SOURCE: "Newton's Optical Papers," in Newton's Papers & Letters on Natural Philosophy and Related Documents, Second Edition, Harvard University Press, 1978, pp. 3-24, 27-45.

[In the following essay, Kuhn examines Newton's optical experiments and publications, commenting on the significance of his findings as well as the limitations of his experimental procedures and his presentation of results.]

The original publication of the optical papers of Isaac Newton marked the beginning of an era in the development of the physical sciences. These papers, reprinted below, were the first public pronouncements by the man who has been to all subsequent generations the archetype of preeminent scientific creativity, and their appearance in early volumes of the Philosophical Transactions of the Royal Society of London constituted the first major contribution to science made through a technical journal, the medium that rapidly became the standard mode of communication among scientists.

Until the last third of the seventeenth century most original contributions to the sciences appeared in books, usually in large books: Copernicus' De Revolutionibus (1543), Kepler's Astronomia Nova (1609), Galileo's Dialogo (1632), Descartes's Dioptrique (1637), or Boyle's Experiments and Considerations Touching Colours (1664). In such books the author's original contributions were usually lost within a systematic exposition of a larger subject matter, so that constructive interchange of scientific experiment and hypothesis was hampered by premature systematization or, as in the case of Boyle, by the mere bulk of the experimental compilation.' Each scientist tended to erect his own system upon his own experiments; those experiments that could not support an entire system were frequently lost to the embryonic profession.

The first important breaches of this traditional mode of presentation occurred in the decade of 1660. The chartering of the Royal Society in 1662 and of the Académie Royale des Sciences in 1666, the first publication of the Journal des Sc, avans and of the Philosophical Transactions in 1665, gave institutional expression and sanction to the new conception of science as a coöperative enterprise with utilitarian goals. The immediate objective of the individual scientist became the experimental contribution to an ultimate reconstruction of a system of nature rather than the construction of the system itself, and the journal article—an immediate report on technical experimentation or a preliminary interpretation of experiments—began to replace the book as the unit communique of the scientist.

Newton was the first to advance through this new medium an experimentally based proposal for the radical reform of a scientific theory, and his proposal was the first to arouse international discussion and debate within the columns of a scientific journal. Through the discussion, in which all the participants modified their positions, a consensus of scientific opinion was obtained. Within this novel pattern of public announcement, discussion, and ultimate achievement of professional consensus science has advanced ever since.

Newton's optical papers have a further importance to the student of the development of scientific thought. These brief and occasionally hasty communications to the editor of the Philosophical Transactions yield an insight into the personality and mental processes of their author that is obscured by the more usual approach to Newton through his Principia (1687) and Opticks (1704). In these later monumental creations, from which has emerged our picture of Newton the Olympian father of modern science, the creative role of the author is deliberately hidden by the superfluity of documentation and illustration and by the formality and impersonality of the organization.² It is primarily in his early papers, as in his letters, his notes, and his largely unpublished manuscripts, that Newton the creative scientist is to be discovered. And the shock of the discovery may be considerable, for this Newton does not always fit our ideal image.

Newton's first paper, the "New Theory about Light and Colors," is almost autobiographical in its development, and so it facilitates, more than any of Newton's other published scientific works, the search for the sources of the novel optical concepts that he drew from the "celebrated phaenomena of colours."³ The prismatic colors to which Newton referred had been well known for centuries: white objects viewed through a triangular glass prism are seen with rainbow fringes at their edges; a beam of sunlight refracted by a prism produces all the colors of the rainbow at the screen upon which it falls. Seneca recorded the observations, which must be as old as shattered glass; Witelo, in the 13th century, employed a water-filled globe to generate rainbow colors; by the 17th century prisms, because of their striking colors, were an important item in the negotiations of the Jesuits in China.⁴ Before Newton began his experiments at least four natural philosophers, Descartes, Marcus Marci, Boyle, and Grimaldi, had discussed in optical treatises the colored iris produced by a prism, and Hooke had based much of his theory of light upon the colors generated by a single refraction of sunlight at an air-water interface.⁵ The "phaenomena" were indeed "celebrated." Newton, when he repeated them for his own edification, can have had no reason to anticipate a result that he would later describe as "the oddest, if not the most considerable detection, which hath hitherto been made in the operations of nature."⁶

But Newton's version of the experiment differed in an essential respect from that employed by most of his predecessors; furthermore, as we shall see, Newton's optical education and experience were not those of the earlier experimentalists who had employed the prism. Previously, when white light had been passed through a prism, the image of the refracted beam had normally been observed on a screen placed close to the prism.⁷ With such an arrangement of the apparatus, the diverging beams of "pure" colors had little opportunity to separate before striking the screen, and the shape of the image cast on the screen was therefore identical with that produced by the unrefracted beam. But in passing through the prism the beam had acquired a red-orange fringe along one edge and a blue-violet fringe along the other.

The colored fringes on an otherwise unaltered beam of white light seemed to bear out an ancient theory of the nature of the rainbow's colors, a theory which held that a succession of modifications of sunlight by the droplets of a rain cloud produced the colors of the bow. In the century and a half preceding Newton's work such a theory was repeatedly and variously reformulated and applied to the colored iris generated by the prism. In all theories the colors were viewed as a minor perturbation restricted primarily to the edges of the homogeneous beam of sunlight. They were due to a mixture of light and shade at the region of contact between the refracted beam and the dark (Descartes); or they were a consequence of the varying "condensation" and "rarefaction" produced at the edges of the beam by the variation in the angle at which rays from the finite sun were incident upon the prism (Grimaldi); or they were generated by some other mechanical modification (Hooke and the later Cartesians).

There was no consensus as to the nature of the particular modification that tinted white light, but there was agreement that there was only one such modification and that its positive or negative application (for example, condensation or rarefaction) to white light could produce only two primary colors. These two colors, usually red and blue, represented the extreme applications of the modification, so that their mixture in appropriate proportions would generate any other color by producing the corresponding intermediate degree of modification. More recent experiments have, of course, shown that two primary colors will not suffice, but color-mixing experiments performed with crude equipment are extremely deceptive, a fact that may also account for Newton's initially surprising assertion that spectral yellow and blue combine to produce a green.⁸

All of the modification theories of prismatic colors fail ultimately because of their inability to account quantitatively for the elongation of the spectrum observed when, as in Newton's version of the experiment, the screen is placed a long distance from the prism. But even with the equipment so arranged, it is not immediately apparent that the elongation of the spectrum is incompatible with the modification theories. For since the sun has a finite breadth, rays from different portions of its disk are incident upon the prism at different angles, and even in the absence of dispersion this difference in angle of incidence will normally produce an elongation of the refracted beam qualitatively similar to that observed by Newton. Those of Newton's predecessors who, like Grimaldi, had noted the elongation of the spectrum had employed this device to account for it, and this was the explanation given by the Jesuit Ignatius Pardies, in his first letter objecting to Newton's theory.⁹ To destroy the modification theory it was necessary to notice a quantitative discrepancy between the elongation predicted by that theory and the elongation actually observed, and this required an experimenter with a knowledge of the mathematical law governing refraction (not announced until 1637) and with considerable experience in applying the law to optical problems. In 1666 these qualifications were uniquely Newton's. Descartes, who shared Newton's mathematical interests, had performed the experiment with the screen close to the prism, and had noted no elongation. Boyle and Hooke, whose apparatus probably generated an elongated spectrum, shared with Grimaldi a prevalent indifference to the power of mathematics in physics.

It was, then, the large elongation produced in the Newtonian version of the experiment plus the recognition that the size of the spectrum was not that predicted by Snel's new law of refraction that transformed a routine repetition of a common experiment into the "oddest … detection, which hath hitherto been made in the operations of nature." The oddity was not the spectrum itself, but the discrepancy between the observed length of the spectrum and the length predicted by existing theory. And this discrepancy, emphasized and investigated with far more mathematical detail in Newton's earlier oral presentations of the experiment, forced Newton to search for a new theory.¹⁰

Newton found the clue to the new theory in the geometrical idealization that he reported as the shape of the spectrum rather than in the elongation that had caused the search. His beam of sunlight was a cylinder ¼ inch in diameter, formed by allowing sunlight to enter his chamber through a circular hole in his "window shuts." After refraction the beam fell upon the opposite wall of the room, distant 22 feet from the prism, where, according to Newton, it produced an elongated spectrum, 13¼ inches in length, bounded by parallel sides 2 inches apart, and capped by semicircular ends. The shape suggested its own interpretation. For the semicircular "caps" could be viewed as the residua of the shape imposed by the circular hole in the shutter, and the spectrum could then be analyzed into an infinite series of differently colored overlapping circles whose centers lay on a straight line perpendicular to the axis of the prism. In his early lectures, as in the later Opticks, Newton frequently sketched the spectrum in this way, one end formed by a pure blue circular image of the original hole, the other formed by a pure red image, and the intermediate region composed of a number of variously colored circles displaced along the axis of the spectrum. By this device the existing laws of refraction, which for Newton's arrangement of the prism predicted a circular image, could be preserved. But the law now had to be applied, not to the incident beam as a whole, but to every one of the colored beams contained in the original beam. Sunlight was a mixture of all the colors of the rainbow; each of the incident colored beams obeyed the laws of optics; but each was refracted through a different angle in its passage through the prism. This was the essence of Newton's new theory, derived primarily from the reported shape of the spectrum.¹¹

The reported shape leaves a puzzle illustrative of the nature of Newton's genius. Though the spectrum described cries aloud for the interpretation that Newton provided, it is very doubtful that he saw any such shape. Only the central 2-inch strip of his 2 -inch-wide spectrum was illuminated uniformly by light from the disk of the sun. The balance of the width of the spectrum consisted of a penumbral region in which the various colors gradually shaded off into the black. Since the eye can distinguish red much farther into the penumbral region than it can distinguish blue, Newton probably saw a figure appreciably narrower and more pointed at the blue end than at the red.¹² This is the shape that Newton's bitterest and least intelligent critic, Franciscus Linus, described, and this is the only one of Linus's criticisms to which Newton never responded.'³ Newton combined a precise and detailed description of his experimental apparatus with an imaginative idealization of his experimental results.

Newton's leap from the full and unintelligible complexity of the observable phenomenon to the geometrical idealization underlying it is symptomatic of the intellectual extrapolations that mark his contributions to science. And he was apparently aware of and concerned with the extrapolation, though he made it explicit in none of his communications to the Royal Society. In the optical lectures, which he delivered in Cambridge prior to the composition of his first published paper, Newton included a description of two experiments that he had designed to investigate the shape of the spectrum produced without a penumbral region. In one of these he used a lens, placed one focal length in front of the screen, to refocus the colored circular sun images of which the spectrum was composed. In a second he utilized the planet Venus, effectively a point source, instead of the sun in order to generate his spectrum. He had justified his extrapolation to himself, but, except for implicit references to the problem in his correspondence with Moray and in the Opticks, he did not tell his readers how to follow him.

Newton's announcement in 1672 of the discoveries made six to eight years earlier induced a great controversy within the columns of the Philosophical Transactions.¹⁴ The prismatic colors that he discussed were well known, at least qualitatively, and there was widespread conviction among 17th-century opticians that they could be adequately treated by existing optical theories. No wonder there was resentment of a newcomer who claimed that precise analysis of a well-known effect necessitated discarding established theories. Opponents could easily find grounds for rejecting the proposals. They could, for example, deny the existence of the experimental effect. The sun is an unreliable and a moving source of light; the prism generates a number of emergent beams, only one of which satisfies Newton's description; quantitative results vary with the sort of glass employed in the prism. Alternatively, they could accept Newton's experimental results, but deny the necessity or even the validity of his interpretation.

The nature and psychological sources of the controversy were typical, but the reaction was less severe than that usually produced by so radical a proposal. Newton's predecessors had all employed some form of modification theory, but, having reached no consensus on the nature of the modification, they lacked a stable base for a counterattack. And Newton's experimental documentation of his theory is a classic in its simplicity and its incisiveness. The modification theorists might finally have explained the elongation of the spectrum, but how could they have evaded the implications of the experimentum crucis? An innovator in the sciences has never stood on surer ground.

As a result the controversy that followed the original announcement is of particular interest today for the light it sheds upon Newton's character.⁵ In particular the controversial literature illuminates the genesis of Newton's relation with the Royal Society's curator, Robert Hooke, with whom he later engaged in a priority battle over the inverse-square law of gravitation.¹⁶ Hooke's claim to the authorship of the inverse-square law almost caused Newton to omit the Third Book of the Principia, and it was apparently Hooke's continuing opposition to Newton's optical theories that caused Newton to delay publication of the Opticks until long after his own active research in the field had ended. Hooke died in 1703, and the Opticks, much of which had existed in manuscript for years, first appeared in the following year.

Newton's first paper was read to the assembled members of the Royal Society on February 8, 1671/2. On February 15 Hooke delivered, at the request of the Society's members, a report on and evaluation of Newton's work. Coming from a senior member of the profession, a man already established as the most original optical experimentalist of the day, the report was most judicious, though it contained important errors and displayed Hooke's typically Baconian indifference to quantitative mathematical formulations. Hooke praised and confirmed Newton's experimental results, and he conceded that the theory which Newton had derived from them was entirely adequate to explain the effects. His only major criticism (excepting the remarks on telescopes, for which see below) is that Newton's interpretation was not a necessary consequence of the experiments. Hooke felt that Newton had performed too few experiments to justify the theory, that another theory (his own) could equally well explain Newton's experiments, and that other experiments (particularly his own on the colors of thin films) could not be explained by Newton's theory.

Hooke's Baconian criticism is an index of the prevalent methodological emphasis upon experimentation, an emphasis that made the "experimental history" a typical scientific product of the day. Most members of the Royal Society would have concurred. But Hooke was quite wrong in thinking that his own version of the modification theory could explain Newton's results; at least he never gave a satisfactory explanation of the production of colors.¹⁷ On the other hand, Hooke was right that Newton's theory could not explain some of the experiments upon which Hooke had based his own theory. In particular, Newton's theory, as of 1672, would not explain either diffraction or the colors of thin sheets of mica, both of which Hooke had described in his Micrographia (1665). Nor would Newton's theory explain the colors produced by confining air between sheets of glass, an observation that Hooke reported to the Society on April 4 and June 19 in his further examination of Newton's doctrine.¹⁸ The latter communication, incidentally, included a clear description of the phenomenon usually known as "Newton's rings," and it seems probable that Newton borrowed it from Hooke and employed it to develop a revised theory adequate to handle Hooke's experiments. For Newton, in his long letters of December and January 1675/6, did succeed in solving Hooke's problems to his own satisfaction and to that of most of his contemporaries. But to do so he had to modify his original theory by the introduction of an explicit Ethereal medium which could transmit impulses as pressure waves, and this was an immense step toward Hooke's theory. Hooke, of course, did not accept even this later modification. He always felt that Newton's use of both corpuscles and Ether impulses violated Occam's injunction against the needless multiplication of conceptual entities.¹⁹

In the final analysis Hooke was wrong. As Newton clearly showed in his belated reply, Hooke's pulse theory of light was incapable of accounting for linear propagation; nor could Hooke's modification theory of color account either for the experimentum crucis or for any of the novel color-mixing experiments that Newton apparently designed specifically to meet Hooke's objections. This much of the reply was effective, and Newton might better have begun and ended with the elaboration of these arguments, for Hooke had challenged neither Newton's experiments nor the adequacy of his theory to resolve the experiments. But this is not what Newton did. In his lengthy and gratuitously caustic response, whose incongruity with Hooke's critique has escaped attention since the two have not before been printed together,²⁰ Newton attacked Hooke on three apparently incompatible grounds: Hooke had attributed to Newton a corpuscular theory that Newton had not developed; Hooke's impulse theory was not basically incompatible with the corpuscular theory (which Newton had disowned); and Hooke's impulse theory was incapable of accounting for the phenomena. Newton might have employed any of these three lines of attack alone—though only the third seems both relevant and accurate—but it is difficult to see how anything but consuming passion could have led him to employ them concurrently.

Newton was a man of passions. It is difficult to read many of his responses to criticism without concurring in a recent judgment of Newton's personality by the late Lord Keynes. After a lengthy examination of Newton's manuscripts Keynes wrote:

For in vulgar modern terms Newton was profoundly neurotic of a not unfamiliar type, but—I should say from the records—a most extreme example. His deepest instincts were occult, esoteric, semantic—with profound shrinking from the world, a paralyzing fear of exposing his thoughts, his beliefs, his discoveries in all nakedness to the inspection and criticism of the world. "Of the most fearful, cautious and suspicious temper that I ever knew," said Whiston, his successor in the Lucasian Chair. The too well-known conflicts and ignoble quarrels with Hooke, Flamsteed, Leibnitz are only too clear an evidence of this. Like all his type he was wholly aloof from women. He parted with and published nothing except under the extreme pressure of friends.²¹

Newton's fear of exposure and the correlated compulsion to be invariably and entirely immune to criticism show throughout the controversial writings. They are apparent in both the tone and the substance of his reply to Hooke, where they are also combined with the beginning of that tendency to deny the apparent implications of earlier writings (rather than either defending them or admitting to a change of mind) which has so consistently misled subsequent students of his work. Did Hooke really misinterpret the intent of Newton's remarks on the difficulties of constructing refracting telescopes? Is Newton honest in rejecting the corpuscular hypothesis that Hooke ascribes to him? Or, to take a later and far clearer example, is not Newton convicted of an irrationally motivated lie in his reply to Huygens's remarks about the composition of the color white? In his first paper Newton had said, in discussing colors:

But the most … wonderful composition is that of Whiteness … 'Tis ever compounded, and to its composition are requisite all the aforesaid primary Colours, mixed in a due proportion … Hence therefore it comes to pass, that Whiteness is the usual colour of Light; for Light is a confused aggregate of Rays indued with all sorts of Colours … if any one predominate, the Light must incline to that colour.

Yet when Huygens suggested that the combination of yellow and blue might generate white, Newton admitted the possibility but claimed that he had never meant anything else. The apparent contradiction he reconciled by saying that Huygens's white would be different from his own by virtue of its composition. Newton's position was correct in the reply, but surely he had changed his mind in reaching it.

The same defensiveness had more serious consequences in Newton's writings on telescopes. Here Newton's influence appears to have been predominantly negative. His own work on telescopes was of little practical importance, and his remarks on design were frequently wrong. Although he built the first working reflector, he was never able to perfect the model sufficiently to enable it to compete with existing refractors, and so his position was not very different from that of the contemporary and independent designers, James Gregory and Guillaume Cassegrain.²² The reflecting telescope remained a curious toy on the shelves of the Royal Society until, in 1722, James Hadley succeeded in grinding a parabolic mirror. But as soon as the reflector could compete with the refractor, Newton's design was discarded in favor of the designs by Gregory and Cassegrain that Newton had so vehemently criticized for essentially irrelevant reasons.²³

Far more important in the development of telescopes were Newton's mistakes in the evaluation of optical aberrations. Having been led to the reflecting telescope by the discovery of the chromatic aberration caused by the variation of refractive index with color, Newton always insisted that chromatic rather than spherical aberration imposed the major limitation upon the power of refracting telescopes. Newton's theoretical comparisons of the two were both mathematically and optically correct, but, as Huygens pointed out in his comment, Newton's interpretation of the calculations was incompatible with the observed performnance of spherical lenses. Newton explained the discrepancy correctly as due to the small effect on the eye of the widely dispersed red and blue rays, but he failed to notice that in practice this made chromatic aberrations little or no more important than spherical. So Newton continued to insist upon the practical superiority of reflectors.²⁴ Subsequent history bore out the judgment expressed by Huygens in his last letter of the optics controversy that until it became possible to grind nonspherical mirrors the future of practical telescopic observations would be associated with refractors of long focal length and consequently low aberrations.²⁵

But among the aspects of Newton's thought that are illuminated by recognition of his dread of controversy, the most important is his attitude toward "hypotheses." Like most of his contemporaries, Newton was guided throughout his scientific career by the conception of the universe as a gigantic machine whose components are microscopic corpuscles moving and interacting in accordance with immutable laws.²⁶ Most of Newton's work in physics can be viewed appropriately as a part of a consistent campaign to discover the mathematical laws governing the aggregation and motion of the corpuscles of a mechanical "clock-work universe," and many of his specifically optical, chemical, or dynamical writings are difficult to comprehend without reference to the corpuscular metaphysic which played an active role in their creation.²⁷ Yet from most of his published writings Newton tried, never completely successfully, to eliminate just these hypothetical and therefore controversial elements.

In the notebook in which he recorded the progress of his early optical research Newton continually referred to light rays as composed of "globules," traveling with finite velocities and interacting in accordance with the known laws of impact.²⁸ But in his first published paper Newton omitted all explicit reference to particular corpuscular mechanisms which determine the behavior of light. He substituted geometrical entities ("rays") for physical entities (corpuscles moving in definite paths); and he contented himself with a retrospective argument showing that the experimentally determined properties of the rays must make light a substance rather than a quality. In his controversy with Hooke, who seems to have known more about the hypotheses than Newton had allowed to enter in his published discussion, he reneged on even this argument, and thus continued a retreat that had begun in his first paper and developed further in his letters to Pardies.

That this is a genuine retreat from the defense of metaphysical hypotheses which Newton believed and employed creatively is amply, if incompletely, attested by the inconsistencies in his discussions and use of hypotheses throughout the optical papers printed below. In the first paper light was a substance. In the letters to Pardies light was either a substance or a quality, but the definition of light rays in terms of "indefinitely small … independent" parts made light again corporeal. In the same letter Newton proclaimed that his observations and theories could be reconciled with the pressure hypotheses of either Hooke or Descartes, but in the letter to Hooke he forcefully demonstrated the inadequacy of all pressure hypotheses to explain the phenomena of light and colors. Newton denied his adherence to the corpuscular hypothesis, and he stated that his credence was restricted to laws that could be proved by experiment, but he returned to the pattern of his notebook by employing implicitly the hypothetical scatterings of corpuscles at points of focus to prove the disadvantages of the Gregorian telescope.²⁹ In 1672 he denied the utility of hypotheses when presenting a theory which he believed could be made independent of them, but in dealing with the colors of thin films in the important letters of 1675/6 he employed explicit hypotheses, presumably because the new subject matter of these letters could not otherwise be elaborated. Significantly, it was just these later letters, from which large segments of Books II and III of the Opticks were transcribed, that Newton refused to publish until after Hooke's death. Of all his optical writings, these letters best reflect the procedures of Newton at work.³⁰

Much of modern science inherits from Newton the admirable pragmatic aim, never completely realized, of eliminating from the final reports of scientific discovery all reference to the more speculative hypotheses that played a role in the process of discovery. The desirability of this Newtonian mode of presenting theories is well illustrated by the subsequent history of Newton's own hypotheses. The next great step in optics, the development of an adequate wave theory, was retarded by the grip of Newton's corpuscular hypotheses upon the scientific mind. But Newton's remarks about the role of hypotheses in science were dictated by personal idiosyncrasy as often as by philosophical acumen; repeatedly he renounces hypotheses simply to avoid debate. And so he has seemed to support the further assertion that scientific research can and should be confined to the experimental pursuit of mathematical regularity—that hypotheses which transcend the immediate evidence of experiment have no place in science. Careful examination of Newton's less systematic published writings provides no evidence that Newton imposed upon himself so drastic a restriction upon scientific imagination.

The achievements initiated by Newton's own imagination are unsurpassed, and it is primarily the magnitude of his achievements that directs attention to the man. If the resulting study displays error and idiosyncrasy in Newton's complex and difficult personality, it cannot lessen his unparalleled accomplishments. It can alter only our image of the requisites for preëminent scientific achievement. But this alteration is a goal worth pursuing: a true image of the successful scientist is a first condition for understanding science.

Notes

¹ For example, Experiments IV and V in Part III of Boyle's Colours are almost identical with the first and last of the three experiments that Newton employed in his first published presentation of the new theory of light and color. In Experiment IV Boyle generates a spectrum and in V he uses a lens to invert the order of the colors. But in Boyle's Baconian compilation these are but two among hundreds of experimental items. There is no evidence that they had the slightest effect on Boyle's contemporaries or successors. See The Works of the Honourable Robert Boyle, ed. Thomas Birch (London, 1744), vol. 2, p. 42.

² The "Queries" that Newton appended to the Opticks are the one portion of his later published scientific works in which he allowed the fecundity of his creative imagination to appear. These speculative postscripts to his last technical work do provide a more intimate view of their author. Of course even the Opticks proper is a less impersonal work than the Principia, but, despite the frequent informality of literary style, the contents and organization are those of a treatise.

³ The phrase is Newton's. See the beginning of the first optical paper, below.

⁴ Joseph Priestley, The History and Present State of Discoveries Relating to Vision, Light, and Colours (London, 1722), pp. 7, 21, 169.

⁵ Descartes's discussion of the prism occurs in Discours VIII of Les météores (1637). For Boyle's experiments see note 1, above. Marci's experiments are described in his Thaumantias liber de arcu coelesti … (Prague, 1648) and are discussed by L. Rosenfeld in Isis 17, 325-330 (1932). Grimaldi's Physico-mathesis de luinine … (Bologna, 1665) includes many discussions of prism experiments. Hooke's theory and experiments appear in his Micrographia (1665), reprinted by R. T. Gunther as vol. XIII of Early Science in Oxford (Oxford, 1938), pp. 47-67. There is no reason to suppose that Newton in 1672 knew of the work of either Marci or Grimaldi, but it is an index of the state of optical experimentation in the 17th century that Grimaldi, Marci, and Boyle had, among them, performed all three of the experiments that Newton employed in his first optical paper.

⁶ Letter from Newton to Oldenburg, the secretary of the Royal Society, dated Cambridge, 18 January, 1671/2. Thomas Birch, The History of the Royal Society of London (London, 1757), vol. 3, p. 5.

⁷ See particularly Descartes's diagrams and discussion, cited in note 5, above.

⁸ In modern terminology, blue and yellow light are complementary; that is, they mix to give white. The green produced when blue and yellow pigments are mixed is the result of subtractive color mixing, a process different from the mixing of spectral colors. But in fact a long-wavelength spectral blue and a short-wave-length spectral red can be combined to produce a light-green tint. By combining in different proportions a blue near the green region of the spectrum with a red near the yellow it is actually possible to produce a number of shades of blue, green, red, yellow, and intermediate colors. The two-color theories were not so foreign to experience as has been imagined.

⁹ Ignace Gaston Pardies, S.J. (1636-1673), was born at Pau in Southern France. At the time of his dispute with Newton he was the professor of rhetoric at the College Louis-le-grand in Paris.

¹⁰ Newton first presented his new theory in a series of lectures delivered at Cambridge during 1669. The lectures were not printed until 1728, after his death, when they appeared in an English translation from the Latin manuscript. A Latin edition, containing lectures for the years 1669, 1670, and 1671, appeared in 1729. Certain of the features emphasized in the present discussion emerge with even greater clarity from the lectures than from the first optical paper. The two may profitably be read together.

¹¹ The preceding reconstruction of Newton's research follows the essentially autobiographical narrative provided by Newton himself in the first of the optical papers. It may require important modification as a result of a recent study of Newton's manuscripts by A. R. Hall, "Sir Isaac Newton's Note-Book, 1661-1665," Cambridge Historical Journal 9, 239-250 (1948). On this topic, see the references to further studies in the Supplement.

Hall believes that Newton discovered the variation of refractive index with color by observing a two-colored thread through a prism, and he suggests that the experiment in which a beam of sunlight is passed through a prism was not performed until a later date. For a variety of reasons I find this portion of Hall's reconstruction implausible. The textual and historical evidence available, though not decisive, persuades me that Newton had already passed a beam of sunlight through a prism when he performed the experiments that Hall has discovered in the "Note-Book."

If so, Newton's account of the development of the new theory remains autobiographical in the sense that the prism experiment did provide the initial impetus as well as an important clue for the new theory, as discussed above. But, as Hall does conclusively show, the implication of Newton's account is wrong in that Newton did not proceed so directly or so immediately from the first prism experiment to the final version of the theory as the first paper would imply. When he made the entries in his college notebook, Newton had not arrived at the final form of the new theory. So far as I can tell from the fragments reproduced by Hall, Newton then believed that different colors were refracted through different angles, but he still held that the individual colors were generated within the prism by modifications of the initially homogeneous white light. This intermediate stage of Newton's thought provides a fascinating field for further study.

¹² It is impossible to be precise about the actual shape of the spectrum viewed by Newton. The sensitivity of the human eye to short-wavelength blue varies from one individual to another, and the relative intensity of the blue in the spectrum is also a function of atmospheric conditions.

¹³ Linus's description occurs midway through the first paragraph of his second letter of criticism. Although the position of Linus's prism was different from that of Newton's, the "sharp cone or pyramis" described by Linus is due to the same penumbral effects that must have caused the sides of Newton's spectrum to deviate from parallelism.

Franciscus Linus (Francis Hall or Line), S.J., was born in London in 1595. During his controversy with Newton he was a teacher of mathematics and Hebrew at the English college of Liege. He spent much of his later life attempting to reconcile the results of 17th-century experimentation with Aristotelian physics. Linus was the author of the "funiculus" hypothesis by which he claimed to explain the results of Boyle's barometer experiments without recourse to the vacuum or atmospheric pressure, and experiments designed to refute him led to the discovery of Boyle's Law. Linus died in 1675, midway through the dispute with Newton, but his cause was taken up by two of his students, Gascoigne and Lucas.

Anthony Lucas (1633-1693), another British Jesuit, appears to have been a meticulous experimenter. His inability to obtain the large dispersion reported by Newton must have been due to his use of a different sort of glass. Lucas's experimental "proofs" of the inadequacy of Newton's theory are a fascinating index of the difficulties in designing unequivocal dispersion experiments. In most experiments the effects are so small that they can be fitted to any theory, so incisive documentation of a particular theory requires careful selection from the multiplicity of available phenomena. At first glance Newton's failure to answer any of Lucas's experimental criticism seems strange, particularly since Newton did respond at such length to the one remark by Lucas that did not reflect at all upon the validity of Newton's conclusions. But see the discussion, below, of Newton's attitude toward controversy.

¹⁴ A. R. Hall, "Sir Isaac Newton's Note-Book," has pointed out that Newton probably intended to write "1665" rather than "1666" for the date of the prism experiment which opens his first paper. He also argues that Newton's work with the prism may have begun as early as 1664.

¹ There are, however, many points of technical interest in the debate. These are discussed more fully in L. Rosenfeld, "La theorie des couleurs de Newton et ses adversaires," Isis 9, 44-65 (1927). A stimulating elementary account of some of the same material has been provided by M. Roberts and E. R. Thomas, Newton and the Origin of Colours (London: G. Bell & Sons, 1934).

¹⁶ For bibliography and a definitive account of the gravitation controversy, see A. Koyré, "An Unpublished Letter of Robert Hooke to Isaac Newton," Isis 43, 312-337 (1952).

¹⁷ The difficulty in adapting a pressure-wave theory of light like Hooke's to the various color phenomena explored by Newton is well illustrated by the experience of Huygens, who brought these theories to their most perfect 17th-century form in his Traité de la lumière (1690). Huygens wrote Leibniz that he had "said nothing respecting colours in my Traité de la lumière, finding this subject very difficult, and particularly from the great number of different ways in which colours are produced." Sir David Brewster, Memoirs of the Life, Writings, and Discoveries of Sir Isaac Newton (Edinburgh, 1855), vol. 1, p. 95 n.

¹⁸ Birch, History of the Royal Society, vol. 3, pp. 41 & 54.

¹⁹Ibid., p. 295.

²⁰ Oldenburg, the secretary of the Royal Society and editor of the Philosophical Transactions, is known to have hated Hooke. This may well explain his failure to print Hooke's critique with Newton's reply. The omission must have seemed a gratuitous insult to Hooke, particularly in view of the tone and substance of Newton's comments.

²¹ J. M. Keynes, "Newton the Man," in the Royal Society's Newton Tercentenary Celebrations (Cambridge, 1947), p. 28. These documents can be put to other uses, however. Examine, for an opinion of the Hooke-Newton exchange directly opposed to the one given above, the analysis provided by Brewster, Memoirs, vol. 1, pp. 86-92. But Brewster cannot avoid providing repeated illustrations of Newton's efforts to escape from controversy (for example, pp. 95-99).

²² James Gregory (1638-1675), a Scottish mathematician, described a reflecting telescope in his Optica Promota (1633), and Newton had studied Gregory's design when he started his own. Sieur Guillaume Cassegrain was a modeler and founder of statues in the employ of Louis XIV. His design was surely independent of Newton's and may have been independent of Gregory's. Both Gregory and Cassegrain tried to build reflectors but were unable to polish adequate mirrors.

²³ On Newton's contributions to the development of telescopes see Louis Bell, The Telescope (New York, 1922).

²⁴ The study of Newton's most important and damaging error in his writings on the telescope is complicated rather than clarified by the papers reprinted below. In his Opticks (Book I, Part II, Experiment 8) Newton "proved" that it was impossible to build an achromatic lens, that is, a lens compounded from two or more materials so differing in dispersive power that they will refract a ray of white light without separating the colors in it. Newton claimed to have found by experiment that when a beam of light was passed through a succession of prisms of glass and water a spectrum was invariably generated unless the emergent and incident beams were parallel. He concluded that any combination of materials which could correct dispersion would also nullify refraction, so that no achromatic lens was possible. The error may well have hindered the development of achromatic lenses.

To get the experimental result Newton must either have shut his eyes, used sugar to raise the refractive index of his water, or employed a variety of glass with unusually low dispersive power. All three of these explanations have been advanced by subsequent historians, most of whom have also expressed surprise at Newton's readiness to draw so general a conclusion from such slight experimental evidence. For a full account of the development of achromatic lenses see N. V. E. Nordenmark and J. Nordstrom, "Om uppfinningen av den akromatiska och aplanatiska linsen," Lychnos 4, 1-52 (1938); 5, 313-384 (1939). The second portion of the article includes some appendices and an abstract in English.

It is apparent from the optical papers below that Newton's theorem concerning the relation of dispersion and refractive index was the best possible refutation for three of his early critics. It nullified the objections of Hooke and Huygens, who had urged that more attention be given to the perfection of refracting telescopes, and it made it certain that Lucas had erred in reporting the small dispersion of his prism. For this reason most historians have argued that the theorem developed in the Opticks was in Newton's mind, at least implicitly, from the beginning of his optical researches and that this is why he failed to consider more seriously the merits of his opponents' positions. But—and this is where the new complication enters—I can find no way of interpreting the text of Newton's response to Hooke without supposing that Newton is there proposing an achromatic lens made by compounding a water lens with two convexo-concave lenses of glass.

On this topic, see the works by D. T. Whiteside and Zev Bechler, referred to in the Supplement.

²⁵ The letters to and from Huygens reprinted below are only a part of a larger correspondence, most of which was not published until recently. L. T. More discusses the complete correspondence more fully in his biography, Isaac Newton (New York, 1934). The letters themselves will be found in volume VII of the Oeuvres completes de Christiaan Huygens (The Hague, 1888-1944).

²⁶ M. Boas, "The Establishment of the Mechanical Philosophy," Osiris 10, 412-541 (1952).

²⁷ For the role of the metaphysic in Newton's chemistry see the next section of this book. For its role in Newton's dynamics, see A. Koyré, "The Significance of the Newtonian Synthesis," Archives internationales d'histoires des sciences 29, 291-311 (1950), and T. S. Kuhn, The Copernican Revolution (Cambridge, Mass., 1957), chap. 7.

²⁸ For example: "Though 2 rays be equally swift yet if one ray be lesse yⁿ y^e other that ray shall have so much lesse effect on y^e sensorium as it has lesse motion yⁿ y^e others &c.

"Whence supposing y' there are loose particles in y^e pores of a body bearing proportion to ye greater rays, as 9:12 & ye less globulus is in proportion to ye greater as 2:9, ye greater globulus by impinging on such a particle will loose 6/⁷ parts of its motion ye less glob, will loose 2/⁷ parts of its motion & ye remaining motion of ye glob. will have almost such a proportion to one another as their quantity have viz. I/⁷: 1/7:: '/7: 1/5 W^ch is almost 2 ye lesse glob. & such a body may produce blews and purples. But if ye particles on wch ye globuli reflect are equal to ye lesse globulus it shall loose its motion & y' greater glob. shall loose 2/parts of its motion and such a body may be red or yellow." Hall, "Sir Isaac Newton's Note-Book," p. 248.

²⁹ Brewster, Memoirs, p. 50 n.

³⁰ These critically important letters, reprinted below, deserve far more study and discussion than they here receive. But such discussion necessarily assumes the proportion of a critical analysis of the second and third books of the Opticks for which these letters provided a draft, and the space for such an analysis is not here available. For a discussion of the central ideas in these later letters, as they emerge in the Opticks, see I. B. Cohen's introduction to the recent reissue of the Opticks (New York, 1952).

Space limitations also prevent my discussing Newton's posthumously published design of "An instrument for observing the Moon's Distance from the fixed Stars at Sea." When written this paper contained important novelties of design, but before it was published these new features had been independently incorporated in practical navigational instruments by several designers. On these instruments see Lloyd Brown, The Story of Maps (Boston, 1949), pp. 191 ff.