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grass are perceived between thy adversary's teeth; thy fame is predominant throughout space; the minds of thy foes are void [of hope]; their route is the desert where men are hindered from passing; O Vigraha Raj'a Déva, in the jubilee occasioned by thy march.

"May thy abode, Ó Vigraha, sovereign of the earth, be fixed, as in reason it ought, in the bosoms fakin to the mansion of dalliance) of the women with beautiful eyebrows, who were married to thy enemies. There is no doubt of thy being the highest of embodied souls. Didst thou not sleep in the lap of Sri, whom thou didst seize from the ocean, having

churned it?

"In the year from the fortunate

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PHILOSOPHICAL PAPERS.

On the Optical PHANOMENON named the MIRAGE

Translated from the French of M. GASPARD MONGE, by the Author of "A NON-MILITARY JOURNAL made in EGYPT."]

"D

URING the march of the French army through the Desert, from Alexandria to Cairo, we had an opportunity of observing a phenomenon daily, that must be considered extraordinary by the greater part of the inhabitants of France. It is necessary for its production, that the spectator should be placed in an extensive plain, wholly, or at least nearly, level; that this plain should be prolonged to the limits of the horizon, and that the soil, by exposure to the sun, should have acquired a very high degree of temperature. It is supposed that these three circumstances may be united in the flats of Bourdeaux, for their level, like that of Lower Egypt, is nearly horizontal; they are not terminated by any mountain, at least in the direction from east to west; and it is probable that, during our long summer days, the arid soil of which they are formed may acquire a sufficient temperature. It is, therefore, not wholly improbable but that this phenomenon may be known to the inhabitants of that department; it is familiar to mariners, who observe it frequently at sea, and have given it the name of mirage.

"In truth, the cause which occasions the mirage in the ocean, may be very different from that which

produces it at land; but the effect being the same in both cases, I have not deemed it proper to introduce a new word. I shall first de scribe the phenomenon, and afterwards endeavour to give an explanation of it.

"The country of Lower Egypt is nearly a level plain, which loses itself, like the sea, in the clouds at the extremity of the horizon: its uniformity is only interrupted by a few eminences, either natural or factitious, on which are situated the villages, thus kept out of the reach of the inundations of the Nile; and these eminences, less usual on the skirts of the desert, more frequently to be seen on the side of the Delta, and which appear like a dark line on a very transparent sky, are rendered still further visible by the date-trees and sycamores, oftener to be met with in such situa tions than elsewhere.

"Both morning and evening the aspect of the country is exactly as it ought to be; and between you and the last villages which present themselves, you perceive nothing but land; but when the surface of the earth is sufficiently heated by the rays of the sun, and indeed until it begins to get cold towards the evening, the land no longer seems to have the same extension, but to be terminated, to within the

distance

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 spectator is 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 the 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, shirinks 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 di rection 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:

1o. 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 perpendicular, 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 maximum,

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 denser medium 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 maximum 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 maximam, 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 maximum 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 maximum, 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 following the rays of light to pass through with rapidity, does not permit it to acquire a very high degree of temperature by its direct exposition to the sun 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 the heated 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 strie, which alter and agitate the images of fixed objects that are situated beyond them.

"In our European climates, we are acquainted with similar striæ, 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 culoric.

"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 molecule 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 making 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 representation of that part of the heavens 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 reffects,) 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 trans mitted 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 sur

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