Dioptrica nova. A Treatise of Dioptricks, in Two Parts. Wherein the Various Effects and Appearances of Spherick Glasses both convex and concave, single and combined, in telescopes and microscopes, together with their usefulness in many concerns of humane life, are explained.

London: for Benj. Tooke, 1692.

First edition of the first treatise on optics in English, “which for many years served as the standard textbook on lenses” (Albury, p. 455); it includes at the end the first publication of Halley’s famous theorem for finding the focal length of a spherical lens. This is an unrestored copy in contemporary binding; three other copies have appeared at auction since Macclesfield, all rebacked or in later binding. Molyneux (1656-98) “was perhaps the single most important figure in the history of Irish science” (McCartney & Whittaker, Physicists of Ireland, p. 22). In the Admonition to the Reader, Molyneux states that he wrote Dioptrica in English because “I am sure there are many ingenious Heads, great Geometers, and masters in Mathematics, who are not so well skill’d in Latin”, and he also notes one of the work’s principal innovations: “the Geometrical Method of calculating a Ray’s Progress, which in many particulars is so amply delivered hereafter, is wholly new, and never before published. And for the first Intimation thereof, I must acknowledge my self obliged to my worthy Friend Mr. Flamsteed”. Dedicated to the Royal Society, the first part of Dioptrica contains one proposition on vision, two on microscopes, and 56 on telescope optics. Proposition 28 explains that an object is perceived as being upright even though the image on the eye is inverted because “’tis the Soul that sees by means of the Eye.” The second part of Dioptrica opens by noting that there is no English language description of optical fabrication, grinding, polishing, tooling or machinery. Molyneux discusses how to find the foci of lenses, and recommends testing a telescope by viewing a printed page set at a distance, as he had seen Cassini do in Paris. On p. 226, Molyneux discusses the “proportioning of the glasses in telescopes and microscopes”, i.e., the relationship between the focal lengths of the objective and the eyepiece. Molyneux enters one of the more contentious debates of his time on p. 228, where he claims that by advocating plain sights for instruments, Hevelius misunderstands the nature of telescopic sights. The next topic is the micrometer, beginning with a historical perspective (p. 246). Molyneux concludes his chapter by describing a glass reticle, to be used instead of cross hairs. Chapter 6 concerns the history of Optick-Glasses. Molyneux concludes his discussion on telescopes with an explanation of how to measure the distance of an object, then thought to be impossible. Halley provided significant corrections to a draft of Dioptrica, and supervised its publication when Molyneux returned to Ireland in 1691. Flamsteed, who had taught optics to Molyneux, was the source of important portions of Dioptrica: Propositions 16, 17, and 18 are followed by Flamsteed’s solutions. Molyneux was the first person to demonstrate the circulation of blood in a living creature, by observing a newt under a microscope. This was reported in Dioptrica (p. 281): “I have been often delighted with the curious Appearance of many Objects seen through the Microscope. But none ever surprised me more, than the visible Circulation of the Blood in Water-Newts (Lacerta aquatica) to be seen as plainly as Water running in a River, and proportionably much more rapid.” The Dioptrica “received the Royal Society’s approbation for printing on June 4, 1690, but copies were not available for distribution until the end of 1691” (Albury, p. 455). It was reviewed positively by both Huygens and Leibniz. The Macclesfield copy realized £7,800 in 2005.

Born in Dublin to a wealthy land-owning family, Molyneux (1656-98) entered Trinity College Dublin in 1671 and received the bachelor’s degree in 1675. He then studied law in London from 1675 to 1678 after which he returned to Ireland. Molyneux held various commissions, including Surveyor General of the King’s Buildings and Works in Ireland, but he occupied much of his time with scientific studies, which he viewed as a way of showing “That God is the Fountain and Original of Truth.”

Molyneux’s wife Lucy went blind in January of 1679, a few months after their marriage in September of 1678. Lucy died in 1691, perhaps due to the strain of the life-threatening illness of their son Samuel, the only one of their three children to survive into adulthood. Molyneux’s concern over Lucy’s vision problem may have led him to pose, in a letter to his good friend John Locke, the question that has since come to be known as the Molyneux problem: a man was born blind but learned to distinguish between a sphere and a cube by touch; if he had his vision restored, would he be able to immediately distinguish between the sphere and the cube by sight without touching them? The Molyneux problem has drawn the attention of numerous leading philosophers ever since.

In the early 1680s, Molyneux undertook studies in mathematics, optics, and astronomy. In a 1682 letter to Flamsteed (1646-1719), Molyneux said that he was “much enamoured with optics, for in them there is such a mixture of physics and mathematics that renders this subject very pleasing.” In the summer of 1685 Molyneux travelled to Europe: at The Hague, Huygens showed him instruments and telescopes; in Delft, Leeuwenhoek displayed microscopes; Cassini at the Paris Observatory showed Molyneux his clock drive for a telescope and his method of testing lenses by reading a printed page set in a distant window; also in Paris, Pierre Borel presented Molyneux with a 24-foot telescope objective. On the way home, Molyneux stopped in London for several weeks in September 1685, when he visited Flamsteed.

Molyneux was taught optics by Halley (1656-1742), but especially by Flamsteed, who in turn credited his knowledge of optics to William Gascoigne (1612-44), who after his early death in war left behind papers that were used by Flamsteed. Molyneux’s description of a previously unpublished geometrical method of ray calculation in Dioptrica was owed to Flamsteed, who had learned it from Gascoigne’s papers.

Due to fighting in Ireland during 1689-90, when Dioptrica was written, Molyneux was in exile in Chester, England. He began writing the book in Latin but switched to English because no similar work had been written in English, and many skilled workers knew no Latin. Halley supervised the publication of Dioptrica when Molyneux returned to Ireland in 1691.

The first part of Dioptrica was dedicated to the Royal Society, for establishing the place of experiment over Aristotlelian dogma. “The commentators on Aristotle … have rendred Physicks an heap of froathy Disputes … by Hypothetical Conjectures, confirmed by plausible Arguments of Wit and Rhetorick … But never studied to prove their Opinions by Experiments … these were the great Dictators of Physics.”

It consists of 59 propositions followed by scholia and corollaries, covering the optics of plano-convex lenses, plano-concave lenses, meniscus lenses, the eye, eye/lens combinations, telescopes, and microscopes. “Proposition 28 deals with the optics of the eye. Molyneux recognized that the eye changes in order to view objects at different distances, but he didn’t take a stand on the mechanism … Molyneux also described how the point of best focus in a myopic eye is a point in front of the retina. He suggested that the cause of myopia was a crystalline lens which was ‘too convex’ (p. 108). He observed that myopes can see near objects clearly without lenses, but they need concave lenses to see distant objects clearly. With regard to presbyopia, Molyneux said that ‘the Eyes of Old Men have their Crystalline too Flat and cannot correct the Divergence of the Rays … ’tis requisite they add the Adventitious Convexity of a Glass … Spectacles help Old Men, not by magnifying an Object, but by making its Appearance Distinct’ (p. 108). Molyneux included a ray diagram showing the point of focus for a near object in presbyopia to be behind the retina” (Goss).

This first part of Dioptrica was an original text, but it included work of Halley, who provided significant corrections to a draft of the work, and of Leibniz and Flamsteed. Leibniz had published a refutation of Descartes’ theory of refraction, and this was included in Dioptrica. (In 1682, Molyneux had published a partial translation of Leibniz’ article ‘Unicum opticae catoptricae et dioptricae principium’.) Propositions 16, 17, and 18 of Dioptrica are followed, with acknowledgement, by the solutions of Flamsteed on lens combinations in telescopes which had been communicated to Molyneux in tutorial letters. After Dioptrica was finished, Molyneux had written to Flamsteed, told him about the book, and requested permission to include the ideas that Flamsteed had earlier communicated to him. This permission was granted, Flamsteed adding that the publication would free him [Flamsteed] from “some fools who are frequently pressing me to give those dioptric propositions, and an account of the telescope, and the effect of compounded glass.” Nevertheless, Flamsteed was offended, and he proceeded to tell others of errors in the text and, according to Molyneux, generally behave like “a man of so much ill-nature and irreligion.” This controversy ended their long friendship.

“‘The Second Part Containing Various Dioptrick Miscellanies’ consists of eight chapters. Chapter 1 discusses the nature of refraction and light. In Chapter 2, ‘A Dioptrick Problem,’ Molyneux explains how four lenses can be used to produce an erect image: a single convex lens inverts the image, the second acts as an eyepiece and does not revert the image, the third erects the image in a second inversion, and the fourth acts as an eyepiece and brings the image out without inversion. The distinct actions are due to placing the lens inside or outside focus.

“Chapter 3 is entitled ‘Of Glasses for defective Eyes.’ In the first paragraph of chapter 3 he extols the virtues of spectacles:

‘Were there no farther Use of Dioptricks than the Invention of Spectacles for the Help of defective Eyes; whether they be those of old Men, or those of pur-blind [myopic] Men; I should think the Advantage that Mankind receives thereby, inferiour to no other Benefit whatsoever, not absolutely requisite to the support of Life’ (p. 207) …

“Molyneux also discussed rules for choosing spectacles. For presbyopia, he advised the least plus power ‘that will possibly help our Eyes’ (p. 209) … For myopia, he noted that the focal length of the correcting lens should be equal to the distance to the person’s far point of clear vision.

“Molyneux also commented in chapter 3 on Robert Hooke’s idea of using a convex lens to correct myopia. We know, as did Molyneux, that any lens so placed as to have its second focal point coincident with the punctum remotum will produce a clear image. Molyneux noted that using a convex lens in that way for myopia would result in objects being seen upside down and backwards, and that the lens would have to be held so far away as to be impractical. The last section of chapter 3 discusses

how the design of telescopes and microscopes could be modified to correct myopia and presbyopia” (Goss).

In Chapter 4, ‘Of Mechanick Dioptricks,’ Molyneux discusses the current literature on the subjects of optical fabrication and telescopes. This includes (p. 215) publications that discuss grinding machines: Hooke, Micrographia; Hevelius, Selenographia. Chapters 1 & 2 (making the forms for grinding glass); Hevelius, Machina Coelestis, Chapter 23 (grinding conic glasses); Schyrleus de Rheita, Oculus Enoch et Eliae, Lib. 4 (conic glasses); Maignan, Perspectiva Horaria (end of book, spherical and conical glasses); Descartes, Dioptrics (conic glasses); Borelly, Journal des Sçavans, July 6, 1676 (grinding ‘great’ glass, in cipher, not yet deciphered); Fatio de Duillier, Journal des Sçavans, November 20, 1684 (making forms for grinding spherical glass); Wren (“our English Archimedes, Apollonius, Diophantus”), Philosophical Transactions, nos. 48 & 53 (hyperbolic glasses). The list continues on p. 223 with Huygens, Astroscopia compendiaria tubi optici molimine liberata, 1684, which describes his method of managing great glasses without a tube; on p. 224, Cusset, Journal des Sçavans, May 18, 1685 (contrivance for managing great glasses); and on p. 225, Boffat of Tolouse, Journal des Sçavans, December 28, 1682 (contrivance for managing great glasses). But Molyneux does not just list books, he reviews some of them. On p. 222, he critically notes, “Père Cherubin, who is often very nice in matters of little moment, and loose enough in those of greater weight and absolute necessity, describes an implicated contrivance for true centring of glasses, Vision Parfait, Tom. II, p. 109.” On p. 237, Cherubin’s ideas about telescopic sights are described as ‘deficient and useless’. However, Cherubin’s procedures for testing glass on p. 25 of Vision Parfait are described in detail by Molyneux, as are Cherubin’s eyepiece configurations, on pp. 222 & 226.

Molyneux continues by discussing how to find the foci of lenses, and the importance of centration of lenses, in great detail. He describes Cassini’s “contrivances for managing great glasses” (p. 224), somewhat similar to Hooke’s in Animadversions onthe first part of the Machina coelestis of Hevelius (1674). On p. 226, Molyneux discusses the ‘proportioning of the glasses in telescopes and microscopes’, by which he means the relationship between the focal lengths of the objective and the eyepiece. In comparing objectives of the same focal length, the glass of superior quality is that which can be used with an eyepiece of greatest convexity, meaning the smallest focal length.

On p. 228, Molyneux echoes Hooke’s criticisms of Hevelius in his Animadversions, stating that by advocating plain sights for instruments, Hevelius misunderstands the nature of telescopic sights. Several pages are spent in establishing that a telescope with a cross hair can have all parts properly aligned, and then describing how to collimate the optical axis of the instrument with the physical axis of the sight. When a cross hair is at the precise focus of the objective, the image of the cross and the image of the object will be immovable on each other, and will not ‘seem to move or dance’.

In Chapter 5, Molyneux discusses the rectification of telescopic sights on sextants and quadrants. On page 245 he counters some objections: “Telescope-Sights are so far from being obnoxious … ’Tis true, the Breath of the Observer, if puft into the Telescope, will sully the Eye-Glass, but how easily is this avoided? Who is it goes purposely to make a Speaking-Trumpet of a Telescope?” It is on p. 243, in the section on telescopic sights, that Molyneux writes an immortal phrase in the annals of telescopy: “I come now to the last thing proposed concerning Telescopick-Sights; and that is, To shew the Dioptrick-Reason of their Performance and Exactness … ’Tis manifest by Experiments, that the ordinary Power of Man’s Eye extends no farther than perceiving what subtends an Angle of about a Minute, or something less. But when an Eye is armed with a Telescope, it may discern an Angle less than a Second. The Telescope that magnifies distinctly the Appearance of a Body, magnifies also distinctly the Appearance of Extension, Space, and Motion through this Space; so if the Minute-Hand of a Watch, which can but just be perceived to move, be looked upon with a Magnifying-Glass, we shall see it give a considerable Leap at every Stroak of the Balance. And thus likewise the slow diurnal Motion of the Sun or Stars, which is hardly perceivable by the bare Eye … is most easily perceived through an ordinary Telescope of 18 inches long: Insomuch that we may determine to the greatest Niceity and Exactness, when a Star passes just over the cross-Hairs, even to the single Beat of a Second-Pendulum. And let an Object in the Heavens rise never so little … and the Eye, by means of the Eye-Glass, perceives this Motion, be it never so small, when an Eye is armed with a Telescope.”

“The next topic is the micrometer, beginning with a historical perspective (p. 246). The first publication to deal with the micrometer was a ‘rough Draught’ of 12 March, 1667, by Monsieur Petit, Surveyor of the Fortifications in France, as noted in Journal des Sçavans, 16 May, 1667. Auzout published in the 28 June, 1667 Journal des Sçavans his measurements of the diameters of planets, crediting the invention to Picard. However, William Gascoigne was the true inventor of the micrometer. The micrometer as an instrument is discussed, with its capabilities, calibration, and use. Molyneux concludes his chapter by describing a glass reticle, to be used instead of cross hairs: ‘I have often used a curious piece of clear, thin, flat Glass, whereon there are drawn two very fine cross-Lines by the curious Point of a Diamond, smaller than the most fine Wyre or Hair; not easily disturbed by a sleight Touch … nor alterable by Heat and Cold’ (p. 250).

“Chapter 6 concerns the history of Optick-Glasses. Optical glasses were not known to the ancients, despite some credulous reports. Roger Bacon in the 13th century probably knew how to combine lenses to make a telescope. On p. 262, part of a section on planets, is another of those immortal phrases that make this early literature so rewarding: “intelligent beings … perhaps are the Inhabitants of these distant Worlds, and of those again infinitely extended beyond these … But in this stupendous Enquiry I stop, as not being able to reach it with the longest Telescope.”

“Molyneux concludes his discussion on telescopes with ‘two remaining uses of the telescope’. First is a note about a modified telescope used to view nearby objects, such as miniature paintings, which is useful to discover ‘the least errors’ … The second ‘remaining use’ was to measure the distance of an object from one station, then thought to be impossible. Molyneux proposes using a needle’s point mounted on a slide and placed at the focus of the objective. Noting the placement when focused at infinity, one focuses on the object in question and measures how far the needle point needs to be moved to be placed back again at the focal point. By moving the eye side to side in front of the eyepiece, the needle will be seen to move against the background of the object, until the needle is at the focal point, when it will not move. One then estimates the distance to the object by noting the change in focus from infinity.

“Chapter 7 is entitled ‘An Optick Problem of Double Vision.’ It includes a careful description of physiological diplopia. Molyneux suggested that ‘we see with both Eyes at once’ (pp. 293-4), and he recognized the importance of binocular vision when he said ‘that which is commonly known and practiced in all Tennis-Courts, that the best Player in the World Hoodwinking one Eye shall be beaten by the greatest Bungler that ever handled a racket; unless he be used to the Trick, and then by Custom he gets an Habit of using one Eye only’ (p. 294)” (Goss).

The work concludes with the Appendix which gives Halley’s now familiar formulas which lie at the heart of geometrical optics: if u and v denote the distance of an object and its image from a lens of focal length f,

1/u + 1/v = 1/f ;

moreover, if the lens consists of two spherical surfaces of radii r and R, and if the glass has refractive index n,

1/f = (n – 1)(1/r – 1/R).

These formulas had been derived by Huygens in 1653 but not published. Molyneux included them in the Appendix, in geometrical form, and Halley published them in algebraic form the next year (1693) in the Philosophical Transactions. Molyneux described Halley’s contributions as follows (p. 295): “Whilst this Book was in the Press my Affairs were such, that I could not attend the Perusal and Correction thereof, but therein have made us of my Friend Mr. E. Halley, who was willing to do me that Service: He, after the first Part hereof was finished, sent me a proposition of his own, which I took to be of that Consequence to Dioptricks, that I importuned him to permit it to be subjoined by way of Appendix to my Treatise”.

Dioptrica was reviewed positively by both Huygens and Leibniz. “In a letter to Bodenhausen of July 22, 1693, Leibniz praised the work Dioptrica Nova published in 1692 by William Molyneux … In Dioptrica Nova … the author had presented parts of Leibniz’s article ‘Unicum opticae catoptricae et dioptricae principium’ (Acta Eruditorum, 1682) in an English translation and had given Leibniz priority for the formulation of Fermat’s principle … in his 1682 article, Leibniz had suggested that light follows the path of least resistance as against Fermat’s principle of least time. Leibniz’s interpretation was also that preferred by William Molyneux in his Dioptrica Nova. Molyneux’s treatise likewise contributed to Huygens’ resumption of his work on dioptrics in the spring of 1692. The latter undertook a detailed examination and critique later published with the title ‘Ex Dioptrica nova Guilielmi Molyneux. Edita 1692’. While Huygens expressed approval of the work in general, Leibniz, for his part, was flattered by Molyneux’s use of his 1682 article and, in in his correspondence and writings, he referred to Dioptrica Nova as an excellent work on a number of occasions” (https://oharas.com/_b_rill/Ohara-brill-chap3.pdf).

“In 1708, the collected correspondence of John Locke was published, and since Molyneux was prominent in this book, renewed attention to him resulted in the reprinting of Dioptrica in 1709, with a new title page, but designated the second edition” (Abrahams).

Wing M-2405; ESTC R3440. Abrahams, ‘When an Eye is armed with a Telescope: The Dioptrics of William and Samuel Molyneux,’ Analytica Chimica Acta 33 (2007), pp. 229-46. Albury, ‘Halley and the Traité de la Lumière of Huygens: new light on Halley’s relationship with Newton,’ Isis 62 (1971), pp. 445-468. Goss, ‘William Molyneux and the optometry content of his 1692 book Dioptrica Nova,’ Hindsight: Journal of Optometry History 39 (2008), pp. 67-71.

4to, pp. [xvi], 301, [2], with 43 folding plates, complete with the initial imprimatur leaf and final advertisement leaf for optical instruments by John Yarwell of London (browning and spotting, heavier on the first and last few leaves, and the last two plates). Contemporary calf, decorated in blind with corner fleurons and red lettering-piece on spine (joints cracked but firm, spine worn with loss at edges and ends, corners worn). A good, genuine copy, unrestored in its first binding.

Item #5246

Price: $15,000.00

See all items by