II. A HYPOTHESIS EXPLAINING THE PROPERTIES OF LIGHT PRESENTED IN SEVERAL OF MY PAPERS.

Sir, in my reply to Mr. Hooke, as you may recall, I had occasion to speak of hypotheses, and there indicated the reason why all admissible hypotheses, in their genuine essence (genuine constitution), must agree with my theories[^16]. With regard to Mr. Hooke’s hypothesis I then said that it may be applied most freely and naturally to phenomena in the following way: the moving particles of bodies, according to their various sizes, figures, and motions, excite in the ether vibrations of various depth or thickness, which, mingling together, propagate through this medium to our eyes, producing in them the sensation of light of white coloration. But if, by some means, vibrations of different breadths are separated from one another, then the broadest produce sensations of red color, and the smallest, or shortest, the sensation of deep violet, while the intermediate ones produce sensations of intermediate colors. In the same way, bodies, according to their various sizes, shapes, and motions, excite in the air vibrations of different breadths, which, in accordance with this breadth, create the various tones of sound, etc. I was glad to learn, from Mr. Hooke’s report[^17], when he was last at one of your meetings, that he had changed his former opinion that all colors are composed only of two original ones, arising from the two sides of an oblique pulsation; he adapted his hypothesis to the aforesaid proposition of mine concerning colors, which, like sounds, differ according to the different breadth of the pulsations. I consider this hypothesis more probable than others described by previous authors, since I do not see how the colors of thin transparent plates, or films, can be satisfactorily explained without recourse to ethereal pulsations; however, I think that another hypothesis, which I had occasion to touch upon in the same letter, is still better, in these words1:

“The hypothesis of the corporeality of light, if I were to propose such a one, has a considerably greater kinship with the opponent’s own hypothesis than is, apparently, known to him; vibrations of the ether are useful and necessary in both the one and the other. For, if one supposes that the rays of light are small bodies emitted in all directions by luminous substances, then these rays, striking a refracting or reflecting surface, must necessarily excite vibrations in the ether just as stones do in water when they are thrown into it.”

“The question of what benefit may be obtained from these vibrations (if it be supposed that they have different depths or thicknesses, in accordance with their being excited by the aforesaid corpuscular rays of different sizes and velocities), for explaining the nature of reflection and refraction, the production of heat by means of solar rays, the emission of light by burning, decaying, and other substances whose particles are in violent motion, for explaining the phenomena of thin transparent plates and bubbles and of all natural bodies, the nature of vision and the difference of colors, their harmony and discord—this question I leave to the consideration of those who may deem it worth the effort to apply this hypothesis to the explanation of phenomena.”

If I had to accept some hypothesis, I would choose this one, but stated in a more general form, without defining what light is, except that it is something capable of exciting vibrations in the ether: for in this form the hypothesis becomes so general and broad in comparison with others that little room remains for the invention of new ones. I have observed that the minds of some valiant men\(^{18}\) are very much inclined toward hypotheses, and in my arguments there was no hypothesis that explained them. I found that some whom I could not persuade of my opinion, when speaking abstractly about the nature of light and colors, would readily agree with it if I explained my reasoning by some hypothesis. For this reason I thought it appropriate to send you a description of the details of this hypothesis, whose aim is only to clarify the memoir sent together with it. I myself shall accept neither this nor any other hypothesis, believing that it does not necessarily concern me whether the properties of light discovered by me are explained by this hypothesis or by Mr. Hooke’s hypothesis, or whether other hypotheses can explain them. However, in setting forth the hypothesis, in order to avoid verbosity and to present it more conveniently, I shall sometimes speak of it as though I accepted and believed it. I think what has been said is sufficient so that no one will confuse the hypothesis with my other arguments, or judge their reliability by the hypothesis, or consider me obliged to answer objections against the present memoir. For I wish to avoid being drawn into such misunderstandings and disputes, which have no significance\(^{19}\).

But I shall turn to the hypothesis: first, it is assumed that there exists a certain ethereal medium, in many respects having the same structure as air, but considerably more rarefied, finer, and more elastic. A not unimportant argument for the existence of such a medium is that the motion of a pendulum in a glass vessel from which the air has been exhausted is almost

just as rapidly as in the open air ^20). It cannot, however, be supposed that this medium is a homogeneous matter; it is composed partly of the principal cosmic ^21) body of the ether, partly of other various ethereal gases ^22), much as air is composed of the cosmic body of air mixed with various vapors or exhalations. In favor of such heterogeneity, apparently, speak the electrical and magnetic effluvia and the origin of gravitation. Perhaps the common basis of nature is nothing other than various interweavings of certain ethereal gases or vapors, condensed as though by precipitation, in the way that vapors thicken into water, or exhalations into coarser substances, though not so easily. After condensation they assume various forms, first directly by the hand of the Creator, and then by the force of nature, which, according to predestination, increases and multiplies, becoming the complete imitator of copies pre-established by the original ^23). Thus, it may be that all things have arisen from ether.

At least elastic effluvia apparently show us that there is something of an ethereal nature, condensed in bodies. I have more than once placed on a table a round piece of glass, about two inches wide, in a brass ring, so that the glass was at a distance from the table of from one eighth to one sixth of an inch. The air between the glass and the table was enclosed on all sides by the ring, as though a small sieve had been placed on the table; then I rapidly rubbed the glass for some time with some coarse, rough cloth, until very small pieces of very thin paper, placed on the table under the glass, began to be attracted and to move briskly to and fro. After the rubbing of the glass had ceased, the bits of paper continued for some time to make various movements; sometimes they leapt up to the glass and remained there for a while, then jumped to the table and remained there; then they again jumped down and up, sometimes along lines that seemed perpendicular to the table, and sometimes along inclined ones; sometimes upward they jumped along one curve and downward along another, with different times, not noticeably stopping in the middle; sometimes they skipped along an arc from one part of the glass to another without touching the table, and sometimes they hung from a corner, often rotating very briskly, as though they were being drawn into a whirlwind; they also moved in other ways, each bit of paper with a different motion. When I slid my finger over the upper side of the glass, moving neither the glass nor the air beneath it, the bits of paper hanging on the glass acquired a certain new motion, inclining to one side or another in accordance with the motion of my finger ^24). I cannot imagine the occurrence of all these irregular motions otherwise than through the mediation of some subtle matter, condensed in the glass and rarefied by rubbing, just as water is rarefied into vapor.

upon heating. This matter, having been carried off and scattered by the surrounding air to a great distance and, being forced to move and circulate in various ways, correspondingly acts upon the bits of paper until it returns again into the glass and there condenses. This condensed matter, when rarefied into an ethereal wind (for, because of the ease of its penetration and circulation in glass, I consider this matter ethereal), may cause irregular motions, and, condensing again, may, upon its return into the glass, produce electrical attractions at the place where it is continually recondensed. The gravitational attraction of the earth may likewise be caused by the continual condensation of some other, similar ethereal gas 25).

This gas is not the main body of the cosmic ether, but something finer and more subtle, dispersed in it, having perhaps an oily or glutinous, viscous and elastic nature; it stands in the same relation to the ether as the vital aerial gas required for maintaining flame and vital motions stands to air. Such an ethereal gas may condense in bodies subjected to fermentation or burning, or in some other way collect in the pores of earth and water into a certain kind of moist active matter for the constant needs of nature, adhering to the walls of these pores just as vapors condense on the walls of a vessel. If this is so, then the vast body of the earth, which everywhere may be an actual center of eternal work, is capable of continually condensing such a quantity of this gas as to cause its descent from above with greater speed for use. In such a descent this gas may carry downward with it bodies through which it passes with a force proportional to the surfaces of all the particles of the bodies upon which it acts 26). Nature creates a circulation by means of the slow ascent of the same quantity of matter from the interior of the earth in an aerial form; this matter for a time constitutes the atmosphere; but it is continually displaced by new air: exhalations and vapors rising from below finally disappear again in the ethereal spaces (with the exception of some part of the vapors, which turn into rain), and here, perhaps, in time melt and sink back into their first principle. For nature is an eternal worker, producing liquids from solid bodies and solids from liquids, stable things from volatile ones and volatile from stable ones, fine from coarse and coarse from fine. Some substances rise and create the upper terrestrial waters, rivers, and the atmosphere, while others, correspondingly, descend to replace the former. The sun, like the earth, may perhaps abundantly absorb gases in order to preserve its radiance and to hold the planets together so that they do not move away from it 27). Those who wish may further suppose that this gas produces or carries with it the sun’s heat and the material principle of light, and that the vast ethereal spaces between us and the stars are a sufficient storehouse for this nourishment of the sun.

and planets. This, among other things, may be said to explain the relations of the ethereal natures.

Secondly, it must be supposed that the ether is an oscillating medium like air, only its oscillations are considerably more rapid and finer; the oscillations of air produced by the ordinary human voice follow one another at a distance of more than half a foot or a foot; the oscillations of the ether, however, at a distance of less than one hundred-thousandth part of an inch. In air some oscillations are somewhat larger than others, but equally rapid (because the sound of any note from a series of bells is heard at a distance of two or three miles in the same sequence as the bells are struck). In the same way, I suppose, ethereal oscillations differ in breadth, but not in velocity. These oscillations, apart from their usefulness in reflection and refraction, may be supposed to be the chief intermediary by means of which the motion of the particles of wandering or decaying substances, of flowing liquids, and of molten, burning, or other heated bodies is maintained. These bodies are struck by ethereal oscillations as a ship is by waves, and are dispersed into vapors, exhalations, or smoke; in these bodies light is released or excited, and they become glowing coals, smoke, and flame. I suppose that flame is nothing other than particles of smoke which, owing to the pressure of light and heat, have turned into incandescent coals, small and innumerable.

Thirdly, air passes through the openings of small glass tubes not so easily as through wide ones, and therefore is within them in a greater degree of rarefaction than in free air spaces; the narrower the tube, the greater the degree of rarefaction, as is known from the rise of water in such tubes to a height considerably greater than the surface of the standing water into which the tubes are immersed[^28]. In a similar way, I suppose, although the ether passes through the pores of crystal, glass, water, and other natural bodies, yet in these pores it is in a greater degree of rarefaction than in free ethereal spaces; the degree of rarefaction of bodies is the greater, the narrower are the pores of the body. Therefore it may be that wine spirit, for example, although it is a light body, nevertheless, having fine particles and consequently smaller pores than water, is a liquid with greater refraction. In this same fact, perhaps, lies the chief cause of the cohesion of the particles of solid and liquid bodies, of the brittleness of glass and of bodies whose particles do not slide relative to one another when bent; in this same fact, perhaps, lies the cause of the fact that in Torricelli’s experiment mercury sometimes reaches the top of the tube, although its height is much greater than twenty-nine inches.

The dense ether surrounding these bodies must press and compress their particles together, just as air surrounding two pieces of marble compresses them if there is little or no air between them.

Further, such a difficult problem as in what manner muscles contract and expand, causing animal motions, may receive from this greater illumination than by any other methods so far devised by men. For if in man there is some ability to compress and rarefy at will the ether that penetrates the muscles, then such compression or expansion must change the compression of the muscle produced by the surrounding ether, correspondingly causing its rising or settling. For although ordinary water is scarcely compressed under pressure and expands when the pressure is weakened, nevertheless (judging from my observations) this occurs in spirit of wine and in oil; for instance, Boyle’s experiment concerning the comparatively great compression of a tadpole under strong pressure upon the water in which it is swimming is an argument in favor of the view that animal fluids exhibit the very same thing. The pressure of the surrounding ether changes; therefore it is clear that compression or expansion must occur to a greater or lesser degree according to the greater or lesser quantity of ether within, which holds and balances the external pressure. If the two ethers are equally dense, the muscle must be free, as though there were no pressure; if there were no ether within, the surrounding ether would compress the muscle with the full force of its elasticity. If the ether within were expanded twofold in comparison with the external ether, having half the elasticity, then only one half of the surrounding force would be balanced, while the other half would act upon the muscle; likewise in other cases the surrounding ether would compress the muscle by the excess of the force of its elasticity over the elasticity of the ether enclosed within. Thus, for the contraction of a muscle and for its raising and lowering, nothing is required except a change in the consistency of the enclosed ether; a very small change is sufficient, provided only that the elasticity of the ether is assumed to be very great; I think that it is many times more elastic than air.

How is the consistency of the ether changed? It is simplest to allow that the soul has immediate power over all the ether in any part of the body, expanding and compressing it at will; but then how does muscular motion depend upon the nerves? To another it may seem more convenient to think of a certain ethereal gas enclosed within the dura mater; the soul can compress or expand this gas at will in any muscle, causing its flow along the nerves.

However, the difficulty remains why this power of the soul does not take away from the ethereal gas its elasticity, thanks to which it must contain, to a greater or lesser extent, the force of the external ether. A third supposition is possible: that the soul has the ability to breathe this gas into a muscle, driving it through the nerves. But this supposition too encounters many difficulties, since it requires a forcible influence upon the elasticity of the ether in the muscles by pressure produced by parts

brain; but it is difficult to imagine how such a delicate matter as the brain can produce such great forces. And, besides, why does this ethereal gas, being quite subtle and subjected to a great force, not pass right through the dura mater and the skin of the muscle, or at least not yield the way to another ether enclosed in the muscle? To remove these difficulties one must make a digression, but, considering that the subject deserves it, I cannot refrain and shall set forth what I think about it.

First, I assume that such a gas exists, i.e., that animal gases are not like liquid, nor like vapors or the gas[^29] of wine spirit: they have an ethereal nature, sufficiently subtle to penetrate the animal fluids as freely as electrical or magnetic effluvia pass through glass. To understand how the tissues of the brain, nerves, and muscles can become a suitable vessel for such subtle gases, remember that liquids and gases have a predisposition to penetrate or not to penetrate through things for reasons other than their subtlety. Water and oil penetrate through wood and stone, but not through mercury; mercury, however, passes through metals, which water and oil cannot do; water and acid spirits[^30] pass through salts, but oil and wine spirit do not; oil and wine spirit penetrate through sulfur, but water and acid spirits do not. Certain liquids, for example oil and water, whose particles are sufficiently free that they could mix with one another, nevertheless remain separate because of a certain hidden principle of immiscibility; other liquids that do mix can become immiscible if a third substance is added to one of them, for example water with wine spirit, if tartaric salt is dissolved in it. A similar immiscibility is also possible in ethereal bodies, as perhaps occurs between the ethers in the vortices of the sun and the planets[^31]; the reason why air is more rarefied in the channels of small glass tubes, and ether more rarefied in the pores of bodies, than outside, may lie not in a lack of subtlety, but in a lack of miscibility[^32]. For this reason, if the ethereal animal gas in man mixes easily with the bone marrow and fluids and does not mix with the tissues of the brain, nerves, and muscles, or with any substances located in the pores of these tissues, then it can be retained, despite its subtlety—especially if one assumes that no great effort is exerted to expel it; that it is, perhaps, not at all as subtle as the fundamental body of ether, although sufficiently subtle to pass through animal fluids; and that, as some of these gases are spent, they are continually replaced by new ones from the heart.

Then, in order to understand how this gas can be used for animal movements, you may take into account that certain immiscible things become miscible by means of a third ...

things. Water, which does not want to dissolve copper, dissolves it if the copper is mixed with sulfur; aqua fortis, which does not penetrate through gold, passes through it if a little ammoniacal salt or spirit of this salt is added; lead does not mix with copper when melted, but if a little tin or antimony is added, they mix easily, though their agreement is again disturbed if the antimony is extracted by saltpeter or by some other method; lead, when alloyed with silver, rapidly penetrates through it and burns it out at a considerably lower heat than is required for melting silver alone; but if the small quantity of the substance that reconciled them is removed or altered, their agreement is again disturbed. In the same way, the ethereal animal gas in man may be the mediator between ordinary ether and the muscular juices, making it easier for them to mix more freely. A little of this gas is sent into the muscle—so little that no noticeable tension of the muscle occurs by its own force. Having made the tissues more miscible with the ordinary external ether, this gas allows the ether for a moment to penetrate freely into the muscle more easily and more abundantly than would have happened without its mediation; the ether again freely exits as soon as the mediator of miscibility is removed. In accordance with what I have said above, owing to this there will occur an extension or contraction of the muscle, and consequently also the animal motion that depends on it.

Thus, by directing this ethereal gas or wind into one nerve or another with the same ease, perhaps, with which air moves in open spaces, the soul can cause all the motions that we see in animals. In order for these motions to be strong, there is no need to suppose a very great condensation or rarefaction of the ether in the muscle, obtained by such means; it is enough that its elasticity be so great that a small change in its density would cause a significant change in pressure. What has been said regarding muscular motion can be applied to the motion of the heart, with only this difference: that here the gas is not sent in, as into the other muscles, but is continuously formed on the spot thanks to the fermentation of the juices with which the flesh is filled; after the gas has been formed, it is directed into the brain through the appropriate channel, producing by its pressure in the muscles those motions which in the heart it produces by its formation. I do not see why fermentation in the heart could not raise from its tissues such a subtle gas as would cause these motions, just as the friction of glass raises a gas that causes electrical attraction, and combustion raises from flame a gas that penetrates through glass, as Mr. Boyle has shown, and, as is known, rusting metals combines with them ^33).

Up to now I have considered the nature of the ether and of ethereal substances with respect to their actions and applications; now I shall add to this considerations on light.

Thus, in the fourth place, I suppose that light is not ether, nor its vibratory motion, but something of another kind, propagated from luminous bodies. Those who wish may suppose it to be an aggregate of various peripatetic properties. Others may suppose that light is a multitude of unimaginably small and swift corpuscles of various sizes, flying off from luminous bodies to great distances from one another, yet without any noticeable interval of time. These corpuscles are continually urged forward by some principle of motion, at first accelerating them until the resistance of the ethereal medium is equal to the force of this principle, just as bodies falling in water accelerate until the resistance of the water becomes equal to the force of gravity. God, who has given animals their own motion, which is beyond our understanding, can undoubtedly also produce other principles of motion in bodies, which we understand just as little. Some will simply regard this principle as spiritual; however, it is possible to indicate a mechanical principle as well, but I prefer to pass over this question.

Those who do not like this may suppose that light is some other corporeal emanation, an impulse or motion of some other medium or ethereal gas scattered through the principal body of the ether, or anything else that they consider suitable for this purpose. To avoid disputes and for the generality of the hypothesis, let everyone keep to his own view. Whatever light may be, I suppose, however, that it consists of rays differing from one another in such accidental features as thickness, form, or force, just as grains of sand on the shore, sea waves, human faces, and all other natural objects of the same kind differ. It is almost impossible to find, among things of one kind, a thing without some accidental difference.

Further, I shall suppose light to be distinct from the vibrations of the ether. If it were such, it would always have to diverge strongly along curved lines into a dark or quiescent medium, breaking all shadows and making its way along curved pores or passages, like sound. But, in addition, I do not understand how, in that case, any surface (for example, the face of a glass prism upon which rays from within fall at an angle greater than forty degrees) can be perfectly dark. For vibrations, striking the refracting boundary of rarer and denser ether, must set this yielding surface into vibration, and these vibrations will excite undulation and propagate it to the other side. Further, how light falling upon very thin films or plates of a transparent body, with successive thicknesses of the plate being in an arithmetic progression, is alternately reflected and transmitted, as I have found—this amazes me just as much. The arithmetic progression of these thicknesses, alternately reflecting and transmitting light, indicates,

that they depend on the number of vibrations between the two surfaces of the plate both upon reflection and upon the passage of the ray. I do not understand, however, in what way the number can alter the character of the phenomenon according as it is greater or smaller, whole or fractional, unless one assumes that light is something different from these vibrations. True, I can somewhat alleviate these last two difficulties, but I do not consider this sufficient.

Fifth, it is assumed that light and ether act mutually upon one another: ether refracts light, and light heats ether, the densest ether acting most strongly of all. Therefore, when a ray moves through ether of nonuniform density, then, I suppose, the medium exerts upon it the greatest pressure, force, or action in the direction of the denser ether; it receives a continuous impulse or bend on this side, retreating toward the more rarefied ether, and is accelerated if it goes along such a path, and retarded on the way back. For this reason, if a ray moves obliquely through such a medium of nonuniform density (i.e., obliquely to those imaginary surfaces which pass through parts of the medium of equal density and may be called refracting surfaces), then it must be curved, as is observed in water*), the lower layers of which gradually become more salty, and consequently denser, than the upper ones. In this may lie the cause of all refraction and reflection. Rarefied air inside a small glass tube and more condensed air outside it ²⁸) are not separated by an exact mathematical surface: between them there is air at the opening of the tube, passing through all intermediate degrees of density. Likewise, I suppose, the refracting surfaces of the ether between media of unequal density are not mathematical; they have a certain thickness, and in them, at the openings of the pores of a solid body, the ether has all intermediate degrees of density between the rarefied and the denser ethereal media. I believe that refraction arises from the continuous curvature of the ray during its passage through physical surfaces. If it is assumed that the motion of the ray in such passage is increased or diminished in some proportion, in accordance with the difference of densities of the ethereal media, and that the increase or diminution of the motion is reckoned along the perpendicular to the refracting surfaces, as it should be, then the sines of incidence and refraction will be proportional, in agreement with what was proved by Descartes ³⁴).

Thus, a ray, passing from a rarefied medium into a denser one, continually inclines more and more toward parallelism with the refracting surface. If the differing densities of the medium do not

) See Hooke’s Micrographia*, where he speaks of the bending of rays.

so great, and the incidence of the ray not so oblique, that the ray succeeds in becoming parallel to the surface before emerging from it, then it passes through and is refracted. But if, for the reasons indicated above, the ray becomes parallel before emerging, then it must turn back and be reflected. Thus, for example, in the triangular glass prism \(OEL\) one may observe that the rays \(An\), passing from glass into air, as their inclination to the refracting surface increases, emerge more and more obliquely until they become infinitely oblique, i.e. parallel to the surface; this occurs at an angle of incidence of about forty degrees; if the rays are inclined a little more, then they are all reflected, as shown by the line \(AV\). In this case, I suppose that the rays become parallel to the surface before they can pass through it. Let \(ABDC\) be the rarer medium (Fig. 2), \(EFHG\) the denser one, and \(CDFE\) the space between them, or the refracting physical surface, in which the ether has all intermediate degrees of density, beginning with the rarest ether at \(CD\) and ending with the densest at \(EF\); \(AmnL\)—

Fig. 1.              Fig. 2.

some ray, \(Am\) its incident part, \(mn\) its curvature due to the refracting surface, \(nL\) its emergent part. If now the ray \(Am\) is curved so much that on emerging at \(n\) it becomes exactly parallel to \(CD\), then it is clear that with a slightly greater incidence it must become parallel to \(CD\) even before reaching \(EF\), the next refracting surface; it has no possibility of approaching closer to \(EF\), and, owing to further curvature, must turn back and be reflected, as is represented by the line \(A\mu V\). The same would occur if the density of the ether increased further from \(EF\) to \(PQ\), and \(PQHG\) were a denser medium than was assumed for \(EFHG\). In the present case the ray, passing from \(m\) to \(n\), is curved so much that at \(n\) it becomes parallel to \(CD\) or \(PQ\); it can no longer approach closer to \(PQ\), but, owing-

then, thanks to the further curvature at \(n\), it returns back and is reflected. If the refracted ray, for example \(nL\), is made incident, then the incident ray \(Am\) will become the refracted one. Therefore, if the ray \(A\mu V\), on arriving at \(V\), where, as I suppose, it becomes parallel to the refracting surface, were reflected perpendicularly backward, then it would return back along the line of incidence \(V\mu A\). Moving forward, it must go along another line \(Vm\); the two cases are similar, and the angle of reflection must be equal to the angle of incidence.

Such, perhaps, is the cause and the manner of reflection when light goes from rarefied ether to dense ether. To understand how light is reflected on its way from dense to rarefied ether, one must recall that liquids near their surfaces are less flexible and yielding than in their inner parts; if they are given the form of thin plates or scales, they become more rigid and viscous than under other conditions. Thus, objects falling freely in water do not easily break through a water bubble, but slide along its sides if they are not too large and heavy. If two well-polished convex glasses, ground to very large spheres, are placed one upon the other, the air between them easily escapes until they almost touch; but thereafter the resistance becomes so great that the weight of the upper glass is too small to bring them together so that a black coloration appears in the middle of the colored rings, of which mention is made in another memoir that I sent you \(^{35}\). If the glasses are plane, but no wider than a two-penny coin, a man with all his strength cannot squeeze out all the air between them so that they fully touch one another. You may also have observed that insects walk upon water without wetting their feet, while the water supports them; dust, falling on water, often lies upon it without being wetted. I suppose that the ether at the boundary of two media is less flexible and yielding than in other places; moreover, the flexibility is the less, the more the media differ in density. In passing from denser ether into rarefied ether, when only a very small layer of dense ether remains to be traversed, the ray thus encounters an unusual difficulty in passing; the difficulty is so great where the media differ very strongly in density that the rays are reflected, because of the curvature, in the same way as described above; the parts of the ether on the side where they are less flexible and yielding act upon the rays as though they were here denser than on the other side. For the resistance of the medium must produce upon the ray one and the same effect, from whatever cause it may arise. Such also, I suppose, may be the cause of the reflection of mercury and other metallic bodies. It must contribute to the reflecting power of bodies also in the case when the rays pass from a rarefied medium into a dense one. In the present case the reflection, having a double cause, must evidently be stronger than in ether. In refraction such a strong visc—

ONE HYPOTHESIS EXPLAINING THE PROPERTIES OF LIGHT

...the viscosity, or rigidity, of the surface may be disregarded, because insofar as the rays are deflected in passing through this most viscous and rigid part of the surface, the deflection is again diminished to the same extent when they pass from there into the neighboring, less viscous parts.

Thus rays are refracted by some surfaces and reflected by others, depending on whether the medium into which they tend is denser or rarer. But it remains further to explain how rays, falling in the same way upon the same surface (say, of crystal, glass, or water), at one and the same time are some of them refracted and others reflected. To explain this I suppose that, on striking a rigid, resisting ethereal surface, the rays upon which the surface acts in turn act upon it, producing oscillations in it, just as stones thrown into water produce oscillations on the surface. These oscillations spread in all directions, both in the rarer and in the denser medium. Like the oscillations of air that produce sound, they are born of the impact and continue most strongly where they began, alternately compressing and expanding the ether in the indicated physical surface. For from the heat produced by light in bodies it is evident that light can set the particles of a body in motion, and all the more can heat and set in motion the more delicate ether; it is more probable that light imparts motion to the coarse particles of a body not directly, but by means of the ether. For example, in mercury, lead, silver, and other very dark bodies, it is more probable that light produces oscillations that pass through these bodies, and does not merely strike the external particles without entering the body. The impact of each separate ray can produce many thousands of oscillations; sending them through the body, the ray moves all the particles and, perhaps, with greater motion than it could have imparted to an individual particle by a direct impact. For oscillations, pushing each particle back and forth, can continuously increase its motion, just as a bell-ringer does with a bell by striking it often; in this way particles can be brought to a great degree of motion, unattainable either by the simple impact of a ray or by any other motion of the ether except oscillatory motion. Thus the motion of particles in air enclosed in a vessel, caused by heating, however strong it may be, is not capable of imparting to bodies suspended in the vessel either oscillatory or translational motion. But if the air is set into oscillatory motion by striking one or two drums, it strikes glass windows, the human body, and other massive objects, especially if the bodies have a consonant tone; indeed, I have observed a clear shaking of the stone floor in a cellar beneath my feet in a large room, such as, I suppose, the direct blows of five hundred drumsticks could not have produced, unless perhaps they followed one another rapidly at regular...

... intervals of time. Therefore ether vibrations are the best means by which so subtle an agent as light can move the coarse particles of solid bodies, heating them. If it is assumed that light, striking a refracting or reflecting surface, brings it into vibratory motion, then the physical surface, owing to the continuous impulses of the rays, is kept all the time in vibratory motion, and the ether in it is alternately expanded and compressed. If a ray strikes the medium at a time of great compression, then, I suppose, the surface is then too dense and rigid to let the ray pass; it reflects it. But rays striking the surface at another time, when it is expanded in the interval between two vibrations, or is not too compressed and condensed, pass through and are refracted.

Such may be the causes of refractions and reflections in all cases. To understand, further, how they can become regular, the following must be taken into account. In a heap of sand the surface is rough, but if water seeps into its pores until all the pores are filled, then the water will envelop the surface evenly, and the more evenly the finer the sand is. In the same way, although the surface of all bodies, even the most polished, is rough, as I believe, nevertheless, where the roughness is not too coarse and jagged, the refracting ether surface can envelop it evenly. One cannot think that, in polishing glass or metal, sand, ash, or other abrasive powders can so regularly smooth the surface that the top of each particle becomes exactly flat, and that all these planes are directed alike, as is needed for well-polished bodies, where reflection is effected by their particles. Such polishing powders first smooth bodies down to a coarse roughness, so that it is perceptible, then down to a roughness finer and finer, until it becomes so fine that the ether surface envelops it evenly and the body takes on the appearance of being polished. This is a very natural and intelligible supposition. It is strange to think that in liquids the surfaces of all their particles must all be flat, and that the planes of all surface particles are always directed alike, despite the fact that they are in eternal motion. Yet without these two assumptions the surfaces of liquids could not be so regularly reflecting as they are, if reflection is caused by the particles themselves and not by ether surfaces evenly enveloping the liquid.

With respect to the regular motion of light, one may further doubt whether the various vibrations of the liquid through which light passes will disturb it. But such doubt, I suppose, will disappear if one takes into account that, even if at some moment the front...

part of the inclined wave begins to deflect the light to the side, the rear part, by the reverse action, will soon again direct it in a straight line[^36].

Finally, there is no doubt that in every transparent body there are pores of various sizes, and I have said that the ether is in the greatest rarefaction in the smallest pores; therefore the ether in each pore must possess a different rarefaction, and the light must be refracted in passing from each pore into the neighboring one, which should lead to the scattering and destruction of the body’s transparency. It must be taken into account, however, that the ether in all dense bodies is constantly agitated by continuous vibrations, and these vibrations can be produced only by compelling the ether to move back and forth from one pore into another by means of a certain kind of shaking; the ether which at a given moment is in a larger pore is compelled at the next moment to pass into the adjacent smaller one, and conversely. This must distribute the ether uniformly through all pores not exceeding a certain definite width—let us suppose, the width of a vibration—and thus the ether will have the same density throughout the transparent body, according to the average kind of pores. But where the pores exceed a definite width, I suppose, the ether has a density corresponding to the width of the pore or to the medium filling it; the density here will be different from that of the surrounding ether; the pore refracts or reflects light at its surface, and a body in which there are many such inclusions appears dark.

What has been said applies to refraction, reflection, transparency, and darkness; now it is necessary to explain colors. Bodies of different sizes, densities, or qualities, when struck or otherwise acted upon, excite sounds of different tones, and consequently also vibrations in the air of different thicknesses. I likewise suppose that rays of light, when striking a rigid refracting surface, excite vibrations in the ether. These rays, whatever they may be in themselves, differ in magnitude, tension, or force, and excite vibrations of different thicknesses. The broadest, most tense, or most powerful rays produce the largest vibrations; the remaining, shorter rays produce vibrations corresponding to their thickness, tension, or force. The ends of the hairs of the optic nerve, with which the retina is paved or clothed, constitute a refracting surface of this kind. When the rays strike these hairs, they must there excite the indicated vibrations. These vibrations (like the sounds of a horn or trumpet) will run along the aqueous pores or crystalline cores of the hairs, through the optic nerves into the sensorium[^37] (light itself cannot do this). In the sensorium, I suppose, they produce the sensation of different colors, according to their thickness and mixture. The broadest vibrations produce the strongest colors—red and yellow; the least broad, the weakest colors—

blue and violet,—the middle ones excite green colors, and the mixture of all—white. In like manner, in the sense of hearing nature makes use of aerial vibrations of various thicknesses for the production of sounds of various tones. For in nature a likeness is observed. Further, just as the harmony and discord of sounds arise from the proportions of aerial vibrations, so too the harmony of certain colors, for example, gold and blue, and the discord of others, for example, red and blue, arise from the proportions of ethereal vibrations. It is possible that colors differ in their principal degrees: red, orange, yellow, green, blue, indigo, and deep violet, on the same basis as sound within the octave is arranged by tones. Some years ago, having cast the prismatic colors in a well-darkened room perpendicularly onto paper, at a distance of twenty-two feet from the prism, I expressed the wish that a friend of mine mark with a pencil the transverse lines or boundaries of the colors on the image, in those places where each of the above-mentioned colors was most full and brilliant, and also where, in his judgment, the truest boundaries of the colors were. At that time I held the paper so that the indicated image fell between certain boundaries marked on it. I did this partly because my own eyes are not very subtle in distinguishing colors, and partly because

Fig. 3.

because another observer, to whom I did not communicate my thoughts on this subject, could have nothing but his own eyes in making such marks. This observation was repeated several times both on the same and on other days, in order to see how far the marks on different papers agreed. The true boundaries of the colors are difficult to mark, since they imperceptibly pass one into another. However, on comparison, the differences of the observations proved to be small, especially at the red end. When the averages of these differences were taken, the length of the image (reckoned, as it should be, not from the vertices of the semicircular ends, but from the centers of these semicircles, i.e., from the straight sides) was divided almost in the same proportion as the string between the end and the middle, when it is made to sound the tones of the octave. You will understand me better if you consider the appended figure, in which $AB$ and $CD$ represent the straight sides, approximately at a distance of ten inches, $APC$ and $BTD$—the semicircular ends, $X$ and $Y$—the centers of these semicircles, and $XZ$—the length of the musical

of a string twice as large as \(XY\), and divided between \(X\) and \(Y\) so that it sounds the tones indicated at the side (i.e. \(XH\)—one half, \(XG\) and \(GI\)—one third, \(YK\)—one fifth, \(YM\)—one eighth, and \(GE\)—one ninth of \(XY\)). The intervals between the subdivisions indicate the spaces occupied by the colors written on them; moreover, the color is most sharply characteristic in the middle part of these spaces\(^{38}\).

Let us now turn to the cause of the various colors produced by refraction. The broadest, or strongest, rays must pass more freely and easily than the weak rays into the refracting surface; they will be bent less to the side, i.e. will be less refracted. This is equivalent to saying that the rays producing the red color are the least refrangible; the rays producing blue and violet are the most refrangible; and the rest are refracted according to their color. Therefore, when rays coming indiscriminately from the sun are refracted by a prism, as in the experiment described above, rays of different kinds are refracted differently and must arrive at different places on the paper or wall placed opposite. Having thus separated, each kind of ray manifests its own colors; together, hiding one another, they cannot do this. Refraction only separates the rays and does not change their breadth or strength; therefore, after the rays have once been well separated, refraction can no longer produce any further changes in their coloration.

On this basis all the phenomena of refraction can be understood; however, to explain the colors obtained in reflections, I must further suppose that, despite the inconceivable swiftness of light, the ethereal vibrations excited by some ray move still faster than the ray itself, and thus overtake and outrun one ray after another. I suppose that to those who are inclined to regard these vibrations themselves as light, such an assumption must seem admissible\(^{39}\). To make it still more acceptable, one may suppose that light is not as swift as some are inclined to think. I know of no argument that would contradict the proposition that the passage of light from the sun to us requires an hour or two, if not more\(^{40}\). With such an assumption about the speed of the vibrations, when light falls upon a thin film or plate of some transparent body, the waves excited by the passage of light through the first surface overtake the rays one after another. When a ray reaches the second surface, the waves will cause it there to be reflected, or refracted, according to which part of the wave is overtaking the ray there—condensed or rarefied. If the thickness of the plate is such that, at the second surface, the ray is overtaken by the condensed part of the first wave, then it must be reflected there. If the thickness is doubled so that the following rarefied part of the wave, i.e. the space between this and the next wave, overtakes the ray, then at the second surface—

will be transmitted. If the thickness is tripled so that the condensed part of the second wave overtakes the ray, then it will be reflected; the same will occur where the plate is five, seven, or nine times as thick. The ray must be reflected there by reason of the third, fourth, and fifth waves overtaking it at the second surface. However, when the thickness is four, six, or eight times greater, so that the ray is overtaken there by an expanded interval between the above-mentioned waves, then it will be transmitted, and so on. The second surface will be capable, or incapable, of reflecting according as it is condensed or expanded by waves. For example, let \(AHQ\) represent the surface of a spherical convex glass placed upon a plane glass \(AIR\); let \(AIRQH\) be the thin plano-concave plate of air between them; let \(BC, DE, FG, HJ\), etc., be the thicknesses of this plate, or the distances between the glasses, lying in the arithmetical progression of the numbers 1, 2, 3, etc. Consequently \(BC\) is the distance at which the ray is overtaken by the most condensed part of the first wave.

Fig. 4.

I assert that the rays incident at \(B, F, K\), and \(O\) must be reflected at \(C, G, L\), and \(P\), and the rays incident at \(D, H, M\), and \(Q\) must be transmitted at \(E, I, N\), and \(R\). This is because the ray \(BC\) reaches the surface \(AC\) when it is condensed by the first wave overtaking the ray; the ray \(DE\) arrives when the surface is rarefied by the interval between the first and second waves; the ray \(FG\), when the surface is condensed by the second wave; the ray \(HI\), when it is rarefied by the interval between the second and third waves, and so on for an indefinite number of alternations. At \(A\), at the center or at the contact of the glasses, the light must be transmitted, because there the ethereal media in both glasses follow continuously one after the other, as though they formed a homogeneous medium. Therefore, if the glasses in this position are viewed from above, at \(A\), where the glasses touch, a black spot should be visible, and around it many concentric light and dark circles, the squares of whose semidiameters are in arithmetical progression. However, not all rays without exception must be reflected or refracted in this way, for sometimes a ray may be overtaken at the second surface by vibrations caused by other

neighboring or immediately following ray; such oscillations, if they are just as strong as or even stronger than the ray’s own oscillations, can cause its reflection or transmission, although its own oscillations alone would have produced the opposite. Therefore a small amount of light will be reflected from the black rings, whereby they become rather black, but not completely dark; a little light is also transmitted by the bright rings, whereby the black rings, seen from the other side of the glass, do not appear as black as they ought to be. At the central black spot, where the glasses do not touch completely, a little light must likewise be reflected, whereby the spot is darkest of all in the middle, and only black at the edges. I observed this by pressing together very strongly two glass prisms which by chance (at least one of them) were slightly convex, and by examining, under illumination with various colors, the black spot at the place of contact. If, behind the candle, at a small distance, a white paper was placed, and the candle and the paper were viewed alternately in the reflected light of the spot, then, in the light of the paper, the edge of the spot appeared just as black as the middle part; in the stronger light of the candle the edge appeared fairly bright, and to the eye the spot became smaller than before, while the middle part remained completely black in both cases, except for a few spots and bands in which, as I suppose, the glasses, owing to some unevenness of the polish, did not touch completely. The same thing I observed when viewing the spot with the same reflection alternately of the sun and of clouds.

But let us return to the bright and black rings. Such rings always appear as described if the light is homogeneous. Thus, illuminating two touching glasses \(A Q\) and \(A R\) in a dark room with homogeneous light obtained by means of a prism, I observed luminous circles, more than twenty in number, with many dark rings between them; the color of the bright circles was the same as that of the light falling on the glasses. When the glasses were placed between the eye and the prismatic colors thrown onto a sheet of white paper, or when any of the prismatic colors was passed directly through the glasses to a sheet of paper placed somewhat behind them, the same rings of color and darkness appeared (in the first case between the glasses, in the second—on the paper), but in the opposite order from the rings seen in reflection. I mean that, whereas in reflected light a dark spot was visible in the middle and then a colored circle, in transmitted light, on the contrary, there was a colored spot in the middle, and behind it a black circle, and so on; the diameters of the colored circles in transmitted light were equal to the diameters of the black rings in reflection.

Such are, and such must be, the rings, I say, when they are produced by means of homogeneous light. In composite light it is otherwise. Rays that appear red and yellow excite, as

As I have said, greater pulsations in the ether than the rays producing blue and violet; consequently, they give broader circles in a definite proportion, as I clearly discovered by illuminating the glasses successively with the above-mentioned colors of the prism in a well-darkened room and without changing the position of my eye or of the glasses. Therefore the circles obtained when the glasses are illuminated by white light should not appear alternately black and white, in the way that circles, when the glasses are illuminated, for example, by red light, appear red and black. The colors composing white light must separate upon reflection; the blue and violet must come closer to the center than the red and yellow, whereby every bright circle must become violet at the inner edge and red at the outer, and in the intermediate parts the colors must be intermediate. The bright circles will become wider than before, scattering colors on both sides, into those spaces which I call black rings; what had earlier appeared black will now be red, yellow, blue, and violet colors, constituting the edges of the rings and appearing from the incident white light illuminating the glasses. For obtaining bright rings only one green color remains. Suppose that \(CB\), \(GD\), \(LF\), \(PM\), \(RN\), \(SX\) represent quadrants of circles obtained in a dark room when illuminated with only the deepest prismatic red color; \(Y\beta\), \(\gamma\delta\), \(\lambda\varphi\), \(\pi\mu\), \(\rho\nu\), \(\sigma\xi\) are quadrants of similar circles obtained also in a dark room when illuminated with only the deepest prismatic violet.

Fig. 5.

If, then, the glasses are illuminated by daylight, in which all sorts of rays conceal one another, it is clear that the first bright ring will be \(Y\beta BC\), the second—\(\gamma\delta DG\), the third—\(\lambda\varphi FL\), the fourth—\(\pi\mu MP\), the fifth—\(\rho\nu NR\), the sixth—\(\sigma\xi XS\), and so on; moreover, in all of them the deepest violet must be reflected at the inner edges, marked by dotted lines, where it would have been reflected if it had been alone; the deepest red must be reflected at the outer edges, represented by black lines, where it would have been reflected if it existed alone; all the intermediate colors will be reflected at the places in order between the indicated edges, at which they would have been reflected,

…if they were alone, separated from all the other colors in a dark room by refraction in a prism. The squares of the semidiameters of the outer edges \(AC\), \(AG\), \(AL\), etc., as well as \(AY\), \(A\gamma\), \(A\lambda\), etc., the semidiameters of the inner edges, are in the arithmetic progression of the numbers 1, 3, 5, 7, 9, 11, etc.; and the squares of the inner ones are to the squares of the outer ones (\(AY^2\) to \(AC^2\), \(A\gamma^2\) to \(AG^2\), \(A\lambda^2\) to \(AL^2\), etc.) as 9 to 14 (as I have found by measuring them carefully and repeatedly, and comparing the observations). Therefore the outer red edge of the second ring and the inner violet edge of the third must border upon one another (as you can find by calculation and see depicted in the figure). The corresponding edges of the third and fourth rings will intersect; the edges of the fourth and fifth will intersect still more, and so on. In reality the colors of each ring must extend somewhat farther in both directions than is shown here, since the quadrant arcs drawn here depict not the edges but the middles of the rings, obtained in a dark room from the extreme violet and red; the violet falls on both sides of the dotted arcs, and the red on both sides of the black arcs. Therefore these rings, or circumferences, follow one another continuously without any black interval, and the colors are pure only in the first three or four rings; farther on they enter into one another and are mixed more and more, dissolving one another to such an extent that after the eighth or ninth ring they can no longer be distinguished, and to the eye they form a uniform whiteness. Meanwhile, when the rings are produced in a dark room in only one of the prismatic colors, I observed, as I have said, more than twenty rings and, undoubtedly, could have seen them in still greater number if I had taken the trouble to make the prismatic light purer. Separating these rings from one another by certain refractions, described in other papers[^35] sent to you, I even discovered more than a hundred rings[^41] in daylight; perhaps they would appear in innumerable quantity if the color illuminating the glasses were absolutely simple, and the pupil of my eye a mathematical point, so that all the rays coming from one and the same point of the glass could enter the eye with the same inclination to the glass.

What has been said thus far about the rings applies to observing them with the eye fixed; if, however, you change the position of the eye, then the more obliquely you look at the glass, the broader the rings appear. The reason for this may be partly that an inclined ray travels a longer path through the first surface, and therefore there is more time for the vibration back and forth on this surface and, consequently, a broader wave is produced; partly the reason may be that the wave, moving between two surfaces, can be accelerated and retarded by the hardness of these surfaces, being attached at both ends; thus it does not overtake…

beam just as fast as a wave moving perpendicularly across the glasses.

In other papers[^35] sent to you, you will find a description of the breadth of the circles for each color at all inclinations of the eye to the glasses and for every thickness of the air, or interval between the glasses, at which each circle is obtained. There I have also described in detail how far these rings enter into, or spread one after another; what colors are visible in each ring, where they are most vivid, where and in what way they dissolve more and more, mixing with the colors of other rings; what are the opposite colors, visible from the back side of the glasses in transmitted light, whereby the glasses transmit light of one color in the same place where they reflect light of another color.

There is no need to add anything further about the colors of other media in the form of thin plates, for example, of water between the above-mentioned glasses, or of water in the form of bubbles bounded in this way by air, or of glass blown into very thin bubbles on a flame, etc.; the circumstances everywhere here are the same, except that where the thickness of the plate is irregular, the rings will not be such; in plates made of denser transparent bodies the rings are obtained at a smaller thickness of the plate (I suppose that the vibrations will be shorter in a more rarefied ether than in a dense one); in dense plates surrounded by a more rarefied body the colors are more vivid than in plates of a rarefied substance surrounded by a denser one. For example, the colors are more vivid in a glass plate surrounded by air than in an air plate surrounded by glass. The reason for this is that the reflection of the second surface, which produces the colors, as was said above, is stronger in the former case than in the latter. For the same reason the colors are most vivid when the difference in densities of the media is greatest.

In the same papers I speak in detail about the colors of natural bodies, and show how the various sizes of the transparent particles of which bodies consist are sufficient for obtaining all colors. These particles reflect or transmit one or another sort of rays according to their thicknesses, similarly to the above-mentioned plates, as though they were fragments of such plates. For I suppose that if one breaks a plate of uniform thickness, and consequently of uniform color, into pieces of the same thickness as the plate, then a heap of such fragments will be a powder of the same color as the plates. Thus, if the particles have the thickness of the water in the black spot at the vertex of the bubble described in the seventeenth of the observations sent to you, then, I suppose, the body must be black. When such blackness arises, I suppose that the particles of the given form are disposed not to reflect almost any light outward; they continuously refract the light as it passes from one particle to the next;

with such a multitude of refractions, the rays have to wander back and forth within the body for so long that, in the end, almost all of them strike the solid particles of the body and thus are stopped and extinguished; these particles do not have the necessary elasticity, or other predisposition, to return quickly enough the sharp blow of the ray back to it.

I could end here, but there is yet another strange phenomenon of colors that deserves attention. I ask you to recall that Mr. Hooke spoke of the irregular scattering of light, caused when light passes near the edge of a razor, a blade, or another opaque body in a dark room[^42]. Rays passing very close to the edge are thereby scattered at all angles into the shadow of the blade.

On this occasion Sir William Petty, then president, posed a very appropriate question: does such scattering not take place along curved lines? This made me say, after I had heard, several days earlier, Mr. Hooke compare such scattering with the scattering of sound within a quiescent medium, that I consider it only a new kind of refraction, caused, perhaps, by the fact that the external ether begins to become somewhat rarefied in comparison with free space even before reaching the dark body; the denser ether outside the body and the rarefied ether inside it are bounded not by a mathematical surface, but pass into one another through intermediate degrees of density. Therefore rays passing so close to the body that they enter the limits where the external ether begins to become rarefied must be refracted, owing to the unequal density, and deflected inward toward the more rarefied medium of the body. Mr. Hooke was pleased to reply to this that, even if this were only a new kind of refraction, nevertheless it was still new. I did not know what to do with this unexpected answer, for I had no other thoughts except that a new kind of refraction could be as noble a discovery as any other matter concerning light. But after this, I do not know on what occasion, I had to say to certain persons who were present at what was taking place that I think I had seen this experiment earlier in an Italian author. This author is Honoratus Fabri; the experiment is described in his dialogue De Lumine, borrowed from Grimaldi[^43]. I mention him because I intend to describe something that is a step forward in comparison—

Fig. 6.

with it, as you will understand from this figure. Let us suppose that the sun shines through the small aperture \(HK\) into a dark room and illuminates the paper \(PQ\). The wedge \(MNO\) holds back all the light except for a small part of the beam. You will then see on the paper six rows of colors \(R, S, T, V, X, Y\), and, besides this, a very weak light scattering in all directions, as would have resulted from the refracted rays in the manner of \(HNZ\). The author describes this at greater length with various diagrams. I have time to mention only the chief point of what he says[^44].

For the (explanation of the) refraction of the ray \(HNZ\), let us suppose that in the following figure \(MNO\) is a solid wedge, \(ABC\) is the inner boundary of homogeneous rarefied ether inside; within these limits the ether passes through all intermediate degrees. It is clear that if the ray travels between \(B\) and \(n\), then in passing there it must deviate from the denser medium toward \(C\), and by so much the more, the closer it approaches \(n\). Further, as for the three rows of colors \(VXY\), they may perhaps arise from the number of oscillations (one, two, or three) overtaking the ray as it passes from \(G\), halfway between \(G\) and \(H\), i.e. at the nearest distance from \(n\), so that the ray touches the circle described about \(n\) with this distance. The last of the indicated oscillations, by correspondingly compressing or expanding the medium there, will enable the ray to move away again from \(n\), proceed farther, and produce colors. If the ray bends around \(n\) and is overtaken by the interval of the next wave, giving it the possibility of moving away from \(n\) along a line of motion very nearly coincident with the one directed toward \(Z\), then there will appear the weak light of which mention was made above. You will understand me somewhat better by comparing this with what was said about the colors of thin transparent plates, and by comparing the greatest distance traversed by the ray from \(GBH\) to \(n\) with the thickness of one of these plates. Something similar is found in Descartes’s explanation of the colors of the rainbow, which may shed further light on this question. But I have no time to develop further details, and I do not propose this with certainty, since I have not made sufficient observations on this subject.

1. Transact. No. 88, p. 5087. ↩