possibility or impossibility of its emergence. These conditions may be established in an abstract manner, by means of the properties which Newton has ascribed to the fits; and their results may be compared with those of experiment. In this manner, the effects of reflection upon the fits are established conformably to the definitions of Newton; and, by applying them to thin plates, nearly parallel, and which exhibit the phenomena of coloured rings, we are enabled to ascertain precisely what takes place before and after interior reflection, by which the rays are produced. This delicate subject can only be suggested here; those who would pursue it further, are referred to the Traité de Physique.

Explanation of Coloured Rings and Fits upon the Hypothesis of the Undulations of Light. Principle of Interferences.

306. Ir light really consist of matter emitted from luminous bodies, the fits are a necessary property, since they are a literal enunciation of the alternations of reflection and transmission, which the coloured rings present. But if we suppose light otherwise constituted, these alternations may be represented differently.

Descartes, and after him Huygens and many other philosophers, have supposed the sensation of light to be produced in us, by undulations excited in a very elastic medium, and propagated to the eye where the sensation takes place, in the same manner as the undulations excited in the air and propagated to the ear, produce the sensation of sound. This medium, if it exist, must fill the celestial spaces, since it is through these spaces that the light of the heavenly bodies comes to the eye. It must also be very elastic, since the transmission of light takes place with so great a velocity. At the same time it must have an infinitely small density, since the most careful examination of ancient and modern astronomical observations, does not indicate in the planetary motions any sensible resistance. This medium must evidently penetrate all terrestial bodies, since all transmit light when they are sufficiently thin, and since they modify, by their contact, its interior reflection. Moreover, its density in different

substances must vary according to their nature, since the unequal refractions which they exert upon the same rays, prove that the propagation of these rays takes place with unequal velocities. But what must be the proportions of these densities, for different substances, crystallized and uncrystallized? How is the luminous ether introduced into each of them in this state, and retained there? How is it confined in such a manner as not to admit of its spreading without? Moreover, how is this medium, so rare, unresisting and intangible, agitated by the particles of bodies which appear to us luminous? These are so many points that must be well understood, or at least well defined, before we can have an exact idea of the conditions by which the undulations are to be produced and propagated; but they have not as yet been distinctly settled.

307. Nevertheless, if we conceive a body endued with the power of exciting an instantaneous agitation in any point of such a medium, supposed for the present to be equally dense throughout its whole extent, this agitation will be propagated spherically by the same laws as that of the air, except that the velocity will be much greater. Each particle of the undulating medium will then be agitated in its turn, and afterwards come to a state of rest.

If these agitations are repeated in the same point, there will result, as in air, a series of undulations analogous to those of sound; and, as in the latter we observe periodical alternations of condensation and rarefaction, corresponding to the alternations of direction which constitute the vibrations of the sonorous body, so we may suppose that the successive and periodical vibrations of luminous bodies produce similar alternations in the luminous undulations. Lastly, as the succession of sonorous undulations, when it is sufficiently rapid, produces on the ear the sensation of continued sound, the quality of which depends upon the rapidity of the opposite vibrations, and the laws of condensation and velocity which the nature of these vibrations excites in each sonorcus wave; so, with analogous conditions, the ethereal undulations may produce sensations of light in the eye, which shall vary with the diversity of the conditions. Hence the difference of colour. In this system the lengths of the luminous undulations correspond to the fits of Newton, and the length of the former is, as we shall see hereafter, precisely quadruple that of the latter; the velocity of propagation, in each case, depends upon the ratio of the elastic force of the fluid to its density.

308. When a sonorous undulation excited in the air, arrives at the surface of a solid body, its impulse produces in the parts of this body an actual though insensible motion, which sends it back. If the body, instead of being solid, be a gas, there is still an impulse, which sends the sonorous undulation back, but a sensible undulation is produced in the gas, depending upon the impression which its surface has received.* The luminous undulations must therefore produce a similar effect, when the medium, traversed by them, is terminated by a body, in which the density of the ethereal fluid is different; that is, there must be produced a reflected wave and a transmitted one; thus giving rise to reflection and refraction. In this system the intensities of the rays must be measured by the moving force of the fluid in motion, that is, by the product of the density of the fluid into the square of the velocity of its particles.

In order to establish these analogies which appear so remarkable, we must follow out the consequences by calculation. We must determine by the laws of motion in fluids, how the direct waves must be refracted when they pass from one medium to another; what is the ratio of the angle of refraction to the angle of incidence in substances crystallized and uncrystallized, and what is the value of this ratio for each simple ray, according to the nature of the vibrations which belong to it. M. Poisson has succeeded in solving completely the two first problems, and his analysis has indicated the same laws of refraction which are established by experiment. He has likewise deduced from it the phenomenon of interior reflection at the point of contact of two media of different refracting powers, a phenomenon which might have seemed, at first view, incompatible with the hypothesis of undulations, by appearing to require that the undulations,

* This phenomenon is observed in the sounds produced with organ pipes, when we have introduced successively strata of gas of unequal densities, for instance, of atmospheric air and hydrogen gas. The sounds which such a compound is capable of producing, have been calculated by M. Poisson, and the law of the succession is found to be perfectly conformable to what direct experiments have shown. Now this same theory indicates the mode in which the agitations, excited in one fluid, are communicated and divided, when they arrive at another contiguous fluid..

excited in the first fluid, should be reflected there without communicating motion to any other contiguous fluid. The analysis of M. Poisson removes this difficulty, by showing that the second medium actually receives condensations and velocities, but so small and decreasing so rapidly with the distance, that they cease to be sensible at any distance physically appreciable. But this analysis, which assigns so exactly and so completely the smallest particulars of the luminous undulations, offers nothing by which we can account for the phenomenon of dispersion, or rather, nothing which is not opposed to it. This circumstance constitutes an objection to the system of undulations as strong as the analysis which leaves it unexplained, is refined and complete. M. Poisson, in the course of his calculations on reflection, remarked also a peculiarity which the system of undulations indicates, and which experiment does not present; but he observes that this disagreement might vanish, if regard were paid to the particular state of the two media in the strata bordering upon their common surface; so that we are not obliged to consider it as a positive objection. He has also applied this analysis to the calculation of the coloured rings formed by homogeneous light, considering each of them as formed, not by the alternations of reflection and transmission, which light experiences at the second surface of the thin lamina, as is done in the system of emission, but by the simultaneous return, in the organ, of the waves reflected at the two surfaces of the lamina, in opposite stages of undulatory motion. We cannot here give a more extended view of this valuable paper; but those who may wish to pursue the subject further, will find an abstract of it, by the author himself, in the 22d volume of the Annales de Chimie et de Physique. They will also find in the same volume the results of the discussion between M. Poisson and M. Fresnel, respecting the manner in which the undulatory system is to be regarded.

309. When the ear hears at the same time two regular and continued sounds, it distinguishes, besides the two sounds, the epochs at which the undulations of the same nature arrive together or separate. If the periods of these returns are very rapid, we hear a third sound, the tone of which may be calculated beforehand from the epochs of the coincidences; but if the returns of these coincidences are more rare, so that the ear can distinguish them separately, we hear a series of beats

which succeed each other with greater or less rapidity. The mixture of two rays which arrive together at the eye, under circumstances properly chosen, produces a similar effect which was first noticed by Grimaldi, but of which Dr Young was the first to show the numerous applications. The best manner of producing this phenomenon is the following, proposed by M. Fresnel.

We introduce into a dark room a solar beam, reflected in a fixed direction by means of a heliostat, and transmit it through a magnifying glass of a very short focal distance, which causes it to converge at its focus almost in a mathematical point. From this the rays of which the pencil is composed, diverge in all directions, and form a cone which increases in magnitude in proportion to the distance. In this cone, at the distance of 7 or 8 feet, we place two metallic mirrors, inclined to each other at a very small angle, so as to receive the rays under nearly the same incidence; and placing the eye at a certain distance, we view at the same time on each mirror the image of the luminous point. In this manner we perceive two images, separated by an angular interval depending upon the inclination of the mirrors, their distance from the luminous point, and the distance at which the observer is placed. But what constitutes the essential circumstance of the phenomenon is, that if we make use of a magnifying glass of a short focus, we perceive between the places of the two images, a series of luminous stripes, parallel to each other, of different colours, and directed perpendicularly to the line which joins the two images. When the incident light is simple, the stripes are of the colour of this light, and separated by dark intervals. Their direction depends simply on the direction of the planes of the mirrors, and not on any influence produced by the physical borders which terminate them; for we can turn each of the mirrors upon itself, which will change the position of the borders without changing the common section of the two planes, and the stripes will suffer no alteration.

310. For the sake of simplicity, let us suppose the incident light homogeneous. This case is easily realized for any of the colours, by decomposing with a prism a beam of light rendered stationary by a heliostat; we may likewise realize the same condition, but only for the red, by looking at the stripes through certain coloured glasses, which suffer none but this colour to Opt.

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