Reading up on the Opticks. Refashioning Newton's Theories Of

Reading up on the Opticks. Refashioning Newton’s Theories of Light and Colors in Eighteenth-Century Textbooks

Fokko Jan Dijksterhuis University of Twente, Netherlands

Robert Smith’s A Compleat System of Opticks (1738) was the most prominent eighteenth-century text-book account of Newton’s optics. By rearranging the ªndings and conclusions of Opticks, it made them accessible to a wider public and at the same time refashioned Newton’s optics into a renewed science of optics. In this process, the optical parts of Principia were integrated, thus blending the experimental inferences and mechanistic hypotheses that Newton had carefully separated. The Compleat System was not isolated in its refashioning of Newton’s optics. Dutch and English promoters of the new philosophy had preceded Smith by giving Opticks a text-book treatment, and they too integrated experimental and mechanistic inferences. In this way eighteenth-century text-books produced a natural philosophical discourse of light, colors and matter. This paper traces the refashioning of Newton’s optics in Dutch and English text-books of natural philosophy during the ªrst half of the eighteenth century. It concludes with the Dutch translation of A Compleat System of Opticks and its reception among innovators of telescope manufacture. The eighteenth century was the age of Newton. Whether or not one agreed with his views of nature and the way to study her, one had to con- front Sir Isaac’s teachings. Those teachings were not always easy. The Principia in particular was a tough study. The age of Newton thus began with teachers unlocking and explaining Newton’s natural philosophy. Al- though Opticks was far more accessible than Principia, Newton’s theories of light and colors were also refashioned for enlightened readers. The Dutch promoters of Newtonianism were the ªrst to give Opticks a textbook treatment, integrating it in their expositions of Newtonian natural philosophy. In A Compleat System of Opticks (1738), Robert Smith devoted exclusive at-

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tention to optics and the Opticks. Yet, Smith too integrated elements of Newton’s natural philosophy beyond the Opticks. And he too, refashioned Newton’s theories of light and colors to meet the needs of didactics. This paper discusses the rearrangements of the Opticks in eighteenth-century textbooks. Smith’s Compleat System will be the centerpiece, as it was the standard text-book on optics of the eighteenth century and beyond. The Dutch reception of Newton’s theories of light and colors provides a prelude and a gigue, but here too Smith plays ªrst violin. Textbooks are important in the history of science. They show how new developments were given a place in, and gave form to the established conception of the sciences.1 In the case of eighteenth-century optics this is particularly interesting. In the preceding century, the mathematical science of optics had undergone a paradigmatic change. At the beginning of the seventeenth century ‘optica’ was a branch of mixed mathematics ana- lyzing the behaviour of light rays and the intricacies of perception. In the work of Descartes, Huygens and Newton a new approach to optics devel- oped in which the focus shifted to questions of the nature of light and the explanation of its behaviour. Huygens’ Traité de la lumière (1690) and Newton’s Opticks (1704) accentuated this shift towards physical optics because both omitted the greater part of their writings on geometrical optics from these works. The old ‘optica’ did not, however, disappear and at the turn of the century the question was open as to what the science of optics would look like, how its physical, geometrical, as well as instrumental parts were ordered and mutually related. Eighteenth-century textbooks reveal what the new optics looked like after the seventeenth-century re- shufºing. This paper is conªned to the physical part of optics. The history of geometrical and instrumental optics is exciting and has still been stud- ied insufªciently, but on the occasion of assessing the legacy of Newton’s Opticks it has to be left aside.

Prelude: Opticks for the Dutch As is well known, the Dutch were the ªrst, and most effective, promoters of Newtonian natural philosophy on the continent (Feingold 2004, pp. 68–75).2 Willem Jacob ‘s Gravesande (1688–1742) was the ªrst to in- corporate Newtonian philosophy in his lessons when he became professor of mathematics and astronomy at Leiden in 1717 (Berkel 1999a, p. 72). He had served on a diplomatic delegation to England in 1715, where he 1. I am using the term ‘textbook’ in a broad sense, indicating books explaining and making accessible bodies of natural philosophy and mathematics to initiates and non- experts. It applies not only to books used in an educational setting but also to those intended for a general audience. 2. For the reception of Newton’s optics in Germany see Hakfoort 1995, pp. 19–26.

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became acquainted with Newton, Desaguliers and Keill and had been deeply impressed with the new natural philosophy (Helden 1999, p. 450). ‘s Gravesande’s Physices Elementa (1720) was the reºection of his lectures at Leiden university and was one of the most important textbooks of Newto- nian natural philosophy. It went through numerous editions and translations. ‘s Gravesande treated the physics of light in a rather cursory way, emphasizing the experimental foundations of his claims and preferring a phenomenological treatment. The contents and organization of the book show that ‘s Gravesande was led by didactic considerations of conceptual clarity. Thus, he ªrst treated inºection of light to show the attraction of matter on light rays, and then discussed refraction prior to reºection (Gravesande 1720, 2: book 5, part 1–3). Likewise he opened the part on colors with a discussion of opacity, arguing that it arose from the conªg- uration of essentially transparent particles of any body. Such deviations from the usual order of optical topics show that ‘s Gravesande organized his argument around what he considered the heart of the matter: the physicomathematics of the interaction of light and matter. By way of ‘introduction to Newtonian philosophy’ this might seem surprising, as New- ton had always been very careful to separate experimental results from mechanistic hypotheses, but it merely shows the way in which ‘s Grave- sande transformed Newton’s achievements. He introduced the cornerstone of Opticks, different refrangibility, in the context of the colors of bodies, which Newton only discussed as part of his account of the nature of colors (Gravesande 1720, 2: book 5, part 4, chapters 19–20). In the third edition of 1742 of Physices Elementa, ‘s Gravesande elaborated a sophisticated adap- tation of Newton’s theory of colored bodies. (Gravesande 1742, 2: book 5, part 4, chapter 26; Shapiro 1993, pp. 228–229). He attributed colors to both the thickness and the refractive force of the intermediate parts of bodies, building on a detailed rendition of Newton’s observations of the colors of thin ªlms. ‘s Gravesande’s argument was mainly phenomenological and he did not draw upon his previous account of refraction in terms of attractive forces to explain different refrangibility. At the time ‘s Gravesande began teaching Newtonian philosophy, Dan- iël Gabriël Fahrenheit (1686–1738) was giving public lectures on optics, hydrostatics and chemistry. His primary interest was instruments, of which he discussed several innovations of his own. He discussed a reºector made with steel mirrors he had devised after having read Newton’s com- plaints in Opticks about the difªculties with making good and durable mirrors (Ploos van Amstel 1718, f. 52r). He was much taken by Newton’s design, not so much because of the solution of chromatic aberration— which he considered to be limited—but because of the possibilities of shortening telescopes (Ploos van Amstel 1718, f. 34v). Fahrenheit’s argu-

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ment was primarily experimental, and he refrained from causal expositions after an initial consideration of the nature of light. This revealed his chem- ical bias, identifying light with luminescent phenomena of vacuum globes and exotic substances. Taking a non-committal position regarding the nature of light, he tended to a Cartesian conception and attributed light to the second element (Ploos van Amstel 1718, f. 6r). ‘s Gravesande was probably instrumental in the trip John Theophilus Desaguliers (1683–1744) made to Holland in 1729–1730, where he lec- tured in Middelburg, The Hague, and Rotterdam (Berkel 1999a, pp. 80– 81). An anonymous listener made notes, elaborated and published them, providing a brief introduction into experimental philosophy “. . . which from its most prominent promoter, the outstanding Sir Isaac Newton, not improperly takes the name Newtonian” (Desaguliers 1732, preface).3 The lessons on optics introduced light as a corporeal substance, rejecting wave conceptions, and explained refraction by an attractive force of the medium. The exposition was straightforward, purely qualitative, and em- ployed some simple experiments and observations. Colors were introduced in terms of the different refrangibility revealed by prisms and the author claimed that these showed light rays to consist of seven different kinds.

The variety of the refraction is certainly caused because the one ray of this kind of light particles being bigger than the other, and propagated with the same speed, has more quantity of motion as the other, and therefore cannot be dispersed from its path so easily (Desaguliers 1732, p. 162).4

Desaguliers added an experiment with balls of various size being diverted by a blast of air. This way of plainly making claims about the mechanistic nature of light and its properties blurred the strict distinction Newton had drawn between experimental inferences and mechanistic speculations. As we show below, it is typical of the way textbooks reworked Newton’s optical teachings. Petrus van Musschenbroek (1692–1761) had also become acquainted with Desaguliers on a trip to England and acknowledged the stimulus the latter’s lectures had given to the pursuit of the new philosophy in the Low Countries: 3. “. . . die van haren voornaemsten bevorderaer den uitmuntenden Ridder Isaak New- ton, niet ten onregt de naem van de Newtoniaensche draegt;...” 4. “De verscheidenheid der strael-buiging ontstaet zekerlyk daer uit, dat de eene strael of het eene soort van ligt-deeltjes grooter als ‘t andere zynde, en met dezelfde snelheid voortgedreven, meerder quantiteit van beweging heeft als het andere, en daerom niet zoo ligt van zynen weg kan worden afgedreven.”

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He demonstrated for them [the Dutch amateurs] to the eye, what they by reading alone had understood and comprehended faintly: here one did not hold up the listener with idle speculations, by which philosophy had been encumbered by Descartes and his fol- lowers, but with matters, that were clearly put before the eyes, and that were proven, with convincing experiments in various ways, or mathematically, whereby they were imprinted deeply in the mem- ory, and excited the desire and ardor to learn still more secrets of Nature (Musschenbroek 1739, preface).5

As professor of mathematics and natural philosophy in Utrecht from 1723, Musschenbroek was a notable promoter of Newtonian philosophy. In a range of textbooks that were promptly translated from Latin into Dutch and other languages, he followed the lead of ‘s Gravesande to whom he was closely linked through his family of instrument makers and whom he succeeded in Leiden in 1742 (Berkel 1999b, p. 538). Beginsels der Natuurkunde, beschreeven ten dienste der Landgenooten (Elements of Physics, described for the beneªt of the countrymen) was ªrst published in 1736 and was a translation of Elementes Physicae (1734).6 Optics occupied a sub- stantial part, and Musschenbroek treated it in a conªdent and straightforward textbook style, developing a causal theory of light, colors, and refractions. He left out details and topics that would complicate matters, like the theory of ªts. His primary goal was to present the teachings of the ‘greatest philosopher’, Isaac Newton (Musschenbroek 1739, preface). Musschenbroek described light as particles streaming like a ºuid along lines. Refraction he explained by an attractive power from a transparent medium that accelerates the motion of light (Musschenbroek 1739, p. 522 (§1018)). Referring to Opticks Book II, Part III, Proposition 10, he added that the force of attraction is proportional to the density of the medium (with the exception of some oily and inºammable substances). Musschenbroek also discussed the alternative views of Descartes, Dechales 5. “Hy toonde hun [de Hollandse liefhebbers] voor het oog, het geen zy alleen door leezen ºaauw begreepen en verstaan hadden: men hieldt hier den Toehoorder niet op met ydele gissingen, waarmee de Wysbegeerte door Descartes en zyne navolgers bezwangerd is geworden, maar met zaaken, welke klaar voor oogen gesteld, en met overtuigende proeven op verscheide manieren, of wiskonstig beweezen wierden, waardoor zy diep in de geheugenis ingeprent raakten, en den lust en yver, om nogh meer verborgentheden der Natuure te leeren, opwekten.” 6. Elementa Physicae had been preceded by Epitome elementorum physico-mathematicorum (1726). Musschenbroek would continue to publish textbooks on natural philosophy, most notably Introductio ad philosophiam naturalem (1762) that was translated into French in 1769 as Cours de physique experimentale et mathematique. A German edition of Elementa in 1747 was much referred to in the second half of the eighteenth century (Hakfoort 1995, pp. 45–46).

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and Barrow (Huygens is not mentioned), but only to reject them. He then derived the sine law of refraction by means of these attractive forces. Mus- schenbroek similarly explained reºection in terms of forces, comparing the attractive and repulsive forces of reºecting materials to those of the mag- net (on which he had done extensive research) (Musschenbroek 1739, p. 605 (§1261)). On colors Musschenbroek reported Newton’s discovery of different refrangibility and gave a causal explanation. Noticing that red rays are least refracted and thus ‘maintain their path more steadily’, he listed three possible reasons: attraction acts less on red rays; the parts of red rays have a larger impulse and are therefore bigger and denser; red rays are swifter. After reviewing these options he concluded that ‘truly the parts of the red rays are bigger and more solid’ (Musschenbroek 1739, p. 556 (§1121)). He saw this conªrmed by the greater clarity of red light. On the colors of thin ªlms, Musschenbroek likewise reported Newton’s experiments and observations. He adopted the explanation of the colors of natural bodies. Colored bodies break up light into colored rays, reºecting some and ‘devouring’ others, their parts being ‘thin bodies, which one can consider as thin plates, of which we have talked [above]’ (Musschenbroek 1739, p. 561 (§1136)). The variety of colors he then explained by the size of the smallest parts of natural bodies in the same way as ªlms of various thicknesses reºect various colors ...asmister Newton has proven very cleverly, which has nearly ex- hausted the doctrine of colors and light by manifold experiments, and shrewd mathematical reasonings; and enriched by such saga- cious concoctions, that we esteem too grave in these elements, to render them sufªciently comprehensible. (Musschenbroek 1739, pp. 563–4 (§1138))7 Whether he actually omitted the theory of ªts because he did not want to burden his students with too much profundity, or thought it unfathom- able himself, cannot be told at this point. In the ªrst edition of the Elementa he had presented the theory of ªts, but he left it out in later editions (Hakfoort 1995, pp. 47–48). In Cours de Physique (1769) Musschen- broek cited Mazéas’ experiments on the colors of thin ªlms and his criti- cism of Newton’s explanation, and concluded that the cause of these colors was unknown (Shapiro 1993, p. 205, n142).8 7.“...,gelyk de Heer Newton zeer spitsvondig beweezen heeft, welke het leerstuk over de kleuren en het licht door meenigvuldige proeven, en schrandere wiskunstige redeneeringen byna uitgeput heeft; en met zulke diepzinnige uitvindingen verrykt, welke wy in deeze beginselen te zwaar rekenen, om ze verstaanbaar genoeg te kunnen maaken.” 8. Shapiro adds that the French translation of Smith’s Compleat System includes a sum- mary of Mazéas’ experiments.

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By the 1730s, Dutch amateurs had several ways to read up on Newton’s Opticks. In the mother tongue, the outline of Desaguliers’s lectures, ‘s Gravesande’s and Musschenbroek’s textbooks were available. Opticks was not translated into Dutch, but many would be able to read the original or the French edition. Furthermore, Desaguliers, whom Musschenbroek had lauded for stimulating the new philosophy in the Low Countries, had treated Newton’s optics in his own works that also found their way over- seas. Desaguliers’ main work was A Course of Experimental Philosophy, an elaboration of his lectures, the ªrst volume of which appeared in 1734. Minutes of his lectures had appeared earlier, with and without his con- sent.9 These conªrm the conclusions from the account of Desaguliers’ Dutch lectures: the main optical subjects were perception and optical instruments, with no or very cursory discussion of causal and physical as- pects of light behavior. Desaguliers ªnally prepared his lectures for publi- cation in 1734, around the time Musschenbroek wrote his Beginsels. The ªrst volume of A Course of Experimental Philosophy covered matter, ma- chines and mechanics, and optics was projected for a later volume. When the second volume ªnally appeared ten years later, it became clear that Desaguliers had abandoned his plan to treat optics. He explained that other topics—hydrology in particular—had expanded so much that there was no longer any room for it. However, his readers were not left empty- handed, for he explained that recently an excellent introduction to Newto- nian optics had been published: A Compleat System of Opticks (Desaguliers 1734, pp. vi–vii). Desaguliers’ Course was promptly noticed by Dutch amateurs. In 1736 the Amsterdam printer Isaak Tirion, a fervent promoter of enlightened texts, began publishing a Dutch translation made by ‘an amateur of physics’. When the translation of the second volume appeared in 1746, the publisher promptly announced a translation of Smith as well (Desa- guliers 1736–1751, message from the translator).10 A market existed for this work, because Tirion’s original plans to translate only the ªrst book quickly changed under pressure of ‘some amateurs of physics’ (Desaguliers 1736–1751, message from the translator). The complete Sys- tem, including the mathematical and instrumental parts would appear in Dutch in 1753.

9. See the preface to Lectures of Experimental Philosophy (1729), which actually was a new edition of A System of Experimental Philosophy (1719), published by Desaguliers’ student Paul Dawson. 10. In the third volume of the Natuurkunde, the publisher included translations of a selection of articles on optics by Desaguliers from Philosophical Transactions.

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Smith’s Compleat System One can imagine the Dutch enthusiasm for Smith’s System. It treated the full spectrum of optics, from the physical underpinnings of light’s actions, through the mathematics of lenses and mirrors, to the practice of optical instruments and a history of telescopic discoveries. As to the physics of light, it ªrmly established Newton as the benchmark of optics, which likewise would have well suited the Dutch Newtonians well. Together with Cotes, Whiston, Bentley and the like, Smith was instrumental in es- tablishing Newtonian natural philosophy in the Cambridge colleges (Rouse Ball 1889, p. 92).11 Smith was a cousin of Roger Cotes, with whom he lived during his studies at Cambridge, and whom he succeeded as Plumian Professor of Astronomy in 1716. He was the literary executor of Cotes’ estate, and left Cambridge the collection of papers of Cotes and Newton. Besides the posthumous works of Cotes and the System, Smith published Harmonics (1749) an interesting work on the mathematical science of music that went through several editions. The central concern of the System was optical instruments. Their theory and construction were clearly Smith’s forte. In the preface he wrote that the reader could expect some original contributions to optics, listing thir- teen topics in geometrical optics, instruments and perception. Perception was the other central interest of Smith, judging from the emphasis he laid throughout the book on issues of perception, and the inclusion of an essay on vision by his colleague James Jurin. This predilection for perception is also apparent in, for example, Desaguliers, and it is historically interesting. Up to Kepler perception was the foundation of optics, but in the seventeenth century it yielded to the physics of light and tended to be rele- gated to a secondary issue. Newton and Huygens only touched lightly on the eye and the manner of vision. Smith presented perception as a substan- tial part of optics, though without restoring its foundational position. The foundation of optics was natural philosophy and the ªrst book of the System provided the necessary explanation of the physics of light and colors. A Compleat System of Opticks offered a thorough treatment of the science of optics, presented as a coherent whole. It was divided into four books: a popular treatise laying the natural philosophical foundation of optics; a mathematical treatise on dioptrics and catoptrics, a mechanical treatise on practical dioptrics and catoptrics, and a philosophical treatise contain- ing a history of telescopic discoveries. The didactic aim is clear from the straightforward exposition of the subject matter that leaves little room for

11. For biographical information see (Morse 1970), (Courtney 1908) and (Barrow- Green 1999, pp. 273–276).

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complicating issues and qualiªcations. Smith’s primary goal was to explain clearly and smoothly the essentials of optics. He did not, however, leave out all mathematical and philosophical subtleties, for he added a long series of ‘remarks upon the preceding books’ in which he discussed further elaborations on experiments, alternative accounts, and the like. He omitted such complexities from the main text in order to prevent the argument from bogging down on side issues. The ªrst book of the System, ‘A Popular Treatise’, introduced optics as a science that was founded upon the question what light is and how its properties may be explained. Smith considered optics to be a mathematical science, geometry being “the preparatory learning that is necessary for a thorough acquaintance of that Science” (Smith 1738, p. i) The popular treatise, however, was intended for a general audience and did not require mathematical knowledge. Instead of geometrical demonstrations it used “that more entertaining and looser sort of proof, that may be drawn from experiment only...”Itwasanexperimental discourse, arranged in observations that substantiated the conclusions put forward, that would initiate the amateur to “no inconsiderable part of the doctrine of Opticks”. The other books had a mathematical structure of propositions and deductions. The popular treatise was an introduction to the rest of the System, but it could be read separately.

Enlightening Opticks The popular treatise drew heavily on Newton. Smith carefully selected and refashioned the contents of Opticks, while adding a few points from Principia. The account of refraction is exemplary in this regard. In the ªrst chapter, Smith introduced refraction in general terms as one of the basic properties of light. Deªning the principal terms of optical analysis—such as incident and refracted rays, and angles of incidence and refraction—he explained what reºection and refraction are. He deªned light as the motion of particles that describe physical lines which compose rays of light. Drawing on Opticks, Book II, Part III, Proposition 10, he stated the proportionality between density and refractive (and reºective) power and then gave ªve ‘laws’ of reºection and refraction “being the principal foundation of the whole science of optics”. These were in fact Newton’s ªrst ªve axi- oms, which Smith adopted while adding some direct consequences. At this stage the sine law was justiªed empirically. Smith described a board that should be immersed half in water, incident, reºected and refracted lines recorded, and the claims concerning reºection and refraction veriªed. This was not, of course, an experimental proof of the said laws, but it served Smith’s didactic purpose of providing easy experiments for his teachings.

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In chapter 7 on ‘the cause of refraction, reºection, inºection and emission of light’, Smith returned to refraction and gave a thorough causal account. By an astute selection of passages scattered throughout Opticks, he presented an explanation of refraction in terms of short-range forces, something which Newton himself avoided in the text of Opticks. Smith adapted these by copying Opticks, Book II, Part III, Proposition 7 in full, but leaving out the ‘considerations’ based on the colors of thin plates (Smith 1738, pp. 86–87 (§183)). He continued with somewhat edited ci- tations of Opticks, Book III, Observations 5 and 6, introducing inºected light as a deªnite proof “that bodies act upon light in some circumstances by an attractive and in others by a repulsive force”. Adding some of New- ton’s ªrst observation, Smith jumped to Query 31, citing the passage on the attraction of particles (Smith 1738, pp. 88–89 (§185)). Drawing on Principia, Book I, Proposition 74, Corollary 2 and Book III, Proposition 8, Smith argued that the power acting on light is inªnitely stronger than gravity but acts at a much shorter range (Smith 1738, pp. 89–90 (§186)). He then returned to Opticks, Book II, Part III Propositions 9 and 10. A passage explaining how these short-range forces act perpendicularly to the refractive surface and bend the course of a ray of light seems mainly a cre- ation of Smith (Smith 1738, pp. 90–93 (§§190–194)). It starts out with an unreferenced allusion to Opticks, Book I, Part I, Proposition 6, where Newton had introduced his (exact) derivation of the sine law. Smith did not present this derivation, only stating the decrease of these forces in lines parallel to the surface and explaining in qualitative terms the gradual bending of a ray by the action of these forces. This resulted in its refraction or reºection, depending on the mass, impulse and direction of the ray. Finally, Smith interjected a quote from Query 29 that explained different refrangibility. In this way, the popular treatise showed how the properties of reºection and refraction may be explained. Smith quite elaborately argued that only short range forces could explain all known phenomena, by drawing on a range of observations that his readers could verify for themselves. Because mathematical subtleties were out of place in the popular discourse, Smith did not reproduce Newton’s derivation of the sine law, and, it should be noted, he did not return to it elsewhere in the System. How- ever, he did indicate to his readers the crucial role mathematics played in Newton’s natural philosophy. Chapter 7 concluded with an intriguing passage on the ‘distinguishing character of Sir Isaac Newton’s philosophy’ that is quite different from the rest of the System:

Now as so exact a conformity of reason and experience is the greatest achievement we can possibly have, that this explication of the

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mechanism of the world is a true explication; and as it is the distinguishing character of his system, which all the philosophers that lived before him could never give of any of theirs, for want of sufªcient skill in geometry; so likewise he has given us the same evidence for the truth of his theory of light. For instance, having shewn by experiments that light and bodies affect one another at a distance, by some power that intercedes them; whatever be the law of this power, he has proved mathematically, by two different meth- ods, that in all refractions the sine of incidence must be to the sine of refraction in a given ratio, and in reºection that the angles and sines are equal. (Smith 1738, pp. 93–94 (§195))

With this passage Smith not only pointed out the slight tension between his own exposition and the teachings of his master, but at the same time indirectly reinforced his account by referring to Opticks, Book I, Part I, Proposition 6 and Principia, Book I, Proposition 94. The universality, as well as the reality, of the principles of Newton’s natural philosophy vindi- cated his discourse. In the light of Sir Isaac’s philosophy, it is not so much the avoidance of mathematical subtleties that strikes us, but rather the neglect of the subtleties of his reasoning. Smith freely assembled passages from all parts of Opticks, refashioning Newton’s argument and creating, from time to time, a heterogeneous mixture of inferential claims. More particularly, he ig- nored the distinction Newton carefully drew between the properties of light proven by reason and experiment and speculative hypotheses. By the physics of light, Smith understood the observable properties of light rays as they could be experimentally established. He adopted Newton’s ex- tended conception of ‘observable properties of light’ that included unob- servables providing that they were experimentally established. Smith transgressed Newtonian boundaries, however, when he freely mixed propositions with queries. Like many of his contemporaries, Smith was far more convinced of the certainty of Newton’s speculations than his master, and he discoursed of unobservable particles just as freely as of observable rays. The popular treatise was an instance of experimental philosophy, in which the account of light and its properties was elaborated systemati- cally, substantiated by experiments and observations that the reader could reproduce. Smith’s main goal was conceptual clarity, developing for his readers step by step the fundamental ideas necessary for understanding the phenomena of optics. The character of the System is well illustrated by its account of different refrangibility. Here too, Smith pointed out to his readers the essentially mathematical nature of Newton’s optics:

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For the discovery of this fundamental property of light, which has opened the whole mystery of colours, we see our author was not only beholden to the experiments themselves, which many others had made before him, but also to his skill in geometry; which was absolutely necessary to determine what the ªgure of the refracted image ought to be upon the old principle of an equal refraction of all rays: but having thus made the discovery he contrived the fol- lowing experiment [Newton’s experimentum crucis] to prove it at sight. (Smith 1738, p. 72 (§172)) However, the popular treatise did not warrant an exposition of the geometrical underpinnings of Newton’s theory of colors. Accordingly, Smith reordered the ªrst book of Opticks drastically and selected only what he regarded to be the essentials. He cut back Newton’s lengthy experimental description to a series of well chosen experiments to elaborate an unequiv- ocal and well-structured account that was conªned to the most important conclusions: sunlight consists of a mixture or colored rays of different refrangibility. For example, where Newton stated different reºectibility in Opticks, Book I, Part I, Proposition III by referring back to previous experiments, Smith gave them as a direct proof. In his account he jumped back and forth between Opticks, Book I, Parts I and II, for example when he con- nected different reºexibility immediately to the colors of bodies. He left out things that would complicate matters, like the observation of a blue- red thread through a prism and the difference between observing the colors of a body in daylight and in homogeneal light. Smith conªned his account to the main issues: different refrangibility and its meaning for the colors of natural bodies.

Textbook Refashioning The textbook nature of A Compleat System of Opticks may better explain its content than natural philosophical convictions supposedly underlying the text. Smith considered the colors of bodies an important topic in optics, devoting the full ªnal chapter of the popular treatise to them. In his account, the colors of thin ªlms were the key, but he did not mention New- ton’s theory of ªts. He merely said ‘the cause of which our author has also considered’ (Smith 1738, p. 93 (§194)). Steffens explains this by Smith’s strong belief in the corporeality of light (Steffens 1977, p. 47).12 I agree with Steffens that Smith eliminated any reference to an ether in his adop- tion of Newton’s optics, but I think he overemphasizes the role of his corpuscular belief. True, Smith’s emission conception is evident, but he con- 12. “Smith was unwilling to compromise his corpuscular theory with a reference to the ‘Fits.’”

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sistently spoke of ‘rays of light’ that behave like bodies. Referring to Query 29, he adopted an emission conception of light: Whoever has considered what a number of properties and effects of light are exactly similar to the properties and effects of bodies of a sensible bulk, will ªnd it difªcult to conceive that light is any thing else but very small and distinct particles of matter. However, he immediately took a noncommittal stance by adding (par- tially quoting Newton’s deªnition of a light ray): But for the present purpose it is sufªcient to observe that light consists of parts, both successive in the same lines and contemporary in several lines. (Smith 1738, p. 1 (§1)) Steffens, it seems to me, sets far too much store on Smith’s notion of attraction, by calling it the starting point of his optics, which he elaborated into a system of corpuscular optics. He has Smith explain rectilinearity by the corpuscular nature of light (Steffens 1977, pp. 34–40). However, Smith uses the empirically evident rectilinearity of light rays as a justi- ªcation to subject rays to the laws of motion (Smith 1738, p. 91 (§191)).13 I think the textbook nature of A Compleat System explains Smith’s unre- served discussion of attractive and repulsive forces in optics. This, com- bined with the imperative to avoid too much mathematics, made him leave out the theory of ªts. A theory that was, after all, avoided by the ma- jority of eighteenth-century optical writers (Shapiro 1993, pp. 202–204). In the course of elaborating an instructive exposition of the foundations of optics, Smith refashioned and rearranged Newton’s optical ideas. He organized the various parts of Opticks into a coherent system and integrated the optical parts of Principia. In so doing, as Steffens aptly points out, he drew together in systematic fashion the force physics of Principia and the ray optics of Opticks (Steffens 1977, p. 28).14 Thus, Smith showed the world the inherent connection between the two that Newton had inten- tionally left implicit. The System was not unique in this regard. On the contrary, ‘s Gravesande and Musschenbroek likewise integrated Newto- nian force physics and optics. And they likewise refashioned Newton’s optical ideas into a purposive natural philosophical discourse in which the 13. “For as light has this property in common with all other bodies, of moving straight forwards, while its motion is not disturbed by any oblique force, so when it is disturbed, we may reasonably conclude, it will follow those other laws of motion, to which all other bodies are equally subject.” 14. Whether he was the ªrst to do so and “fundamentally responsible for this incorpo- ration of ideas from the Principia into the optics” (Steffens 1977, p. 33) and therefore established eighteenth-century ‘Newtonian optics’ I cannot judge at this moment.

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colors of bodies were the central issue. Textbooks maintained a clear, didactic style in which the argument followed a ‘natural order’ of reasoning and qualiªcations and complications were left out or put in appendices. In eighteenth-century textbooks optics had become a mathematical science founded upon the natural philosophy of the nature of light and its behavior. In this regard, the seventeenth-century transformation of optics had indeed culminated. This transformation was fully attributed to New- ton. Huygens had virtually disappeared from view. No mention of Traité de la lumière was made, and his wave theory was not discussed. Even ‘s Gravesande, who edited Huygens’ Opera varia (1724) and Opera reliqua (1728), which included a Latin translation of Traité de la lumière, did not deem the wave theory worthy of discussion. Newton constituted the physical part of optics in the eighteenth century, and Descartes entered only to be refuted. Despite its natural philosophical foundation, the main substance of optics remained good old geometrical optics. All books discussed here elaborately treated lenses, mirrors and instruments with a marked predilection for issues of perception. In these parts Huygens ªgured prom- inently on the merits of his extensive and searching writings on dioptrics. A Compleat System of Opticks was regarded as the principal textbook on optics in the eighteenth century. It gave Smith the nickname ‘Old Focus’ (Courtney 1908). In his Histoire des Mathematiques Montucla opened the section on optics with Smith, although he was critical of its composition and the choice of subjects (Montucla 1799, p. 430).15 Smith continued to be read well into the nineteenth century; Helmholtz and Mach still referred to it well into the nineteenth century. In 1889 Rouse Ball could still write of Smith: “His Opticks published in 1728 is one of the best textbooks on the subject that has yet appeared, and with a few additions might be usefully reprinted now” (Rouse Ball 1889, p. 91). Throughout the eighteenth century the System was used as a textbook at Cambridge. Around 1730 it was listed with Gregory and Newton in a tutor’s reading scheme and a list with disputation topics from the end of the century explicitly referred to Smith in a question on focal distances (Rouse Ball 1889, pp. 92–93, 180). A description of the senate-house examination for the general level from 1772 mentioned Smith as the textbook for optics (Rouse Ball 1889, pp. 190–192). In these mathematics examinations optics was conªned to geometrical optics, but it is clear that Cambridge students were familiar with Smith. In the 1770s the System had become quite

15. “Cet ouvrage, il faut en convenir, n’est pas un modèle pour la redaction; il y règne beaucoup de désordre et beaucoup de diffusion. Une de ses parties qui traite de divers instruments astronomiques et des découvertes faites par leur moyen, y est entièrement superºue;...”

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scarce, but a reprint of the whole treatise was not deemed feasible. An outline was compiled and subsequently published for the beneªt of students of the whole university in 1778 (Smith 1778, p. iii). The Elementary Parts of Dr. Smith’s Compleat System of Opticks consisted of selections from Smith arranged to meet the plan of lectures of the Cambridge tutors. Some selections from other authors were added and the whole was presented as a guide to ‘modern optics’ (Smith 1778, pp. ii–ii). In the meantime several foreign editions of the System had appeared: Dutch (1753, with a reprint in 1764), German (1755) and French (expanded; 1767, 1783). Which brings us back to Holland.

Gigue: The Usefulness of the System Through Desaguliers’ intercession, Tirion had projected a Dutch translation of the ‘Popular Treatise’ in 1746, expanding his plans to a translation of the full System in 1751. When the response to this prospectus was satisfactory—176 people had subscribed—Volkomen Samenstel der Optica of Gezigtkunde appeared in 1753 (Zuidervaart 1999, p. 77, and appendix 11). The translation was faithful and did not add to the original. It was, however, widely read and exerted some inºuence in the Dutch Republic. In the middle of the eighteenth century, the Dutch were successfully producing reºecting telescopes (Zuidervaart 2004). The market for optical instruments evidently also formed an outlet for books on optics. In 1758, Dutch optics enthusiasts also became captivated by Dollond’s invention of the achromatic telescope. Whereas prominent telescope makers responded by trying to make even better reºectors, in Amsterdam de Van Deijl workshop successfully began producing achromatic telescopes (Zuider- vaart 2004, pp. 434–443; Zuidervaart 1999: 306–307). Jan van Deijl had managed to understand the ‘secret’ in collaboration with his fellow towns- man Carl Ulrich Bley. They had experimented with lens combinations and in 1765 Bley published an article reporting on their trials as well as explaining the theory. Dollond had revealed little detail about his telescopes. The Dutch translation of his original article called upon the readers to un- cover the secret of the achromatic telescope (Houttuyn 1760).16 To this Bley and Van Deijl replied, and they found a solution in 1761 (Zuider- vaart 2004, p. 434). In his article, Bley discussed experiments in combining various kinds of glasses and gave a mathematical analysis of his study. He claimed he had found the way to improve refractors and understood it theoretically. He wrote that he had commissioned Van Deijl to build a telescope accord- 16. In his article Bley also replied to a 1762 prize contest of the St. Petersburg Acad- emy of Sciences (Bley 1765, pp. 417–418).

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ing to his design. It did not fully remove colors, but this, Bley maintained, was because the lenses were not proportioned exactly to his instructions. It did, however, surpass the best reºectors as regards mag- niªcation, clarity, ªeld of view and distinctness (Bley 1765, pp. 461–463). Bley had been educated in the Amsterdam lecture circuit, which Mus- schenbroek had noted and in which Newton’s optics had played a prominent role (Zuidervaart 1999, pp. 304–305). In his analysis of the amount of chromatic aberration he referred to both Smith’s and Newton’s account. Although he may have drawn on Smith for Newton, it is clear that he was well acquainted with Opticks. Bley discussed refraction in terms of a short range attraction on the ray of light, reproducing Newton’s argument in Opticks, Book II, Part III, Proposition 10. In other words, he ªlled in the mathematical part of Newton’s explanation of refraction that Smith had omitted from his popular treatise. Central to Bley’s solution of the chromatic aberration of lenses, was the proportionality between refractive power and color dispersion and the density of the kind of glass used. He drew explicitly on Smith’s analysis in the mathematical treatise of the Sys- tem. In his analysis of spherical aberration, Bley too built on Smith’s mathematical treatise, who in turn built on Huygens’ dioptrics (Smith 1738, pp. 652–669 (§§ 329–333)). Bley’s article makes it clear that A Compleat System was a valuable elaboration of Newton’s Opticks applied to the mathematics of lenses and instruments.17 Telescopes continued to engage Dutch minds, but the dominance of Newton slowly declined towards the end of the eighteenth century. In 1774, the Utrecht mathematics professor Hennert published an extensive article on the theory of achromatic telescopes. The article consisted of three parts, of which the ªrst was a general introduction that, according to the author, did not bring much news for those familiar with Smith. I will not discuss the content of the article but will only point out the remark- able introduction. Hennert was astonished that English opticians had only endeavored to improve reºectors. Apparently the conclusions of Opticks had restrained them from considering refracting telescopes. In the meantime alternative conceptions in optics had been proposed. Euler had elaborated a wave conception of light, including an account of colors (Hakfoort 1995). Euler had made clear that options existed to improving refracting telescopes, Hennert argued and then concluded: When the students of the science are controlled by the power of prejudices, they can only be liberated from that tyranny by the ef- forts of excellent minds whose judgments equal the commands of 17. The same can be said for Dollond; for his reading of A Compleat System see (Sorrensen 2001, p. 10).

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the Most High: thus Cartesius disturbed the tyranny of the Scholas- tics, thus Euler stood up against Newton (Hennert 1774, p. 280).18

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