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distance of about a league, by a general inundation. “The villages placed beyond that appear like so many islands stationed in the midst of a great lake,from which the spectatoris separated by an extent of land, more or less considerable, according to circumstances. You then behold the image of each of these villages reflected exactly as if it were exhibited on a clear surface of water, with only this difference, that as the representation is at a considerable distance, the smaller objects are invisible, and the masses alone distinct; in addition to this, the edges of the reversed image are rather ill-defined, and such as they would be if the surface of the reflecting medium happened to be a little agitated. * “In proportion as, one approaches a village, which appears to be placed in §. midst of an inundation, the margin of the water seems to recede, and the arm of the sea, separating you as it were from the village, shrinks back by degrees: it at length, disappears entirely, and the phenomenon which now ceases, in respect to the first village, is instantly reproduced by a new one, which you discover at a due distance in the rear. Thus every thing contributes to complete an illusion, which is sometimes cruel, more especially in the Desert, because it tantalises you with the appearance of water, at a time when you experience the greatest want of that element. “The explanation which I propose to give of the mirage, is founded on some of the principles of optics, that, indeed, apply equally to all the elements, but which it may be, perhaps, proper to explain here. “When a ray of light traverses a

transparent and uniform medium, its direction is in a straight line. When a ray passes from a transparent medium into another, the density of which is greater, if its direction in the first be perpendicular to the surface that separates it from the two media, this direction will not experience any alteration; that is to say, so long as the right line which the ray forms in the second medium, is a prolongation of that followed in the first. But if the direction of the incidental ray makes

an angle with the perpendicular at

the surface: 1°. The ray will divide in its passage in such a manner, that the angle which it forms, with the perpendicular in the second medium, becomes smaller; and “2°. In respect to the two media, whatever may be the extent of the angle which the incidental ray forms with the ndicular, the sinus of this angle, and that of the angle of the refracted ray, are always in a correspondent ratio. “But the sinus of a large angle does not increase so rapidly as that of a small one. When the angle, therefore, that is formed by the incidental ray and the perpendicular happens to increase, the sinus of the angle, formed by the broken ray, increases in the ratio of the sinus of the former, and the increase of the angle itself is less than that of the angle of the incidental ray. Thus, in proportion as the angle of incidence augments, the angle formed by the broken ray augments also, but always by little and little; so that when the angle of incidence hath arrived at its largest dimensions, that is to say, when it is within an infinitely small space of 90°, the angle which the broken ray makes with the perpendicular is less than 90°: this is a marimum, Or,

or, in other words, no ray of light can pass from the first medium into a second, under a greater angle. “When the ray of light passes, on the contrary, from a densermedium into one less so, it exactly follows the same line as in the first case, but in a contrary direction; that is to say, if in the dense medium it has the same direction as the broken ray in the first case, it divides at the surface, and assumes the direction which has been also followed by the incidental ray. “In consequence of this it may be inferred, that on the passage from a more to a less dense medium, “1°. If the ray of light be comprehended between the perpendicular and the direction of the diverging ray which constitutes the marimum angle; this ray will project into the less dense medium. “2°. If the ray of light possesses the same direction as the diverging ray, the angle of which is the maximum, it will again issue forth, by making an angle of 90° with the perpendicular, or by remaining in the plane, which serves as a tangent to the surface. But if the angle which the ray of light forms with the perpendicular, be greater than the marimum of the angle of refraction, or what amounts to the same, if the ray be compressed between the surface and the diverging ray, the angle of which is the marimum, it will not leave the dense medium : it will reflect itself to the surface, and re-enter the same medium, by making the angle of reflection equal to the angle of incidence, these two angles being in the same plane, perpendicular to the surface. It is on this last proposition that the explanation of the mirage is principally founded. “The transparency of the at

mosphere, that is to say, the faculty which it possesses of followin the rays of light to pass j with rapidity, does not permit it to acquire a very high degree of temperature by its direct exposition to the sum alone; but when, after having traversed the atmosphere, the light becoming extinguished by an arid soil, that serves only in a very small degree as a conductor, hath considerably warmed the surface of this earth; it is then that the inferior stratum of the atmosphere, by its contact with theheated surface of the soil, contracts a very high degree of temperature. “This stratum dilates itself; its specific weight diminishes; and in consequence of the laws of hydrostatics, it elevates, itself, until, by becoming cool, it hath recovered a density equal to that of the surrounding element. It is then succeeded by the stratum immediately above it, through which it passes, and the other soon experiences a similar operation. Thence is produced a continual efflux of rarefied air, always elevating itself through

a denser medium, that in its turn

experiences a depression; and this efflux is rendered sensible by the stria, which alter and agitate the images of fixed objects that are situated beyond them. “In our European climates, we are acquainted with similar striar, produced by the same cause; but they are not so numerous, and do not possess such an ascensional rapidity as in the Desert, where the altitude of the sun is greater, and the aridity of the soil, by depriving it of evaporation, does not permit any other employment of the caloric. “Thus towards the middle of the day, and during the greatest degrees of heat, the stratum of the atmo

atmosphere, in contact with the soil, is of an evidently less degree of density than the strata immediately above it. “The brilliancy of the sky proceeds merely from the rays of the sun being reflected in every direction by the transparent molecular of the atmosphere. Such of the rays of light as are transmitted by the more elevated part of the sky, and which descend to the earth after makin a considerable angle with the horizon, take a new direction on entering the inferior dilated stratum, and encounter the element on which we live, by means of a much smaller angle. But those that proceed from the lower parts of the sky, and form small angles with the horizon, when they reach the surface which separates the inferior and dilated stratum of the atmosphere, from the more dense stratum above, are unable to leave the latter; in conformity, therefore, to the principle of optics already alluded to, they reflect themselves in an ascending direction, by making an angle of reflection equal to the angle of incidence, as if the surface which separates the two strata constituted a mirror: and they then represent to the eye placed in the dense stratum, the inverted image of the lower parts of the sky, which appear as if below the real horizon. , “In this case, if you were not advertised of your error, as the reF. of that part of the eavens perceived by means of reflection is almost of the same brilliancy as that seen directly, you would imagine that the sky was greatly prolonged, and far nigher than it really is. “If this phenomenon were to occur at sea, it would alter the altitude of the sun, taken by an instrument, and augment it in the

ratio of the quantity of the apparent limit of the horizon depressed. “But if some terrestrial objects, such as villages, trees, or little hills, give you notice that the limits of the horizon are more distant, and that the sky is not really so near, (as the surface of the water is not usually visible under a small angle, but by the image of the sky which it reflects,) you will perceive the representation of the sky, and imagine that you behold a superficies of reflecting water. “The villages and trees that are

at a proper distance, by intercepting

a portion of the rays of light transmitted by the lower regions of the heavens, occasion so many voids in the image of the sky, produced by reflection. These voids are wholly occupied by the inverted images of the same objects, because such of the rays of light as are transmitted by them, and which form angles with the horizon, equal to those constituted by the intercepted rays, are reflected back in the same manner as those would have been. But" as the reflecting surface which separates the two strata of air, of different densities, is neither perfectly level, nor perfectly motionless; the last images will, of course, appear badly defined, and agitated towards the edges, like those produced by the surface of water which may have contracted slight undulations. “It is easily to be discovered why this phenomenon cannot take place when the horizon is terminated by an elevated chain of mountains; for those mountains intercept all the rays of light transmitted by the lower parts of the sky, and only allow those to pass above them which form sufficiently large angles with the dilated surface, to prevent the reflection from taking place. “In an uniform state, that is te say, by supposing that the density and thickness of the dilated stratum are constant, and the temperature of the superior stratum invariable, the greatest possible angle under which the rays of light could be thus reflected, would be determined with precision: for the largeness of this angle depends entirely on the immediate connection between the sinus of the angles of incidence and reflection for §. two *nedia. But of all the rays reflected, those which form the greatest angle with the horizon, appear to issue from the nearest point to that where the phenomenon commences. “In an uniform state them, the point at which the phenomenon commences, is always at a certain distance from the observer: accordingly, if he should happen to advance, the spot at which the inundation seems to begin, appears to advance also in the same direction, and with the same celerity. If the line of march should, therefore, be directed towards a village, which appears to be situated in the midst of the inundation, the limits of the inundation will seem to recede insensibly from this village, and are soon after seen to stretch beyond 1t. “When the sum is near the horizon at his rising, the earth cannot have been sufficiently warmed; and at his setting it has become too cold for the phenomenon of the mirage. It then appears to be extremely difficult to perceive both a direct and reflected image of the sun, on account of the elevated temperature of the inferior stratum of the atmosphere. But during the second quarter of the moon,

that planet rises in the afternoon, a time when circumstances are more favourable to the mirage. If it then happens that the brilliancy of the sun and the clearness of the atmosphere should permit the moon to

be discerned at her rising, two

images of that planet will be observed, one above the other, in the same vertical line. This phenomenon is known by the name of paraselene. “The transparency of the sea allows the rays of the sun to pene. trate to a considerable depth; its surface, from its exposition, does not, however, become near so warm as an arid soil in the same circumstances; it cannot communicate, therefore, to the stratum of air that reposes upon it so elevated a temperature; and on this account the mirage is not so common at sea as in the Desert. But the elevation of the temperature is not the sole cause which, under a constant pressure, may dilate the inferior stratum of the atmosphere. In fact, the air possesses i. faculty of dissolv. ing water, so far, even as to attain the point of saturation without losing its transparency; and Saussure hath proved that the specificweight of the air decreases in proportion to the quantity of water kept in dissolution. When, therefore, any wind at sea is not impregnated with water, the inferior stratum of the atmosphere, which is in contact with the surface of the ocean, dissolves water anew, and thus becomes dilated. This cause, added to the slight augmentation of the temperature, may, however, produce a casioned by the dissolution of a large quantity of water, may take place every moment of the day, as well when the sun is near the horizon, as when he approaches the meridian. It is possible that a parh, lion might then be produced, a phenomenon in consequence of which, either at the rising or setting of the sun, one beholds two images of that luminous body above the apparent horizon at the same time. But I never had occasion to observe this latter phenomenon, which is very unfrequent, or to remark the circumstances that accompany it. I therefore propose this latter explanation with a certain degree of reserve, and merely with an intent of furnishing the means of making useful observations.

state of things favourable to the

mirage, which mariners, indeed,

frequently observe. “This last cause, or, in other words, the dilatation of the infeirior stratum of the atmosphere, occasioned

Addi TiON.

“Sincereading the above memoir, I have had frequent opportunities of observing the mirage at land; this has occurred in various seasons, as well as under different circumstances, and the result, even including the minutest details, has always been in conformity to the explanation already given by me. Of all these observations, there is one only, the relation of which may prove useful here.

“I was along with general Bonaparte in the valley of Suez, when he discovered the canal that formerly united the Red Sea with the Mediterranean. This valley, which is some leagues in length, is bounded on the east by that chain of mountains that extends from Syria to Mount Sinai; and on the west by the mountains of Egypt. These mountains are in general sufficiently elevated to exclude the rays of light transmitted by the inferior parts of the sky, and such of the

rays as are not thus intercepted,

reach the earth under too large an angle to be reflected by the inferior dilated stratum of the atmosphere. Thus in the hottest part of the day one does not perceive the reflected surface of any portion of the sky, nor is the appearance of an inundation any where to be seen. “ Notwithstanding this, the ef. fect of the mirage is not entirely lost; the visible objects placed generally on an ascent, whose position corresponds with the inferior parts of the sky, the image of which reflects itself, participates in the effect, although in a less striking manner, on account of their small extent, and also with less force, because the colour is far more obscure than that of the sky. Independently of the representation o by the direct rays of ight, the rays which have emanated from these objects, and are directed towards the earth, become reflected by the inferior stratuin of the air, in the same manner as the rays proceeding from the inferior parts of the atmosphere, of which they occupy the place; thus producing a second image of these objects inverted, and placed vertically above the former. “This duplication of images produces optical illusions, against which it is proper to be on our guard in a desert that may be occupied by an enemy, while no one is at hand to give information relative to such alarming appearances. “I shall take advantage of this opportunity to mention another optical phenomenon, which is not sufficiently interesting to be made the subject of a particular memoir. “During our return from Egypt, when we approached the European climates, one morning, a few hinutes after sun-rise, the sky was clear towards the east; it rained at

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