attend to the most simple case, namely, that in which the rings are formed of a single kind of rays, the red, for example. Then, if we observe them formed upon a lamina, the thickness of which gradually increases from the centre to the circumference, such as those of water and air comprehended between two spherical surfaces, we shall see that the first rings are the farthest separated from one another; the differences of their diameters grow less and less, as they become more distant from the central spot; and lastly, at a certain distance from this spot they are so close to each other, that the eye can no longer discern any intervals, and they appear to compose one continuous colour. If we view these rings through a prism, they will not experience any sensible separation, because the rays which compose them being equally refracted by the prism, all their images appear equally displaced, at least if we neglect the small differences which arise from the unequal incidence of these rays upon the faces of the prism. If we now cause the assemblage of all the colours which compose white light to fall upon these same laminæ, we shall constantly perceive, if we still view them directly with the naked eye, much fewer distinct rings than before, owing to the superposition of these rings and to their encroaching upon each other, as we explained above when speaking of the experiments of Newton on this subject, made in the dark room. But if we view the laminæ through a prism, refraction will transfer all the images in the same direction, but to unequal distances, the violet rays which are most refrangible, being removed farthest, and the red rays least. Then if we suppose the prism placed as represented in figure 161, the consequence will be that in all the parts of the rings situated beyond the centre C, the violet rings, which before were by their nature smaller in each order than the red, will be found to approach nearer to them; and if the difference of dispersion is sufficiently great to compensate entirely for their primitive inferiority they may finally join them; and as the same will take place very nearly with respect to all the intermediate colours between the red and the violet rings, the result will be that all these rings, being thus concentrated together, will appear white and separated by dark intervals. The case will then be the same as if they had been formed by rays of a single colour, and consequently we shall be able to perceive a much greater number than before the prism was interposed. But in

the position of the prism which we have supposed, this increase of distinctness will only take place with respect to the parts of the rings situated beyond their centre, relatively to the prism; and, on the contrary, with respect to the parts situated on this side the centre, the prism will only render them more confused; for its effect, in this part, will be to bring still nearer to the centre, the violet rings which before were the nearest, and thus remove them still further from the red rings; and this extension of the coloured fringes, by causing them to encroach more upon one another, will contribute to mix them more together, and will sooner compose an uniform white tint, in which no colour will be sufficiently distinct to be perceptible. It is evident, therefore, that if we wish to separate this part of the rings, we must change the direction of the prism. This is done in figure 162. But reciprocally, the parts situated beyond the centre will now become more confused and indistinct, as we find by observation.

277. Now since we are, in this manner, enabled to see rings in the part of the plate of air where we could not see them with the naked eye, it follows that such a plate may appear to the eye to be of a continuous and uniform white, when, in reality, the rays of light form rings there which the prism would separate and render sensible. This may be observed, not only in lamina of air comprehended between two object-glasses, but also in soap bubbles; for before they have attained the degree of thinness necessary to reflect sensible colours, the prism enables us to discover in them concentric rings. In the same manner, laminæ of mica, water, or glass blown by means of a lamp, although they are not thin enough to appear coloured to the naked eye, exhibit, when viewed by the prism, a vast number of small irregular rings, which undulate in a thousand different ways upon their surface, according to the insensible inequalities of their thickness. And, as observed by Newton, we shall easily comprehend the reason of these phenomena, if we consider that all these rings, infinite in number, already exist in the lamina when we view them with the naked eye, although on account of the extent of their circumference and the high order to which they correspond, they are so mixed and confounded together, that they appear to compose an uniform white; whereas the prism recovers them from this confusion by separating them. To perform this experiment in a satisfactory manner, we must place the thin lamina over some

black body, and view them through the prism disposed as in figure 163.

In fine, all the phenomena described in Newton's theory of coloured rings, confirm us in the conclusions to which we were before led, respecting the nature of the luminous rays themselves; namely, that the colorific properties of these rays do not depend upon any alteration or modification produced in them by the media which they traverse; but that they belong to the nature of the rays themselves, and exist in them at the moment they emanate from luminous bodies; that they are transported with the rays to all distances indefinitely, and preserved without alteration in all media.

Fits of easy Reflection and easy Transmission.

278. AFTER having established by experiment the fundamental laws which regulate the distribution and succession of the coloured rings formed upon thin laminæ, Newton recognised, by means of them, a new physical property in the particles of light, a property which not only accounts for all the particular phenomena observed by this great man, but also explains a multitude of other facts apparently of a totally different nature, and which were entirely unknown to him. In order to make it evident that this property results necessarily from the phenomena without the intervention of any hypothesis, I shall state in their order the propositions of Newton, adding only such explanations and remarks as are necessary to prove that they are general; and I shall afterwards show how each of them is a faithful expression of some phenomenon observed in the rings.

279. In the first place it must be remembered that the transmission of light is progressive. This fact was first made known by the eclipses of Jupiter's satellites, and has since been confirmed by the aberration of the fixed stars. These phenomena agree in proving that light employs 8′ 13′′ in traversing the mean distance of the earth from the sun. We find, moreover, that the motion of light is uniform through the whole of this space, and indeed throughout the extent of Jupiter's orbit. Observations of this kind do not indicate a sensible difference in the velocities of the luminous particles of different refrangibilities; for if there Opt.

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were a sensible difference in this respect, when a satellite entered the shadow or emerged from it, its disc would appear successively tinged with the different prismatic colours, which is not the case. The common velocity thus determined is that which light has in a vacuum; for the celestial spaces may be considered as destitute of all ponderable or refracting matter. When the luminous particles traverse media, the parts of which act upon them by attractions at a small distance, their velocity in these media is to their velocity in a vacuum, as the sine of incidence. in the vacuum is to the sine of refraction in the material medium. Whence it follows that the velocity of light in bodies, is always greater than in a vacuum, and increases with their refracting power.

280. We are now prepared to attend to the new properties of light which Newton established as consequences of his observations upon thin laminæ.

First proposition. Every luminous particle, which traverses a refracting surface of whatever kind, acquires by this very act a certain transient disposition, which, from that time, during the whole course of the particle in the same medium, is periodically reproduced at equal intervals; and the consequence of each return of this disposition, is, that the luminous particle is easily transmitted through a second refracting surface, if one then presents itself; while, on the contrary, at each intermission of this state, it is easily though not necessarily reflected by such a surface. These successive states or dispositions, Newton calls fits of easy transmission and easy reflection; and the distance traversed by the particle between the returns of two fits of the same nature, he calls the interval of the fits; so that the length of each fit is half of one of these intervals. If these definitions be expressed analytically, we can predict the kind and stage of the fit, which a luminous particle will be found in at any instant whatever, in a given medium, when we know these elements for the instant of its entrance into the medium, and also the length of the fits for this particle. In the Traité de Physique, I have given formulas which express the dependance in question.

This is only a general enunciation of the fact and the law of the alternate transmissions and reflections, which occur at different thicknesses, in the same place, under each given incidence. Only Newton represents these alternations as indefinite,

and attributes them to a physical property of the luminous particles, which renders them susceptible of being thus modified by the refracting surfaces of bodies; these are the two points which we are to examine.

281. When we observe the compound rings with the naked eye, we are unable to perceive more than 7 or 8 distinct successions or alternations; and we can predict beforehand, that in every other series of phenomena which follows similar laws, we can never perceive more. But the analysis, and if we may so express it, dissection, which we havemade of the phenomenon, has taught us that this limitation is owing simply to the encroachment and superposition of rings of all colours, formed by the different simple rays of which white light is composed. Accordingly, we have discovered a much greater number of rings, when we have formed them with a beam of simple light, and we have arrived at the same object in a still easier manner, by taking rings themselves compound, and separating them by the prism, in virtue of their unequal refrangibility. These observations prove that the alternations of reflection and transmission extend to thicknesses much greater than we at first suspected; and from the manner in which the rings crowd upon each other according as the thickness increases, we may conclude that the alternations are still produced, at thicknesses much greater than those at which we cease, even with the prism, to distinguish them. Indeed, other experiments of Newton, which may be seen in the Traité de Physique, show that these alternations exist in glass, at thicknesses which amount even to a quarter of an inch; and the same process might be employed to make known their existence at still greater thicknesses. Now, as such thicknesses exceed by many thousand times, the distance at which the variability of the attractive and repulsive forces of media can be sensible, we are obliged to conclude that the alternations of reflection and transmission, if continued so far, must be continued indefinitely.

282. Hence it becomes evident that these alternations depend upon some physical modification impressed upon the luminous particles, in their passage through the first refracting surface; and which they afterwards preserve throughout the whole extent of the medium which they traverse; for otherwise, when the luminous particles came to the second surface of this medium, their reflection or transmission would no longer depend upon