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Pieter van Musschenbroek on laws of nature


In this article, we discuss the development of the concept of a ‘law’ (of nature) in the work of the Dutch natural philosopher and experimenter Petrus van Musschenbroek (1692–1761). Since Van Musschenbroek is commonly described as one of the first ‘Newtonians’ on the Continent in the secondary literature, we focus more specifically on its relation to Newton's views on this issue. Although he was certainly indebted to Newton for his thinking on laws (of nature), Van Musschenbroek's views can be seen to diverge from Newton's on crucial points. We show, moreover, how his thinking on laws of nature was shaped by both international and local factors. We start with a brief discussion of Newton's concept of ‘laws of nature’ in order to set the stage for Van Musschenbroek's. We then document the development of Van Musschenbroek's views on laws of nature in chronological order. We demonstrate how his thinking on laws of nature was tied to institutional, theological and scientific factors. We conclude by pointing to the broader significance of this case study for our understanding of the development of the concept ‘law of nature’ during the eighteenth century.

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1 It is impossible to do justice to the enormous amount of philosophical literature that this subject has spawned. A good starting point is to be found in John W. Carroll, ‘Laws of nature’, in Edward N. Zalta (ed.), The Stanford Encyclopedia of Philosophy, Fall 2016 edition, at, accessed 9 September 2016.

2 Frans van Lunteren, ‘The missing history of the “laws of nature”’, Shells and Pebbles, 7 November 2016, at, accessed 9 November 2016.

3 The only exception we are aware of is Ruestow, Edward G., Physics at Seventeenth and Eighteenth-Century Leiden: Philosophy and the New Science in the University, The Hague: Martinus Nijhoff, 1973, pp. 129130 . It should be noted that Ruestow does not provide a detailed account of Van Musschenbroek's views on laws of nature, let alone offer a chronological overview of their development.

4 Here we will restrict ourselves to those parts of Newton's corpus that were available to Van Musschenbroek, i.e. Newton's published work, and those that are relevant in view of what is to follow in the next section. We will not provide a full-blown discussion of Newton's stance of forces, causes and explanations. For a treatment of these issues see Ducheyne, Steffen, ‘ The Main Business of Natural Philosophy ’: Isaac Newton's Natural-Philosophical Methodology, Dordrecht: Springer, 2012 .

5 Newton, Isaac, The Principia, Mathematical Principles of Natural Philosophy: A New Translation by I. Bernard Cohen and Anne Whitman, Assisted by Julia Budenz, Berkeley: University of California Press, 1999, pp. 939, 381.

6 The most insightful analysis of Van Musschenbroek's study of magnetism is Cornelis de Pater, Petrus van Musschenbroek (1692–1761): Een newtoniaans natuuronderzoeker (PhD dissertation, Utrecht University), Utrecht: Elinkwijk, 1979, Chapter 4.

7 Heilbron, John L., Electricity in the 17th and 18th Centuries: A Study in Early Modern Physics, New York: Dover, 1999 ; first published 1979, p. 90; de Pater, op. cit. (6), p. 159; Home, Roderick Weir, ‘Physical principles and the possibility of a mathematical science of electricity and magnetism’, in Métivier, Michel, Costabel, Pierre and Dugas, Pierre (eds.), Siméon Denis Poisson et la science de son temps, Paris: Ecole polytechnique, 1981, pp. 151166, 159160 ; de Pater, Kees, ‘“The wisest man to whom this earth has as yet given birth”: Petrus van Musschenbroek and the limits of Newtonian philosophy’, in Jorink, Eric and Maas, Ad (eds.), Newton and the Netherlands: How Isaac Newton Was Fashioned in the Dutch Republic, Amsterdam: Leiden University Press, 2012, pp. 139157, 148.

8 Newton, op. cit. (5), p. 940.

9 Newton, op. cit. (5), p. 942, italics added. That everything is dependent on God's will is also emphasized in Roger Cotes's editorial introduction to the second edition of the Principia (Newton, op. cit. (5), p. 397).

10 Newton, Isaac, Opticks, or a treatise of the reflections, refractions, inflections & colours of light, New York: Dover, 1952 ; first published 1730, p. 403, italics added.

11 Newton, op. cit. (10), p. 397, p. 401. On Newton's active principles see, for instance, McGuire, J.E., ‘Force, active principles, and Newton's invisible realm’, Ambix (1968) 15, pp. 154208 ; Dobbs, Betty Jo Teeter, The Janus Faces of Genius: The Role of Alchemy in Newton's Thought, Cambridge: Cambridge University Press, 1991 ; and Ducheyne, Steffen, ‘Newton on action at a distance’, Journal of the History of Philosophy (2014) 52, pp. 675702 .

12 Newton, op. cit. (10), pp. 399, 401.

13 Newton, op. cit. (10), p. 401. Newton used the term ‘laws of nature’ for the first time in print in the 1718 edition of the Opticks ( Newton, Isaac, Opticks, or a treatise of the reflections, refractions, inflections & colours of light, London: Printed for W. and L. Innys, 1718, p. 377 ). The selling catalogue of Van Musschenbroek's library contains a copy of this edition (anon., Bibliotheca Musschenbroekiana, sive catalogus librorum, Leiden: Per S. et J. Luchtmans, 1762, p. 58 , item 486).

14 van Musschenbroek, Petrus, Physicae experimentales, et geometricae: De magnete, tuborum capillarium vitreorumque speculorum attractione, magnitudine terræ, cohaerentia corporum firmorum dissertationes: ut et ephemerides meteorologicae Ultrajectinae, Leiden: Apud Samuelem Luchtmans, 1729, pp. 12 .

15 Newton, op. cit. (10), p. 369. This point has been made in detail in Janiak, Andrew, ‘Newton and the reality of force’, Journal for the History of Philosophy (2007) 45, pp. 127147 ; and Ducheyne, op. cit. (4), Chapter 1.

16 Newton, op. cit. (10), p. 404.

17 De Pater, op. cit. (6), pp. 26–27; and Kernkamp, Gerhard Wilhelm, Acta en decreta senatus: vroedschapresolutiën en andere bescheiden betreffende de Utrechtse Academie, 3 vols., Utrecht: Broekhoff N.V. v/h Kemink en zoon, 1936–1940, vol. 2, p. 278 .

18 van Musschenbroek, Petrus, De certa methodo philosophiae experimentalis, Utrecht: Apud Guilielmum Vande Water, 1723, p. 10 .

19 Sassen, Ferdinand, Geschiedenis van de wijsbegeerte in Nederland tot het einde der negentiende eeuw, Amsterdam: Elsevier, 1959, p. 147 .

20 Van Musschenbroek, op. cit. (18), p. 7.

21 Van Musschenbroek, op. cit. (18), p. 10.

22 Van Musschenbroek, op. cit. (18), pp. 10–14. Due to space constraints, we cannot treat Van Musschenbroek's argument against innate ideas in full. In the oration, Van Musschenbroek focuses on our ideas of the properties of bodies. On the one hand, he shows how they depend on sensory input, and on the other he argues that a priori reasoning could never allow us to infer other properties from the idea of ‘extension’ (Van Musschenbroek, op. cit. (18), pp. 15–18). Van Musschenbroek's library contained a printed version of a disputation defended by a student of Serrurier on the topic of innate ideas: Thierens, Hadrianus, Disputatio philosophia de ideis innatis, Utrecht: Guilelmi vande Water, 1707 . In the selling catalogue of Van Musschenbroek's library, Serrurier is listed as the author. It was common practice that in their disputations students defended their supervisors’ ideas. Anon., op. cit. (13), p. 15, item 71.

23 Van Musschenbroek, op. cit. (18), p. 22.

24 Van Musschenbroek, op. cit. (18), p. 23.

25 Van Musschenbroek, op. cit. (18), pp. 27–28.

26 Van Musschenbroek, op. cit. (18), p. 28.

27 Van Musschenbroek, op. cit. (18), pp. 43–44, italics added in our translation.

28 Van Musschenbroek, op. cit. (18), p. 9.

29 van Musschenbroek, Petrus, Epitome elementorum physico-mathematicorum, Leiden: Apud Samuelem Lugtmans, 1726, p. 1 .

30 In 1729 Van Musschenbroek also characterized gravity as a ‘law of nature’. Van Musschenbroek, op. cit. (14), p. 2.

31 Van Musschenbroek, op. cit. (29), pp. 1–3.

32 Van Musschenbroek, op. cit. (29), p. 3.

33 Van Musschenbroek, op. cit. (29), p. 3.

34 The definition goes as follows: ‘We call “phenomena” all positions, actions and changes of bodies, which we observe with one, or with multiple senses, [and which] therefore do not differ from what is observed by the senses’. Van Musschenbroek, op. cit. (29), pp. 2–3.

35 Ducheyne, op. cit. (4), pp. 22–25.

36 Ducheyne, op. cit. (11).

37 Van Musschenbroek, op. cit. (29), p. 3.

38 Van Musschenbroek, op. cit. (29), p. 4.

39 Van Musschenbroek, op. cit. (29), p. 4. Van Musschenbroek's claim is problematic, for according to his own criterion of a universal law, the law of universal gravitation cannot be considered a universal law, since the law of universal gravitation was established through an inductive generalization from a limited set of data based on Newton's third regula philosophandi (Newton, op. cit. (5), p. 809). However, later in his career Van Musschenbroek became aware of the importance of the third regula. Ducheyne, Steffen, ‘Petrus van Musschenbroek and Newton's “vera stabilisque Philosophandi methodus”’, Berichte zur Wissenschaftsgeschichte (2015) 38, pp. 279304, 284286 ).

40 Van Musschenbroek, op. cit. (29), p. 130. He repeated these points in Van Musschenbroek, op. cit. (14), pp. 2, 451–452, which was published three years later. The claim that attraction is ‘instilled’ in bodies by God is a statement that Van Musschenbroek cannot legitimately uphold according to his own epistemological standards. According to his own empiricist methodology, this statement is to be considered a mere hypothesis.

41 Van Musschenbroek, op. cit. (29), pp. 131–132.

42 Van Musschenbroek, op. cit. (29), p. 4.

43 Van Musschenbroek, op. cit. (29), pp. 4–5. Three years later Van Musschenbroek repeated both points in Van Musschenbroek, op. cit. (14), pp. 2, 451–452. One year thereafter, he reiterated the first point in Van Musschenbroek, Petrus, ‘Oratio de methodo instituendi experimenta physica’, in Van Musschenbroek, Tentamina experimentorum naturalium captorum in academia del cimento, Leiden: Johan. et Herm. Verbeek, 1731, p. xxxii.

44 van Musschenbroek, Petrus, Elementa physicae conscripta in usus academicos, Leiden: Apud Samuelem Luchtmans, 1734, p. 2 .

45 Van Musschenbroek, op. cit. (44), p. 3.

46 Van Musschenbroek, op. cit. (44), p. 3, italics added in our translation.

47 van Musschenbroek, Petrus, Elementa physicae conscripta in usus academicos, Leiden, Apud Samuelem Luchtmans, 1741, p. 4 . A draft version of this definition can be found in Van Musschenbroek's annotated copy of the first edition of Elementa physicae and in his annotated copy of Beginsels der natuurkunde (Leiden University Library, Special Collections (subsequently LUL), BPL 240.54, verso side of the interleaved folio between pp. 2 and 3, and LUL, BPL 240.61, p. 7). Van Musschenbroek used ‘apparitiones’ as synonymous to ‘phenomena’ (Van Musschenbroek, op. cit., p. 3). This sentence is similar to the definition he gave in the Epitome: ‘Lex nobis idem audit quam Regula, juxta quam Deus voluit, ut constantissime ejusmodi phænomena in talibus corporum conditionibus contingerent’. Van Musschenbroek, op. cit. (29), p. 3, original emphasis.

48 Van Musschenbroek, op. cit. (44), p. 4.

49 Van Musschenbroek, op. cit. (44), p. 4. In the second edition, the last sentence is changed to explicitly state that the laws are most constant ‘because the divine will is most constant’. Van Musschenbroek, op. cit. (47), p. 5.

50 Van Musschenbroek, op. cit. (44), p. 4.

51 Van Musschenbroek, op. cit. (44), p. 4. In Institutiones, Van Musschenbroek added the disjunct ‘or occur contrary to the regular course of nature’. van Musschenbroek, Petrus, Institutiones physicae conscriptae in usus academicos, Leiden: Apud Samuelem Luchtmans et filium, 1748, p. 6 . For a discussion of the debates on miracles and laws of nature in the context of Dutch Newtonianism see Rienk Vermij, ‘Defining the supernatural: the Dutch Newtonians, the Bible and the laws of nature’, in Jorink and Maas, op. cit. (7), pp. 185–206.

52 Our translation of ‘We kennen het boven natuurlijke niet, tenzy wy eerst het natuurlyke geleerd hebben.’ LUL, BPL 240.60, recto and verso side of first interleaved folio between pp. 12 and 13.

53 Van Musschenbroek, op. cit. (44), p. 5.

54 Van Musschenbroek, op. cit. (44), p. 5.

55 Van Musschenbroek, op. cit. (44), pp. 5–6. For a discussion of his take on Newton's regulae see Ducheyne, op. cit. (39).

56 On Newton's regulae philosophandi see Ducheyne, op. cit. (4), pp. 109–120.

57 Van Musschenbroek, op. cit. (44), pp. 139–140.

58 See Vermij, Rienk, ‘The formation of the Newtonian philosophy: the case of the Amsterdam mathematical amateurs’, BJHS (2003) 36, pp. 183200 ; Vermij, op. cit. (51), pp. 190–193; Eric Jorink (2009), “Honouring Sir Isaac, or, exorcising the ghost of Spinoza”: some recent remarks on the success of Newton in the Dutch Republic’, in Ducheyne, Steffen (ed.), Future Perspectives on Newton Scholarship and the Newtonian Legacy, Brussels: Koninklijke Vlaamse Academie van België voor Wetenschappen en Kunsten, 2009, pp. 2334 ; van Bunge, Wiep, ‘The waning of radical Enlightenment in the Dutch Republic’, in Ducheyne, Steffen (ed.), Reassessing the Radical Enlightenment, London: Routledge, pp. 178193 ; and Steffen Ducheyne and Jip van Besouw, ‘Newton and the Dutch “Newtonians”: 1713–1750’, in Chris Smeenk and Eric Schliesser (eds.), The Oxford Handbook of Newton, Oxford: Oxford University Press, in print.

59 de Spinoza, Benedictus, The Collected Works of Spinoza (ed. and tr. Curley, Edwin), 2 vols., Princeton, NJ: Princeton University Press, 1985–2016, vol. 1, p. 435 , original emphasis. However, given Definition 7, God is ‘free’, according to Spinoza, in the sense that he exists from the necessity of his nature alone, while things that are necessary by contrast are determined by something else to exist. Spinoza, op. cit., p. 409.

60 Cf. Spinoza, op. cit. (59), p. 437.

61 Spinoza, op. cit. (59), p. 436, original emphasis.

62 The contents of these lectures are discussed in Ducheyne, Steffen, ‘“Celeberrimus Atheismi Patronus Praecedentis Saeculi”: Petrus van Musschenbroek's anti-Spinozism unveiled’, Lias: Journal of Early Modern Intellectual Culture and Its Sources (2014) 41, pp. 173197 .

63 LUL, BPL 240.12, f. 51r.

64 LUL, BPL 240.12, f. 51v; Ducheyne, op. cit. (62), p. 180.

65 van Musschenbroek, Pieter, Beginselen der natuurkunde, Leiden: Samuel Luchtmans, 1736, p. 7 . This was, of course, what Descartes had proclaimed to be possible. Descartes, René, La description du corps humain et de la formation de l'animal, in Oeuvres de Descartes (ed. Adam, Charles and Tannery, Paul), 12 vols., Paris: Léopold Cerf, 1897–1913, vol. 11, pp. 223290, 277. This text was published posthumously in 1664. Van Musschenbroek owned the edition of 1680. Anon., op. cit. (13), p. 33, item 626.

66 Van Musschenbroek, op. cit. (65), p. 7.

67 Cf. Vermij, Rienk, ‘Een nieuw concept: De wetten der natuur’, in Egmond, Florike, Jorink, Eric and Vermij, Rienk (eds.), Kometen, monsters en muilezels: Het veranderende natuurbeeld en de natuurwetenschap in de zeventiende eeuw, Haarlem: Uitgeverij Arcadia, 1999, pp. 105119, 114–115.

68 Van Musschenbroek, op. cit. (65), p. 8.

69 Van Musschenbroek, op. cit. (65), p. 8.

70 Van Musschenbroek, op. cit. (65), pp. 8–9.

71 Van Musschenbroek, op. cit. (65), p. 9.

72 Van Musschenbroek, op. cit. (65), p. 10.

73 van Musschenbroek, Pieter, Beginsels der natuurkunde, Leiden: Samuel Luchtmans, 1739, pp. 812 .

74 LUL, BPL 240.60.

75 Van Musschenbroek, op. cit. (73), pp. 11–12.

76 Our translation of ‘non sum prorsus convictus eandem atque universalem in omnibus, quos Terrarum orbis gerit, magnetibus legem obtinere’. LUL, BPL 240.42, f. 57v. On the dating of this manuscript see de Pater, op. cit. (6), p. 148.

77 Van Musschenbroek, op. cit. (51), p. 4.

78 Van Musschenbroek, op. cit. (51), pp. 6–8.

79 Van Musschenbroek, op. cit. (51), p. 6, italics added in our translation.

80 LUL, BPL 240.55, interleaved folio facing p. 10. Rule 3 states, ‘Those qualities of bodies that cannot be intended and remittedand that belong to all bodies on which experiments can be made should be taken as qualities of all bodies universally’. Newton, op. cit. (5), p. 795, original emphasis.

81 Needham, John Turberville, ‘A summary of some late observations upon the generation, composition, and decomposition of animal and vegetable substances; communicated in a letter to Martin Folkes Esq; President of the Royal Society, by Mr. Turberville Needham, Fellow of the same Society’, Philosophical Transactions (1748) 45, pp. 615666 .

82 van Musschenbroek, Petrus, Introductio ad philosophiam naturalem, 2 vols., Leiden: Apud Sam. et Joh. Luchtmans, 1762, vol. 1, pp. 1516 .

83 This episode has been covered by one of us. See Ducheyne, op. cit. (39), pp. 287–288.

84 Cf. Ratcliff, Marc J., The Quest for the Invisible: Microscopy in the Enlightenment, London and New York: Routledge, 2009, p. 109 n. 33; and Gronovius, Jan Frederik, ‘Extract of a Letter from J.F. Gronovius, M.D. at Leyden, November 1742 to Peter Collinson, F.R.S. concerning a Water Insect, which, being cut into several Pieces, becomes so many perfect animals’, Philosophical Transactions (1742–1743) 42, pp. 218220 .

85 LUL, BPL 240.61, p. 9.

86 LUL, BPL 240.61, p. 9.

87 van Musschenbroek, Petrus, Oratio de sapientia divina, Leiden, Apud Samuelem Luchtmans & Filium, 1744, p. 27 .

88 Van Musschenbroek, op. cit. (51), p. 5. A draft version of this addition is to be found in his annotated copy of the second edition of Elementa physicae. LUL, BPL 240.57, p. 5. An important source of inspiration for Van Musschenbroek was Gravesande, Willem Jacob ’s, Physices elementa mathematica experimentis confirmata, sive introductio ad philosophiam Newtoniam, 2 vols., Leiden: Johannes Arnoldus Langerak and Johannes and Herman Verbeek, 1742, vol. 1, pp. 23 . Space does not permit us to develop this point.

89 Van Musschenbroek, op. cit. (47), p. 5.

90 Van Musschenbroek, op. cit. (82), pp. 6–7.

91 Van Musschenbroek, op. cit. (82), p. 7. The notion of a vis plastica features significantly in the work of the Cambridge Platonists Ralph Cudworth and Henry More. See e.g. Hunter, William B., ‘The seventeenth-century doctrine of plastic nature’, Harvard Theological Review (1950) 43, pp. 197213 .

92 Van Musschenbroek, op. cit. (82), p. 7. To aid the comparison with the edition of 1748, we have put the words which were added in the 1762 edition between asterisks.

93 LUL, BPL 240.61, interleaved folio between ***2 and ***3.

94 Van Musschenbroek, op. cit. (82), p. 8.

95 Van Musschenbroek, op. cit. (82), pp. 9–10.

96 Van Musschenbroek, op. cit. (82), pp. 9–11.

97 van Musschenbroek, Petrus, Compendium physicae experimentalis conscriptum in usus academicos, Leiden: Apud S. et J. Luchtmans, 1762, pp. 23 .

98 Darrignol, Olivier, Physics & Necessity: Rationalist Pursuits from the Cartesian Past to the Quantum Present, Oxford: Oxford University Press, 2014, Chapter 1.

99 de Maupertuis, Pierre Louis Moreau, ‘Les loix du mouvement et du repos déduites d'un principe metaphysique’, Histoire de l'Académie royale des sciences et des belles lettres, Année MDCCXLVI, Berlin: Chez Ambroise Haude, 1748, pp. 267294 .

100 ‘Lors qu'il arrive quelque changement dans la Nature, la Quantité d'Action, nécessaire pour ce changement, est la plus petite qu'il soit possible’. Maupertuis, op. cit. (99), p. 290.

101 ‘To these laws we deservedly add the principle discovered by the noble Maupertuis. Every natural effect that arises from one or several causes, is always performed with the least action’. Our translation of ‘Hisce legibus merito addimus Principium a Nob. Maupertuisio inventum. Omnis effectus naturalis qui ab una causa, vel â pluribus causis efficitur, semper peragitur actione minima’. LUL, BPL 240.55, recto side of eleventh interleaved folio between pp. 80 and 81.

102 Van Musschenbroek, op. cit. (82), p. 236.

103 Schmaltz, Tad M., ‘From causes to laws’, in Clarke, Desmond M. and Wilson, Catherine (eds.), The Oxford Handbook of Philosophy in the Eighteenth Century, Oxford: Oxford University Press, 2011, pp. 3250, 45; cf. Buchdahl, Gerd, Metaphysics and the Philosophy of Science: The Classical Origins, Descartes to Kant, Oxford: Blackwell, 1969, p. 315 .

104 During the second half of the eighteenth century, Thomas Reid, for instance, stripped laws of nature from their remaining causal and theological connotations, thereby paving the way to a regularity view of laws. On this matter see Ducheyne, Steffen, ‘Reid's adaptation and radicalization of Newton's natural philosophy’, History of European Ideas (2006) 32, pp. 173189 . On 16 December 1780 Reid wrote to Henry Home, Lord Kames, as follows: ‘By the cause of a phenomenon, nothing is meant but the law of nature, of which that phenomenon is an instance, or a necessary consequence … In natural philosophy, therefore, we seek only the general laws, according to which nature works, and these we call the causes of what is done according to them. But such laws cannot be the efficient cause of anything. They are only the rule according to which the efficient cause operates. A natural philosopher may search after the cause of a law of nature; but this means no more than searching for a more general law, which includes that particular law, and perhaps many others under it … Efficient causes, properly so called, are not within the sphere of natural philosophy’. Reid, Thomas, Philosophical Works (ed. Hamilton, William), 2 vols., Hildesheim: Georg Olms Verlag, 1983; first published 1895), vol. 1, pp. 5758 , italics added. It should be noted that Reid endorsed a metaphysical agent-causal notion that applies outside the realm of natural philosophy. Reid was familiar with Van Musschenbroek's work in the context of his study of the vis viva debate. Wood, Paul, ‘Thomas Reid and the culture of science’, in Cuneo, Terence and van Woudenberg, René (eds.), The Cambridge Companion to Thomas Reid, Cambridge: Cambridge University Press, 2004, pp. 5376, 59. To the best of our knowledge, there is no direct evidence to suggest that Reid was influenced by Van Musschenbroek's take on laws of nature.

105 For an overview of these different editions and translations see de Pater, op. cit. (6), pp. 349–360.

106 On the parts of Van Musschenbroek's work incorporated in the Encyclopédie see section 4 of Pierre Crépel, ‘La “physique” dans l’Encyclopédie’, Recherches sur Diderot et sur l'Encyclopédie (1 October 2006), 40–41, at, accessed 27 June 2017.

107 Kant, Immanuel, Kant: Natural Science (ed. Watkins, Eric), Cambridge: Cambridge University Press, 2012, p. 103 ; original in Kant, Immanuel, Gesammelte Schriften, vol. 1, Berlin: Königlich Preußische Akademie der Wissenschaften, 1902, p. 118, lines 10–11.

Nature hath no gaole, though she hath law.

John Donne, The Progress of the Soul (1612)

This article is collaborative work and no significance attaches to the alphabetical order of the authors’ names. All translations are ours. Steffen Ducheyne's research is sponsored by the Vrije Universiteit Brussel under the form of a research professorship. Pieter Present's research is financed by the Research Fund – Flanders (project: G.0271.15N). The first two sections and the final one were written by Steffen Ducheyne. All other sections were written by Pieter Present. We are highly indebted to Frans van Lunteren for useful exchanges of thought, the anonymous referees for useful feedback, and the Special Collections Department at Leiden University Library for permission to quote from the material in their care.

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