definitive history of the waterwheel, Stronger than a Hundred Men (Baltimore: Johns Hopkins University Press, 1983), analyzes Smeaton’s work in its historical context, as a stepping stone toward a full understanding of the waterwheel. Reynolds also examines the impact of science on technology in his work, concluding that Smeaton did not radically depart from the methodology of earlier engineers and that merely by the fact that he used experiment it could not be inferred that he was significantly influenced by the more strictly scientific practice of his day (p. 286). Since his interests lie elsewhere, however, Reynolds does not treat of the vis viva controversy in any great detail.

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waterwheel was an important source of power in Europe, and its improvement contributed to the early technological advances of the Industrial Revolution. In 1704, Antoine Parent, a lesser-known French natural philosopher, provided a groundbreaking, yet ultimately flawed, analysis of the optimal functioning of waterwheels based on an understanding of motive force as momentum.11 Influential British Newtonians J. T. Desaguliers and Colin Maclaurin had both relied on Parent’s study when composing their own accounts of waterwheels.12 Smeaton, a practicing engineer, carried out extensive scale model experiments in order to put Parent’s results to the test, with a view to constructing more efficient waterwheels. He was also the first to compare different types of waterwheel. His results helped him to become a leading engineer of the Industrial Revolution in Britain. The eighteenth century also saw a gradual breakdown of the social categories which structured scientific practice. In particular, the distinction between natural philosophers and artisans, which represented the “ancient ideological boundaries between hand and mind,” began to give way, as various hybrid figures emerged who combined both theoretical knowledge and practical knowhow.13 Natural philosophers, who had traditionally focused on analytically derived theoretical knowledge based on first principles, began to turn their attention to engineering problems, while traditional artisans made increasing use of the principles of mechanics to understand their work. This change also brought with it a narrowing of the social divide separating theoreticians and practicians, intellectuals and skilled laborers. In this paper I will argue that Smeaton’s contribution to the vis viva controversy was to establish a clear difference between momentum and vis viva by showing that, in the context of waterwheels, the concept of vis viva possessed an explanatory power that the concept of momentum did not.14 I will further contend that this explanatory power only emerged when determining the efficiency of waterwheels was given priority over merely understanding their functioning, and therefore that it was only once natural philosophy turned toward more practical, industrial applications that vis viva found a role. Finally, I  11. Antoine Parent, “Sur la plus grande perfection possible des machines,” Mémoires de l’académie des sciences (1704): 323–38.   12. J. T. Desaguliers, A Course of Experimental Philosophy, 2 vols. (London: W. Innys, M. Senex and T. Longman, 1734–44) II, art. 424; Colin Maclaurin, A Treatise on Fluxions, 2 vols. (Edinburgh: W. Baynes and W. Davis, 1742) II, art. 907. In The Conflict between Atomism and Conservation Theory 1644 to 1860 (New York: Science History Publications, 1970), Wilson L. Scott looks at Smeaton’s innovations in the context of the debate about hard inelastic bodies. Of particular importance to Scott, and to us, is the question of whether vis viva is conserved or lost in impulse waterwheels (that is, those where the wheel is propelled by collisions between the water and the blades) (cf. Chapter seven). Scott’s wideranging study is important insofar as it charts the development of thinking about motive force throughout the eighteenth century. However, Scott subordinates the vis viva controversy to the broader debate over hard bodies.  13. Ursula Klein, “Hybrid Experts,” in Matteo Valleriani (ed.) The Structures of Practical Knowledge (Basel: Springer, 2017), pp.287–306, 303.   14. Jip Van Besouw comes to a similar conclusion regarding the role of vis viva for understanding the wedge in his detailed study “The Wedge and Vis viva Controversy,” Archive for History of Exact Sciences 71 (2017): 109–56.

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will show how this turn toward practical mechanics in Britain led to disagreement about the relationship between theoretical and practical mechanics.15 Much recent historiography has focused on the complex interplay of natural philosophy, technology, and industry during the period considered in this article.16 I intend to contribute to this historiography by showing that Smeaton’s breakthrough in the understanding of motive force only came about because of the influence science, technology, and industry exerted on one another. We will see that Smeaton was what Ursula Klein calls a “hybrid expert,” because he was active in these three fields, and his work grew out of their intersection. I will focus in particular on the influence technology and industry exerted on natural philosophy, which was exemplified in the loss of motive force in inelastic collisions – a loss which could be made sense of as labor’s transformation of brute matter into commodities.

Earlier British studies of the waterwheel: Desaguliers J. T. Desaguliers frs was a prominent lecturer in natural philosophy, known for promoting Newton’s theories and their applicability to practical concerns. He took a great interest in what became known as engineering, studying the designs of early steam engines and waterwheels.17 Desaguliers provided the most extensive analysis of waterwheels in the second volume of his Course of Experimental Philosophy of 1744, where he not only gave an account of waterwheel functioning, but used the waterwheel as an example of how to apply the rules governing the collision of bodies to diverse phenomena. This method had been used since at least as early as Descartes’ Principles of Philosophy.18 Because of the emphasis on the rules governing collisions, any dispute concerning those rules would also have an impact on other fields of enquiry. In the sixth lecture of A Course in Experimental Philosophy Vol. 2, Desaguliers provided the rules for collisions between bodies. He noted that these rules could be widely applied, and that they were of special use in their application to machines. Desaguliers   15. Simon Schaffer discusses this disagreement in his important work “Machine Philosophy: Demonstration Devices in Georgian Mechanics,” Osiris 9 (1994): 157–82. I will contest Schaffer’s interpretation of Smeaton’s work.   16. See for example Paola Bertucci and Olivier Courcelle, “Artisanal Knowledge, Expertise and Patronage in Early Eighteenth-century Paris: the Société des Arts (1728–36),” EighteenthCentury Studies 48 (2015): 159–79; Margaret C. Jacob, “Mechanical Science on the Factory Floor: The Early Industrial Revolution in Leeds,” History of Science 45 (2007): 197–221; Klein, “Hybrid Experts,” and Larry Stewart, “A Meaning for Machines: Modernity, Utility, and the Eighteenth-Century British Public,” The Journal of Modern History 70 (1998): 259–94.   17. A detailed account of Desaguliers’ forays into practical mechanics can be found in Larry Stewart, The Rise of Public Science: Rhetoric, Technology, and Natural Philosophy in Newtonian Britain, 1660–1750 (Cambridge: Cambridge University Press, 1992). This is also discussed in Carlo Poni, “The Craftsman and the Good Engineer,” History and Technology 10 (1993): 215–32.   18. See Descartes, “Principia Philosophiæ” part two: “Of the Principles of Material Things.”

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explained that, through the use of his rules for collisions, the practical artist would be able to design machines without the need for extensive testing by common trial and error.19 He even appeared to value the practical applications of his doctrine of the congress of bodies above its theoretical importance when he wrote that “there is hardly any machine […] contriv’d for the Uses of Life, to which it is not applicable: and several Philosophical Truths are also deduc’d from it.”20 Desaguliers did not attempt to break with orthodoxy in his rules for the collision of bodies, holding instead that his rules were corollaries of Newton’s third law of motion.21 Desaguliers also took a Newtonian position with respect to motive force, arguing that force was proportional to velocity, not velocity squared: “Therefore the Magnitude of the Blow in given Bodies is always proportional to their Velocities respectively.”22 This was no surprise since he had defended momentum as the measure of motive force from as early as 1722.23 In his annotations to the sixth lecture, Desaguliers illustrated the much vaunted practical utility of the rules governing collisions by showing how the action of water on the paddles of an undershot waterwheel was governed by these very rules. He argued that, if a given quantity of water were to strike an undershot wheel, and if this wheel were counterbalanced with a weight (which would represent the resistance of the mill machinery attached to the waterwheel) making it equal to the weight of the water, then the collision between the water and the wheel would obey the rules for an inelastic collision between two equal bodies.24 After the stroke, the water and the paddle of the waterwheel would move together with half the velocity possessed by the water before the stroke.25 Desaguliers went on to argue that, for a working mill, the flow of water powering the mill could be reduced to a succession of collisions, against which the paddles of the waterwheel provided a succession of instantaneous resistances. This analysis of waterwheel functioning will be crucial for grasping how Smeaton ultimately improved our understanding of the workings of waterwheels. Since Desaguliers attached great importance to the practical uses of natural philosophy, he devoted a considerable part of his Course of Experimental Philosophy to describing various machines, with the twelfth lecture focusing on machines which used water. In the annotations to this lecture, he gave an account of the efficiency of overshot waterwheels compared to undershot wheels. Desaguliers compared an overshot mill observed at Nuneaton (Warwickshire, UK) with an undershot mill described by Bernard Forest de Bélidor in his Architecture Hydraulique of 1737.26 He acknowledged that the overshot  19.  20.   21.   22.  23.

Desaguliers, Course Vol. 2, p.1. Ibid. Ibid., p.9. Ibid., p.16. Cf. Desaguliers, “An Account of Some Experiments Made to Prove, That the Force of Moving Bodies is Proportionable to Their Velocities,” Philosophical Transactions 32 (1722): 269–79.  24. Desaguliers, Course Vol. 2, p.35.   25. “If A be equal to B, and B is at rest, A+B: will be to A as 2 to 1, therefore the Velocity of the impinging Body will, before the Stroke, be the Double of what it will be afterwards.” Desaguliers, Course Vol. 2, p.13. Reynolds, in Stronger than a Hundred Men, briefly discusses Desaguliers, but does not touch on this application of rules governing collisions.   26. Bernard Forest de Bélidor, Architecture Hydraulique, 2 vols. (Paris, 1737–9) 2, art. 635. Desaguliers cites Bélidor’s text at length.

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wheel was more efficient than the undershot, noting that “a well-made Over-shot Mill ground as much Corn in the same time as an Under-shot Mill with ten times less Water: supposing the Fall of Water at the Over-shot to be 20 Feet, and at the Under-shot to be about six or seven Feet.”27 Thus, Desaguliers estimated the overshot wheel to be around three and a half times more efficient than the undershot.28 Desaguliers did not attempt to explain why the overshot wheel was more efficient than the undershot. The evidence suggests he would have been unable to do so. Desaguliers implied that he favored impulse over gravity as the source of motive force for waterwheels when he quoted the analysis of Henry Beighton frs – an English engineer who specialized in detailed descriptions and technical drawings of machines – who said: “Of so much more service is the Impulse, Stroke, or Momentum of the Water, than is its bare Statical Weight.”29 Yet when Desaguliers considered whether it would be preferable to add some impulse to the overshot wheel, he concluded that this could only be done to a limited extent, where the water struck the paddles directly, instead of “dashing in the Water that is already in the Bucket, and making a Froth.”30 Here Desaguliers was tacitly recognizing that an inelastic collision – water striking water in the bucket – was less efficient than an elastic collision. Such would be anathema to a Newtonian who believed that motive force was measured by momentum, which was conserved in both elastic and inelastic collisions. This admission, combined with the fact that overshot wheels were more efficient than undershot wheels, appeared to contradict Beighton’s claim – cited by Desaguliers – that impulse was of greater service than gravity for propelling waterwheels. In other words, Desaguliers seemed to accept that (1) the most efficient waterwheels were overshot, and (2) overshot wheels worked primarily with gravity, only allowing a small proportion of impulse, yet (3) impulse was better than gravity for providing motive force to waterwheels.31

Measuring efficiency: motive force as power to raise weights Desaguliers was unable to explain the difference in efficiency between overshot and undershot waterwheels because, when he adopted Parent’s theory, he also inherited the paradoxes which could be found in Parent’s work. Parent, in his article from 1704, gave

 27. Desaguliers, Course Vol. 2, p.532.   28. This is also noted in Reynolds, Stronger than a Hundred Men, p.215. Schaffer, “Machine Philosophy,” pp.174–5, appears to suggest that Desaguliers was able to establish the superior efficiency of the overshot wheel from experiments on model reaction wheels. However, Desaguliers’ comparison in his Course of Experimental Philosophy is derived from observations of working watermills, not demonstration devices.  29. Desaguliers, Course Vol. 2, p.453.   30. Ibid., p.532.  31. Reynolds, Stronger than a Hundred Men, pp.214–16, discusses these passages without drawing attention to the contradiction. He does note, however, that the mechanical philosophy of the period “made the problem of impact a central issue to scientists of the era, and thus, the impact or impulse wheel was more likely to attract attention” (p.212).

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a momentum-based account of the optimal functioning of waterwheels – that is, in terms of the product of mass and velocity. Yet in the opening paragraphs of this article he revealed that the function of waterwheels was not to generate velocity in bodies, but rather to raise bodies to certain heights.32 He said: Given a machine which has as its motive force some fluid body, like, for example, water, wind or flames, etc., and which serves to raise solid or liquid weights, such as stones or water etc., we propose to find the charge that should be given to this machine, and the proportion the different parts must have, in order that it produce the greatest possible effect, which is to say, that it raise the greatest quantity of weight in a given time.33

The waterwheel was not an experimental apparatus, but an industrial machine whose use did not depend on the opinions of natural philosophers. It depended on the practices of raising water out of mineshafts or grinding corn, and it was these practical applications of the waterwheel that determined that its efficiency should best be measured by the height to which it raised a given weight, not the velocity attained by this weight.34 Through its application to industrial machines, natural philosophy came to be exposed to the exigencies of industry. Measuring the efficiency of waterwheels did not merely consist in applying theoretical principles to concrete cases, as Desaguliers presumed. This presupposition dogged both early natural philosophers, who tried to derive their practical mechanics from first principles, and the early historiography, which tended to understand technology as the application of these first principles to specific problems.35 Measuring efficiency actually involved a twofold transformation of natural philosophy, in order to take account of the notion of mechanical efficiency necessary for comparing machines, and the uses to which the machines in question were put. Harnessing a power source (humans, animals, steam, water, and so forth) involved developing an apparatus which transformed the work done by this power source into a form that could be used.36

  32. Donald Cardwell, “Some Factors in the Early Development of the Concepts of Power, Work and Energy,” British Journal for the History of Science 3.03 (1967): 209–24, 211, credits Parent as the originator of the idea of mechanical efficiency. It is thus understandable that the idea lacked clarity.   33. Parent, “Sur la plus grande perfection possible des machines,” p.325 (my translation).  34. Cardwell, “Some Factors,” p.215, is the only commentator to emphasize the industrial importance of mgh as a measure of work. He says: “Mining, the great power-using industry, required, as a natural measure, the raising of a given weight a given distance in a given time […] it is clear that craft practice could not give rise to such a measure.”  35. Nathan Rosenberg, Inside the Black Box: Technology and Economics (Cambridge: Cambridge University Press, 1982), p.143, makes the case for rejecting the view according to which “it is common to think of technology as if it were reducible to the application of prior scientific knowledge.”   36. Liliane Hilaire-Pérez, La pièce et le geste (Paris: Albin Michel, 2013), p.4, identifies the social forces at work in the rise of the notion of efficiency: “Together with the need for precision in production and the rise of machine science, technology, as an industrial science, is based on calculating the useful effect, or ‘quantity of action’, of machines, or, more generally, of bodies put to work” (my translation).

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Thus a flowing river, with the installation of a waterwheel and a system of pulleys or gears, could be used to raise water out of a mine or to grind corn. To evaluate the efficiency of this waterwheel system, it would be necessary to establish a way of measuring the output of the system – water raised or corn ground – and compare it to a compatible measure for the input of the flowing river – the quantity of descending water. In other words, it was the practical application of the waterwheel which determined how its efficiency was to be measured, and this was best expressed by the product of weight (mass) and vertical displacement. The efficiency of a waterwheel was thus calculated by comparing the weight of water falling a certain distance with the weight that could be raised by this quantity of water. Importantly for the vis viva debate, vis viva, not momentum, was proportional to weight times height. And, according to this measure of efficiency, the undershot wheel was less efficient than the overshot wheel. If the efficiency of waterwheels was measured using momentum, there would be a much smaller difference in efficiency between the overshot and the undershot wheel. However, since it was accepted by both sides of the debate (Desaguliers and Smeaton in this case) that the overshot wheel was much more efficient than the undershot, once it was demonstrated that vis viva was lost in undershot wheels, but conserved in overshot wheels, then partisans of momentum would be obliged to accept that vis viva was a better measure of motive force than momentum. This was what was at stake in the question of waterwheel efficiency.

Smeaton’s improvement of the waterwheel John Smeaton frs was a pioneer of civil engineering who possessed both the practical knowhow and the theoretical knowledge to make improvements in a number of technological domains, such as the waterwheel, the lighthouse, and the steam engine. He was perhaps one of the most famous examples of the “hybrid expert” who bridged the gap between theory and practice.37 According to Ursula Klein, the hybrid expert was an artisan who also “borrowed knowledge from books; they were experimenters and inventors; they often kept experimental notebooks; and they also gained experience through travelling and through conversations with experienced merchants, men of science and all kinds of researchers and inventors.”38 Smeaton, born in 1724 in the parish of Austhorpe in Leeds (which was, incidentally, a major mill town in West Yorkshire during the Industrial Revolution), came from an upwardly mobile family – his father was an attorney at law – but decided to devote himself to instrument making, against the wishes of his father.39 He did not restrict himself

  37. Klein, “Hybrid Experts,” p.288: “Experts did not carry out hard physical work, but all of them did some handiwork, for example, in the context of measuring, testing, experimenting and so on. And all of them mobilized propositional knowledge for organizing and carrying out their practical enterprises. Thus the social figure of the expert undermined the ancient ideological distinction between hand and mind.”   38. Klein, “Hybrid Experts,” p.288.  39. Trevor Turner and A. W. Skempton, “John Smeaton,” in A. W. Skempton (ed.) John Smeaton, FRS (London: T. Telford, 1981), pp.7–34, 8.

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to becoming an artisan, however. He learned French (he had already learned Latin at school) in order to read the latest treatises on natural philosophy or engineering.40 As an adolescent, he had already begun to master the techniques of the instrument maker, forging steel, grinding lenses, and making himself familiar with the tools of the trade, and he achieved early success by improving the vacuum pump.41 Smeaton kept a detailed record of his work throughout his lifetime, amassing 200 reports and 1,000 technical drawings, as well as numerous published articles.42 In addition to reading widely, he traveled to the Low Countries to study the engineering works there.43 Later in his career, Smeaton was a founding member of the Society of Civil Engineers, as well as an active member of the Royal Society. According to his biographers Trevor Turner and A. W. Skempton: He was a man who met as equals Joseph Priestley and Henry Cavendish, who proposed James Watt for Fellowship of the Royal Society, who counted among his closest friends such distinguished men as John Michell and Alexander Aubert, and who had his portrait painted by Romney, Gainsborough and several other artists of note; but who, in turn, never failed to meet his fellow engineers at their club whenever he was in town.44

Despite starting his career in what was considered to be a lowly position of instrument maker, Smeaton did not turn his back on his past as an artisan, even making sure to equip a workshop with his tools when traveling to London later in life.45 It was in this role of hybrid expert that Smeaton investigated the efficiency of waterwheels. He intended his work to clarify the contradictory theoretical analyses of waterwheel functioning which were dominant at the time, with a view to constructing the most efficient waterwheels in Britain. Overshot and undershot wheels had seldom been compared since it had always been presupposed that equal quantities of water produced equal effects. According to Smeaton, “[i]n reasoning without experiment, one might be led to imagine, that however different the mode of application is; yet that whenever the same quantity of water descends thro’ the same perpendicular space, that the natural effective power would be equal.”46 This despite the fact that overshot and undershot wheels had already been recognized as differing in one important respect: the undershot wheel was powered by impulse, whereas the overshot wheel was powered by gravitation. And as we have seen, impulse was thought to be better than gravity at transmitting motive force. In order to determine the difference in efficiency between undershot and overshot waterwheels, Smeaton constructed a miniature waterwheel apparatus to test both types of waterwheel by adapting the apparatus (Figure 1).47 The water was stored in a column   40.   41.   42.   43.   44.   45.   46.

Ibid., p.9. Ibid., p.10. Ibid., p.16. Ibid., p.13. Ibid., p.26. Ibid., p.30. Smeaton, “An Experimental Enquiry concerning the Natural Powers of Water and Wind to Turn Mills, and Other Machines, Depending on a Circular Motion,” Philosophical Transactions 51 (1759): 100–174, 124.  47. Reynolds, Stronger than a Hundred Men, pp.223–6, provides a concise summary of Smeaton’s experiments on waterwheel efficiency.

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Figure 1.  Smeaton’s waterwheel apparatus, set up as an undershot wheel. From Smeaton, “An Experimental Enquiry concerning the Natural Powers of Water and Wind to Turn Mills, and Other Machines, Depending on a Circular Motion,” Philosophical Transactions 51 (1759): 100–174, 101, courtesy of the Royal Society.

to the right of the wheel and, in the case of the undershot wheel, flowed out of an aperture at the foot of the column, along a trough under the wheel. This water turned the wheel, which then lifted the weight by means of a pulley. The force of the water was measured by the product of the height of the water’s fall and the size of the aperture, which controlled the quantity of water released. This system meant that Smeaton could then adapt the apparatus to test the efficiency of an overshot wheel by adding a sluice which released the water on to the top of the waterwheel. To calculate efficiency, Smeaton compared the mass falling from a certain height in one minute to the mass that was raised in one minute. In other words, he multiplied the quantity of water which powered the wheel for one minute by the height from which that water had fallen to provide what he called the “power of the water to produce mechanical effects.”48 Smeaton stated that “by multiplying the quantity, or weight of water, really expended in a given time, by the height of the head so obtained; which must be considered as the height from which that weight of water had descended in that given time; we shall have a product, equal to the original power of the water; and clear of all uncertainty.”49 To find the mechanical effect, Smeaton then took the product of the weight raised in one minute and the height to which that weight was   48. Smeaton, “An Experimental Enquiry,” p.111.   49. Ibid., p.106.

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raised. The ratio of power to effect gave the efficiency of the waterwheel under consideration. Yet even this apparently straightforward approach did not earn unanimous approval. John Playfair frs, a respected mathematician and geologist, writing in the Edinburgh Review of 1808, argued that, by taking time into consideration, Smeaton was merely reintroducing the notion of momentum which he was trying to exclude: “Thus, in the very outset of the investigation, the principle of the vis viva, or mechanical power, is in fact abandoned, in consequence of including time in the measure of the effect, without which, however, that measure would be imperfect.”50 Vis viva alone, according to Playfair, would not be enough to provide a satisfactory analysis of mechanical efficiency, so Smeaton had no choice but to include time, and therefore momentum, in his study. Peter Ewart frs, an engineer and colleague of Matthew Boulton and James Watt, and a staunch defender of Smeaton’s ideas in the early nineteenth century, gave a rebuttal of this argument in his “On the Measure of Moving Force,” which he read to the Manchester Literary and Philosophical Society later that year. He contended that, although the time was included by Smeaton, it was merely as a means to determine the quantity of water under consideration: Now the time of one minute is taken merely because it is known that a certain quantity of water passes in that time – the effect which is to be estimated being produced in the same time. But the time is by no means a necessary element in the estimation of the effect; for the height to which a weight is raised by any other given quantity of the running water, may easily be determined without reference to the time, and the result will be the same as when time is considered.51

In order to give an accurate account of the efficiency of overshot and undershot wheels, Smeaton tested a wide range of weights in order to find the optimal performance – where “the effect is a maximum” – of both wheels.52 Smeaton also used a counterweight to calculate the amount of friction and resistance found in the workings of the wheel, in order to eliminate it, thus ensuring that his experiments were not only applicable to the particular waterwheel used, but to all waterwheels.53 Any waterwheel which achieved a 1:1 ratio between power and effect would be perfectly efficient. Smeaton’s results tell us that the overshot wheel was more than twice as efficient as the undershot wheel, because it had an efficiency of 10:6.6, whereas the undershot wheel’s efficiency was only 10:3.2.54

 50. [John Playfair], “Bakerian Lecture on the Force of Percussion,” Edinburgh Review 12 (1808): 120–30, 123.   51. Peter Ewart, “On the Measure of Moving Force (Read Nov. 18, 1808),” Memoirs of the Manchester Literary and Philosophical Society 2 (1813): 105–258, 146.   52. Smeaton, “An Experimental Enquiry,” p.107.   53. Ibid, pp.107–9. Schaffer, “Machine Philosophy,” p.175, calls this “Smeaton’s most important technique,” making it the centerpiece of his analysis, although I would argue that it was the loss of vis viva in inelastic collisions, not friction, which was at the core of Smeaton’s research.   54. Smeaton, “An Experimental Enquiry,” pp.111–28. According to Reynolds, Stronger than a Hundred Men, p.226, “Smeaton found, to his surprise, that his model overshot-gravity wheel had an efficiency roughly twice that of his undershot wheel.”

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The collision which occurred between the water and the paddles of the undershot wheel was an inelastic collision. Smeaton concluded that the difference in efficiency between the different types of waterwheel could be explained by the production of turbulence – and thus loss of force – in this inelastic collision between the water and the wheel, and since momentum was conserved in inelastic collisions, it was therefore the loss of vis viva which explained the difference.55 He said: The effect therefore of overshot wheels, under the same circumstances of quantity and fall, is at a medium double to that of the undershot: and, as a consequence thereof, that nonelastic bodies, when acting by their impulse or collision, communicate only a part of their original power; the other part being spent in changing their figure in consequence of the stroke.56

This conclusion was only possible because the industrial use of waterwheels demanded that efficiency be understood in terms of the raising of bodies to a certain height. As a hybrid expert who had firsthand knowledge of the growing congestion on the waterways of Britain, Smeaton was sensitive to the needs of industry, and the crucial importance of efficiency. The proliferation of waterwheels in the eighteenth century meant that each waterwheel needed to be more efficient in order to extract the most power from the increasingly clogged and slow waterways. Because efficiency was measured by the product of mass and vertical displacement, there was a large difference in efficiency between over and undershot wheels. And since mass times height was proportional to vis viva, not momentum, it was the loss of vis viva in inelastic collisions which explained the difference in efficiency between undershot wheels (which involved inelastic collisions) and overshot wheels (which did not involve inelastic collisions). If efficiency had been measured by the product of the mass and velocity of the water, there would have been a much smaller difference in efficiency between over and undershot wheels, since mass times velocity was proportional to momentum, and momentum was conserved in inelastic collisions.57 The influence of industrial applications also led to a broader conclusion: given that loss of vis viva accounted for the difference in efficiency between the undershot and overshot waterwheel, then vis viva, not momentum, was the true measure of motive force. This was why Smeaton’s contribution to the understanding of waterwheels became a part of the vis viva controversy. It is important to remember, however, that by using momentum it was still possible to give a mathematically accurate account of the functioning of a waterwheel, except that,   55. Smeaton, “An Experimental Enquiry,” p.130.   56. Ibid. (my emphasis). cf. Reynolds, Stronger than a Hundred Men, p.226: “He suggested that most of the difference was probably due to the power wasted by the water in turbulent impact against the blades of the undershot wheel.”   57. As we shall see, the overshot wheel was more efficient than the undershot for two reasons. The first was the loss of vis viva in the collision between the water and the paddles, and the second was the relatively high velocity of the water as it left the undershot waterwheel, which amounted to lost motive force. However, the loss of vis viva was greater than the loss of motive force in the velocity of the water exiting the wheel.

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since momentum was conserved in inelastic collisions, the difference in efficiency between overshot wheels and undershot wheels would remain unexplained.58 As we shall see in the second half of this paper, Smeaton’s understanding of motive force became intuitively appealing during the eighteenth century. Since changing the figure of bodies through the expenditure of force – producing commodities – was central to manufacturing, it made sense to postulate that motive force was lost in collisions where there was a change of figure. Earlier natural philosophers, by contrast, could not accept a loss of motive force in inelastic collisions because they presupposed that motive force was always conserved.

Loss of motive force in inelastic collisions Smeaton’s conclusion regarding the difference in efficiency between undershot and overshot waterwheels, although a groundbreaking discovery in the study of water power, had already been put forward in the debates about vis viva. Indeed, the thesis that vis viva was lost in inelastic collisions was rejected by the earliest partisans of vis viva, Leibniz and Johann Bernoulli.59 Leibniz argued for the conservation of vis viva in all collisions since he thought vis viva should replace Descartes’ quantity of motion as that which God always conserved in the universe. He postulated that vis viva was not lost in inelastic collisions, but that it was dispersed into the parts of the inelastic body.60 However, this view ran up against atomism, the theory according to which the ultimate constituents of matter were indivisible, and so did not have any parts into which the vis viva could be dispersed. Leibniz and Bernoulli were forced to reject the existence of hard, inelastic bodies in order to hold on to the claim that vis viva was always conserved. With ’s Gravesande, however, a theoretical shift occurred. He argued that vis viva was lost in inelastic collisions because motive force was expended in changing the figure of the inelastic body: “Whilst the Parts of Bodies are pressed inwards, the Force is destroyed, which exceeds the Pressure, by which they cohere […] No Force is destroy’d in the Collision of Bodies, besides that by which the Parts are pressed inwards.”61 Indeed, this new position put Newtonians on the back foot, since ’s Gravesande was dutifully  58. For Schaffer, “Machine Philosophy,” p.176, “[b]aldly expressed as mathematical proportionalities, Smeaton’s results could easily have been absorbed into academic rational mechanics. However, the gentlemanly engineer presented them as major challenges to received machine philosophy.” As Cardwell, “Some Factors,” p.223, puts it, “the orthodox tradition was less suggestive, it gave less insight, than the newer mechanics.” One of our tasks in this paper is to explain why Smeaton’s understanding of waterwheel functioning provided more insight than the orthodox tradition.  59. Scott, Conflict, p.33, writes of “deliberate efforts to avoid accounting for permanent loss or change.” It is worth noting that Scott restricts his analysis to the question of hard bodies, without really focusing on inelastic soft bodies.   60. See for example: Samuel Clarke and Gottfried Leibniz, The Leibniz-Clarke Correspondence, H. G. Alexander (ed.) (Manchester: Manchester University Press, 1956), art. 99.   61. ’s Gravesande, Mathematical Elements of Natural Philosophy, Confirm’d by Experiments, 2 vols., trans. into English by J. Desaguliers (London: W. Innys, T. Longman et al., 1747) I, 217–18 (arts. 932–4) (my emphasis).

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applying an interpretation of Newton’s third law, according to which there was no effect without a cause.62 This argument was compelling because, as the vis viva controversy developed, the elasticity of bodies came to be assimilated to that of a spring, and effort was required to compress a spring. If the body that was compressed did not return to its original form (that is, if it was inelastic) then the force used to compress it was lost. However, if the Newtonians accepted that motive force was lost in inelastic collisions, they would be identifying motive force with vis viva, not momentum, since momentum was not lost in inelastic collisions. Desaguliers said he came close to being convinced by this reasoning before reconsidering the matter: [T]o make use of the old Opinion, which gave the same Quantity of Motion after the Stroke as before, was to neglect an evident Phaenomenon, and admit a visible Effect, (the denting in of the Bodies) without believing that any Part of the Cause was lost in producing it. These Reasons at first appear’d to me so probable, that I was almost ready to quit the old Opinion.63

Colin Maclaurin frs, a respected Scottish mathematician and Newtonian natural philosopher, considered this position only to reject it. He said: Because the parts yield, in their collisions, certain philosophers have imagined that some force must be lost in producing this effect: but there is no motion communicated to any one part that it can lose without communicating it to others […] a body acting upon a soft body can lose no force but what must be communicated to the parts of that body, which therefore must be accumulated to the force of the whole.64

Interestingly, both Desaguliers and Maclaurin adopted Leibniz’s argument, according to which the motive force was not lost in the collision, but merely transferred to the parts of the body which had changed its figure.65 This was an interesting volteface. At the beginning of the controversy, partisans of vis viva argued for the conservation of vis viva in the small parts of the inelastic body because the loss of vis viva in inelastic collisions was seen as a weakness of the theory. By the mid eighteenth century, however, it was the partisans of momentum who argued for the conservation of motive force in the small parts of the inelastic body because the loss of vis viva in inelastic collisions had come to be seen as one of the principal strengths of the theory. This reversal came about as a result of the increasing importance of manufacturing and the central role of commodity-producing labor, which I will discuss in the final section of this paper.   62. This is an interesting example of how scientists needed to develop a theory which appears to us to be false (the non-conservation of energy) in order to progress toward a deeper understanding (the conversion of kinetic energy into heat).  63. Desaguliers, Course Vol. 2, p.54.   64. Colin Maclaurin, An Account of Sir Isaac Newton’s Philosophical Discoveries (London: J. Nourse, W. Strahan et al., 1748), p.196.  65. Desaguliers, Course Vol. 2, p.55, and Maclaurin, Account, p.196. For a brief statement of Leibniz’s position, see the fifth letter to Clarke.

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Figure 2.  Smeaton’s experimental device for testing inelastic collisions. The curved springs at the ends of the rods (e and g) are compressed in the collision, and then held in place by the ratchets above them. From Smeaton, “New Fundamental Experiments upon the Collision of Bodies,” Philosophical Transactions 72 (1782): 337–54, 354, courtesy of the Royal Society.

Smeaton, after having shown by experiment that the overshot wheel was more efficient than the undershot, entered into the vis viva controversy in earnest when he published two more papers which he intended to provide experimental proof that motive force was measured by vis viva, not momentum. In his second paper, Smeaton defined the mechanical power of a body as the weight of that body multiplied by the height from which it could descend. He provided a series of experimental results showing the different velocities obtained when a body was accelerated from rest by various different falling weights.66 His   66. John Smeaton, “An Experimental Examination of the Quantity and Proportion of Mechanic Power Necessary to be Employed in Giving Different Degrees of Velocity to Heavy Bodies from a State of Rest,” Philosophical Transactions 66 (1776): 450–75, 458.

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third paper is of more interest to us, since there he carried out experiments on inelastic collisions. Following the conclusions of his first article on waterwheels, according to which the undershot waterwheel was less efficient than the overshot because motive force was lost in the striking of the water against the paddles of the wheel, Smeaton sought to confirm and refine this result with further experiments on colliding bodies.67 Since his first article, it was also clear that Smeaton had begun to take an interest in the vis viva controversy, as both his later articles provided much more contextual information than his first article, which had simply stated his methods and results. Smeaton tried to correct two mistakes he thought participants in the vis viva controversy had made. Firstly, he claimed that it was not possible to deny a priori the existence of inelastic hard bodies, as partisans of vis viva had tended to do; and secondly, he claimed that it would be absurd to deny that the shape of a body could be changed without any loss of motive force.68 To support these two claims, Smeaton carried out experiments on inelastic collisions using an apparatus equipped with a spring and a ratchet mechanism for measuring the amount of force used up in inelastic collisions (Figure 2). As a collision occurred, the spring would be bent back and the ratchet would hold the spring in place, instead of it springing back as it would in an elastic collision. Smeaton’s experiment was guided by the idea that an inelastic collision was an elastic collision where the body did not return to its original shape.69 In other words, he conceived the inelastic collision as an incomplete elastic collision, because the bodies involved were compressed, but did not return to their original shapes, as in an elastic collision. After taking into consideration the friction of the ratchet and springs, and the elasticity remaining in the apparatus (which prevented Smeaton from achieving a fully inelastic collision using springs), Smeaton was able to determine the force used to compress the spring by looking at the force imparted by the spring when it was subsequently released, since “the power of restitution of a perfect spring is exactly equal to the power that bends it.”70 He concluded, confirming the results of his first article on waterwheels, that “in the collision of non elastic soft bodies, one half of the mechanic power residing in the striking body is lost in the stroke.”71 It was this conclusion which provoked debate among British natural philosophers, since it could not be easily assimilated by Newtonian mechanics.72 According to the broadly Newtonian position, momentum, and therefore

  67. Schaffer, “Machine Philosophy,” p.177, neglects this aspect of Smeaton’s research, despite calling it “crucial.”   68. John Smeaton, “New Fundamental Experiments upon the Collision of Bodies,” Philosophical Transactions 72 (1782): 337–54, 342. Scott, Conflict, pp.147–9, analyzes this article exclusively in terms of the controversy about hard bodies, ignoring Smeaton’s central conclusion concerning inelastic soft body collisions.   69. Smeaton, “New Fundamental Experiments,” p.346.   70. Ibid., p.352.  71. Ibid.   72. According to Cardwell, “Some Factors,” p.213, “[t]he received Newtonian doctrine was that momentum is conserved in all collisions; and this gives no immediate measure or indication of the power, or ‘duty’ lost by generation of spray or turbulence.”

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force, was conserved in both elastic and inelastic collisions, but Smeaton’s conclusions appeared to show that force was actually lost in inelastic collisions.

Difficulties adopting a practical approach in mechanics The shift toward a more practically oriented natural philosophy posed difficulties for even the most practical of thinkers. Although Smeaton was the first to propose that undershot waterwheels were less efficient because they involved an inelastic collision, it was Jean-Charles Borda, a French mathematician, natural philosopher, and naval engineer, who, in 1767, was the first to notice that the relatively high velocity of the water leaving the undershot wheel contributed to its inefficiency, since this amounted to unused motive force.73 On Desaguliers’ schema, which understood the waterwheel in terms of an inelastic collision where momentum was conserved, this loss of motive force – in the velocity of the water leaving the waterwheel – equaled half the vis viva which Smeaton had shown to be lost in the inelastic collision. Yet no one before Borda noticed this loss of motive force, despite the fact that one did not need to theorize waterwheels in terms of vis viva to detect it. This oversight indicates to us that the natural philosophers of the eighteenth century had difficulties taking a more practical stance. As we have seen, using momentum alone it was possible to correctly determine the velocities of the water before and after entering the waterwheel, as well as the velocity of the wheel itself.74 However, it was only by distinguishing between that which propelled the waterwheel and that which did not, or, in other words, by attending to the efficiency of the waterwheel, that it became possible to improve it. The difficulties faced by natural philosophers when trying to take a more practical approach suggest that the new approach had not yet been fully assimilated. Indeed, it was toward the beginning of the nineteenth century that British natural philosophers began to advocate for the practical attitude, with some going so far as to presuppose that the interests of science aligned perfectly with those of industry.75 This movement was already well underway when Desaguliers published his Course in Experimental Philosophy in 1734.76 Recent research has focused on how a number of institutions emerged during this period that embodied this hybridization of science, technology, and industry, thus helping to remove the ideological barrier separating theory from practice.77   73. Jean-Charles Borda, “Mémoire sur les roues hydrauliques,” Mémoires de l’académie des sciences (1767): 270–87, 283. For a discussion of this issue, see Reynolds, Stronger than a Hundred Men, p.240.   74. Borda demonstrated this clearly in his “Mémoire sur les roues hydrauliques.”  75. Rupert Hall, “Engineering and the Scientific Revolution,” Technology and Culture 2.4 (1961): 333–41, 338, tells of “a new race of engineers” who began to emerge at the end of the eighteenth century, and who bridged the gap between science and technology.  76. Stewart, The Rise of Public Science, shows how Desaguliers placed great importance on the practical applications of natural philosophy: “If there was a gap between theory and practice, Desaguliers bridged it” (p.220).  77. See Bertucci and Courcelle, “Artisanal Knowledge,” and Joel Mokyr, “The Intellectual Origins of Modern Economic Growth,” The Journal of Economic History 65 (2005): 285– 351, who develops the notion of an Industrial Enlightenment.

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Yet the move toward a practical natural philosophy did not go unopposed. Partisans of momentum, aware that vis viva seemed to more accurately measure motive force for certain practical applications, began to try to separate theory and practice in natural philosophy.78 George Atwood frs, a Newtonian mathematician and natural philosopher, was the most outspoken critic of attempts by engineers such as Smeaton to intervene in debates about the general principles of mechanics. He argued that natural philosophy and practical mechanics were not closely related. Since Atwood clearly expressed the increasingly outdated view of the separation between theoretical and practical mechanics, it is worth quoting him at length: It is not probable that the theory of motion, however incontestable its principles may be, can afford much assistance to the practical mechanic; and there appears as little reason to imagine that any errors or misconceptions which may have been propagated concerning the effects of forces considered in a theoretical view, have at all impeded the due construction of useful machines, such as are impelled by the force of wind or water, by springs, or any other kind of motive power. Machines of this sort, owe their origin and improvement to other sources: it is from long experience of repeated trials, errors, deliberations, corrections, continued throughout the lives of individuals, and by successive generations of them, that the sciences strictly called practical, derive their gradual advancement from feeble and awkward beginnings, to their most perfect state of excellence.79

Atwood advocated for a complete separation of practical and theoretical mechanics. His mention of wind, water, and springs was a reference to partisans of vis viva who tried to use results obtained in practical mechanics to argue a position in the vis viva controversy, which concerned the foundational principles of theoretical mechanics.80 By arguing that practical mechanics could not be used to provide the general principles of theoretical mechanics, certain British Newtonians of the late eighteenth and early nineteenth centuries hoped to preserve the primacy of momentum over vis viva as the measure of motive force. Isaac Milner frs, a Newtonian natural philosopher and inventor, Thomas Parkinson frs, an English clergyman and Newtonian natural philosopher, and the renowned polymath Thomas Young frs, all attempted to establish a similar separation, without going so far as to argue that theoretical mechanics was of no help to practical mechanics.81 Milner  78. Scott, Conflict, p.140, does not take into account the resistance from orthodox British Newtonians, arguing that, “[f]rom an historical point of view, this signifies the growing union in Great Britain between the practical engineering tradition and the scholarly lucubrations on vis viva, representing a marked industrial advance.”   79. George Atwood, A Treatise on the Rectilinear Motion and Rotation of Bodies (Cambridge: J. Archdeacon, 1784), pp.380–1. Cardwell, “Some Factors,” p.214, is astonished that Atwood would reject the union of theoretical and practical mechanics: “It is almost as if a modern physicist were to assert that physics can throw little light on the processes of a nuclear reactor.”   80. Smeaton discussed wind and water, and J. Bernoulli analyzed springs.   81. Contrary to the position advanced by Schaffer, “Machine Philosophy,” pp.172–8, the British academic reaction to Smeaton’s research did not only focus on friction, but emphasized the more general distinction between the ideal world of theoretical mechanics and the messy

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held that, while natural philosophy did provide the theoretical foundation for practical mechanics, their results may diverge because the theoretician worked with an idealized model of reality which did not take into account the true behavior of bodies.82 A similar point was also made by Atwood, who insisted that the “friction, tenacity, the irregular action of the impelling force, and of the resistances” made it impossible to compare the results obtained in theory and in practice.83 For Parkinson, “[t]heory is very seldom confirmed by practice,” since there were too many conditional circumstances attached to the practical applications of theoretical principles; the truth of such applications could only compare unfavorably to the “experimental proofs clearly comprehended” which were at the center of theoretical mechanics.84 In addition, Milner argued, the collisions studied by theoretical mechanics were not suited to the needs of practical mechanics because “[t]he collisions of bodies are too violent operations to enter into the composition of useful machines, in which motions are rather to be preserved by the gradual effects of weights and pressures.”85 Young held that the most persuasive arguments of theoretical mechanics favored momentum, but practical mechanics, which was more concerned with resistance and less with idealized collisions, was better served using vis viva (which he famously called energy): “In almost all cases of the forces employed in practical mechanics, the labour expended in producing any motion, is proportional, not to the momentum, but to the energy which is obtained.”86 This backlash against the hybridization of mechanics had its source in the threat to Newtonian orthodoxy posed by Smeaton’s rethinking of motive force. By separating practical from theoretical mechanics, these Newtonians hoped to save the central tenets of their master’s teachings while giving up only that which they considered to be relatively inessential: the practical uses of Newtonian mechanics.

Natural philosophy in the service of industry The attempt to maintain a firm distinction between theoretical and practical mechanics – in the way that natural philosophy had formerly been distinguished from the mechanical arts – seemed doomed to failure, however. Over the course of the eighteenth century, this distinction gradually began to disappear as natural philosophers, such as Desaguliers,

  82.  83.  84.   85.   86.

reality of practical mechanics. Neither Isaac Milner, “Reflections on the Communication of Motion by Impact and Gravity,” Philosophical Transactions 68 (1778): 344–79, 371, nor Thomas Parkinson, A System of Mechanics (Cambridge: J. Archdeacon, 1785), p. 70 (both cited by Schaffer), discuss friction directly, preferring to refer to “collateral circumstances” or “collateral causes,” the same that Smeaton (“An Experimental Examination,” p.452) himself mentioned – rather diplomatically – to explain the difference between Newtonian orthodoxy and his own conclusions. Milner, “Reflections,” p.371. Atwood, Treatise, p.381. Parkinson, System of Mechanics, p.70. Milner, “Reflections,” pp.363–4. Thomas Young, A Course of Lectures on Natural Philosophy and the Mechanical Arts (London: Johnson, 1807), p.60.

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embarked on practical enterprises, and engineers, such as Smeaton, turned their attention toward the principles of theoretical mechanics.87 The transformation of the relationship between natural philosophy, technology, and industry in the eighteenth century has been widely discussed in the recent literature. Much emphasis has been placed on the false dichotomy between theory and practice, and the older historiographical tendency to cultivate this dichotomy.88 I would argue that a real distinction did exist between artisans and natural philosophers, but that the eighteenth century opened up a space for the evolution of these social identities through the sharing of knowledge and practices, which was spurred on by the incentives offered by industry. This new trend toward the unification of industry and natural philosophy was exemplified in the notion of efficiency, which only emerged when it became necessary to evaluate nature’s capacity to do work.89 Thus even scientists such as Milner and Young, who defended the distinction between practical and theoretical mechanics, emphasized the importance of natural philosophy for practical mechanics and the interests of industry.90 For Milner, “[t]he right understanding of these laws [the laws of theoretical mechanics] is of the last importance in practice: the good or bad success of some very expensive projects has depended upon it.”91 Young, in preparing a series of lectures for the Royal Institution of Great Britain, drew inspiration from the role of this newly formed institution, which was to “apply to domestic convenience the improvements which have been made in science, and to introduce into general practice such mechanical inventions as are of decided utility.”92 Natural philosophy, according to Young, provided the theoretical principles which underpinned not only the speculative understanding of the cosmos, but also the most prosaic of machines and industrial processes.93 Young also argued that theoretical mechanics was necessary as a corrective to overzealous engineers who made extravagant claims about their inventions: “We need only read over the monthly accounts of patents; intended for securing the pecuniary advantages of useful discoveries, in order to be convinced what expense of time and fortune is continually lavished on the feeblest attempts to innovate and improve.”94 More than sixty   87. Margaret C. Jacob and Larry Stewart, Practical Matter: Newton’s Science in the Service of Industry and Empire 1687-1851 (Boston: Harvard University Press, 2004), charts the rise of Newtonian natural philosophy in the eighteenth century.  88. See in particular Stewart, “A Meaning for Machines,” p.262, and Jacob, “Mechanical Science,” p.210.   89. Jennifer Karns Alexander, The Mantra of Efficiency: From Waterwheel to Social Control (Baltimore: Johns Hopkins University Press, 2008), traces the genesis of this notion to the study of waterwheels in the late eighteenth and early nineteenth centuries.   90. According to Scott, Conflict, p.141, “[t]he start made by Great Britain early in the century was to bring her world leadership in industry by 1850.”   91. Milner, “Reflections,” p.348.  92. Young, Lectures, p.1. Mokyr, “The Intellectual Origins of Modern Economic Growth,” p.316, notes how the Society of Arts and the Royal Institution were at the center of the Industrial Enlightenment project. Bertucci and Courcelle, “Artisanal Knowledge,” discuss the French equivalent, the Société des Arts.   93. Ibid., p.3.  94. Ibid.

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years earlier, Desaguliers prefaced his Course of Experimental Philosophy by warning the reader of “boasting” engineers who swindled investors by promising impossible improvements in efficiency without being able to follow through.95 Desaguliers suggested to these engineers that we could not change the laws of nature and we could not add or take away from the gravity of bodies. This wariness, shared by Desaguliers and Young, concerning claims about practical mechanics was founded on a belief in the central role natural philosophy played in the service of industry. Thus Smeaton’s work on waterwheels was representative of a broader transformation of natural philosophy that occurred as a result of the increasing importance of natural philosophy to industry.96 This transformation had three interrelated moments: first, the increasing importance of economic considerations in the evaluation of theories of natural philosophy; second, the growing importance of the applications of theories in natural philosophy to concrete problems; and third, the emergence of a new paradigm for natural philosophy in the form of labor.97 These issues emerged in the late eighteenth and early nineteenth centuries as Smeaton’s approach began to be adopted by other practically oriented British natural philosophers such as Ewart and William Hyde Wollaston prs, a chemist and industrialist, whose scientific outlook was informed by the Industrial Revolution. The economic role of natural philosophy was first mentioned by Smeaton in his paper of 1776, where he stated that the errors occasioned by the confusion over motive force – as part of the vis viva controversy – were “also of great consequence to the public, as they tend greatly to mislead the practical artist in works that occur daily, and which often require very great sums of money in their execution.”98 Peter Ewart, a partisan of Smeaton’s view, also thought this a pressing matter, noting that “inconsistent rules have often been adopted, in the construction of expensive machines.”99 As we have already seen, this attitude toward the economic role of practical mechanics had already been developed by Desaguliers in his Course of Experimental Philosophy, and was at least partially accepted by Milner and Young, who both favored momentum over vis viva.

 95. Desaguliers, Course Vol. 2, p.viii. Stewart, in The Rise of Public Science, shows how Desaguliers pioneered an approach combining the principles of theoretical mechanics and the practical applications of these principles. Of this union, he writes, “Natural philosophy and commerce were locked together in the embrace of the incipient industrial ventures of Hanoverian England” (p.361).   96. For Cardwell, “Some Factors,” p.223, “[t]he rise of practical mechanics, the diversity of power machines in the closing decades of the eighteenth century and the opening ones of the nineteenth emphasized increasingly the practical and then, in the hands of French engineers and mathematicians, the theoretical importance of the concept that came to be called ‘work’.” The influence of technology on scientific practice has been emphasized by Rosenberg, Inside the Black Box, and Derek deS Price, “The Science/Technology Relationship, the Craft of Experimental Science, and Policy for the Improvement of High Technology Innovation,” Research Policy 13 (1984): 3–20.   97. On the importance of economic considerations, see Stewart, “A Meaning for Machines,” p.269, and Jacob, “Mechanical Science,” p.201.   98. Smeaton, “An Experimental Examination,” p.452.   99. Ewart, “On the Measure of Moving Force,” p.112.

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Figure 3.  Smeaton’s device for measuring the amount of mechanical power, or vis viva, used in accelerating a body from rest. From Smeaton, “An Experimental Examination of the Quantity and Proportion of Mechanic Power Necessary to be Employed in Giving Different Degrees of Velocity to Heavy Bodies from a State of Rest,” Philosophical Transactions 66 (1776): 450–75, 466, courtesy of the Royal Society.

Ideal versus concrete bodies: resistance, labor, and change of figure The shift toward profitable, practical applications of natural philosophy produced a deeper methodological transformation. Desaguliers, following a tradition dating back at least as far as Descartes, established the rules governing collisions between point-like bodies as the cornerstone of his natural philosophy. On this account, the phenomena of the material world could theoretically be reduced to a series of collisions between atoms or corpuscles. This was why the question of the behavior of hard inelastic bodies became so important – because the ultimate constituents of matter could neither be elastic nor soft, since they were supposedly indivisible. Unfortunately, the atomistic, corpuscular schema had its limits, such as when the paradigm of collisions between idealized, punctual bodies did not adequately model the phenomenon under consideration. This was what happened at the beginning of the Industrial Revolution. Although the partisans of momentum we are considering here claimed that the most general, certain principles of mechanics could only be derived from the idealized behavior of simplified bodies, the partisans of vis viva argued that it was the practical application of principles to concrete cases which could determine the value of those principles. Characteristically, Smeaton

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carried out his waterwheel experiments on a miniature apparatus, but waited to be able to test his conclusions in the field before publishing.100 Smeaton’s different outlook brought with it a new way of practicing natural philosophy. Instead of starting with general rules of theoretical mechanics which were then applied to different questions (as was the case with Descartes, Newton, Desaguliers, Atwood, Parkinson, and Young), Smeaton started with a concrete case – the watermill – and worked his way toward the general principles. Thus, in his first article he used a miniature waterwheel to model waterwheel behavior. In his second and third articles, he built experimental devices to test the more abstract principles he claimed to have discovered in his experiments on waterwheels (such as the device in Figure 3). Yet he never lost sight of what was truly important: the application of those rules to concrete cases.101 He prefaced his third article (on inelastic collisions) thus: “It is universally acknowledged, that the first simple principles of science cannot be too critically examined, in order to their being firmly established; more especially those which relate to the practical and operative parts of mechanics, upon which much of the active business of mankind depends.”102 Although Smeaton recognized that the general principles of theoretical mechanics were necessary for practical mechanics, he shifted the relation by arguing that the general principles of theoretical mechanics must be correct in order to guarantee the effectiveness of practical mechanics, and that the effectiveness of practical mechanics was what mattered. In other words, according to Smeaton, we must judge the truthfulness of the general principles of theoretical mechanics by their successful use in practical mechanics.103 This can be contrasted with the methodology most clearly articulated by Parkinson, according to which the analytic search for first principles is distinct from, and superior to, the synthetic application of these principles to practical matters.104 100. Smeaton, “An Experimental Enquiry,” p.101. Stewart, “Meaning for Machines,” p.275, draws attention to Smeaton’s concerns about the accuracy of scale models. 101. Terry S Reynolds, “Scientific Influences on Technology: The Case of the Overshot Water Wheel, 1752-1754,” Technology and Culture 20 (1979): 270–95, 294, explains why Johann Euler’s analysis of waterwheels did not influence the broader debate: “In working with waterwheels, he started from the basic laws of motion and derived his conclusions entirely by analytical means. He felt that mathematical demonstrations were sufficient proof of the validity of his ideas, and they may have been to the scientific community […] They [engineers such as Smeaton] started from actual machines, appealed to basic mechanical intuition, and supported their conclusions with model experiments.” The problem was that these engineers also began to question the basic laws of motion, instead of restricting themselves to building watermills. 102. Smeaton, “New Fundamental Experiments,” p.338. 103. Alexander, The Mantra of Efficiency, pp.31–2, underestimates the extent to which Smeaton’s approach differed from that of eighteenth century natural philosophers by ignoring the fact that Smeaton was only interested in the laws of motion insofar as they might help him to perfect his waterwheels. 104. Parkinson, System of Mechanics, p.i: “In all natural science, the analytic method of reasoning necessarily precedes the synthetic, and the converse of this order would terminate in uncertainty and chimera.” See also p.32.

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This is where we can see most clearly Smeaton’s role as a hybrid expert. His work on waterwheels mobilized theoretical mechanics, but to practical ends, insofar as he was capable of conceptualizing waterwheel functioning using the physical categories of the period. However, he also brought practical considerations to bear on foundational questions in theoretical mechanics, by using results obtained in experiments on both scale model and real waterwheels, to take a position in the debate about vis viva.105 This new attitude appealed to other practically oriented scientists. Ewart, defending Smeaton’s legacy against partisans of momentum, argued that the fact that very few undershot mills were built in Britain after Smeaton’s results were published demonstrated that Smeaton had, for all intents and purposes, resolved the question of loss of motive force in inelastic collisions. He wrote: “So that all the points in question, as far as they relate to undershot water-wheels, although highly important at the time when Mr. Smeaton wrote his first paper, are now become matters of mere speculative curiosity, and, in this country at least, they can no longer be of any practical use.”106 As natural philosophy began to be used as a tool to improve industrial productivity, practically minded natural philosophers, such as Wollaston, recognized that it needed to adapt: The former conception of a quantity dependent on the continuance of a given vis motrix for a certain time may have its use, when correctly applied, in certain philosophical considerations; but the latter idea of a quantity resulting from the same force exerted through a determinate space is of greater practical utility, as it occurs daily in the usual occupations of men; since any quantity of work performed is always appreciated by the extent of effect resulting from their exertions.107

For Smeaton, as for Wollaston, mechanical power was best measured by the raising of a weight to a given height, irrespective of the velocity of that weight, because the needs of industry dictated it to be so. Momentum thus became an unsatisfactory measure of mechanical power because the velocity of a body falling from a certain height was not proportional to the labor required to raise it to that height.108 The notion of labor makes all the difference here, since it had become central to the understanding of motive force. Natural philosophy had begun to understand the world not as an idealized system of point-like bodies which interacted in a vacuum, but as a system of concrete bodies which resisted any transformation or change. Harnessing the potential of this kind of world required labor. This was underlined in the treatment of inelastic collisions. In the view which took the collision of abstract bodies as its paradigm, motive force should have been conserved in 105. Klein, “Hybrid Experts,” p.303, highlights this crossover: “At meetings of academies and in their publications they reported what they had experienced at sites of practice, unfamiliar to most academicians.” The results obtained did not always please those academicians, however. 106. Ewart, “On the Measure of Moving Force,” p.162. 107. William Hyde Wollaston, “Bakerian Lecture on the Force of Percussion (Read 1805),” Philosophical Transactions 96 (1806): 13–22, 15. 108. Ibid., p.16.

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inelastic collisions. As we have already seen, even Leibniz himself felt the need to explain away the apparent loss of vis viva in inelastic collisions as the dispersion of vis viva into the moving parts of the inelastic body. The conservation of motive force in inelastic collisions seemed to be self-evident. Smeaton, following ’s Gravesande, turned this schema on its head. He asked how it was possible that no motive force be lost in an inelastic collision, even though this collision also produced a change in the shape of the colliding bodies. He explained: If it can be shewn, that the figure of a body can be changed, without a power, then, by the same law, we might be able to make a forge hammer work upon a mass of soft iron, without any other power than that necessary to overcome the friction, resistance, and original vis inertiae, of the parts of the machine to be put in motion.109

Since hammering a piece of iron into shape cannot be performed effortlessly, it stood to reason that a certain quantity of force was expended in each collision between the hammer and the iron. It was thus the changing shape of the iron which accounted for the loss of motive force, and if motive force was lost in inelastic collisions then motive force was measured by vis viva, not momentum. This was a radically new way of understanding the transmission of motive force.110 With the new emphasis placed on the role of labor, it was the loss of motive force in inelastic collisions that appeared to be intuitively correct, and the conservation of motive force in such circumstances would be, as Smeaton noted, “an idea so very contrary to all experience, and even apprehension, of both the philosopher and the vulgar artist.”111 This novel understanding of motive force was a product of the breakdown of the distinction between the ‘philosopher’ and the ‘vulgar artist’, as the natural philosopher began to consider practical questions and the artisan deployed the philosopher’s concepts in order to better understand his creations. In eighteenth-century France, the hybrid philosopher–artisan was embodied in the artiste, who possessed the theoretical knowledge which distinguished her from ordinary artisans or craftsmen.112 This hybrid expert, or artiste, promoted the transformation of both industry and natural philosophy by selectively combining the two fields. Natural philosophy transformed industry by rationalizing it, and industry transformed natural philosophy by providing it with new problems to solve.113 109. Smeaton, “New Fundamental Experiments,” p.343. 110. Scott, who has written extensively on this subject, fails to fully understand this historical transformation because his focus is on theoretical mechanics. He writes in Conflict, p.48: “Such questions [concerning loss of vis viva] were embarrassing to the conservationists and were not completely resolved for another century.” 111. Smeaton, “New Fundamental Experiments,” p.343. 112. Bertucci and Courcelle, “Artisanal Knowledge,” p.161: “L’artiste was a new expert who could contribute to the public good with his knowledge, grounded in the world of knowing as well as in the world of doing.” 113. Rosenberg, Inside the Black Box, pp.144–52, looks at how technology opens up new fields of scientific research.

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On the crucial question of the loss of motive force in the changing shape of bodies, Desaguliers and Maclaurin found themselves on the wrong side of history – arguing that no force was used up changing the shape of a body – just as the industrial point of view was taking hold, according to which matter was transformed, and commodities were manufactured, by the expenditure of labor (and, by implication, force).114 Ewart described the situation very clearly: “The application and measurement of mechanical force producing changes of figure are indeed the chief occupations of practical men, in the construction and management of machinery.”115 He added further on that: The fabrication of every thing that is useful or convenient to us is accomplished chiefly by the application of mechanical force to produce change of figure. The grinding of corn, the expressing of oil from seed, the sawing of timber, the hammering and rolling of metals, the driving of piles – all are examples of moving force producing changes of figure.116

Conclusion Vis viva found favor in Britain at the end of the eighteenth century because natural philosophy began to be influenced by the practical mechanics which served the interests of industry. The application of natural philosophy to engineering problems meant that natural philosophy began to absorb industrial concepts, such as efficiency, via industrial practices such as raising water or grinding corn. This in turn began to have a bearing on debates concerning the more strictly theoretical principles of mechanics, such as the vis viva controversy. We have seen that, because of their industrial usage as tools for raising bodies, the efficiency of watermills needed to be measured by the raising of a mass m to height h. Measured in this way, overshot wheels were more efficient than undershot wheels. Smeaton, a hybrid expert who straddled the worlds of science, technology, and industry, carried out experiments to understand this difference in efficiency, finding that motive force was lost by undershot wheels in the production of turbulence in the inelastic collision between the water and the waterwheel paddles. The idea that motive force was lost in inelastic collisions was not generally accepted, because it was thought that motive force was always conserved. However, the new practical approach to natural philosophy, which served to maximize industrial efficiency, made sense of this loss by conceiving it as the labor expended on a body to transform it into something useful or valuable. Indeed, the central preoccupation of industry was to expend motive force in the transformation of raw materials into objects of use or value. So although the natural philosophers who labeled the vis viva controversy a mere dispute over definitions were technically correct, they neglected to consider the fact that

114. Lilian Hilaire-Pérez, La pièce et le geste, p.4, charts the rise of this manufacturing mindset in the nineteenth century, which she calls “operative industry.” It is uniquely focused on the “transformation of raw materials, either mechanically or chemically, into objects with exchange value” (my translation). 115. Ewart, “On the Measure of Moving Force,” p.189. 116. Ibid., p.220.

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changing practices of mechanics – driven by the hybridization of science, technology, and industry – meant adopting different definitions of motive force. Thus, in the second half of the eighteenth century, vis viva became an appropriate definition of motive force as a consequence of the application of natural philosophy to the understanding of industrial processes. This was why partisans of momentum attempted to distinguish theoretical and practical mechanics: if they could show that practical mechanics was unrelated to, or subordinate to, theoretical mechanics, they could refuse to accept vis viva as the true measure of motive force. This rejection of vis viva eventually fell out of favor as the concepts of momentum, potential energy, kinetic energy, work, and force came to be more clearly defined during the course of the nineteenth century, allowing for the cohabitation of both vis viva (once it had been factored by half) and momentum in the same conceptual framework. Acknowledgements I would like to thank Steffen Ducheyne (Vrije Universiteit Brussel) for his helpful guidance in writing this paper. I would also like to thank Maarten Van Dyck (Universiteit Gent), who provided valuable advice in the early stages of this project. I am very grateful to the two anonymous reviewers for their detailed comments. Finally, I would like to thank my father, Michael Morris, for his many helpful suggestions.

Declaration of conflicting interests The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding The author(s) received no financial support for the research, authorship, and/or publication of this article.

ORCID iD Andrew M. A. Morris

http://orcid.org/0000-0002-6033-3769

Author biography Andrew M. A. Morris earned a bachelors degree in philosophy at the University of Warwick in the UK., then moved to Belgium where he completed an M.A. at the Katholieke Universiteit Leuven and a two-year research masters, with a focus on the philosophy of science, at the Université libre de Bruxelles. He is currently applying for funding for a doctoral degree on the vis viva controversy under the supervision of Steffen Ducheyne at the Vrije Universiteit Brussel.