Marat's Science

4: Marat's Investigations of Light



The second volume of Marat's trilogy, published later in 1780, was devoted to the science of optics. In the time between the appearance earlier that year of the volume on fire and the publication in 1782 of the volume on electricity, a qualitative change for the worse had occurred in Marat's relationship with the French scientific elite. That change is reflected in the general tone of Marat's writing, which in the first two parts of the trilogy displays a more “professional” neutrality, whereas the third volume turns more polemical and antagonistic toward scientific opponents in general and members of the Academy of Sciences in particular.

Since the heightened hostility manifested itself in the third book of the series, the one on electricity, C.C. Gillispie attributes the change to a loss of psychological control on Marat's part that occurred while he was writing up his electrical experiments. A closer examination suggests, however, that Marat's change in attitude originated with his optical studies and derived less from his internal mental state than from the hostile reception the academicians gave his revisionist optical notions.

In Découvertes sur la lumière (Discoveries about Light), Marat explicitly stated his intention to revise a fundamental tenet of Newton's theory of colors. Newton's authority in this field was so great in the eighteenth century as to be virtually absolute. Marat's challenge was regarded as an act of effrontery and rejected without a real hearing. The leaders of the Academy apparently deemed Marat's innovations to be worthless without conscientiously examining them. They closed ranks against him and his later writings reflected his anger at being rebuffed.

Later commentators who have defended the Academy's cold shoulder to Marat have done so on the grounds that subsequent developments in optics proved Marat wrong in his case against Newton. These judgments based on hindsight, however, do not address the question of whether dismissing Marat's contributions out of hand was justifiable in terms of contemporary knowledge of optics.

In fact, Marat's work targeted a problem in optical science that Newton had explicitly left unresolved in his Opticks. Marat’s investigations of the deviation of light as it passed close to the surface of objects—reminiscent of what Newton called “inflexion” and others have called “diffraction”—recalled attention to a neglected class of phenomena that would eventually prove to be of critical importance to optical science.[1] Although Marat insisted that the deviation of light he was describing was not the same as diffraction/inflexion, it was certainly very similar since it referred to the same observed behavior of light.

Deviation? Inflexion? Diffraction?

Whether called deviation, inflexion, or diffraction, it is not a readily apparent phenomenon. Unlike reflection and refraction it is not part of everyday visual perception and was never noticed by the natural philosophers of antiquity. The first to detect this subtle manifestation of light was the Jesuit natural philosopher Francesco Grimaldi, whose Physico-Mathesis reported it for the first time and gave it the name diffraction.[2] Grimaldi's book was published posthumously in 1665; he had died two years earlier.

The commonplace observation that a strong light source casts a sharply defined shadow leads naturally to the assumption that rays of light travel in perfectly straight lines. In darkroom experiments, however, Grimaldi detected a very slight bending of light as it passes the edges of objects.

Imagine sunlight entering a darkroom through a very small hole in the window shutters and projecting a luminous disk upon the opposite wall of the room. A knife blade placed between the hole and the disk of light produces a shadow within the disk. One would expect, if the commonsense assumption holds true, that a perfectly straight line would connect the hole, the edge of the knife blade, and the edge of the knife blade's shadow. A careful experimenter, however, will find this not to be so. The shadow will be slightly displaced from its anticipated position. Furthermore, the shadow will not be sharply defined, as would be expected, but will exhibit what appear to be a series of overlapping fringes.

Grimaldi gave the name “diffraction” to this unexpected behavior of light, and said it implied that light is a wave phenomenon. Perhaps even more surprising was his observation of barely perceptible bands of colors in the fringes of shadows projected onto the walls of his darkroom. In 1672, seven years after the publication of Grimaldi's book, Robert Hooke detected this same peculiar bending of light and the colored fringes, but apparently without knowledge of Grimaldi's work.

Meanwhile, Newton had begun his optical investigations. His primary attention was directed toward the production of colors by the passage of sunlight through a prism. As a result of a series of classic darkroom experiments, he announced that the various colors of the spectrum were all originally present in the beam of sunlight; they were separated and spread out into a rainbow-like continuum by the prism because each color is refracted a little more or less than every other color as the rays pass through the prism. He called this phenomenon “differential refrangibility.”

Although Newton thus placed refraction at the center of his color doctrine, he also showed an interest in the unexpected bending of light around objects. Instead of using Grimaldi's term, diffraction, he used the term inflexion to describe it.

Newton’s earliest announcement of his optical conclusions, in 1672 in the Royal Society's Transactions, provoked heated opposition, which was not at all to Newton’s liking. He did not accept criticism graciously. Among other things, Hooke charged Newton with stealing his ideas about inflexion. Newton denied the charge of plagiarism, saying he had given credit to Hooke for his observations.

Newton acknowledged the reality of inflexion, conceded that he was not sure how it could be reconciled with the rest of his optical doctrines, and left it as an unsolved problem for physicists of the future to probe. Nonetheless, the early investigations into diffraction by Grimaldi, Hooke, and Newton had had no significant sequel by the time Marat began studying the phenomenon.

A useful source for determining the specific content of optical knowledge at the beginning of the last quarter of the eighteenth century is Joseph Priestley's History and Present State of Discoveries Relating to Vision, Light, and Colours. Priestley's account of the invention of the solar microscope was noted in the previous chapter. Published in 1772, this work represented the conscientious effort of a leading physicist to survey and analyze the entire body of his predecessors' accomplishments in the field of optics. Priestley's personal prestige as a scientist assured a wide readership among practitioners in the field and thereby helped to establish a standard history to which the community of physical scientists and optical craftsmen could refer.[3]

Priestley introduced Grimaldi’s discovery of diffraction by describing it as “such an effect as could hardly have been suspected without actual observation.”

Had Descartes, or any other philosopher before this period, been asked, what would have become of a ray of light, which should pass as near as possible to any body, but without actually impinging upon it; he would have replied, without hesitation, that it would proceed in a straight line, without being affected by its approach. But it was now found, that light coming within a certain distance of any body, will either be bent from it, or towards it.[4]

Aside from Robert Hooke's investigations, “little use had been made of Grimaldi's observations” before Newton took an interest in them. In the last section of his Opticks, Newton reported replicating Grimaldi's experiments, which Priestley says he did “with the greatest care, diversified them, and pursued them much farther.” Priestley emphasizes that

as these experiments were the last that [Newton] made, and are acknowledged by himself to be incomplete, it is the more necessary to be particular in relating the circumstance of them; that others may be enabled to repeat them, and carry them still further.[5]

This gives strong testimony to the legitimacy of Marat's work in the field of optics. First of all it indicates that, in Priestley’s well-informed opinion, the understanding of this subtle bending of light had not been advanced as of 1772; secondly, it is an explicit call for physicists to engage in precisely the kind of investigation that Marat was to undertake a few years later.

Newton's doctrine of color as a function of the differential refrangibility of individual rays of light achieved the status of an unchallengeable paradigm early in the eighteenth century. After 1728, Priestley says,

no person, who chose to give his name to the public, or whose name is worth recording, made any opposition to it; so that, at present, no hypothesis in philosophy stands upon surer ground, or is more generally acquiesced in, than that of the differential refrangibility of light.[6]

While presented and widely accepted as a complete and satisfying explanation of the nature of color, disturbing anomalies remained unaccounted for. If light consists, as Newton believed, of “solid, massy, hard, impenetrable, moveable Particles,”[7] what force deflects them as they pass edges of objects? And if colors are made visible by the prism's power to deflect those particles at different angles depending upon their individual colors, then how can the colors produced in diffraction experiments be explained?

Newton’s “Queries”

Newton attempted to suggest some preliminary answers in the queries appended to his Opticks. By relegating them to the queries, he acknowledged that they were provisional and hypothetical; in other words, that the bending of light around objects remained an unsolved problem for the science of optics.

Newton's Opticks is divided into three sections, or “books,” which are in turn divided into parts. The first two books are devoted to the reflection and refraction of light, and include consideration of the colors visible on the surfaces of soap bubbles and other such “thin transparent Bodies.” Book III, Part I is devoted to inflexion. Book III has no Part II, however; this is an indication of the unfinished character of the work. In fact, Newton says as much, because after describing and discussing his investigations of inflexion, he states:

When I made the foregoing Observations, I design’d to repeat most of them with more care and exactness, and to make some new ones for determining the manner how the Rays of Light are bent in their passage by Bodies, for making the Fringes of Colours with the dark lines between them. But I was then interrupted, and cannot now think of taking these things into farther Consideration. And since I have not finish’d this part of my Design, I shall conclude with proposing only some Queries, in order to a farther search to be made by others.[8]

The queries, eventually totaling 31 in number by the 1717 edition, appear directly after this apology and constitute the ending of the Opticks. Only the first few queries are directly concerned with inflexion, but it is clear that inflexion was what Newton was referring to when he said “I have not finish’d this part of my Design.”

The title of Book III, Part I is “Observations concerning the Inflexions of the Rays of Light, and the Colours made thereby,” and the problem is stated at the outset:

Grimaldo has inform’d us, that if a beam of the Sun’s Light be let into a dark Room through a very small hole, the Shadows of things in this Light will be larger than they ought to be if the Rays went on by the Bodies in straight Lines, and that these Shadows have three parallel Fringes, Bands or Ranks of colour’d Light adjacent to them.[9]

It should be noted that if the shadows of things in the light are larger than they ought to be, the implication is that the light is bending away from the objects it passes; if it were bending toward the objects, the shadows would be smaller. Grimaldi and Newton both recognized, however, that in fact some light rays appear to bend toward objects and some appear to bend away.

After carefully describing his inflexion experiments and apologizing for being unable to conclude the investigation to his satisfaction, Newton began listing his queries. The use of the question form was a bit of a ruse; as I.B. Cohen has pointed out, it “may have been adopted in order to allay criticism, but it does not hide the extent of Newton's belief.”[10]

Newton's difficulty with inflexion is manifested in the way in which he directly contradicted himself in the queries. In Query 29 he asked:

Are not the Rays of Light very small Bodies emitted from shining Substances? For such Bodies will pass through uniform Mediums in right Lines without bending into the Shadow, which is the Nature of the Rays of Light.[11]

Here Newton explicitly stated that light rays, by their very nature, move in straight lines and therefore do not bend into the shadow. He had already suggested in earlier queries, however, that light not only bends into the shadow; it bends away from the shadow as well. In Query 3 he asked:

Are not the Rays of Light in passing by the edges and sides of Bodies, bent several times backwards and forwards, with a motion like that of an Eel? And do not the three Fringes of colour’d Light above-mention’d arise from three such bendings?[12]

What was to be made of this extraordinary eel-like behavior of light rays? Priestley reported that physicists heeded Newton's call to follow up on his investigations into inflexion: “We are much obliged to several ingenious foreigners who have made experiments similar to his.” Among these ingenious foreigners were Maraldi, Mairan, Du Tour, Le Cat, and Muschenbroek.[13] Nonetheless, Priestley concluded, these investigations “cannot be said to be completed.”[14]

“The doctrine of the inflection of light seems to be capable of much farther illustration,” Priestley continued. “The origin of the three coloured streaks, on each side of the termination of the shadows of bodies, has not been satisfactorily traced.”[15] Newton's conjecture “that light bends in its motion, like an eel . . . seems to be a kind of hypothesis that one would not chuse to have recourse to without necessity.”[16]

Marat and the Academy: Round Two

Marat’s choice of the bending of light around objects as a focus of scientific inquiry, then, was certainly reasonable by any contemporary standards. His patron the comte de Maillebois, the honorary member of the Academy of Sciences who had arranged for a commission to evaluate Marat’s experiments with heat and fire, once again approached the Academy and requested that Marat’s optical work be examined as well. As a result, another commission was named to witness demonstrations of his experiments and to issue a report on them. According to Marat, the commission’s first visit took place on June 22, 1779, and the last one on January 30, 1780:

My experiments were performed during a seven-month period under the eyes of the academicians, and in that time they were all repeated a very great number of times.[17]

One reason the commission's work took so long to complete was that most of Marat’s experiments could only be demonstrated on sunny days. Although the commission was officially composed of five members, most of the work devolved upon two of them: J.B. Le Roy and J.A.J. Cousin. Le Roy was assigned to write the final report.[18]

After the commission completed its observations at the end of January, Marat awaited their report. Hearing nothing but excuses from Le Roy and Cousin for several weeks, he began writing to Condorcet to ask when he might expect it to be issued. As time passed, Marat’s letters became more impatient and persistent: Why the inordinate delay?[19]

The report was finally issued on May 10, 1780, and consisted of three rather brief paragraphs. Marat had it printed in its entirety at the front of his Découvertes sur la lumière and followed it with a commentary of his own.

The report began by acknowledging that inflexion was a valid topic of optical investigation:

These experiments, which are very numerous, touch upon various phenomena of light, and particularly with those having to do with its inflexion when it passes along the length of bodies.[20]

By careful wording and judicious use of phrases such as “according to the author,” however, the report avoids saying anything that could be interpreted as praise for Marat’s work or endorsement of his conclusions. The conclusion the commissioners were most concerned to dissociate themselves from was Marat’s assertion that the decomposition of colors attributed by Newton to refraction should in fact be attributed to the deviation of light at the boundaries of objects. The separation of colors from sunlight that Newton observed, according to Marat, did not occur in his prisms but at the edges of the hole that admitted the sunlight into the room in the first place. The prism simply served to amplify the phenomenon. (This contention will be discussed further below.)

This was a rather bold hypothesis aimed at eliminating a long-standing anomaly from the science of optics by incorporating reflection, refraction, and inflexion (or “deviation”) into a single explanatory model of color production. The Academy's report, however, explicitly avoided evaluating Marat’s synthesis:

But since these experiments are so very numerous, as we have said, that we have not been able for that reason to verify all of them (in spite of all the attention that we have paid to them) with the necessary precision; since, moreover, they do not appear to us to prove what the author believes they establish; and since they are generally contrary to what is best known in the field of optics . . . we do not regard them as being of the nature of that which the Academy could give its sanction or its approval.[21]

The report was signed by Le Roy, Cousin, and Sage, and was certified by Condorcet. It is significant that the report does not explicitly deny the validity of Marat’s theory; it simply refuses to take a position on the issue.

In reply, Marat said that he had neither asked for nor expected the Academy to endorse his conclusions; he had merely requested that the commissioners verify matters of fact. “But I had the right to expect that this scientific society would state an opinion on the precision and novelty of my experiments.”[22]

As for the commissioners’ charge that his conclusions “are generally contrary to what is best known in the field of optics,” Marat’s response was, in effect, so be it; he had stated the conclusions his experiments had led him to, and he considered that to be a positive gain for science: “Is it necessary to defend the old opinions,” he asked, if they can be shown to be erroneous? “There is no scientific society in the world whose judgment can make true what is false or false what is true.”[23]

Although neither the Academy’s report nor Marat’s response mentioned Newton’s name, the authority of Newton was at the root of the dispute here. “What is best known in the field of optics” was a euphemism for Newton’s doctrine of differential refrangibility. Marat’s attempt to replace it with his own doctrine of deviability—promoting what had previously been a mere curiosity to the central principle of optics—was a clear challenge to Newtonian orthodoxy.

Marat’s response reflects disappointment, but it did not express the bitterness toward the Academy that he later displayed.[24] His resentment apparently increased over time. He later charged that the Academy had acted dishonestly in this affair. Le Roy, he asserted, had told a friend of Marat’s that he, Le Roy, had in fact written a 45-page, detailed report on Marat’s experiments, but that it had been suppressed by the geometers’ faction within the Academy.[25]

There is no independent evidence that such a report had ever existed, but it is not at all an implausible supposition. For the three-paragraph report that was actually released to have taken more than three months to prepare seemed preposterous to Marat. Had Le Roy not repeatedly assured him that the report was taking a lot of time and effort?[26] Had Cousin not told him that the reading of the report had required more than a single session of the Academy?[27] Why would so much time be needed to read three brief paragraphs?

Even if there had been no such report, the delay could well have been due to disputes between Le Roy, Cousin, and other academicians over how to formulate the report that did appear. Le Roy had previously complained openly to Marat that a “spirit of chicanery in the Academy” was making it difficult for him to write it.[28] It is conceivable that one or more members of the Academy recognized that Marat’s exposition of the deviation of light did indeed raise questions that could not be answered within the confines of the standard Newtonian paradigm. If so, that was an admission that the central leaders of the Academy were unwilling to make. Their attitude was represented by Condorcet’s later reference to “the Marat incident” as a shining example of the way the Academy should deal with “charlatans,” i.e., dismissively.[29]

In any event, Marat could hardly be blamed for believing that he had been rebuffed by a conservative priesthood of science blindly defending its entrenched orthodoxy. Was the Academy's refusal to really examine the light-bending anomaly any different in principle from the refusal of Vatican astronomers to look through Galileo's telescope? Both seemed afraid to confront empirical evidence that threatened a cherished paradigm. The Galileo tale, however, had developed into one of the central myths underlying the ideology of modern science. Galileo's telescope symbolized Truth and those who refused to look through it represented ignorance and superstition. In Marat’s case, it was the Academy of Sciences rather than the Catholic Church that proved unwilling to face up to empirical evidence.

Young and Fresnel

To assess Marat’s value as a scientist in terms of later developments in optics would be anachronistic. Nevertheless, the inappropriateness of the charlatan and pseudoscientist labels that have often been affixed to him by later writers can be appreciated by considering how the diffraction issue evolved in the following generation.

In England, about a decade after Marat's death, the following challenge appeared in the Philosophical Transactions published by the Royal Society of London:

The experiment of Grimaldi, on the crested fringes within the shadow, together with several others of his observations, equally important, has been left unnoticed by Newton. Those who are attached to the Newtonian theory of light, or to the hypotheses of modern opticians, founded on views still less enlarged, would do well to endeavour to imagine any thing like an explanation of these experiments, derived from their own doctrines, and, if they fail in the attempt, to refrain at least from idle declamation against a system which is founded on the accuracy of its application to all these facts, and to a thousand others of a similar nature.[30]

The author of this blast, Thomas Young, was mistaken in his supposition that Grimaldi’s discoveries had “been left unnoticed by Newton.” His misperception in this regard is an indication of the state of neglect into which the study of diffraction phenomena had fallen. Grimaldi had been all but forgotten.

Young’s optical investigations resulted in a theory able to account for diffraction by assuming that light is fundamentally wavelike in nature. Young’s hypothesis did not have to ignore diffraction; it could explain it, and Newton’s soap bubble colors as well, as patterns of mutual reinforcement and interference characteristic of interacting waves. At the same time, of course, Young’s theory represented the ultimate challenge to Newton’s concept of light rays as hard, massy particles.

Like Marat, Young did not receive an open-minded hearing from his contemporaries, as his angry rejoinder to their “idle declamations” against his system illustrates. Unlike Marat, however, he lived to see his ideas vindicated, though not through his own efforts.

About 1814 a Frenchman, Augustin Fresnel, began studying the problem of diffraction without knowing of either Marat's or Young's previous work. His first contributions to the Academy of Sciences, reporting his observations on the fringes of shadows cast by opaque objects, received a thoroughly negative response, especially from Laplace, J.B. Biot, and S.D. Poisson.[31]

Unlike their dismissive reaction to Marat, however, the academicians took the trouble to try to refute Fresnel and ultimately discovered they could not. The mathematician Poisson carefully studied Fresnel’s explanation of diffraction as a consequence of the wave nature of light and demonstrated that it led to an obvious absurdity: that under certain circumstances the shadow of a small opaque disk would be brighter at the center than at the edges. Fresnel concurred with Poisson’s inference, but denied that it was absurd. To the contrary, it is true; such circular shadows can indeed have bright spots at their centers. This physical fact was demonstrated in the laboratory of Fresnel’s ally, François Arago, lending strong support to Fresnel’s contentions.[32]

When the wave theory became dominant in the 1830s, the pendulum of Academic prejudice that had blindly shielded Newton’s Opticks from criticism swung in the opposite direction. Throughout the rest of the nineteenth century the Opticks was treated as an embarrassment and downgraded to the status of a minor work representing a lapse in the great scientist's judgment.[33]

Again, the point of recounting the histories of Young and Fresnel is not to credit Marat with prescience or to identify him as their predecessor in the “march toward modern science,” but to illustrate the degree to which nonscientific considerations intervened in the process of scientists coming to grips with diffraction phenomena. Until Fresnel’s theory gained acceptance, the empirical facts of diffraction were subordinated for a century and a half to various social and personal biases that prevented their recognition and due consideration.

Marat, in fact, made no direct contribution to the later discoveries by Young and Fresnel, but not because his efforts were intrinsically worthless. The blame for its lack of influence is not Marat’s; he did not suppress his own work. The Academy of Sciences did indeed function as a blind defender of orthodoxy in this affair, and its actions represented, to some degree, a lost opportunity for science.

Découvertes sur la Lumière

The fullest statement of Marat’s investigation of the deviability of light is his Découvertes sur la lumière, published in 1780. It was not his last word on the subject, however; he would continue to study and write about optics up to the eve of the Revolution. In 1784 he published a 44-page synopsis as a study guide for people taking courses on his optical theories.[34] In December of that same year his new translation of Newton’s Opticks was presented (anonymously) to the Academy of Sciences for its stamp of approval; it was published in 1787.[35] In 1785 he set out to bring to completion what he had begun with Découvertes sur la lumière. That work, he had said, was simply an “extract” of a larger work to follow that would include practical applications of his principles with regard to lens-making and other useful occupations. The Revolution intervened before he could make good on this promise, but the unfinished manuscript of the Traité d’optique is in the Bibliothèque Nationale in Paris.[36]

In 1787 he published a collection of four essays on optical problems—all had been entries in provincial academies’ competitions—as Mémoires académiques. They tackled specific problems, such as how colors are produced in soap bubbles and rainbows, but Marat explained in the introduction that all four have the same purpose: to challenge Newton’s doctrine of differential refrangibility. The essence of Marat’s optical theories, then, is best presented in his Découvertes sur la lumière.

Unlike Marat’s previous volume on fire, Découvertes sur la lumière does not bear the royal approbation that would have permitted its legal publication in France. According to the title page it was printed in London and could be purchased in Paris at the offices of the bookseller/publisher Jombert. Either Marat could not get the official censor to approve it, or he did not want to spend the time and effort to do so. Although the book certainly represented no political challenge to the crown, it is possible that its anti-Newtonian contents had alienated certain academicians enough to put its approval in doubt. It is perhaps significant that the royal censor who has earlier accepted Marat’s book on fire was Sage, a member of the commission that reviewed Marat’s optical experiments. On the other hand, his book on electricity seems to have had no problem gaining the censor’s approval two years later. Whatever the case, it is possible that Jombert was the actual publisher and the claim of London publication was simply the standard ruse employed in old-regime France to bypass official censorship channels.

Marat did not put forward a wave theory of light. Although his work was entitled Découvertes sur la lumière, he was more directly concerned with the origins of colors than with the nature of light per se. Marat had no need of the wave hypothesis, since he accounted for the bending of light at surfaces of objects by assuming the existence of specific atmospheres surrounding objects. Later, before adopting the wave theory, Thomas Young would first find it necessary to experimentally reject “the presence of such an inflecting medium in the neighbourhood of dense substances as I was formerly inclined to attribute to them.”[37]

In Découvertes sur la lumière, Marat once again utilized the familiar format of numbered experiments; the total in this book was 202. As would be expected, given the nature of the inquiry, almost all make use of the darkroom. Marat’s innovation was to bring his solar microscope to bear on the subject.

Experiment number one identifies the central phenomenon that defines the focus of the work as a whole:

When one exposes any body whatsoever to the solar rays, focused in the darkroom with the use of a simple objective lens, one sees its shadow surrounded by a luminous band that is more or less bright and more or less wide depending upon the distance that it is from the screen.[38]

Marat uses the word “aureole” to denote that luminous band. To what can the appearance of this aureole be attributed? Experiment two shows that it “does not depend upon a double refraction since it occurs no less when a steel mirror is used.”[39] Experiment three eliminates the configuration of the ambient air, which he had first suspected to be the cause, since the aureole “is no less perceived surrounding extremely thin bodies than it is surrounding spherical bodies.”[40]

After having tested and rejected two hypotheses, Marat was left with one that he believed would prove successful. The aureole was to be attributed to “the principle of attraction that brings together at the surface of a body the rays of light that surround it.”[41]

He reasoned that the rays cannot be brought together at the surface of an object unless they are subtracted from somewhere else, namely from the surrounding medium. The area farther away from the object should appear less bright, then, but in a large space the difference in brightness is generally imperceptible. Marat said that this difficulty can be overcome by making the field of light very small, which is a simple matter: “Instead of forming it outside the body, it must be formed inside.”[42] By this he meant that rather than shining a light behind an object to produce a shadow surrounded by a field of light, the light should instead be directed through a small hole in a flat card. The spot on the screen will then be the field of light and the shadow will surround it. Marat did not claim this as an original idea; Grimaldi’s classic experiments utilized a similar method, as did Newton’s, among others.

In the next three experiments he utilized this technique and in each case found the shadow surrounding the hole bordered by a bright band. He varied the size of the hole and concluded that “the rays that pass through the hole are principally attracted toward its edges.”[43]

If the hole is made very small, the luminous band circumscribes a small area. One would expect this area to be a very bright point, but it is not; it is dark. “What is the cause of this privation of light?”[44] It indicates an attraction of the rays toward the edges of the hole. This counterintuitive fact that Marat demonstrated is the inverse of the one that helped Fresnel support his case against Poisson, Laplace, and Biot several decades later.[45]

Marat’s “Perioptrics”

“From these experiments and a thousand more like them,” he said, “we conclude that bodies attract light.”[46] Marat believed that the terminology of optics should acknowledge that this phenomenon was as important as reflection and refraction. To the recognized terms “catoptrics” (signifying reflection phenomena) and “dioptrics” (signifying refraction phenomena) he proposed adding “perioptrics” to designate “the part of optics that deals with the deviation of rays of light at the edges of bodies.”[47] Marat's neologism never achieved the status of an accepted term, first of all because his optical work as a whole was suppressed, and secondly because the usefulness of such a term diminished in the nineteenth century with the rise of the wave theory of light. Nonetheless, at the time it was put forward by Marat it was a reasonable suggestion for a useful addition to the lexicon of optics.

In the course of introducing the new term, Marat stated:

No doubt the deviation of the rays of light that I have just spoken of are nothing, in truth, but an external refraction, and it should be considered as related to the same principle.[48]

This was an echo of Newton's suggestion that inflexion may perhaps be but a special case of reflection and refraction. Priestley agreed with this view and stated it more positively:

The same power that disposes the light which actually falls upon bodies to be reflected from them, or refracted into them, affects the light which only passes very near to them; some of the rays being thereby made to bend from them, which is similar to reflexion, and others to bend towards them, which is a kind of partial refraction.[49]

But whereas Newton and Priestley considered the bending of light around objects to be subordinate to refraction, Marat thought it should be the other way around: If anything, refraction was but a special case of deviation. Either way, “however similar these principles [refraction and deviation] may be, their laws are different and it is important not to confuse the phenomena.”[50] Hence the need for the term perioptrics as distinct from dioptrics.

Marat devoted considerable attention to the force of attraction that he believed underlies this phenomenon. “Since all bodies attract light,” he wrote, “each therefore has a particular atmosphere. This atmosphere becomes perceptible due to the aureole that appears to surround their shadows.”[51] As always, the ocular demonstration ranks high among the elements that count for evidence to Marat.

If the attraction that draws light to objects is at all akin to gravitational attraction, one would expect it to vary relative to the mass of the objects. Indeed, Marat believed this would be found to be so, “because it is a consistent law that the attractive force is deployed proportionately to mass.”[52] This is not the only factor, however, because “it is no less consistent a law that this force is deployed proportionately to the affinity between bodies.”[53]

Marat was apparently making some assumptions about the attractive force that are not stated explicitly here. It would seem that he thought of it as a composite of gravitational force in the usual sense with the forces that cause the smallest particles of matter to bind together: the forces of chemical affinity.

Of the two factors—mass and chemical affinity—the latter clearly seemed by far the more powerful to Marat. Experiment 31 revealed that

after having introduced solar rays into a darkroom . . . if you present on the same line, at four feet from the screen, some objects of the same dimensions but different density, you will not necessarily find the most extensive aureoles around the denser objects; in fact, some of the denser objects have much less extensive aureoles.[54]

If mass were the only consideration, the denser objects would be expected to exert a greater attractive force and would therefore have broader luminous bands surrounding them, but Marat found that not to be so. More important than mass is the kind of material the object is made of:

After a multitude of experiments of this kind it was ascertained that certain materials, such as white wood, resin, paper, cotton cloth, wax, tallow, plaster, and above all the igneous fluid, attract light more than metals do.[55]

For example, Marat compared the shadows of objects made of lead and cork that were identical in size and shape. He found in both cases that the shadows were slightly smaller than would be expected if light traveled in perfectly straight lines past the objects. However, the amount of diminution of the shadows hardly differed at all between the two objects. This illustrated that neither the density of objects nor the specific characteristics of their materials has much influence on the attraction of light.

Marat discovered another variable, however, that proved to be a more significant factor:

The size of the surfaces influences the attraction of light much more than either of the two aforementioned causes. . . . The deviation of rays tangent to the circumference of spherical bodies is related to the lengths of their circumferences, not to their masses.[56]

Regardless of the density of the material, “the attractive force always deploys itself in inverse ratio to the square of the distance.”[57] Therefore, it is always at a maximum right at the surface of an object. Since it is evenly distributed over that surface, increasing the surface area decreases the force per unit of area. “Thus the attraction of light is proportionately more intense in smaller as opposed to larger objects.”[58] This assertion is supported by experiments 32 through 35.

Which Way Does the Light Bend?

Marat’s emphasis on the attraction of light seems to place him somewhat at odds with earlier experimenters. If light is simply attracted to the objects it passes, then it would bend toward those objects and their shadows would appear smaller than if light traveled in perfectly straight lines. Marat reported that this is what he saw in the darkroom: smaller shadows.

Grimaldi’s initial reports were quite the opposite: The diffraction of light produced larger shadows, and therefore indicated that the light was somehow deflected away from the edges of objects.

Newton, it will be recalled, suggested that light is deflected both ways; that in passing close to edges of objects rays of light are “bent several times backwards and forwards, with a motion like that of an Eel.”[59]

The discrepancy between Marat’s smaller shadows and the larger shadows reported by others can be accounted for by their differing definitions of the shadow. Marat did not include what he called the aureole as part of the shadow while the other investigators did. Some of the alternating light and dark bands or colored fringes lie inside and some lie outside the ideal shadow that would be made if the light’s trajectory were perfectly straight; that is why Newton conceived of light bending backward and forward.

Marat, however, treated the bending of the light and its dissociation into colors as distinct phenomena—associated, to be sure, but not identical. To him, only the completely solid dark area counted as part of the shadow, and by that definition his claim that light always bends into the shadow and never away from it is comprehensible.

According to Marat, the colored bands outside the shadow (and even those that appeared black were really very dark blue) resulted from the decomposition of light. “All known bodies decompose light in attracting it,” he declared, offering experiment number 42 into evidence:

Place some of these bodies four feet from the screen and in the cone of light; their aureole will appear distinct. Fix this aureole carefully; it will appear to be divided into three small bands, an inside one of dark blue, an outside one of pale yellow, and a white one in the middle.[60]

He found that he could increase color production by shining light through a solid object cut in such a way that it became a grid of narrow openings (un solide découpé en réseau):

But it is important that the little slits that make it up be parallel and separated only by small intervals. Then when at three feet from the screen you expose to the solar rays a card, a metal plate, or an ivory plaque cut up in this manner, the shadow of the grid is plainly seen bordered by bands of various colors. The colors that are consistently distinguishable are blue, straw, and pink.[61]

Marat had devised what would later be called a diffraction grating. Priestley's history of optics relates that a number of investigators had found colors in the shadows of very narrow objects such as needles, wires, or thin openings between straightedges, but none are reported to have arranged such objects to form a series of parallel slits, as Marat did. If color production were believed to be a function of light passing close to edges, it was a logical step to multiply the effect by multiplying the number of edges, which is what Marat accomplished with his solide découpé en réseau.

An interesting variant is described later in the book; experiments 118 and 119 utilize “a small disk with several very thin concentric circles cut out of it.” The shadow of this device shows “each circle covered with three colored bands of equal width and intensity.”[62]

While the color phenomena brought forth by most diffraction demonstrations in the eighteenth century were modest and no doubt unimpressive to skeptical observers, Marat’s diffraction gratings could potentially have produced a more dramatic display of colors that would be harder to ignore. One of Marat’s aristocratic backers, the vicomte de Montigny, wrote an ecstatic letter to the Journal de Littérature, des Sciences et des Arts raving about the colorful magic Marat could work with “white cards cut up in a certain manner.” The “brilliant bursts of color and the bewitching nuances,” the vicomte exclaimed, outshine “anything that Holland, anything that the Amazon River, anything that India can offer in their most magnificent flowers, butterflies, and birds.”[63]

If the Academy's commissioners had been prone to discount Marat's claims, the colors produced by his novel apparatus may have given some of them pause. If Le Roy did indeed struggle over preparing his report, his difficulty might well have arisen from trying to interpret effects produced by the diffraction grating according to orthodox Newtonian principles. This, however, is a matter of speculation.

How Many Primary Colors Are There?

The first of Marat's two frontal assaults on Newtonian orthodoxy had to do with the number of primary colors. Marat disputed the prevailing belief, based on Newton's teaching, that there are seven primary colors. The truly primary colors, he said,

are limited to yellow, red, and blue, because when the light rays to which any isolated body is exposed are decomposed, they always come to have only these three different colors, whether it is in the darkroom or outdoors, by the light of the sun or that of a candle.[64]

Marat believed, as Newton had, that different colors of light are composed of qualitatively different kinds of rays. But whereas Newton believed that there could be different kinds for every perceptible color, Marat held that there could only be three: one kind for yellow light, another for red, and another for blue. All other hues are composites of these, he said, including the indigo, violet, orange, and green that the Newtonians considered primary. “Even the prism gives no more than three inalterable colors; all the others are decompositions of those.”[65] This is shown by setting up a prism demonstration in the usual way, but moving it back and forth, toward and away from the screen. As the prism moves, the green band (for example) can be seen to weaken and finally disappear into the encroaching yellow and red bands.

Continuing to move the prism in the same direction results in even the yellow band fading away into the encroaching blue and red bands. This seems to imply that among the three primary colors, two of them, red and blue, are more primary than the third.

C.C. Gillispie, although critical of Marat's contentions regarding the primary colors, acknowledges that they merited more attention than the commissioners of the Academy of Sciences gave them.[66]

Newton’s treatment of primary colors was certainly vulnerable, but Marat never gave his criticism any development. There is no hint of the distinction Goethe called for between the study of color as produced in light and as perceived in the eye.[67]

In fact, however, Marat did call attention to the physiological basis of color perception:

Properly speaking, the colors consist of the elemental impressions of light on the organ of sight, because the light per se does not include any color within itself.[68]

The subtle fluid of light, he continued,

is composed of parts that differ essentially among themselves, since they consistently affect the organ of sight in different manners. Thus, each ray of light is composed of three others, one of which produces the sensation of yellow, another that of red, and another that of blue; from their various combinations result a great number of composite sensations.[69]

Marat did not dwell on these points. Découvertes sur la lumière was, after all, a book about physics rather than physiology. It is worth recalling, though, that Marat's earlier publications in England included a tract on eye disease and revealed considerable knowledge (by contemporary standards) of the physiology of vision.

The Origin of Color

Marat’s second major challenge to the Newtonians concerned the role of the prism in producing color. Newton’s most admired experiment was the one where he showed that white light refracted through a prism divides up into a spectrum of light of various colors. He clinched his argument by showing that the beams of colored light could be refracted in an inverse manner to reproduce the original white light. This experiment was so straightforward that Newton’s interpretation seemed self-evident to later generations.

Although the Newtonian explanation had attained the force of dogma and had remained virtually unchallenged for more than half a century, Marat was not convinced. The appearance of color, he contended, owes absolutely nothing to refraction; it is entirely due to the decomposition of light at the edges of objects. The colors that Newton saw on the wall did not originate in his prism but in the hole in the window shutters where the light entered the room. The light was decomposed into colors as it passed the edges of the hole; the colors already existed before the light reached the prism.

Marat anticipated some objections to this hypothesis. Admitting the light by means of a larger hole can allow white light—light that has not been decomposed—to pass through the prism; when that light reaches the screen it, too, will be seen to have separated into a spectrum of colors. Were those colors not produced by the prism?

Yes, Marat replied, but not in the way Newton thought; not by means of refraction. In this case the colors are decomposed by the light’s deviation at the edges of the prism itself. As the red, blue, and yellow light then travels through the prism, it is refracted, but not differentially, as Newton would have it; all three are refracted exactly the same amount.

If some of them appear afterwards to have been refracted more than others, it is because their angles of incidence were unequal.[70]

Marat also used this explanation to account for why the images produced by prisms appear far more colorful than those produced by edges of objects. The light in the prism experiments is decomposed twice; once at the edges of the window hole and again at the edges of the prism. The diagram below illustrates the differences between Newton’s and Marat’s theories of how colors are produced.[71]

As proof of his contention that Newton was wrong about differential refrangibility, Marat proposed to measure and compare the focal distances of “the various rays of which light is composed.” The ideal way to do this, he acknowledged, would be to use pure rays of blue, red, or yellow light. Unfortunately it is not feasible to do so, “since it is extremely difficult to gather a bundle of rays of each kind large enough to cover the entire surface of a lens.”[72] As an alternative to “rays decomposed at the edges of objects” he suggests using “rays decomposed at their surface; that is to say, the heterogeneous reflected rays.”[73] Red reflected rays, for example, are those that are seen when looking at a red object, such as an apple.

For experimental simplicity, Marat utilized colored disks; one red, one blue, and one yellow. The images of these disks were projected through a lens onto a plane parallel to the disk. “Since the focal distances are the same no matter what the color of the bodies, the heterogeneous rays are equally refrangible.”[74] Q.E.D.

Marat noted that Newton had likewise tried to measure focal lengths of light of different colors, but reported an exactly opposite result: that the focal lengths were not the same. “I am very far from suspecting that great man of untruthfulness,” Marat declared, “but I cannot fail to point out that the manner in which he proceeded was very defective.”[75]

It is here that Newton’s partisans must have found Marat's presentation most offensive. Marat expressed wonder that Newton could have repeated his prism experiments for thirty years, and that other physicists had repeated them for another fifty or so, without understanding where the colors were coming from: “It is regrettable that such a great genius wasted so much time in vain in this research.”[76]

As for his own theory attributing all color separation to deviation rather than refraction, Marat stated:

I know that this assertion is entirely opposite to that of all authors who have written on this subject, but it is founded on a multitude of simple, clear, and consistent experiments, whereas the other authors have established their opinion only on the results of experiments that are complicated, illusory, and based upon the most superficial understanding of a principle that plays a great role in nature.[77]

These were strong words, and the “other authors” could not have been expected to find them congenial. Nonetheless, Marat’s demeanor should not be considered sufficient cause for other scientists’ refusal to come to grips with his critique of Newtonian optics. His experiments did indeed demonstrate significant anomalies for the accepted paradigm; Marat was justified in claiming that the apparent bending of light at the edges of objects is “a principle that plays a great role in nature.” The rejection of Marat’s ideas seems to have been based more upon personal antipathies than upon rational scientific criteria.

Addendum: Goethe and Marat

Wolfgang von Goethe devoted some thirty years to developing and defending a theory of colors in opposition to the received Newtonian doctrine on the nature of color. The explanation of color phenomena that Newton had advanced in his Opticks was so impressive to most scientists that it had tended to discourage further inquiry. Goethe, however, challenged the Newtonian orthodoxy in a long ideological struggle that culminated in the publication of his massive Zur Farbenlehre in 1810. Historians of science have traditionally dismissed Goethe's color theories as bad science, but recent studies have begun to force a new appreciation of Zur Farbenlehre.[78]

A central focus of Goethe’s critique was the Newtonians’ erroneous treatment of color as solely a physical property of light. If that were true, then color would be perfectly determined by some measurable quantity, such as Newton’s “differential refrangibility” or, later, wavelength. To measure that property of light would be to know all there is to know about the color it produces. The reduction of color to a quantifiable aspect of light is seductive in its simplicity, but Goethe demonstrated that it simply does not accord with a great body of observational and experimental fact.

The Newtonian reduction leaves the undeniable facts of color perception out of account. Goethe’s critique pointed the way toward understanding that the study of color cannot be exclusively restricted to the science of physics, but must be extended to the sciences of physiology and psychology as well. While light of varying measurable characteristics does exist external to the eye and brain, color does not.

The limitations of the Newtonian color doctrine exemplify the more general fallacy inherent in reductionism: the habit of declaring that a complex phenomenon is “nothing but” an aggregate of simple parts. Much of the anger that Goethe expressed toward the Newtonians derived from his understandable irritation at seeing the mantle of science being claimed exclusively for the narrow metaphysics of the “nothing-but.”

It is worth noting a common theme in the traditional dismissal of both Goethe's color theory and the Mesmerists' animal magnetism. In both cases, scientific orthodoxy held that only objective phenomena qualify as worthy of scientific attention, and to be objective a phenomenon must exist “out there”; i.e., external to the human observer. By this criterion neither the crises induced by the Mesmerists in their patients nor color per se are objective. The refusal to acknowledge their reality and the need to investigate them does not indicate scientific maturity, but conservatism and narrowness of view.

Goethe devoted considerable space in Zur Farbenlehre to critically examining the ideas of his predecessors on the subject of colors. He summarized the central theses of Marat’s optical theories in five pages.[79] In addition to Découvertes sur la lumière, Goethe cited two of Marat’s shorter works on optics as well.[80]

Goethe believed that Marat’s work had constituted a significant challenge to the Newtonian hegemony in the field of optics. He hailed Marat’s opposition to the “accepted teachings” of the Academy of Sciences. As for the Academy’s commission that had passed judgment on Marat’s ideas, Goethe considered its “expert opinion” to be “an example of bad faith on the part of those confronted with something that cannot be totally denied, in an attempt to at least do away with it.”[81]

In Goethe's opinion, Marat's writings revealed an admirable degree of “perceptiveness and insight” on his part:

As far as we are concerned, we think that Marat has, with a great deal of intelligence and good observations, brought the doctrine of color . . . to a very critical point, worthy of more observations, the clarification of which we can hope will lead to genuine progress in the doctrine of color.[82]

Marat’s and Goethe’s ideas on colors were by no means identical, however. “Those who are familiar with our views,” Goethe wrote, “know where we stand with regard to the work of this researcher.”[83] One of Goethe’s main criticisms of the Newtonians was their notion that white light is a composite that can be analyzed into rays of various colors by refraction through a prism. Goethe held that white light was primary and indivisible. Marat substituted deviation for refraction as the agent of decomposition, but the very notion of decomposition was unacceptable to Goethe.

On the other hand, Goethe believed (in much the same way that Aristotle had) that color phenomena arise from a contrast of light and darkness, or black and white. Since Marat’s perioptrics drew attention to color production at the edges of objects—that is, at the juncture between a dark object and the light—Goethe felt that Marat’s doctrine represented an improvement over Newton’s.

Goethe was no more successful than Marat in breaking through the wall of academic prejudice that shielded the Newtonian doctrine and sustained its hegemony. The recent scholarship that has recognized valuable and sophisticated insights in Goethe’s ideas about color puts Marat’s scientific work in a more favorable light as well.


[1] The terms “diffraction” and “inflexion” will be used interchangeably here. Its discoverer, Grimaldi, used the word “diffraction”; Newton, Marat, and Priestley all preferred “inflexion.” Fresnel went back to “diffraction,” which then became the universally preferred term.

[2] F. M. Grimaldi, Physico-Mathesis de Lumine Coloribus et Iride.

[3] I. B. Cohen says, “Joseph Priestley’s value judgments are notable because he was a great scientist and a splendid historian.” Priestley’s History and Present State of Electricity “has the particular merit of expressing the point of view and the foci of interest of the third quarter of the eighteenth century.” On the other hand, “it should be pointed out . . . that Priestley’s history of optics is a poorer book than his history of electricity.” Cohen, Franklin and Newton, 429–30.

[4] Priestley, History and Present State of . . . Vision, Light, and Colours, 171.

[5] Ibid., 317.

[6] Ibid., 351.

[7] Newton, Opticks (Query 31), 400.

[8] Ibid., 338–9.

[9] Ibid., 317.

[10] Cohen, “Preface” to Newton’s Opticks, xxxv.

[11] Newton, Opticks (Query 29), 370.

[12] Ibid. (Query 3), 339.

[13] Priestley, History and Present State of . . . Vision, Light, and Colours, 521. The spellings are Priestley’s. The scientists he discusses are Giacomo Filippo Maraldi (1665–1729); Jean Jacques Dortous de Mairan (1678–1771); Etienne François Dutour de Salvert (1711–89); Claude Nicolas Le Cat (1700–68); and Pieter van Musschenbroek (1692–1761).

[14] Ibid., 520–40.

[15] Ibid., 780.

[16] Ibid., 780–1.

[17] Marat, Découvertes sur la lumière, 5.

[18] Maillebois, Sage, and Montigny were the other members of the commission. Gillispie identifies Montigny as an honorary member of the Academy, J. C. P. Trudaine de Montigny (Science and Polity, 304), which is impossible because he died in 1777. The Montigny in question was in fact a regular member, the mathematician-engineer Étienne Mignot de Montigny.

[19] See Correspondance de Marat, 5–7 and 58–64.

[20] Marat, Découvertes sur la lumière, 3. The commission’s report was originally printed in the Registres de l’Académie des Sciences, dated 10 May 1780.

[21] Marat, Découvertes sur la lumière, 3–4.

[22] Ibid., 5.

[23] Ibid., 6.

[24] Most notably in Les Charlatans modernes.

[25] Letter to Roume de Saint-Laurent (20 November 1783), in Correspondance de Marat, 66–7.

[26] Correspondance de Marat, 58–61.

[27] Ibid., 61.

[28] Ibid., 6. Letter of Le Roy to Marat (13 February 1780).

[29] Hahn, Anatomy of a Scientific Institution, 158. Original source: Bibliothèque de l’Institute, MS. 876, fols. 95-6.

[30] Thomas Young, “The Bakerian Lecture: Experiments and Calculations Relative to Physical Optics” (Philosophical Transactions of the Royal Society of London XCIV [1804]), 11; emphasis added.

[31] Jean Baptiste Biot (1774–1862), mathematician, elected to the Academy of Sciences in 1800; Siméon Denis Poisson (1781–1840), physicist, elected to the Academy of Sciences in 1812.

[32] John Worrall has recounted this episode—and debunked the traditional account—in “Fresnel, Poisson and the White Spot: The Role of Successful Predictions in the Acceptance of Scientific Theories” (in The Uses of Experiment: Studies in the Natural Sciences, edited by Gooding, Pinch, and Schaffer). According to Worrall the demonstration of the white spot did not force a dramatic, immediate about-face on the part of the academicians in favor of Fresnel’s wave theory of light, as is often suggested. It was simply another nail in the coffin, so to speak, of the Newtonian paradigm, perhaps no more important than the century-old problem of diffraction. See also, in the same volume, Geoffrey Cantor’s comments on Worrall’s paper in “The Rhetoric of Experiment.”

[33] See Cohen, “Preface” to Newton’s Opticks, xi.

[34] Marat, Notions élémentaires d’optique.

[35] Marat’s translation of Newton’s Opticks is discussed in Chapter 2 on this website.

[36] Bibliothèque Nationale. Manuscripts: “Nouvelles acquisitions françaises” 309.

[37] Young, “Experiments and Calculations Relative to Physical Optics,” 11, 12.

[38] Marat, Découvertes sur la lumière, 1.

[39] Ibid., 1–2.

[40] Ibid., 2.

[41] Ibid.

[42] Ibid.

[43] Ibid., 3.

[44] Ibid., 4.

[45] Fresnel predicted the black spot as well as the white spot: “Fresnel had found that his theory entails that if light from a point source is shone on an opaque screen in which there is a small circular opening, then at certain points beyond the screen but along the axis of the aperture (that is, the extension of the line from the source to the centre of the aperture) there is total darkness. This ‘black spot’ prediction is ‘complementary’ to the white spot case—it is just as counterintuitive as the latter and its empirical success just as unexpected and remarkable.” Worrall, “Fresnel, Poisson and the White Spot,” 145.

[46] Marat, Découvertes sur la lumière, 5.

[47] Ibid., 6.

[48] Ibid.

[49] Priestley, History and Present State of . . . Vision, Light, and Colours, 520; emphasis in the original.

[50] Marat, Découvertes sur la lumière, 6.

[51] Ibid., 13.

[52] Ibid., 22.

[53] Ibid.

[54] Ibid., 23.

[55] Ibid., 23–4.

[56] Ibid., 29–30; see experiment 41.

[57] Ibid., 24.

[58] Ibid.

[59] Newton, Opticks (Query 3), 339.

[60] Marat, Découvertes sur la lumière, 30.

[61] Ibid., 31–2.

[62] Ibid., 66.

[63] Journal de Littérature, des Sciences et des Arts, vol. II (1781), 230–1.

[64] Marat, Découvertes sur la lumière, 51.

[65] Ibid., 52.

[66] Gillispie, Science and Polity, 307.

[67] Ibid., 328. Gillispie was commenting on Marat’s Mémoires académiques, not his Découvertes sur la lumière. On Goethe, see the addendum at the end of this chapter.

[68] Marat, Découvertes sur la lumière, 133.

[69] Ibid., 133–4.

[70] Ibid., 67.

[71] Source: Mme. M. A. Tonnelat, “The Spread of Newtonian Optics,” in René Taton, The Beginnings of Modern Science, 459.

[72] Marat, Découvertes sur la lumière, 67.

[73] Ibid.

[74] Ibid., 69.

[75] Ibid., 70.

[76] Ibid., 77.

[77] Ibid., 99–100.

[78] C.C. Gillispie wrote: “It is impossible to read the Farbenlehre without an acute sense of embarrassment at the painful spectacle of the author, a great man, making a fool of himself” (Gillispie, The Edge of Objectivity, 196). A number of scholars have recently reinvestigated this work of Goethe’s and have concluded that he was not so foolish after all; see Sepper, Goethe Contra Newton; and Amrine, Zucker, and Wheeler, Goethe and the Sciences: A Reappraisal.

[79] Goethe, Zur Farbenlehre, vol. II, 601–6.

[80] The other two works were Découvertes de M. Marat sur le feu, l’électricité, et la lumière and Notions élémentaires d’optique. Goethe cited the original French edition of Découvertes sur la lumière but also noted Weigel’s 1783 German translation.

[81] Goethe, Zur Farbenlehre, vol. II, 605.

[82] Ibid.

[83] Ibid.