PRINCIPLES AND HYPOTHESES OF NEWTON’S OPTICS

S. I. Vavilov, Moscow.

Ego vero incerta certis miscere nolo.
I. Newton.

The words placed above were written by Newton in 1671, in his first memoir; the more decisive “hypotheses non fingo” appeared in the second edition of the Principia, in 1713, toward the end of his life. The rule—not to mix conjectures with certainties, hypotheses with principles—was unfailingly observed by Newton. But “hypotheses non fingo” is only the conclusion of many years of experience, a method indicated by the old Newton to the young generation. Newton himself devised no few hypotheses, but they are always sharply separated from what is certain, from principles and theory. Newton’s hypotheses are set forth in the memoir of 1675, printed only 30 years after his death, in the Questions of the Opticks, outwardly quite detached from the main text and by their very heading containing something uncertain, and, finally, in private letters to Boyle, Bentley, Burnet, and others, and in theological writings. The official part of Newton’s writings—the Principia, the main text of the Opticks, the Optical Lectures, the mathematical works, and the memoirs printed in the Philosophical Transactions—contain no hypotheses, at least no intentional ones. Newton’s hypotheses are temporary mechanisms used for discovering principles and then removed as unreliable or unnecessary. Newton also indicates another, popularizing meaning of his hypotheses. In the memoir of 1675 he wrote: “I have found that some, whom I cannot convince in my ...”

...opinion, speaking abstractly about the nature of light and colors, would easily have agreed with him, had I explained my reasoning by some hypothesis. For this reason I thought it appropriate to send you a description of the details of a hypothesis whose only purpose is to explain the memoir being sent along with it. I myself shall accept neither this nor any other hypothesis...” Having removed, or rendered harmless, hypotheses, Newton secured for his scientific legacy that durability which the further development of physics has not destroyed and cannot destroy. Newton’s principles are as long-lived as the infallible experience of which they are the equivalent; they may be supplemented, generalized, subjected to some correction, but in their foundation they are indestructible.

Fig. 1. Monument to Newton in Cambridge.

In the quarter of a millennium that has passed since Newton’s first works, the relations between principles and hypotheses as methods of natural science have become completely peaceful. As flawless examples of the physics of principles there developed mechanics, thermodynamics, electrodynamics, the theory of relativity, and alongside them models of the physics of hypotheses: the molecular theory, the theory of electrons, the optics of Young–Fresnel, and others. Sometimes a hypothesis became a principle, a certainty (atoms). Theories arose that immediately made use of both methods, in which there are both principles and hypotheses (Bohr’s theory). Both methods proved necessary, but they are still very far from merging into that single physics toward which people strove in the seventeenth century (Descartes, Newton).

Especially in optics, with which Newton began, the situation in general remains almost the same as in his time. The hypotheses of waves and corpuscles still contend; compromise solutions are still being sought, and the principles—the properties of light—are not absorbed in their entirety by any single hypothesis. In what follows, the principles and hypotheses of Newton’s optics are recalled, and their subsequent historical fate is briefly outlined.

1. The Origin of Newton’s Optical Works

The source of Newton’s scientific pursuits, in which three principal channels intersect—optics, celestial mechanics, and mathematical investigations—was the reflecting telescope. The search for its perfect form...

of optical glass with the least aberrational error—the probable practical occasion for Newton’s first geometrical work. The discovery of the dispersion of light was a direct consequence of work on improving telescopic glass. The very object of the telescope—the planets and their satellites—drew Newton’s attention to celestial mechanics. Finally, the long chemical investigations, of whose results we know very little, initially had as their aim the search for alloys suitable for making the metallic mirrors of reflectors. These chemical experiments later proved useful to Newton at the London Mint. Thus it is natural to seek the external occasion for the development of Newton’s thought in the technical problem of improving telescopes.

Fig. 2. Newton’s telescope.

It is difficult to establish any strong influences upon Newton, or any continuity, except perhaps for the mathematical tradition of Barrow. Newton read Descartes, Kepler, de Dominis, but only negligible traces of these books can be found in Newton’s first optical memoirs. He set about studying nature as though nothing had been done before him. Descartes’ first principle: “For the investigation of truth it is necessary, once in one’s life, to doubt as far as possible all things,” was carried out by Newton to a greater degree than by Descartes. But “ideas were in the air”; if one cannot speak of the influence of individual persons, then the general tendency of the age is beyond doubt also in Newton’s exceptional activity. It is enough to compare several dates in the history of optics in the seventeenth century:

1660: Grimaldi in Italy discovers the diffraction of light.
1665: Hooke in England describes interference phenomena in thin plates.

1666–1667. Newton discovers the dispersion of light and simple colors.

1. Bartholinus in Denmark discovers the double refraction of Iceland spar.

2. Newton proves the periodicity of light.

3. Rømer in Paris determines the speed of light.

In the course of 15 years, by different people, who knew almost nothing of one another, in different countries, the foundations of physical optics were laid and almost all the principal properties of light were discovered. In this sense Newton was a man of his epoch.

Newton’s optical writings are numerous. In 1672 his first memoir, “A Theory of Light and Colors,” was printed; in 1675 another large memoir was presented to the Royal Society, containing a hypothesis on the nature of light and a description of experiments with interference rings1. In the interval, in the Philosophical Transactions, he carried on a lengthy polemic with his numerous opponents. After Newton’s death, in 1729, his “Optical Lectures,” delivered at Cambridge in 1669, 1670, and 1671, were published from the manuscript. In 1704 Newton for the first time published his Opticks. In it are gathered almost all of Newton’s investigations in the field of luminous phenomena. Finally, the mathematical theory of the refraction of light was set forth by Newton in the Principia; there, too, are found other observations of an optical character, for example concerning light pressure. Newton’s correspondence also contains a large amount of optical material, relating in particular to questions of physiological optics. Newton’s optical writings, with the exception of the memoir of 1675 and the letters, were published in full in 1749 in Padua as a separate book in Latin.

2. The Principle of the Immutability of Simple Color

In Newton’s method of principles there are two sides—the analytical and the synthetical: the finding of the principles themselves and the derivation from them of mathematical consequences. The first of these is experimental, the second mathematical. In the Principia, in the field of mechanics, both tasks were carried out. In the Opticks only the first part was done—the analytical one: the principles, the fundamental properties of light, were found. Fontenelle called Newton’s work the “anatomy of light.” In the changes of daylight, in the constant changes of chromaticity and brightness, Newton found the invariable—simple colors. From them any light is composed, and they are constant, a kind of atoms of optics. “The species of color,” Newton wrote in his “doctrine” of 1671, “belonging to each separate kind of rays, is not changed either by refraction or by reflection from natural bodies,

by any other cause which I could observe.” The green color of verdigris and the red of azure, when illuminated through the monochromator by the corresponding light, proved a complete surprise both to Newton and, all the more, to his contemporaries and descendants. Even in the eighteenth century the echo of this astonishing discovery had not died away. The invariability of simple colors was celebrated in verse.^1

Mais quoi? De ces rayons la subtile structure
Ne peut ni s’altérer, ni changer de nature.
L’art ne la détruit point, et des efforts vainqueurs,
Le rayon rouge ou bleu conserve sa couleur.
D’eau, de lumière, d’air la plus faible parcelle
Ne peut être détruite. Oh, Sagesse éternelle
Tout Être corporel, de tes trésors sorti,
Par ton pouvoir lui seul peut être anéanti.

From the last lines it is clear that even poets drew from this the conclusion as to the corporeality of light, comparing light with atoms: the same conclusion, though in an extremely cautious form, was expressed by Newton in his memoir.

The invariability of simple color is the first and chief principle of Newtonian optics. With what precision and reliability was it established? Apparently, the yellow tincture of nephritic wood, which glows with a blue color in daylight (the fluorescence of aesculin), caused Newton no small difficulty. If it had been possible to illuminate the tincture with pure extreme violet light, Newton’s principle, at least for a physicist of the seventeenth century, would have been violated: under violet illumination a blue glow would have appeared. But Newton’s monochromator proved insufficiently perfect, although he did use a collimator arrangement with a narrow slit; under homogeneous illumination Newton did not notice fluorescence, and the principle was saved. We have before us a rare example of how the imperfection of an experiment promotes the development of science. It is hard to imagine the confusion of optical conceptions that would have arisen had Stokes’s shift been discovered in the seventeenth century.

Newton judged the constancy and change of color by coloration and refraction, i.e. the principle was established with an accuracy scarcely exceeding 10 μμ, or approximately 1–2 percent of the wavelength. What happened to Newton’s principle over the 250 years of the development of optics? Was it confirmed with greater accuracy, or did it undergo modifications? Both occurred.

^1 Dulard. La grandeur de Dieu dans les merveilles de la nature, poème. Paris, 1758, p. 29. Russian translation: “But what is this? The subtle essence of these rays cannot change according to its nature! No art is able to destroy it, and the red or blue ray preserves its color, overcoming all efforts. The smallest particle of water, light, air cannot be destroyed. O eternal wisdom, everything corporeal that has issued from thee can be annihilated only by thy power.”

For stationary mirrors and refracting bodies in the visible region of the spectrum, the color of the ray (more precisely, its frequency) remains unchanged with a colossal degree of accuracy. This can be verified by the simplest interference experiment: let light from a luminous point \(S\) (Fig. 3) enter the eye \(P\). Part of the beam goes directly; another part, coherent with it, is reflected from the mirror at \(A\). The eye observes interference fringes. If, upon reflection from the mirror, even a small change in the frequency of the light occurred, then rays of different frequencies would interfere at \(P\), and “beats” would arise, i.e. the fringes would appear to be moving. A continuous train of waves is emitted only for approximately one hundred-millionth part of a second; therefore, for a small change in frequency, the motions of the fringes cannot be perceptible; instead, the interference fringes would be blurred, they would become less sharp or would practically disappear altogether. It is not hard to calculate that if the wavelength of visible light changed upon reflection by \(10^{-5}\)—\(10^{-6}\ \mu\mu\), then the blurring of the fringes would become noticeable. In experiment this does not occur, and consequently it may be asserted that Newton’s principle is fulfilled with an accuracy of approximately one millionth of a percent (of the wavelength). Direct spectroscopic observation confirms Newton’s principle with an accuracy of approximately one hundred-thousandth of a percent.

Fig. 3.

The theoretical meaning of the principle is immediately clear in the wave theory of light: it is an obvious result of the theory of forced oscillations. But on the basis of the same wave theory, Newton’s principle requires correction for moving systems (the Doppler–Fizeau–Michelson effect). A. A. Belopolsky’s experiments with multiple reflection of light from moving mirrors showed this in direct experiment1. The color, or wavelength, changes appreciably upon reflection from a moving mirror. Recently Schrödinger has shown that the Doppler effect follows not only from the wave theory, but also from the theory of light quanta, if, while asserting the conservation of energy and momentum, one postulates the invariance of the constant \(h\).

The Doppler effect, of course, does not eliminate Newton’s principle; it only generalizes it to the case of moving systems. We have before us a typical case of the evolution of a principle.

Much more sensitively, in its very essence, Newton’s principle is affected by the Compton phenomenon2. According to Compton’s theory—

Debye, a light ray, being scattered by free or weakly bound electrons, undergoes a percentage change in wavelength:

\[ \frac{\Delta\lambda}{\lambda}=0.00482\,\frac{\sin^2\frac{\theta}{2}}{\lambda}\,\mu\mu, \]

where \(\theta\) is the angle between the incident and the reflected ray. The theory has been splendidly confirmed by experiment. The change of wavelength, or of color, may attain colossal percentage values for rays of high frequency, changing by a factor of two, three, or dozens. For the visible region the percentage change is vanishingly small and lies beyond the limits indicated above. Compton’s theory to some extent unites the phenomena of light scattering and fluorescence (or resonance radiation). In both cases, in the “collision” of a quantum with an atom, a displacement of an electron in the atom takes place, and the energy acquired by the electron is subtracted from the quantum \(h\nu\); the postulate of the constancy of \(h\) leads to the necessity of a decrease in \(\nu\). From this point of view, Newton’s experiments with tincture of guaiacum wood—a remote prototype of Compton’s experiments. In any case Newton’s principle proved to be only a special case of a broader principle, in its general form little resembling the principles of constancy. But, like every principle based on exact experiment, it has only been generalized and has retained its real force within definite limits.

3. The principle of periodicity of light.

Grimaldi, in the treatise Physico-Mathesis de lumine, coloribus et iride (Bologna, 1665), was the first to suspect the possibility of interference phenomena: “Sometimes light makes the surface of a body, already illuminated earlier, darker” (prop. XXII). He adduces in evidence experiments somewhat similar to Young’s well-known experiments with two apertures. But the darkening observed by him was, obviously, of diffraction origin; under the conditions of his experiment pure interference could not be observed. With Newton the opposite occurred. He found a pure interference phenomenon in the dark and bright rings, in thin and thick plates, but did not recognize in it a violation of the principle of superposition of intensities. His “energetic” interpretation of the dark and bright rings is clear from Fig. 4 (p. 94), taken from the second book of the Opticks. The dark rings correspond to the absence of reflection; in these places the light passes through. There is no violation of superposition; there is only an alternation of transmissions and reflections. The principle of superposition is confirmed by ordinary experience (for incoherent beams), and Newton had no grounds to suppose

possibility of its violations. Only since the doctrine of wave motion took on real forms and the concept of coherence became clear has a local violation of the superposition of light become possible in principle. For Newton, the interpretation of the rings as alternating transmissions and reflections was the only one. Subsequently, Euler explained Newton’s rings from the point of view of the wave theory by the resonance of thin layers to the incident waves. The alternation of rings was interpreted as overtonal resonance. But even in this conception Newton’s energy scheme was the only one. Resonating layers give reflected light; nonresonating ones transmit it. In our time, of course, it is not difficult to refute Newton’s scheme photometrically or, for example, by the following experiment. If the layer between

Fig. 4.

the lens and the glass is filled with a fluorescent solution, then, according to Newton, the fluorescence should have alternating brightness (according to the law of the rings). Where a bright ring is visible in the reflected light, the solution inside the gap absorbs, approximately, twice as much light as in the neighboring regions. The experiment gives no fluorescence rings and, consequently, Newton is not right. Thus, having seen interference, Newton did not discover it, because for this a hypothesis, or an experiment, was needed which in Newton’s time was difficult to carry out.

But, without finding interference, Newton discovered the periodicity of light; it appeared with the precision and simplicity of the law of alternation of the rings. With astonishing thoroughness for his time, Newton measured the lengths of the periods for different colors (for the boundaries between the colors of the solar spectrum), compared the results for thin and thick plates, and obtained identical figures. The table gives Newton’s data, recalculated in modern terms, for the boundaries of certain colors and compares them with the figures for wavelengths by which these boundaries are now estimated:

How did Newton interpret his new discovery? In its final form, in the Optics—as an empirical principle: “Every ray of light, in passing through a refracting surface, assumes a certain temporary structure, or state, which returns again at equal intervals as the ray proceeds; each time this state returns, it disposes the ray to pass through; in the interval between the returns of such a state the ray is reflected... The returns of the predisposition to reflection in the ray I call fits of easy reflection, and the predispositions to transmission—fits of easy transmission; the space traversed between each two returns I call the interval of the fits... I shall not here examine wherein a predisposition of this kind consists, whether it consists in a rotary or vibratory motion of the ray, or of the medium, or in something else. For me it is enough of the simple discovery that rays of light are disposed to refraction or reflection by some cause, or by something else.”

The principle of periodicity has survived to our day in full inviolability; only the “intervals of the fits” have come to be called wavelengths. This is the fundamental property of light, uniting the whole diversity of radiations from radio-telegraph waves to the millimicron penetrating cosmic rays. Dividing Newton’s “interval” by the speed of light, we obtain the frequency, which, according to Newton’s first principle, must remain unchanged. Classical wave theory gave a simple interpretation of frequency. In quantum theory the frequency of light is a mysterious, purely empirical factor, the quotient of the division of the quantum energy by the constant $h$.

The method for analyzing light frequencies—spectroscopy—was to a considerable degree created by Newton. He indicated all three methods of decomposing light: refraction, interference, and diffraction.

The prism with a collimator, slit, and lens was the first model of a spectroscope; Newton’s rings were an interference apparatus, by means of which the first spectral [[unclear: continuation cut off at bottom of page]]

table cited above; finally, the slit between the razor blades—a prototype of the diffraction grating. Newton devised and used, when great homogeneity of light was required, a collimating arrangement, and clearly understood the conditions for increasing resolving power. It is unclear why he did not discover the dark lines in the solar spectrum before Wollaston.

4. Diffraction.

The diffraction of light was discovered by Grimaldi. The description of his experiments appeared in a posthumous treatise printed in 1665. Grimaldi gives a somewhat vague qualitative explanation of bending, comparing light with sound. Newton had not read Grimaldi’s book, at least not before 1675, and cited Grimaldi as presented by Fabri, Grimaldi’s opponent. The immediate occasion for Newton’s own diffraction experiments was the work of Hooke, who, likewise knowing nothing of Grimaldi, laid claim to the discovery of bending. Newton did little work on diffraction. His experiments were, to a considerable extent, a repetition of Grimaldi’s experiments. The step forward was the quantitative study of the phenomenon, as always with Newton, and the application of the idea of the complexity of white light. To explain colored diffraction fringes Newton carried out experiments in monochromatic light. He showed that the substance of the diffracting body does not affect the character of the phenomenon. “In making these observations,” Newton concludes the description of his experiments in the Opticks, “I intended to repeat them with greater accuracy and care, and to make new experiments... However, at that time I was interrupted in my work and now have no opportunity to take up the investigations again. Leaving this part of my work unfinished, I wish in conclusion to propose some questions so that others may investigate this subject further.” From this point begin the famous Queries of the Opticks.

What could diffraction have been for Newton, given his adopted rule “not to mix conjectures with certainties”? Only a principle. Light, passing near bodies, bends, and the rectilinearity of its motion is violated. Hence the first question of the Opticks: “Do not bodies act upon light at some distance, bending the rays of light? And will not this action, other things being equal, be the stronger the smaller the distance?” The supposition that light rays are deflected when passing near material bodies was expressed by Newton many times; it is stated in the Principia and mentioned in letters to Boyle. Newton explained regular reflection by the action of bodies on light at a distance (the natural “roughness” of every surface would otherwise turn every reflection into a diffuse one). We were brought up on the wave theory of light, but if one tries to

at the moment distract ourselves from any theory and formulate the phenomenon of diffraction in a purely empirical way, we shall hardly be able to invent anything other than “the deflection of light by material bodies.” Just as in mechanics a deviation from rectilinearity is for us a sign of the presence of a force, so in optics diffraction was for Newton proof of the action of a body upon light at a distance (in 1675 this action was explained by the hypothesis of the ether). Newton knew that behind this lay either proof of the materiality of light, or at least a hypothesis about this materiality. Therefore the conclusion is placed not in the text of the Opticks, but in the queries. The 4th query of the Opticks contains, in laconic form, a general theory of diffraction, reflection, and refraction: “Do not the rays of light which fall upon a body and are reflected or refracted in it begin to bend even before they reach the body, and do not reflection, refraction, and inflection occur by means of one and the same force, manifesting itself differently in different circumstances?”

Diffraction is a fundamental, not accidental property of light, a principle, as Grimaldi already emphasized. It is a necessary characteristic of all light, from radio-telegraph waves to X-rays. For Newton, inflection was an argument for the corporeality of light, while historically it became the basis of the wave theory. True, the visual theory of Young–Fresnel could not fully cope with the fact of the rectilinear propagation of light and with the diffraction problem. Only the wave equation, much broader than any particular form of wave theory, gave, in the mathematical treatment of Kirchhoff and then Sommerfeld, the solution of the problem. The wave equation in itself is not a hypothesis, but a principle, a generalized fact of the same kind as the equations of thermodynamics or electrodynamics, not connected with this or that form of the wave hypothesis.

5. The principle of the polarization of light.

The 25th query of the Opticks begins as follows: “Have not the rays of light, besides the properties described, other original properties?” And further Newton proves the existence of the polarization of light on the basis of an analysis of Huygens’ observations on double refraction in Iceland spar. Huygens, in the Treatise on Light, gave a well-known formal construction, based on the wave theory, for determining the direction of the extraordinary ray. In this case the wave theory not only explained the behavior of the extraordinary ray, but was almost an inevitable theory. Newton gives his own, completely incorrect rule for the refraction of the extraordinary ray, without mentioning Huygens’ construction. We encounter a hard-to-explain caprice of the great physicist. It can be explained either by a little characteristic

for Newton by carelessness, or by a desire to bypass the wave theory. Huygens himself, in one letter to Leibniz, calls his experiments with double refraction an “experimentum crucis” of the wave theory. Later, however, Laplace, Biot, and others also provided a corpuscular mathematical theory of double refraction. Huygens, however, could not explain from the standpoint of his theory the fact that if one of the rays, ordinary or extraordinary, falls upon a second crystalline plate, then it either again undergoes double refraction, or passes through in the form of a single ray, depending on the rotation of the plate. Newton gives a formal explanation in two lines: “Do not light rays have different sides with different original properties?” In Query 28 the “sides” of the ray are compared with the poles of a magnet, which is why in 1808 Malus named the whole phenomenon polarization. The name immortalized the tendency as well: Newton regarded polarization as a strong argument for the corpuscular theory: “I do not say,” writes Newton, “that this force is magnetic; its nature is probably different. But whatever it may be, it is difficult to understand how light rays, if they do not consist of corpuscles, can have two sides that constantly exhibit forces such as are not present on the other sides.”

Polarization proved to be a great difficulty on the path of development of the wave hypothesis in the true sense—that is, the hypothesis based on a visual hydrodynamic conception. Fresnel’s doctrine of transverse vibrations of the ether met with sharp hydrodynamic objections from Poisson. Only the formal wave theory, with a wave equation but without a concrete medium, peacefully accepted polarization as an empirical principle.

Newton was not mistaken in including polarization among the fundamental original properties of light. In the light spectrum all rays can exhibit polarization, and attempts to find longitudinal light waves proved futile.

If to the principles of periodicity, invariability of periods, diffraction, and polarization one adds the empirical velocity of light and the transfer of energy, the principles of the doctrine of light in itself (independently of the actions of light upon matter) will be almost exhausted.

Newton was the first to define the very subject of optics, discovering almost all the basic properties of light. But the synthetic part of the problem remained unsolved. It was necessary to find that higher general principle from which all the properties would follow unambiguously.

Newton’s light ray, with its “fits,” its “poles,” its infinite variety of periods, and its special attractive or repulsive properties, needed a unifying image or at least a general mathematical expression. To achieve this

has not been possible to do to this day. Formal wave theory has encompassed only part of the phenomena. In another part, strange quantum laws prevail. What remains is to construct hypotheses.

6. Newton’s corpuscular-wave hypothesis.

History confirmed the farsightedness of Newton, when he cautiously gave preference to the correct method of principles over hypotheses in the study of light and gravitation. The nature of light and the nature of gravitation remain incomprehensible even now. The number of possible mechanical hypotheses concerning light is small; this was clearly known both in the seventeenth and in the eighteenth centuries. Let us allow ourselves to make an excerpt from Lomonosov’s “Discourse on the Origin of Light,” delivered in 1756:

“Having posited a fluid, most subtle and imperceptible matter of light, about which no one now has any doubt, we find in it three possible motions, which will be seen later to exist in reality or not. The first motion may be current, or translatory, as Gassendi and Newton think, by which the ether (as the ancients and many moderns call the matter of light) moves from the sun and from other great and small luminous bodies in all directions, like a river, incessantly. The second motion may be in the ether an undulatory one, according to the opinion of Descartes and Huygens, by which it acts in all directions from the sun in the manner of very small and frequent waves... The third motion may be vortical, when each insensible particle composing the ether rotates about its own center or axis.” Such hypotheses have arisen in various modifications ever since man began to reflect on the nature of light. These hypotheses received quantitative treatment only in the nineteenth century.

For us now the conclusion made by Newton at the end of the 13 points of his empirical doctrine of 1671 seems very obscure: “We recognize bodies as substances only by their sensible qualities, and when the chief qualities of something have been found, we have sufficient grounds to suppose that this something is likewise a substance.” But in the seventeenth century it was immediately understood that Newton was asserting the materiality of light, and he confirmed this in his dispute with Hooke, while nevertheless indicating the hypothetical character of his conclusion. The rectilinearity of light rays, their invariability, attractions and repulsions manifested, according to Newton, in diffraction, reflection and appearance, and finally, later, polarization, which for the seventeenth century could only be the manifestation of a solid corpuscle—all these were the arguments that coherently combined for Newton in the image of a flying material particle. There was also a certain, perhaps unconscious, tradition; from the Opticks, the Principia, and the letters one may judge that Newton was an atomist, although in a definite form he did not express atomism. The teaching of Epicurus, Lucretius, Gassendi, perhaps

be, and not in a direct form, was known to Newton. In setting forth the history of the discovery of dispersion, Newton, anticipating the doctrine, compares a ray of light with a flying tennis ball.

Such was the origin of the emission hypothesis. Newton remained faithful to it to the end, down to the last edition of the Opticks in 1721, but it was never stated in an affirmative form. “The most that can be said is that it is a very probable consequence of the doctrine,” was said in 1672, and this opinion remained unchanged. What remained doubtful in the emission hypothesis for Newton—we do not know.

Newton knew the merits of the wave representation better than its apologists Huygens and Hooke; this can be judged from his polemic with Hooke, from the memoir of 1675, and from the Principia. The chief objection to it was the rectilinearity of light. This obstacle was completely removed only by Kirchhoff’s formal wave theory. In the memoir of 1675 and in the Opticks (Question 29) other objections are also given: total internal reflection, polarization, and the mechanical incomprehensibility of the ether.

“If there is no use whatever in such a fluid, and it only hinders and weakens the actions of nature (the motions of the luminaries), then there is no basis for its existence and, consequently, it must be rejected.” The ether of our time is compromised far more than in Newton’s time; we know absolutely nothing and refuse to understand its properties, and Newton’s objection remains unremoved.

But in the phenomena of periodicity (and diffraction in 1675) Newton clearly saw the presence of a certain wave element in light rays. On this point the wave hypothesis was vivid and useful. And Newton creates a hypothesis of a completely new type, in which there are both corpuscles and waves. In the ether filling bodies, light corpuscles excite waves, propagating with a velocity somewhat greater than the velocity of the corpuscle. Overtaking the corpuscles, the waves bring them now to a phase of condensation, now to a phase of rarefaction, causing fits of alternating reflections and transmissions. The hypothesis is set forth in the memoir of 1675, translated here; we refer the reader to it for details.

Newton’s hypothesis is unusually broad; it is a typical “system” of the seventeenth century, in which light, gravitation, electricity, living processes, molecular phenomena, and so on are all explained at once. The principal agent of this system, the ether, was outlined by Newton after the image and likeness of a real fluid with viscosity, surface tension, and so forth. The corpuscular-wave hypothesis, it is true, is set forth also in the Opticks, in a more abstract and still less affirmative form.

Newton’s hypothesis has been appreciated only by our own time, for its principal merit—the idea of compromise. Newton’s followers in the eighteenth and nineteenth centuries developed a pure emission theory.

Few people know that a scheme of the compromise theory of light was outlined in 1842 by Lobachevsky1. On the occasion of observing a solar eclipse in Penza, he wrote: “The system of waves cannot properly be called a theory, but only an expression of those phenomena which it wishes to explain... The wave theory correctly represents certain laws in the phenomena of light, but does not yet give a notion of wherein their essence consists.” The formalism of wave theory has grown considerably since Lobachevsky’s time, and his doubts have still greater grounds. “To speak of waves means to base the whole judgment on something that, in the strict sense, does not exist, just as when we speak of lines and surfaces, whereas in nature there are only bodies.” Lobachevsky supposes, like Newton, that the theory of waves and that of emission should be combined. “A stream of ether,” he writes, “encountering obstacles on its way, enters into undulation, just as water in a river does when it meets a dam”... The progressive motion of the stream of ether is the cause of heating and illumination; its oscillations explain diffraction, interference, colors, and polarization.

In our time the combination of waves and corpuscles is the only remaining way out in the question of the nature of light. We have several attempts at such a combination: the theory of Sir J. J. Thomson2, the theory of de Broglie3, and the wholly abstract and formal theory of Schrödinger4. The results of such a combination are more satisfactory than those of each theory separately, but it is still too early to speak of a final solution of the problem. Only Newton’s principles remain as unshaken and firm as before.

7. The Emission Hypothesis.

For an unprepared reader, reading the questions of the Opticks will produce a strange impression. One hypothesis is replaced by another, quite unlike it. In one question the hypothesis of the ether is set forth in an affirmative sense, in another in a negative one. The corpuscular-wave conception is replaced, after the rejection of the ether, by a purely corpuscular one (Questions 28 and 29). The key to understanding these contradictions is always the same: “I do not feign hypotheses,” or, more precisely, “I shall not confuse conjectures with certainties.” The juxtaposition of opposite hypotheses, equally plausible, is to some extent a mockery of hypotheses and a defense of the method of principles.

But hypotheses had a greater, similar significance for Newton himself as well. The first ideas about gravitation, about the quadratic la—

... arose on the basis of the hydrodynamic hypothesis of the ether (letters to Boyle, memoir of 1675), and the emergence of the idea of polarization would hardly have been possible without the notion of light corpuscles.

The appearance of the Principia marks a sharp turning point in the history of Newton’s hypotheses. Up to that time the scheme of Newton’s working hypotheses was: particles of matter and the ether (the sun and ether vortices around it in gravitation, light corpuscles and waves in the ether excited by them in optics, etc.).

The astounding success of the Principia, the derivation of the laws of gravitation and of the system of the world without hypotheses, from principles of mechanics alone and from Kepler’s empirical laws, compelled one to treat hypotheses with still greater skepticism than before. The hypothetical mechanism of the interaction of masses was replaced by the rigorous formal concept of central forces. The Democritean world—atoms moving in a void—was replaced first by atoms in the ether, and finally by a formal conception of atoms: force centers attracting or repelling at a distance.

In the Principia Newton bypasses the question of the possible causes of gravitation, confining himself to the fact and to its mathematical formulation: “It is enough that gravity really exists and acts according to the laws we have set forth, and is fully sufficient for explaining all the motions of the heavenly bodies and the sea.” Contemporaries in many cases did not understand Newton’s formalism and accused him of introducing hidden, or, as they said in the eighteenth century, “occult,” qualities. Cotes gave a brilliant reply to these accusations in the preface to the second edition of the Principia: “I hear,” he wrote, “how some people ... mutter about occult qualities. They constantly maintain that gravity is a hidden, secret quality, whereas hidden qualities have no place in philosophy. To this it is easy to reply: hidden are not those causes whose existence is discovered by observations with the greatest clarity, but only those whose very existence is unknown and is confirmed by nothing. Consequently gravity is not a hidden cause of the motion of the heavenly bodies, for the phenomena show that this cause actually exists. It would be more correct to admit that those resort to hidden causes who ascribe the laws of these motions to certain vortices of some purely imaginary matter, utterly inaccessible to the senses.” The accusation was turned around: the ether proved to be the occult quality. In the heat of struggle and defense Cotes fell into another extreme, asserting—though, it is true, not altogether definitely—the primacy and further incomprehensibility of gravitation, attributing to the central forces a real and not merely formal significance. Newton himself was very cautious on this question: “I by no means assert that gravity is essential to bodies,” he wrote in the third edition of the Principia, “under the...

...by an innate force I understand solely the force of inertia.” The Principia ends with a remarkable paragraph: “It would now be proper to add something concerning a certain very subtle aether, which penetrates all solid bodies and is contained in them, by whose force and actions the particles of bodies, at very small1 distances, attract one another, and, when in contact, cohere; electrified bodies act at greater distances, both repelling and attracting neighboring small bodies; light is emitted, reflected, refracted, inflected, and heats bodies... but this cannot be set forth briefly; moreover, there is not a sufficient store of experiments by which the laws of the action of this aether could be exactly determined and demonstrated.” At first glance this passage may seem a simple résumé of the memoir of 1675. In fact, however, it speaks only of actions at small distances, i.e., of an aether concentrated in matter; gravitation is not mentioned in this scheme.

The disciples, or rather the followers, of Newton in many respects failed to understand his extreme caution and crudely transformed the formal principle of central forces into a hypothesis, making gravitation a primary, and hence inexplicable, principle.

In any case, even the formal idea of central forces connected with masses could be extended, in addition to gravitation, to a broad class of phenomena: cohesion, capillarity, chemical processes, electricity, and, finally, optics. Newton gave a brilliant sketch of such a universal theory in the extensive 31st Query of the Opticks. In this universal scheme there remained room only for a purely corpuscular hypothesis of light. For waves there was no mechanism in it once the aether had been removed. The desirability of a purely corpuscular theory was called forth by the requirements of the rigor and unity of Newton’s new mechanics, in which there were only atoms—force centers in empty space. Optics was adapted to mechanics, to the general scheme of the Principia.

Newton himself, impartially and very briefly, set forth the purely corpuscular hypothesis alongside the corpuscular-wave one in the Queries of the Opticks. The processes of emission, reflection, and diffraction of light were explained as manifestations of repulsive forces acting at a distance between particles of light and matter. Conversely, in simple and double refraction mutual attractions are manifested. Light can turn into matter, and matter into light; they are akin to one another, and heating, together with the luminosity accompanying it, is the result of such a transformation. Several causes are indicated to explain the periodic “fits.” The rotation of a two-poled particle, similar to a bar magnet, is quite sufficient for this purpose.

In our time it has almost been forgotten that the corpuscular theory was developed mathematically as well, and sometimes in very great detail, in the works of Laplace, Poisson, Biot, Brewster, Malus, and others.

Boscovich came closest of all to the conception of the Newtonian mechanics of central forces. Boscovich’s optical excursions are scattered through his numerous books and memoirs. Boscovich’s optical theory is set forth most fully in his Dissertation on Light1. It is difficult to find in the eighteenth century another analyst so subtle in the fundamental concepts of physics concerning space, motion, matter, and forces. The dissertation begins with an analysis of the concept of the rectilinearity of light. Boscovich proves the vicious circle in this definition. The physical concept of rectilinearity is always reduced to an optical definition, and with the aid of this concept we wish, in turn, to judge the rectilinearity of a ray! According to Boscovich, support for the concept of rectilinearity is provided only by the mechanical principle of inertia. The path along which a body moves by inertia should be called rectilinear. Conversely, the coincidence of the path of light with the trajectory of inertial motion testifies, according to Boscovich, to the corporeality of light.

Fig. 5.

The foundation of Boscovich’s theory is the conception of particles of matter. These are “indivisible and unextended points, standing apart from one another at distances” and interacting by forces of the Newtonian type. These particles are immutable, since, being points, they have no parts. They are always identical; this may be judged from the immutability of the constant of the law of gravitation. The particles act upon one another according to the law of forces depicted in Fig. 5. Along the abscissas is plotted the distance from the particle \(O\), and along the ordinates the magnitudes of the forces. Positive values of the ordinates correspond to repulsion, negative ones to attraction; the asymptotically decreasing attraction at the end of the curve represents Newtonian gravitation. The concept of a central force is generalized, and Newton’s law is only a segment of the universal curve. “Such a form of curve best explains all the fundamental mechanical properties of bodies, both in general and in particular: the mobility, impenetrability, and extension of bodies; the equality of action and reaction; the interactions of particles of matter at small distances; gravitation, cohesion, hardness and fluidity, elasticity and softness, and all optical prop—

hood.” In the treatise “On Living Forces,” Bošković gives an analytical expression for his curve:

\[ y = a + bx^m + cx + dx^r + \ldots \]

Bošković’s light corpuscles do not differ in any way from other points—centers of matter. Only in connection with the phenomenon of polarization does Bošković indicate the possibility of a dipolar character of the corpuscle, comparing it, like Newton, with a rotating magnet. If the corpuscle-point is near the position \(A\) on the curve, it can perform oscillations; an insignificant external impulse can transfer it to the steep repelling part of the curve near the center \(O\), and then emission will occur—the repulsion of the particle. Absorption is the capture of a corpuscle in the region of strong attraction near the center. An absorbed corpuscle, as a result of internal motions of matter, may enter the zone of repulsion and be emitted again. In this way Bošković explains phosphorescence. In Bošković’s curve there are enough bends to interpret qualitatively reflection, refraction, and various cases of diffraction. Periodicity is explained, as in Newton, by the rotational motion of corpuscle-dipoles, or by certain changes in the medium itself, “ex mutatione aliqua facta in ipso medio,” as Bošković obscurely puts it. This indefiniteness is understandable, since the changes of the medium that may be in question are Newtonian waves in the ether excited by corpuscles, but ether is superfluous in Bošković’s system.

The idea of Bošković’s complex but single force function, in one form or another, is still used in physics. Lord Kelvin1 used it in the dynamics of crystals.

In Born’s theory of the solid body, a special case of Bošković’s function again appears. To explain stationary states of the atom and the laws of spectral series, Sir J. J. Thomson recently proposed a generalization of Coulomb’s law similar to Bošković’s curve2. From time to time universal hypotheses arise that are entirely in the spirit of Bošković, usually without mention of his name3.

It should be remembered, however, that Newton’s conception was formal; in Bošković it is treated as a reality and becomes a hypothesis.

The history of optics over two and a half centuries has been both complex and in many respects unexpected. But if we speak of the main point: of the properties and pri-

...nature of light, then here almost everything was anticipated by Newton. He established all the principal properties of light, gave the criteria for the subject matter of optics, and by these criteria, in the nineteenth and twentieth centuries, physicists had to include in optics ever newer domains of phenomena. He considered three possible theories of light—the wave, the corpuscular, and the corpuscular-wave—and was satisfied with none of them; all three remained hypotheses, i.e., unproven. The following centuries devised no fundamentally new hypotheses, and the question of which hypothesis is correct, and whether even one of them is correct, has remained unresolved.

Lagrange, who often called Newton the greatest genius who had ever existed, added: “He was the most fortunate: the system of the world can be established only once.” Almost the same must be repeated with regard to the doctrine of light.

1. Lord Kelvin. Baltimore lectures, p. 667, 1904. ↩↩↩↩↩↩

2. Sir J. J. Thomson. Phil. Mag. 38, 1919. ↩↩↩

3. Cf., for example, H. Strache. Die Einheit der Materie. Leipzig, 1919. ↩↩

4. Cf. E. Schrödinger, Abhandlungen zur Wellenmechanik. 1927. ↩