About the Work
This book is a treatise on the system of the world, presented as a comprehensive scientific work. The text is a later edition of a work originally composed in the late seventeenth century, with the author’s own advertisements dated 1704 and 1717, indicating the material was written over a period beginning in 1675. The edition described is printed from a third edition, corrected by the author’s hand, with citations added from his earlier lectures on optics read at Cambridge in 1669-1671. The work is structured as a formal scientific treatise, divided into books and parts, containing propositions, theorems, problems, experiments, observations, and queries. It is written in the style of a mathematical and experimental philosophy, with the author declaring his design to propose and prove properties of light by reason and experiments, not hypotheses. The book includes numerous figures, tables of measurements, and detailed descriptions of experimental apparatus and procedures. The author also includes an account of his earlier invention of a reflecting telescope and his methods for polishing metals and glasses for optical instruments. The work concludes with a series of queries that extend beyond optics into questions of natural philosophy, including the nature of gravity, the existence of a vacuum, and the attributes of a first cause.
Context
The work emerges from a period of intense scientific inquiry in the late seventeenth and early eighteenth centuries. The author, Isaac Newton, was a central figure in the scientific revolution, and this text reflects his engagement with the Royal Society, to which part of the discourse was communicated in 1675. The author delayed printing the work to avoid disputes, but published due to the importunity of friends. The text engages with the work of other natural philosophers, including Grimaldo, whose supposition of ray dilatation is refuted, and Des-Cartes, whose explanation of the rainbow is cited and built upon. The author also references the work of Antonius de Dominis on the rainbow, Hugenius on halos and the parhelia, Roemer on the finite speed of light, and Mr. Halley’s observations on the color of seawater at depth. The author also mentions his communication of a method for squaring curvilinear figures to Mr. Leibnitz in 1679, which was later published by Dr. Wallis. The work is set against a background of debate about the nature of light, with the author arguing against the hypothesis that light is mere pressure or motion propagated through a uniform aether. The author also cites the experiments of Mr. Boyle with the air-pump and the observations of ancient Greek and Phoenician philosophers who posited a vacuum and atoms. The context is one of establishing a new science of optics and natural philosophy based on experiment and mathematics, while also engaging with theological questions about the nature of God as a first cause.
Structure of the Book
The book is organized into three main books, each divided into parts. The First Book, Part I, begins with definitions of key terms such as Rays of Light, Refrangibility, Reflexibility, and Homogeneal and Compound Light and Colours, followed by axioms covering the laws of reflection and refraction, including the constant sine ratio for different media. It then presents propositions and theorems, supported by experiments, proving that lights differing in colour differ in refrangibility and that the Sun’s light consists of rays differently refrangible. This part includes detailed experimental procedures, such as using a prism to project a spectrum and measuring the angles of refraction. It also contains a mathematical demonstration that the sine of incidence is in a given ratio to the sine of refraction, assuming the refracting body acts perpendicularly to its surface. The First Book, Part II, addresses the composition of white light and the nature of colour, with propositions proving that colours are not caused by new modifications of light by shadows, that homogeneal light has a proper colour that cannot be changed, and that whiteness is compounded of all primary colours. This section includes experiments with a comb-like instrument to intercept parts of the spectrum, the mixing of painters’ powders, and a rule for finding the colour of a compound using a circle divided into seven parts proportional to musical tones. It also explains prismatic colours, the rainbow, and the permanent colours of natural bodies, with a proposition on compounding a white beam from coloured lights.
The Second Book addresses the colours produced by thin and thick transparent plates. Part I contains observations on the coloured rings produced between two object-glasses, with experiments using prismatic light to show that rings made by red light are bigger than those by blue or violet. The observations detail the order of colours, the arithmetical progression of the squares of the diameters of the rings, and the relationship between the thickness of the air between the glasses and the colours produced. Part II discusses the permanent colours of natural bodies and their analogy to thin transparent plates, with propositions on the reflection of light by surfaces of different refracting power, the transparency of the least parts of natural bodies, and the spaces between the parts of opake and coloured bodies. This part includes a table of refracting bodies with their refractive powers and densities. Part III introduces the concept of Fits of easy Reflexion and easy Transmission, with propositions on the propagation of light in time, the transient constitution of rays, and the intervals of these fits. Part IV contains observations on the reflections and colours of thick transparent polished plates, including experiments with a concavo-convex glass speculum that produced concentric rings of colours.
The Third Book, Part I, addresses the inflections of light, with observations on the shadows cast by hairs and knife edges, which show fringes of colours and demonstrate that light bends as it passes near edges. The book concludes with a series of Queries, numbered 28 through 31, which explore broader questions of natural philosophy. These queries discuss the unusual refraction of Island Crystal, argue against the existence of dense fluid mediums filling the heavens, ask whether rays of light are small bodies emitted from shining substances, ask whether bodies and light are convertible, and ask whether particles have powers acting at a distance. The final query argues from phenomena to a first cause, an incorporeal, living, intelligent, omnipresent Being. The book ends with this theological argument, concluding that God perceives all things immediately, as we perceive images in our sensoriums.
Detailed Section-by-Section Summary
Opening Advertisements and Definitions
The 1730 fourth edition of Newton’s Opticks opens with the title page and the author’s own preliminary remarks. In the first advertisement, dated April 1, 1704, Newton explains that part of the discourse was written in 1675 for the Royal Society, with the remainder added about twelve years later, except for the third book and the last proposition of the second, which were compiled from scattered papers. He delayed printing to avoid disputes but published due to the importunity of friends. He also mentions a method for squaring curvilinear figures, communicated to Mr. Leibnitz in 1679 and published by Dr. Wallis, now made public with an introduction and scholium. A second advertisement, dated July 16, 1717, notes the omission of mathematical tracts and the addition of Questions, including one on gravity’s cause, proposed as a question due to a lack of experiments. The advertisement to this fourth edition states it is printed from the third edition, corrected by the author’s hand, with citations added from his Lectiones Opticae, read at Cambridge from 1669 to 1671.
The main text begins with Book One, Part I. Newton declares his design is to propose and prove the properties of light by reason and experiments, not hypotheses. Definitions I through VIII define rays of light, refrangibility, reflexibility, angles of incidence, reflexion, and refraction, sines, and homogeneal and compound light and colours. Axioms I through VII cover the plane of reflection and refraction, the equality of angles, reversibility, refraction towards the perpendicular in denser media, the constant sine ratio (such as 4 to 3 for air to water and 17 to 11 for air to glass), and the formation of foci and pictures. Axiom VII explains vision, the camera obscura, the eye’s anatomy, and the causes of long and short sight. Axiom VIII explains the apparent location of objects seen by reflection or refraction. Proposition I, Theorem I, proves by Experiments 1 and 2 that lights differing in colour differ in refrangibility. Proposition II, Theorem II, through Experiments 3, 4, and 5, proves that the Sun’s light consists of rays differently refrangible, refuting Grimaldo’s supposition of ray dilatation.
Refining the Experiments and Proving Regular Refraction
Newton continues his optical experiments, describing how a triangular hole may replace the parallelogram hole, with its base about a tenth of an inch and its height an inch or more. With the prism’s axis parallel to the triangle’s perpendicular, the image is formed of equicrural triangles lying in a series between parallel lines. These triangles intermingle at their bases but not at their vertices, so light is compounded near the brighter side but uncompounded near the darker side, with composition proportional to distance from the darker side. For such experiments, the chamber must be very dark to prevent foreign light from mixing with the spectrum, especially near the fainter side. The lens must be optically good, and the prism should have a large angle of 65 or 70 degrees, be well-wrought glass free from bubbles and veins, with truly plane sides and elaborate polish, not the usual putty polish that leaves wave-like risings. Prism and lens edges must be covered with black paper, and all useless sunlight must be intercepted. Newton sometimes used prismatic vessels of broken looking-glass filled with rain water, sometimes impregnated with Saccharum Saturni to increase refraction.
Proposition V, Theorem IV states that homogeneal light is refracted regularly without dilatation, and that confused vision through refracting bodies arises from the different refrangibility of rays. In Experiment 12, a round hole is made in black paper, and homogeneal spectrum light passed through it, refracted by a prism behind, falls on white paper two or three feet away—the spectrum is perfectly circular, not oblong. In Experiment 13, a paper circle in homogeneal light viewed through a prism appears circular, while the same circle in the Sun’s heterogeneal white light appears very oblong. In Experiment 14, flies and small print viewed through a prism in homogeneal light appear distinct, but in heterogeneal light they appear confused and unreadable. In all three experiments, the colour of homogeneal light is never changed by refraction.
The Constant Ratio of Sines and the Limits of Telescopes
Proposition VI, Theorem V states that the sine of incidence of every ray apart is to its sine of refraction in a given ratio. Rays most refracted at equal incidences in the first refraction are also most refracted in following refractions, as shown by Experiments 5 through 9. In Experiment 15, the Sun shining through a hole produces a round white image and an oblong coloured image from a first prism, and images from a second cross prism of increasing angles. All spectrums converge nearly to the round image, and the axes of the spectrums pass through its middle. With equal refractions, the axis of the third image also passes through the round image; with lesser second refraction, the axes cut the produced axis of the first image at points beyond it. The proportions of the lines give tangents of refractions, and deriving sines, they come out equal. Newton then gives a mathematical demonstration: if bodies refract light by acting perpendicularly to surfaces, the perpendicular velocity at emergence equals the square root of the sum of squares of the incident perpendicular velocity and the velocity if incidence were infinitely little. Using the sines of incidence and refraction, he derives that the sine of incidence is to the sine of refraction as a given ratio. This demonstration is general, assuming only that the refracting body acts perpendicularly to its surface.
Proposition VII, Theorem VI states that the perfection of telescopes is impeded by different refrangibility. The imperfection is vulgarly attributed to spherical figures, and mathematicians proposed conical sections. Newton determines measures: in Experiment 3, the prism’s refracting angle was 62-1/2 degrees; half is 31 degrees 15 minutes, the angle of incidence at emergence, with a sine of 5188 (radius 10000). The emergent rays contained with incident an angle of 44 degrees 40 minutes; half added to incidence gives a refraction angle of 53 degrees 35 minutes, with a sine of 8047, giving a proportion in round numbers of 20 to 31. A second prism of clear white glass with an angle of 63-1/2 degrees gave an emergent angle of 45 degrees 50 minutes, with sines 5262 and 8157, a proportion also of 20 to 31. From the image length of 9-3/4 or 10 inches, subducting the breadth of 2-1/8 inches, the remainder 7-3/4 inches would be the length if the Sun were a point, subtending 2 degrees 0 minutes 7 seconds at 18-1/2 feet. Half this angle is between the emergent most and least refrangible and mean rays, and a quarter of it is the angle if coincident within the glass. Adding and subducting this from 53 degrees 35 minutes gives the refractions of the most and least refrangible rays: 54 degrees 5 minutes 2 seconds and 53 degrees 4 minutes 58 seconds, with sines 8099 and 7995, and a common incidence sine of 5188, giving in least round numbers 78 and 77 to 50. Subducting 50 from 77 and 78 gives remainders 27 and 28, showing the small difference in refrangibility.
The Reflecting Telescope and Its Construction
Newton describes his earlier invention of a reflecting telescope, using a concave metal instead of an object-glass. The metal’s sphere was about 25 English inches in diameter, making the instrument about six and a quarter inches long. The eye-glass was plano-convex, magnifying between 30 and 40 times, measured at about 35 times. The aperture was limited by an opake circle placed between the eyeglass and the eye, which stopped erroneous light. He could read at a greater distance with his instrument than with a four-foot perspective with a concave eye-glass, though objects appeared darker. He made two such instruments about 16 years ago, and an artist in London failed to imitate them. He details his polishing method using two round copper plates, pitch, and fine putty, grinding the object-metal to avoid bending. He proposes using a glass ground concave on the foreside and convex on the backside, quick-silver’d over, to avoid tarnishing. A trial with a four-foot telescope magnifying about 150 times failed due to inequalities in the glass, as errors of reflected rays are about six times greater than refracted ones.
In Proposition VIII, he describes shortening telescopes with a glass speculum and a prism, placed so rays reflect to a common focus. A six-foot instrument would bear an aperture of six inches and magnify between two and three hundred times. The object will be inverted but can be erected with spherically convex prism sides. He notes the air is in perpetual tremor, causing stars to twinkle, but large apertures prevent this. The only remedy is a serene air on high mountains.
The Nature of Colours and the Composition of White Light
The text shifts to the First Book of Opticks, Part II. Proposition I states that colours are not caused by new modifications of light by shadows, demonstrated by Experiments 1 through 4, including using a prism and holes and the colours of bubbles. Proposition II states that homogeneal light has a proper colour that cannot be changed by reflections or refractions, proven by Experiments 5 and 6. A definition explains that rays are not coloured but have a power to stir up sensations. Proposition III defines refrangibility, with Experiment 7 mapping colours to a musical chord and giving sine ratios from 50 to 77 and 78. Experiment 8 establishes two theorems on refraction. Proposition IV states that compounded colours may resemble homogeneal ones but are not immutable. Proposition V proves that whiteness is compounded of all primary colours, using Experiments 9 and 10 with a lens and focus.
An instrument shaped like a comb with sixteen teeth, each about 1.5 inches broad with intervals about 2 inches wide, is interposed near a lens to intercept parts of the coloured spectrum projected onto paper. When the comb is moved slowly, the paper shows a perpetual succession of colours—red, yellow, green, blue, purple. When moved quickly, the individual colours are no longer distinguishable, and a uniform white arises from their confusion. The text asserts no part of this white light is really white; each part retains its proper colour until it strikes the Sensorium. If impressions follow slowly, distinct sensations occur; if quickly, they are confounded in the Sensorium, producing a mixed sensation of whiteness. The analogy of a burning coal moved in a circle appearing as fire is given, as the impression remains until the coal returns.
The passage then describes using two prisms instead of a lens to make diverging rays converge and mix into white light. Experiment 11 involves viewing the coloured image through a prism; at a certain distance, the spectrum becomes perfectly round and white when rays from different parts converge and mingle at one point in the eye. Experiment 12 uses a comb with equal teeth and intervals; when the paper is moved about a foot away, the ranges of colours dilute each other to become white. Intercepting one range causes the others to expand into its place, and restoring it restores whiteness. Inclining the paper reflects more of certain rays, changing white to blue or violet or yellow or red, proving rays retain their colourific qualities. Experiment 13 compounds whiteness using two or three prisms, detailing the geometric conditions for uniform mixing of all ray sorts. Experiment 14 shows soapy water froth appears white when viewed from afar. Experiment 15 mixes painters’ powders; coloured powders suppress much light, yielding only grey or dun colours, not perfect white. A mixture of Orpiment, Purple, Bise, and Viride AEris rubbed on a floor appeared intensely white in sunlight, surpassing white paper, as confirmed by a visiting friend. The passage concludes the Sun’s whiteness is compounded of all colours.
Rules for Compound Colours and the Rainbow
Proposition VI presents a rule for finding the colour of a compound from given quantities of primary colours, using a circle divided into seven parts proportional to musical tones, with centres of gravity determining the resulting colour and its intensity. Proposition VII states all colours in the universe are either homogeneal or compounded according to this rule, summarizing prior proofs about the immutability of colours and their mixture in the Sensorium. Proposition VIII explains prismatic colours by the different refrangibility of rays, detailing the expected colour sequence. Experiment 16 describes a blue bow seen by reflecting cloud light through a prism, explained by the limits of total reflection for different ray types. Proposition IX explains the rainbow, citing Antonius de Dominis and Des-Cartes, and computes the angles—42 degrees 2 minutes and 40 degrees 17 minutes for one reflexion, and 50 degrees 57 minutes and 54 degrees 7 minutes for two—at which different rays emerge most copiously, producing the two bows’ colour orders.
The Rainbow’s Geometry and the Colors of Natural Bodies
The analysis of the rainbow’s geometry reveals a precise structure. Two bows are formed: an interior, stronger one by a single reflection within the raindrops, and an exterior, fainter one by two reflections, as light weakens with each reflection. Their colors lie in a contrary order, with the red of both bows bordering the space between them. The interior bow measures 1°45′ across, the exterior 3°10′, and the distance between them is 8°15′. The greatest semi-diameter of the innermost bow is 42°2′, while the least of the outermost is 50°57′. These figures assume the Sun is a point; the Sun’s breadth increases the bow widths and decreases their distance by half a degree. The author measured the interior iris at about 42°, with its red-yellow-green breadth at 63–64 minutes, blue about 40 minutes, and a total breadth of about 2¼ degrees. This is confirmed by the experiment of Antonius de Dominis and Des-Cartes, where a water-filled glass globe viewed at angles of 42 or 50 degrees shows red, then yellow, green, and blue as the angle decreases, and at about 50° red appears on the Sun-side, followed by other colors as the angle increases. The author disputes a claim about prism-refracted candlelight, attributing the phenomenon to faintness; he observed the spectator always sees the color falling on the eye, with red appearing first as the prism moves.
The Permanent Colors of Natural Bodies
Proposition X, Problem V explains the permanent colors of natural bodies: they reflect some rays more copiously than others. Minium appears red because it reflects the least refrangible rays, and violets appear violet because they reflect the most refrangible. In homogeneal lights, every body looks most splendid in its own color—Cinnaber in red, Indigo in violet-blue. Homogeneal light cannot be changed by reflection, so the reflection of own-color rays is the only reason for these appearances. Transparently colored liquors vary with thickness: a red liquor in a conical glass looks pale yellow when thin, then orange, then red, and finally deep red, as it stops violet and indigo most easily, blue less, green still less, and red most difficultly. Mr. Halley, diving deep in a diving vessel, saw his hand red from direct sunlight through water and the water below green from reflected light, showing seawater reflects violet and blue most easily and lets red pass to depths. Gold leaf is yellow by reflected light and greenish-blue by transmitted light, while massy gold is yellow in all positions. Some liquors, such as Tincture of Lignum Nephriticum, and some glasses transmit one light and reflect another.
Compounding a White Beam from Colored Lights
Proposition XI, Problem VI describes compounding a white beam from colored lights. A prism refracts sunlight through a lens, painting colors—violet, blue, green, yellow, red—which converge at a point and compound white. A second prism at that point refracts the white upward, making a parallel beam perfectly white like sunlight. Stopping any color at the lens makes the corresponding color vanish at the paper, showing colors arise from the separation or mixture of rays with original color-making qualities, not from new modifications. Testing natural bodies in this beam, Cinnaber appears red as in daylight; intercepting green and blue makes the red fuller, while intercepting red makes it yellow or green. Gold appears yellow; intercepting the yellow-making rays makes it white like silver. An infusion of Lignum Nephriticum looks blue by reflection and red by transmission; intercepting the blue removes the reflected color.
Observations on the Colored Rings with Prismatic Light
Observations 13–24 continue experiments on the colored rings produced between two object-glasses, now using prismatic light. With an assistant rotating a prism so each color fell successively on the rings, Newton found rings made by red light were manifestly bigger than those by blue or violet. The interval of the glasses at any ring for utmost red versus utmost violet was greater than 3 to 2, less than 13 to 8, and by most observations as 14 to 9. This proportion held nearly the same at all obliquities, unless two prisms replaced the object-glasses; then at a great obliquity the violet rings became bigger than the red, because the prism’s refraction made the most refrangible rays fall more obliquely on the air-plate. Turning the prism uniformly, the contraction and dilatation of each ring was swiftest in red and slowest in violet. The whole contraction of a ring’s diameter by all degrees of red versus all degrees of violet was about 4 to 3 or 5 to 4. When light was the middle color between yellow and green, the ring’s diameter was nearly an arithmetical mean between the greatest diameter (utmost red) and least (utmost violet). He collected that the thicknesses of air where the ring is made by the limits of the five principal colors are nearly as the sixth lengths of a chord sounding notes in a sixth major, but it agrees better to say the thicknesses for the seven colors are as the cube roots of the squares of the eight lengths of a chord sounding an eighth. These rings were not variously colored but appeared all over of the single prismatic color illuminating them. Light falling on the dark spaces between colored rings was transmitted through the glasses without color variation, painting on white paper behind rings of the same color and bigness as their immediate spaces. The squares of the diameters of rings made by any prismatic color were in arithmetical progression.
Observations on Soap Bubbles and Thin Plates
The preceding observations used a rarer thin medium terminated by a denser one; the following concern a denser medium thinned within a rarer, such as plates of Muscovy Glass, bubbles of water, and other thin substances terminated on all sides with air. If a bubble is blown with water made tenacious by dissolving soap, it commonly appears tinged with many colors. To defend bubbles from external air agitation, Newton covered each blown bubble with a clear glass; then colors emerged in regular order like concentric rings encompassing the top. As the bubble grew thinner by water subsiding, the rings dilated slowly, overspread the whole bubble, descended to the bottom, and vanished successively. After all colors emerged at the top, a small round black spot grew in the center, dilating sometimes to more than ½ or ¾ inch before the bubble broke. He could see images of a candle or the sun faintly reflected from the great black spot and from the smaller dark spots within it. Because bubble colors were more extended and lively than those of air thinned between glasses, Newton describes their order as observed by reflection of white skies: red, blue; red, blue; red, blue; red, green; red, yellow, green, blue, purple; red, yellow, green, blue, violet; red, yellow, white, blue, black. The first three successions of red and blue were very dilute and dirty, the first red seeming almost white. The fourth red was dilute but less so; after it followed little or no yellow, but a copious green. The fifth red at first inclined much to purple, then became brighter but not very pure; it was succeeded by a very bright intense yellow, little in quantity, soon changing to green.
The Cause of Colors in Thin Plates and the Nature of Light
The phenomena in small fragments of thin glass plates, when lying flat and turned while viewed through a prism, exhibit waves of various colors. The reason is that such surfaces are uneven, with cavities and swellings that vary plate thickness, producing waves at several sides of cavities. These phenomena depend on properties of light previously delivered. By the 24th Observation, rays of several colors have several degrees of refrangibility, so those of each order intermixed with others are separated by refraction and become visible as arcs. If rays were all alike refrangible, whiteness could not be transposed into black and white arcs. Unequal refractions of difform rays do not proceed from contingent irregularities, for such would make rings indistinct. Therefore every ray has a proper, constant, connate degree of refrangibility; several rays have several degrees. The same holds for reflexibility—dispositions to be reflected at greater or lesser thicknesses—also connate and immutable. Whiteness is a dissimilar mixture of all colors; light is a mixture of rays endued with all colors. Though only eight or nine rings appear in Observations 4 and 18, there are really far more, which interfere and mingle, diluting one another into uniform whiteness. By the 24th Observation, there is constant relation between colors and refrangibility: most refrangible rays are violet, least refrangible red, intermediates proportionally intermediate. Thus colorific dispositions are connate and immutable; all color productions derive not from physical change in light by refraction or reflection, but from various mixtures or separations of rays by their different refrangibility or reflexibility. The science of colors becomes truly mathematical, so far as colors depend on light’s nature, not imagination or eye pressure.
The Second Book, Part III: On the Permanent Colors of Natural Bodies
Proposition I states that surfaces of transparent bodies reflect the greatest quantity of light which have the greatest refracting power, interceding mediums differing most in refractive densities; in confines of equally refracting mediums there is no reflection. The analogy appears because when light passes obliquely out of one medium into another refracting from the perpendicular, the greater the difference of refractive density, the less obliquity of incidence causes total reflection. As the sines measure refraction, so is the sine of incidence at total reflection to the radius. Thus in passing out of Water into Air, total reflection begins at about 48 degrees 35 minutes; out of Glass into Air, at 40 degrees 10 minutes; out of Crystal or more strongly refracting mediums into Air, still less obliquity. Surfaces which refract most reflect all incident light soonest. The truth appears by observing that in surfaces interceding two transparent mediums, reflection is stronger or weaker as the surface has greater or less refracting power. In the confine of Air and Sal-gem it’s stronger than Air and Water, stronger in Air and common Glass or Crystal, stronger in Air and Diamond. If immersed in Water, reflection becomes much weaker; still weaker in strongly refracting liquors. If Water be distinguished into two parts by an imaginary surface, reflection in their confine is none. In Water and Ice it’s very little; Water and Oil something greater; Water and Sal-gem still greater; Water and Glass, Crystal, or denser substances still greater, as mediums differ in refracting powers. In two Glasses of equal density there is no sensible reflection, as shown in the first Observation. Uniform pellucid mediums have no sensible reflection but in external surfaces adjacent to mediums of different density, because all contiguous parts have one degree of density.
Proposition II states that the least parts of almost all natural bodies are in some measure transparent; opacity arises from multitude of reflections in internal parts. This has been observed by others and may be tried by applying any substance to a hole through which light is imitted into a dark room; however opake in open air, it appears transparent if sufficiently thin. White metalline bodies are excepted, which by excessive density reflect almost all light on their first surface, unless reduced into very small particles by solution in Menstruums, then they become transparent.
Proposition III states that between parts of opake and coloured bodies are many spaces, either empty or replenished with mediums of other densities: Water between tinging Corpuscles of liquors, Air between aqueous Globules constituting Clouds or Mists, and for the most part spaces void of both Air and Water, but perhaps not wholly void of all substance, between parts of hard bodies. This is evinced by the two precedent propositions: by the second there are many reflections by internal parts, which by the first would not happen if parts were continued without interstices, since reflections are caused only in surfaces.
A Table of Refractive Powers and the Fits of easy Reflexion and Transmission
A table lists various refracting bodies, giving for each the proportion of the sines of incidence and refraction of yellow light, the square of BR (to which the refracting force is proportionate), the density and specifick gravity, and the refractive power of the body in respect of its density. The text explains that the refraction of Air is determined by that of the Atmosphere observed by Astronomers, arguing that the sum of refractions through many parallel-surfaced mediums equals a single refraction from the first into the last medium, even if the number of mediums is infinite. It notes that terrestrial stony alcalizate concretes and Air have refractive powers almost proportional to their densities, though Island Crystal’s refraction is a little bigger. Fat sulphureous unctuous Bodies and a Diamond have refractive powers proportional to their densities, but two or three times greater in respect of their densities than the former substances. Water has a refractive power in a middle degree, as do Salts and Vitriols, and Spirit of Wine is in a middle degree between water and oily substances. The text concludes that all bodies seem to have refractive powers proportional to their densities, excepting so far as they partake of sulphureous oily Particles, and it seems rational to attribute the refractive power chiefly to sulphureous parts.
Prop. XI states that Light is propagated from luminous Bodies in time, spending about seven or eight Minutes passing from the Sun to the Earth, observed first by Roemer via the Eclipses of the Satellites of Jupiter. Prop. XII states that every Ray of Light in passing through any refracting Surface is put into a transient Constitution or State, returning at equal Intervals, disposing the Ray to be easily transmitted or reflected. The returns of the disposition to be reflected are called Fits of easy Reflexion, and those to be transmitted Fits of easy Transmission, with the space between returns being the Interval of its Fits. Prop. XIII states that thick transparent Bodies reflect part of the Light and refract the rest because some Rays are in Fits of easy Reflexion and others in Fits of easy Transmission. Prop. XIV states that surfaces which refract most strongly also reflect most easily. Prop. XV gives a formula for the Interval of Fits involving secants. Prop. XVI relates the Intervals to the Cube-Roots of the Squares of the lengths of a Chord sounding the Notes in an Eight. Prop. XVII states that Intervals in different mediums are as the Sine of Incidence to the Sine of Refraction. Prop. XVIII states that for rays in the confine of yellow and orange passing into Air, the Intervals are the 1/89000th part of an Inch. Prop. XIX states that for reflected Rays, the Fits of easy Reflexion continue to return at distances in the arithmetical progression 2, 4, 6, 8, etc. Prop. XX states that the Intervals of Fits propagated from points of Reflexion are equal to those the same Rays would have if refracted into the same Medium in Angles of Refraction equal to their Angles of Reflexion.
The Second Book, Part IV: Observations on the Reflexions and Colours of thick transparent polish’d Plates
Obs. 1 describes an experiment with a Glass Speculum ground concave on one side and convex on the other, quick-silver’d on the convex side, where concentric Irises or Rings of Colours were observed on a Chart. Obs. 2 describes the colours of these Rain-bows succeeding one another from the center outwards. Obs. 3 gives measurements of the Diameters of these Rings, finding their Squares in arithmetical progression. Obs. 4 describes viewing the Rings through a Prism to see them more distinctly. Obs. 5 describes illuminating the Speculum with a single Colour from a Prism, finding the Rings of that Colour only, with their sizes varying with the colour. Obs. 6 describes seeing the Speculum tinged with Waves of Colours, whose appearance depended on the position of the Eye. Obs. 7 explains that these Colours are produced by the thick Plate of Glass, depending on its two surfaces and thickness, and gives the reasons for the Rings, relating them to the Fits of easy Reflexion and Transmission.
Observation 8: The Concavo-Convex Glass Plate
Newton details precise measurements of a concavo-convex glass plate, a quarter-inch thick, correlating its thickness with the transmission of bright yellow light from the first ring. He establishes that the required thickness for transmitting successive rings is a simple multiple of the first, and that for oblique rays, the thickness relates to the secant of a specific angle derived from the sines of incidence and refraction. The computed ring diameters, derived from these increasing thicknesses, match his measured values at a distance of six feet, and he extends the calculation to other colours using a subduplicate proportion of fits, which he links to the cube-roots of numbers corresponding to monochord lengths.
Observation 9: A Thinner Plate
Testing a thinner plate, Newton finds that the ring diameters are reciprocally in a subduplicate proportion to the plate’s thickness. This confirms that the phenomena depend on both the reflecting surfaces and the distance between them, solidifying the geometric relationship between thickness and ring size.
Observation 10: Offset Reflected Beam
When the reflected beam is offset, Newton observes that the center of the rings falls midway between the incident and reflected beams. The rings enlarge, new rings emerge from the center, and the central white spot transforms into a white ring. He notes that while the angles of reflection equal the angles of incidence, they do not lie in the same plane.
Observation 11: Contrary Order of Colours
As the distance between the incident and reflected beams increases, Newton records the appearance of new rings with a contrary order of colours. He provides specific diameters and colour sequences—violet, indigo, blue, green, yellow, red—that invert as the rings expand, demonstrating the systematic progression of the fits of easy transmission and reflection.
Observation 12: Prismatic Colours and Ring Sizes
Using prismatic colours, Newton finds that the central white ring is the same size in all colours, but the exterior rings are largest in red and the interior rings are smallest in red. This is due to the fits of the least refrangible rays, which have longer intervals and thus produce larger rings at greater obliquities.
Observation 13: Halos in Water Globules
Newton extends his theory to water globules, predicting the formation of concentric rings. He reports having seen three halos about the Sun in June 1692 and two about the Moon in February 1664, including a notable elliptical halo with a diameter of 22°35′, providing observational confirmation of his theoretical predictions.
The Third Book, Part I: Observations on Inflection
The Third Book opens with Grimaldo’s report of broad shadows with three parallel fringes. Newton’s first observation uses a hair one-280th of an inch thick, which casts shadows four, ten, and thirty-five times broader at increasing distances, and wetting the glass does not alter this. The second observation details the fringes’ colours—violet, indigo, pale blue, green, yellow, red—and the third provides tabulated measurements. The fourth observation shows that the fringe proportions follow the numbers 1, the square root of one-third, and the square root of one-fifth.
Observations on Knife-Edges
Newton’s fifth observation describes a knife edge producing two comet-like streams of light. The sixth shows that two knives create a central shadow, with light bending more when nearer the edges. The seventh observation reveals that fringes appear and enlarge as the knives approach each other. The eighth, with fixed-angle knives, shows fringes crossing after meeting. The ninth provides tables of knife-edge distances, demonstrating that the fringes depend on the distance of the paper, indicating a varying degree of bending.
Queries 28–31: The Nature of Light and the Universe
Addressing the unusual refraction of Island Crystal, Newton notes that only Huygens attempted an explanation via two vibrating mediums, but Huygens confessed failure after experiments with two successive pieces. Newton argues that if light were mere pressure or motion through a uniform aether, rays could not have different properties on different sides, and Huygens’ suspected modifications cannot account for dispositions present before incidence. He finds this inexplicable under the pressure/motion hypothesis.
He then argues against two aethers causing fits of easy reflection and transmission, calling their interaction inconceivable. He objects to filling the heavens with fluid mediums because planets and comets show no sensible resistance, distinguishing resistance from attrition (proportional to diameter and velocity) from resistance from vis inertiae (proportional to the square of that product), asserting the latter dominates in air, water, and quicksilver. Citing pendulum experiments and Boyle’s air-pump trials where feathers fall as fast as lead in a vacuum, he computes air density decreasing with altitude. Since a dense aether would retard planets, the heavens must be empty except for rare vapours and an exceedingly rare aether, rejecting dense fluid mediums as useless and unauthoritative, and citing ancient Greek and Phoenician philosophers who posited vacuum and atoms.
Query 29 asks whether rays are small bodies emitted from shining substances, arguing they pass in right lines, conserve properties, and act at a distance. Refraction by attraction gives the sine law, and total reflection from glass into vacuum is attributed to the glass’s attractive power, shown by moistening the surface with water or oil. Different ray sizes produce colours, and fits arise from vibrations stirred up by rays. Island-crystal refraction suggests a polar virtue in rays and crystal particles, like magnet poles, though not magnetic.
Query 30 asks whether bodies and light are convertible, citing water turning to fixed earth and various transmutations in nature. Query 31 asks whether particles have powers acting at a distance, citing gravity, magnetism, electricity, and chemical attractions. He infers attraction from cohesion of polished marbles in vacuo, barometer mercury standing high, water rising between glass plates, and oil drops moving between inclined plates. He concludes that particles are hard, and hardness is a universal property of uncompounded matter, rejecting hooked atoms and occult qualities in favour of attraction. Finally, he argues from phenomena to a first cause: an incorporeal, living, intelligent, omnipresent Being who perceives all things immediately, as we perceive images in our sensoriums.
Main Arguments
The central argument of the work is that light is not a simple, uniform substance but a mixture of rays that differ in their refrangibility and reflexibility, and that these differences are the cause of colours. The author proves through a series of experiments that lights differing in colour differ in refrangibility, and that the Sun’s light consists of rays that are differently refrangible. He refutes the supposition that the oblong spectrum is caused by the dilatation of rays, showing instead that it is due to the different degrees of refraction of different rays. A key argument is that homogeneal light is refracted regularly without dilatation, and that confused vision through refracting bodies arises from the different refrangibility of rays. The author demonstrates that the sine of incidence of every ray apart is to its sine of refraction in a given ratio, and that rays most refracted at equal incidences are also most refracted in following refractions. He argues that the perfection of telescopes is impeded by this different refrangibility, not by spherical aberration as vulgarly supposed, and he describes his invention of a reflecting telescope to overcome this problem.
Another major argument is that colours are not created by modifications of light but are original properties of the rays themselves. The author proves that homogeneal light has a proper colour that cannot be changed by reflections or refractions, and that compounded colours may resemble homogeneal ones but are not immutable. He demonstrates that whiteness is compounded of all primary colours, using experiments where the colours of the spectrum are mixed together to produce white light. He also provides a rule for finding the colour of a compound from given quantities of primary colours, using a circle divided into seven parts proportional to musical tones. The author argues that all colours in the universe are either homogeneal or compounded according to this rule. He explains the rainbow by the different refrangibility of rays, computing the angles at which different rays emerge most copiously. He also explains the permanent colours of natural bodies by their reflecting some rays more copiously than others.
The author argues for a particulate theory of light, asking whether rays are not small bodies emitted from shining substances. He supports this by noting that rays pass in right lines, conserve their properties, and act at a distance. He argues that refraction is caused by an attractive force, which gives the sine law, and that total reflection is due to the attractive power of the glass. He also argues that the heavens must be empty of dense fluid mediums, as planets and comets show no sensible resistance, and that a dense aether would retard their motions. He rejects the hypothesis that light is mere pressure or motion propagated through a uniform aether, as it cannot explain the different properties of rays on different sides, as seen in the unusual refraction of Island Crystal. Finally, he argues from the phenomena of nature to a first cause, an incorporeal, living, intelligent, omnipresent Being, who perceives all things immediately.
Key Concepts
The work introduces and develops several specific named concepts. Refrangibility is the property of rays to be refracted, with different rays having different degrees of refrangibility, which is the cause of colours. Reflexibility is the analogous property for reflection. Homogeneal light is light consisting of rays that are all alike in refrangibility and colour, while Compound light is a mixture of different sorts of rays. The author defines Fits of easy Reflexion and Fits of easy Transmission, which are transient states or constitutions that every ray of light is put into when passing through a refracting surface, returning at equal intervals and disposing the ray to be easily reflected or transmitted. The Interval of its Fits is the space between these returns. The author also introduces the concept of the Sensorium, the seat of sensation where impressions of colours are received and confounded. The work also discusses the concept of the vis inertiae, the force of inactivity, which is distinguished from attrition as a source of resistance. The author also refers to the concept of a polar virtue in rays and crystal particles to explain the unusual refraction of Island Crystal, likening it to magnet poles. The concept of attraction is central, including gravity, magnetism, electricity, and chemical attractions, which the author infers from various phenomena such as cohesion, capillary action, and chemical reactions. The author also discusses the concept of a vacuum, arguing for the existence of empty space in the heavens and between the parts of bodies.
Themes
A recurring theme is the establishment of a mathematical and experimental science of nature, in contrast to speculative hypotheses. The author repeatedly emphasizes that his conclusions are drawn from experiments and mathematical demonstrations, not from hypotheses. He states that the science of colours becomes truly mathematical, so far as colours depend on light’s nature. This theme is tied to a critique of hypothetical explanations, such as the supposition of ray dilatation or the existence of dense aethers, which are rejected because they do not account for the phenomena. The theme of order and proportion is also prominent, seen in the relationships between colours and musical tones, the arithmetical progressions of ring diameters, and the constant ratios of sines of incidence and refraction. This suggests a universe governed by regular, discoverable laws. The theme of the inadequacy of the senses and the need for careful experimentation is present, as the author describes the need for dark chambers, well-wrought prisms, and careful measurement to avoid errors. The theme of the unity of natural phenomena is explored through the analogy between the colours of thin plates and the permanent colours of natural bodies, and through the extension of the theory of fits to explain the colours of thick plates and halos. The theme of the limits of human knowledge is also present, as the author proposes questions about the cause of gravity and the nature of the first cause, acknowledging that these are beyond the reach of experiment. The theme of the divine creation is a final, culminating theme, as the author argues from the order and design of the universe to the existence of an incorporeal, living, intelligent, omnipresent Being who perceives all things immediately. This is presented as the ultimate conclusion of the natural philosophy, grounding the mathematical order of the world in a divine intelligence.
The Author’s Conclusions
The author concludes that light is a mixture of rays that differ in their refrangibility and reflexibility, and that these differences are the immutable, connate properties of the rays. He concludes that colours are not produced by modifications of light but are original properties of the rays, and that whiteness is a dissimilar mixture of all colours. He concludes that the science of colours is mathematical, as it depends on the nature of light. He concludes that the perfection of telescopes is impeded by the different refrangibility of rays, and that reflecting telescopes are a remedy. He concludes that the least parts of natural bodies are transparent, and that opacity arises from the multitude of reflections in their internal parts. He concludes that light is propagated in time, spending about seven or eight minutes passing from the Sun to the Earth. He concludes that every ray of light is put into a transient constitution of Fits of easy Reflexion and easy Transmission, and he provides a formula for the intervals of these fits. He concludes that the heavens are empty of dense fluid mediums, as they would retard the motions of planets and comets. He argues that rays of light are small bodies emitted from shining substances, and that refraction and reflection are caused by attractive forces acting at a distance. He concludes that particles of matter are hard, and that hardness is a universal property of uncompounded matter. Finally, he concludes that from the phenomena of nature, one must argue to a first cause, an incorporeal, living, intelligent, omnipresent Being, who perceives all things immediately, as we perceive images in our sensoriums. The book ends with this theological conclusion, asserting that God is the ultimate ground of the order and intelligibility of the natural world.
Significance
The significance of this work lies in its comprehensive and rigorous establishment of the science of optics on a new foundation. It presents a systematic experimental and mathematical investigation of the nature of light and colour, overturning previous assumptions and providing a framework that would dominate the field for centuries. The work’s demonstration that white light is composed of all the colours of the spectrum was a fundamental discovery, and its explanation of the rainbow and the colours of natural bodies showed the power of the new experimental philosophy. The concept of Fits of easy Reflexion and easy Transmission, while later superseded, was an important step in the development of theories of light. The work’s arguments for a particulate theory of light and for the existence of a vacuum engaged with the deepest questions of natural philosophy. The book’s influence extended beyond optics, as its methodology and its conclusions about the nature of matter, force, and the cosmos contributed to the broader scientific revolution. The final queries, which range over gravity, chemistry, and the attributes of God, show the author’s ambition to unify all of natural philosophy under a single set of principles, and they set an agenda for future research. The work is a landmark in the history of science, representing a high point of the mathematical and experimental approach to nature and a profound statement of a mechanistic yet divinely ordered worldview.
