Lectiones opticae annis MDCLXIX, MDCLXIX, MDCLXX & MDCLXXI. In scholis publicis habitae: et nunce primum ex MSS. In lucem editae.
London: William Innys for the Royal Society, 1729. First edition of the complete text, in the original Latin, of Newton’s inaugural lectures as the second Lucasian professor of mathematics at Cambridge, and the first publication of his lectures on his new mathematical science of colour, including his discovery of the compound nature of white light. It was from this material that Newton composed his Opticks of 1704, although in the Opticks he left out the specifically mathematical parts of the lectures which are included here. Newton “was obliged by the statutes of the post to lecture and to deposit the lectures in the University Library. For the period 1670-72 Newton lectured on optics and deposited the lectures in the ULC in October 1674. At one time Newton seemed to be contemplating publishing the lectures together with the mathematical work De methodis, but by May 1672 he had decided otherwise and wrote to Collins: ‘I have now determined otherwise of them; finding already by the little use I have made of the Presse, that I shall not enjoy my former serene liberty till I have done with it’ (Correspondence, I, p 161). Consequently, … the lectures remained unpublished until after his death [as did the De methodis]” (Gjertsen, pp. 409-410). Following Newton’s death in March 1727, his followers decided to publish the lectures, both in the original Latin and in English. In fact, only Part I, on the mathematical theory of reflection and refraction, was translated and published in English, in 1728; part II, on colours, was omitted. The present Latin edition, which includes both parts, is thus the editio princeps of the complete series of Newton’s lectures, including the first publication of his lectures on colours. Based on a copy belonging to David Gregory, it was discovered during the printing that there were discrepancies between Gregory’s copy and the copy deposited by Newton in the ULC, which necessitated the inclusion of a five-page ‘Addenda and Corrigenda’. “Today we can appreciate [the Lectiones] as an invaluable document of Newton’s investigations of optics that reveals his ideas in the midst of his most productive period of research. In the inevitable comparison with the Opticks (1704), which recounts research for the most part carried out twenty to thirty years earlier and since refined – sometimes overrefined – the lectures must be judged neither as carefully developed nor as polished. But whatever polish it may lack is more than compensated for by its vitality, as Newton boldly attempts in the following pages to create a new mathematical science of color” (Shapiro, p. 25). Since the Lectiones “was his first and most comprehensive account of his theory of color, he naturally drew upon it in his later writings. It served as the immediate source for his ‘New theory of light and colors’ (1672) in the Philosophical Transactions, his first public statement of his theory outside the Cambridge lecture halls. And twenty years later it remained the foundation for the ‘definitive’ statement of his theory in Book I of the Opticks” (ibid., p. 1). This was the only separate edition of Newton’s complete lectures: the text was published six more times in the eighteenth century, in various collections of Newton’s works. Provenance: ‘Ex-libris Dutour’ on front free endpaper, followed by a price; some marginal notes in Latin. “Upon his appointment as [Isaac] Barrow’s successor to the Lucasian chair in the late autumn of 1669, Newton was confronted with developing a series of lectures to begin the following January. In a natural extension to Barrow’s prior series of optical lectures [published as Lectiones XVIII, 1669] he took the opportunity to make the first formal presentation of his new mathematical science of color. The Lucasian Professor was required to give one lecture for about one hour each week during the term and to submit annually not fewer than ten of those lectures to the Vice-Chancellor for deposit in the University Library for public use. Newton complied with this regulation somewhat tardily in October 1674, when he delivered to the Vice-Chancellor his Optica divided into two parts with a total of thirty-one lectures. According to the marginal annotations, the first lecture of Part I was delivered in January 1670, at the beginning of Lent term, and Lecture 9 of Part I and Lectures 4 and 14 of Part II opened the Michaelmas terms (beginning in October) of 1670, 1671, and 1672” (Shapiro, p. 16). As noted above, by the winter of 1671-2 Newton had decided to publish the Optica, together with his mathematical treatise De methodis serierum et fluxionum [the latter was not actually published until 1736]. However, following the publication of his ‘New theory of light and colours’ in the Philosophical Transactions a few months later, Newton changed his mind: his ‘New theory’ had resulted in controversy which he was loathe to encourage by further publications. “In September 1672 Newton had decided to recast his theory in a more formal structure ‘in imitation of the Method by wch Mathematicians are wont to prove their doctrines.’ The next year, in outlining his restructured theory for Christiaan Huygens, he recognized that it needed a more rigorous proof … Instead, Newton was planning a work very much like the later Opticks … In this newly projected work, the sections of the Optica on color were to be extensively rewritten and its mathematical part omitted. There is no evidence that Newton wrote such a discourse during this period, but when in the early 1690s he eventually composed the Opticks, he in essence followed the plan he had proposed in the mid-1670s … When, after still another postponement, the Opticks was finally published in 1704, Newton felt it necessary to warn that, ‘If any other Papers writ on this Subject are got out of my Hands they are imperfect, and were perhaps written before I had tried all the Experiments here set down, and fully satisfied my self about the Laws of Refractions and Composition of Colours, I have here Published what I think proper to come abroad.’ He is here inter alia surely referring to his Optica, deposited thirty years earlier in the Cambridge University Library … During his lifetime Newton’s disavowal was respected by eager members of the Newtonian circle, but an English translation of Part I appeared in 1728, the year after his death, followed in the next year by the editio princeps of the complete Latin text of the Optica … The editor of the Latin edition emphasized the significance of the geometrical demonstrations and philosophical arguments in Part I, because in the Opticks Newton ‘seems to have been as careful as possible not to mix geometrical demonstrations with philosophical arguments, and when it was necessary to set forth a mathematical proposition, its demonstration scarcely ever occurs’ … [He] also perceptively recognized that with respect to color, ‘many things are found in each with the same meaning but are explained in a different manner’” (ibid., pp. 21-23). “After briefly paying tribute to Barrow and deriding efforts to improve refracting telescopes by the use of nonspherical lenses, Newton devotes the first two lectures [of Part I] to laying the foundations for the whole of the Lectures: a demonstration that direct sunlight consists of rays that differ in their degree of refrangibility. Virtually the entire burden of his demonstration is borne by an analysis of the elongated spectrum formed by passing a narrow beam of sunlight through a prism. Newton’s major insight, and the key to his demonstration, was to recognize that when a prism is placed symmetrically with respect to the incident and emergent beams, or at minimum deviation, the sun’s image would be circular rather than elongated if all rays were refracted equally. An exact solution for the shape of the sun’s image with monochromatic rays is exceedingly difficult, involving a finite source and aperture and rays incident out of the principal plane; but he is able to demonstrate that under particular conditions, such as with a point aperture, the image is nearly circular. This was sufficient for his purpose, for he had found the spectrum’s length to be five times its breadth, thus making small deviations from the assumed condition inconsequential. “Newton begins Lecture 2 by describing the shape of the spectrum to be an oblong bounded by straight edges and semicircular ends and, he argues, formed by innumerable overlapping circular images of the sun, each consisting of rays of a different refrangibility … The thrust of the remainder of the lecture describes how to decrease the effective size of the source, and thus the circular images, and to approach the ideal spectrum – a straight line with no breadth – formed by a point source. By this mode of demonstration, culminating in the observation of Venus’s spectrum, he makes the actually observed shape of the sun’s spectrum inessential to his proof that its elongation is caused by unequal refrangibility (ibid., pp. 26-27). “Newton begins his ‘dissertation on the measure of refractions’, which constitutes the next three lectures, with an explanation of Descartes’s sine law of refraction, which he extends – without experimental demonstration – to rays of each color … Next, in two lemmas he derives the equations for his preferred method to measure the index of refraction, that of minimum deviation in prisms, one of his most important contributions to quantitative experimental optics … Newton opens Lecture 10 by extending the method of minimum deviation to fluids with the use of a hollow prism with glass sides, and he illustrates this method by a measurement of the mean index of refraction of water … He then advances to the next phase of his investigation of refraction: to determine the indices of refraction of the extreme rays, or the chromatic dispersion … When the prism is placed at minimum deviation for the mean refrangible rays, he measure the length of the spectrum and thereby determines the angular dispersion. He presents a simple measurement and calculation for the dispersion of glass … “Newton concludes his ‘dissertation on the measures of refraction’ in Lecture 11 by setting forth a dispersion law, which serves as the foundation for the rest of the Lectures. He freely admits that it is a purely theoretical construct that he has not yet experimentally tested. Though he presents his dispersion law solely in mathematical terms without any mechanical interpretation, it is evidently a modification of Descartes’s projectile model for a single sort of ray extended to apply to polychromatic rays. It represents the very ideal of a rational optics, for the indices of refraction of rays of every color in any medium can be determined with only a single measurement, as Newton illustrates with water … “In [Lectures 12 and 13] on refraction at a single plane surface Newton attempts to uncover the physical implications of the laws of refraction, the sine law and his dispersion law, by a thorough mathematical analysis. Since that dispersion law was so tenuously founded and is the starting point for much of his analysis, these lectures are now as notable for their mathematical analyses as for their contributions to optics. “Lecture 12 is … devoted to the single problem in Proposition 3 of determining the position of a luminous point viewed obliquely across a plane reflecting surface. Newton’s recognition here that there are two image points effectively begins the study of astigmatism … Lecture 13 … [studies] a natural extension of Proposition 3: to determine the shape of the extended image of a point source due to the varying index of refraction when the point is viewed across a plane surface. He elegantly demonstrates that the images of the point lie on a Dioclean cissoid … “In the next two pairs of Lectures, 14, 15 and 16, 17, Newton continues his attempt to create a rational science of color by investigating the variation of angular dispersion as the index of refractions and hence the chromatic dispersion of the refracting media vary … [The brief Lecture 18] treats refraction in prisms … “Section 4, on refraction at curved surfaces, the conclusion of the mathematical part of the Optica, is its highpoint, an intimate blend of mathematics and physics consistently yielding novel, interesting results … He effectively begins this section in Proposition 29 by determining the image point (in a form equivalent to the Gaussian formula) for paraxial rays incident upon a single spherical surface; and then in Proposition 30 he extends this result to any curved surface by substituting the center of curvature (determined in Lemma 9) in the immediate neighborhood of the incident rays for the center of the spherical surface. In Proposition 31 Newton applies many of the newly wrought mathematical methods, such as series expansions and the determination of extrema, to find the longitudinal spherical aberration for rays incident on the plane face of a plano-convex lens, and then the circle of least confusion. Because of its algebraic formulation, this proposition is particularly accessible to the modern reader and provides a fine example of Newton’s application of mathematics to physics. In the next proposition he elegantly derives the location of the primary image point, or caustic locus, for rays obliquely incident upon a spherical surface while also noting the existence and location of the secondary image point. Proposition 33 extends this result to any curved refracting surface. In Proposition 34 he presents his own solution to a problem posed and solved by Descartes: to find the aplanatic surface (a Cartesian oval) that refracts rays perfectly from a given point to a given point. Pursuing the Cartesian theme, in Propositions 35 and 36 he derives the radii of the primary and secondary rainbows, and then moving beyond all his contemporaries he generalizes his solution to bows of any order. And to conclude, Newton in Proposition 37 calculates the chromatic aberration to show that it is much more enormous – some 1500 times greater – than spherical aberration, and once again stresses the significance of his discovery of unequal refrangibility for practical optics” (ibid., pp. 36-41). In Part II Newton begins the ‘dissertation on colors’ by reiterating his inaugural remarks on the defects of contemporary telescopes and the impediment presented by chromatic aberration, and in prelude to his own theory he vigorously attacks both Aristotelian and more recent modification theories of colour. He then presents his theory in five propositions. The first proposition, that to differently refrangible rays there correspond different colors, had already been established in Part I. Its converse states that different colors are unequally refracted. “To demonstrate this he introduces his crossed-prism experiments, where spectra cast on a second, transverse prism become inclined to their original orientation because the blue end is always refracted more than the red. Initially he places the second prism transverse to the first one to minimize the unequal incidence arising from the refraction of the first prism; but by passing the refracted rays through two holes far apart so that they fall on the second prism at very nearly the same angle of incidence, he eliminated the requirement for any particular orientation of the second prism and arrives at an experimental arrangement virtually identical to the experimentum crucis of the ‘New theory’ … “Proposition 2, on the immutability of monochromatic colors, [is established] by first separating the spectral colors from one another and then demonstrating that the more completely they are separated the smaller are their changes after additional refractions. He first separates the colors with two parallel prisms and observes some color change, because the adjacent colors are still intermingled, but when he adds two more prisms he is unable to detect any further sensible change … “In [Lectures 4-7] Newton carries out the first part of his demonstration of Proposition 3, that white light, in particular sunlight, is composed of rays of every color, by showing five different ways to make white from a mixture of spectral colors: (i) colors from three prisms are cast onto a screen where they are mixed; (ii) one face of a prism is covered with an opaque paper with six slits, each functioning as one of the prisms in the preceding experiment, and then the colors from the various slits mix on a screen; (iii) light scattered from a screen on which a spectrum has been projected is received on a second screen where the scattered rays mix; (iv) the colors dispersed by a prism are transmitted through a lens and brought together at its focus; (v) in a variant of the preceding way a mirror is substituted for the lens. He also illustrates the compound nature of white by a mixture of colored powders, and by a froth of soap bubbles … “Newton now applies himself to the second and more difficult part of his demonstration of Proposition 3, namely, to show that the sun’s direct light is compounded of colors even before they are apparent. He bases his demonstration on the phenomenon of total reflection, for, as he discovered, the critical angle of reflection varies for each color. In the first and simplest experiment, a beam of sunlight is partially reflected and partially refracted at the base of a prism. As the prism is rotated the colors are totally reflected in sequence, and the reflected and transmitted beams change color until, when the red rays are at last totally reflected and the transmitted beam vanishes, the reflective beam is restored to white. Newton argues, implicitly appealing to the emission theory of light, that this reveals that the colors are in the rays as they arrive from the sun, since they preserve and exhibit the same color whether they are reflected refracted. Furthermore, this shows that reflected light is compound, since white is restored when the last color, red, is totally reflected. To make this interpretation still more certain he introduces three variants of this basic experiment, one of which is an exact analog of the experimentum crucis, but with total reflection replacing the second refraction … Newton concludes the proof of Proposition 3 by briefly explaining why the sun’s light is yellowish rather than white, and then by showing that black is compounded from all colors, grey from white and black, and all other compound colors from the painter’s primaries, red, yellow and blue. Despite the need for some restrictions and the brevity of its demonstration, Proposition 4, that spectral colors can be compounded from their neighbouring colors, is an important contribution to the theory of compound colors and displays Newton’s keen experimental skill. “Newton now turns to his fifth and final proposition, that natural bodies derive their color from the sort of rays they reflect most. By the principle of color immutability, the color of a ray cannot be changed my reflection, so that bodies can appear only the color of the rays illuminating them. To explain why all bodies are not therefore the same color in daylight, as this principle alone would demand, he adds that bodies reflect more of their own daylight color than others. After demonstrating this by illuminating various bodies with monochromatic light, he moves beyond this phenomenological account and attributes two distinct powers to bodies: to reflect rays and to transmit them. These rays are complementary, for the rays that are not reflected pass through the body, and he illustrates this with the colors of such substances as gold leaf, which reflects yellow light and transmits blue. Newton did recognize that most bodies are not of this sort, but are the same color all around, and to explain this he introduces a third power – and a new concept in optics – selective absorption … “In the concluding section of the Optica, Newton considers the colors generated by refractions at curved surfaces, namely lenses, the eye, and raindrops, or the rainbow. He first describes the chromatic aberration of a plano-convex lens and gives a simple physical derivation and numerical estimate of its magnitude. Observing that the eye is a lens of sorts, which should likewise suffer from chromatic aberration, he presents a simple experimental demonstration of its existence. In the last article of Lecture 14, and in all of Lecture 15, Newton indulges in the sort of speculative or hypothetical natural philosophy that he frequently and vigorously decried yet could not always resist. Exhibiting a firm command of Cartesian natural philosophy, he explains the cause of the colored circles or coronas that Descartes saw around a candle after he had pressed his eye shut for a long time. While Newton recognizes that an infinity of causes may be devised to explain these colored circles, he ascribes them to refractions in wrinkles impressed on the cornea and, invoking the principles of hydrostatics, rejects Descartes’s own suggestion that they are impressed on the crystalline lens. He concludes the Optica in Lecture 16 with a far more notable achievement, an explanation of the dimensions and colors of the rainbow based on the mathematical results derived in Part I” (ibid., pp. 28-36). Babson 155; Wallis 191; ESTC t18664. Gjertsen, The Newton Handbook, 1986. Shapiro (ed.), The Optical Papers of Isaac Newton, Vol. 1, The Optical Lectures 1670-1672, 1984.
4to (221 x 165 mm), pp xii, 144, [145-152], 153-291, [5, Addenda and corrigenda], with 24 folding engraved plates (some spotting, scattered foxing). Contemporary marbled sheep, spine gilt in compartments, red morocco spine label, marbled endpapers, red edges (a little rubbed, minor abrasion to upper board).
Item #6375
Price: $9,500.00
