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bent. The barometer shows that the density of the atmosphere decreases as the height above the earth increases; and direct experiments prove, that the refractive power of the air increases with its density; it follows, therefore, that if the temperature be uniform, the refractive power of the air is greatest at the earth's surface and diminishes upwards.

A ray of light from a celestial object falling obliquely on this variable atmosphere, instead of being refracted at once from its course, is gradually more and more bent during its passage through it, so as to move in a vertical -curved line, in the same manner as if the atmosphere consisted of an infinite number of strata of different densities. The object is seen in the direction of a tangent to that part of the curve which meets the eye, consequently the apparent altitude of the heavenly bodies is always greater than their true altitude. Owing to this circumstance, the stars are seen above the horizon after they are set, and the day is lengthened from a part of the sun being visible, though he really is behind the rotundity of the earth. It would be easy to determine the direction of a ray of light through the atmosphere, if the law of the density were known; but as this law is perpetually varying with the temperature, the cause is very complicated. When rays pass perpendicularly from one medium into another, they are not bent; and experience shows, that in the same surface, though the sines of the angles of incidence and refraction retain the same ratio, the refraction increases with the obliquity of incidence. Hence it appears, from what precedes, that the refraction is greatest at the horizon, and at the zenith there is none; but it is proved that at all heights above ten degrees, refraction varies nearly as the

tangent of the angular distance of the object from the zenith, and wholly depends upon the heights of the barometer and thermometer; for the quantity of refraction at the same distance from the zenith varies nearly as the height of the barometer, the temperature being constant; and the effect of the variation of temperature is to diminish the quantity of refraction by about its 480th part for every degree in the rise of Fahrenheit's thermometer. Not much reliance can be placed on celestial observations within less than ten or twelve degrees of the horizon, on account of irregular variations in the density of the air near the surface of the earth, which are sometimes the cause of very singular phenomena. The humidity of the air produces no sensible effect on its refractive powers.

Bodies, whether luminous or not, are only visible by the rays which proceed from them; and as the rays must pass through strata of different densities in coming to us, it follows that, with the exception of stars in the zenith, no object either in or beyond our atmosphere is seen in its true place; but the deviation is so small in ordinary cases, that it causes no inconvenience, though in astronomical and trigonometrical observations a due allowance must be made for the effects of refraction. Dr. Bradley's tables of refraction were formed by observing the zenith distances of the sun at his greatest declinations, and the zenith distances of the pole-star above and below the pole; the sum of these four quantities is equal to 180°, diminished by the sum of the four refractions; whence the sum of the four refractions was obtained; and from the law of the variation of refraction determined by theory, he assigned the quantity due to each altitude. The mean horizontal refraction is about 35' 6", and at the height of

forty-five degrees it is 58" 36. The effect of refraction upon the same star above and below the pole was noticed by Alhazen, a Saracen astronomer of Spain, in the ninth century; but its existence was known to Ptolmey in the second, though he was ignorant of its quantity.

The refraction of a terrestrial object is estimated differently from that of a celestial body; it is measured by the angle contained between the tangent to the curvilineal path of the ray, where it meets the eye, and the straight line joining the eye and the object. Near the earth's sur face the path of the ray may be supposed to be circular; and the angle of this path between tangents at the two extremities of this arc is called the horizontal angle. The quantity of terrestrial refraction is obtained by measuring contemporaneously the elevation of the top of a mountain above a point in the plain at its base, and the depression of that below the top of the mountain. The distance between these two stations is the chord of the horizontal angle; and it is easy to prove that double the refraction is equal to the horizontal angle, diminished by the difference between the apparent elevation and the apparent depression. Whence it appears that, in the mean state of the atmosphere, the refraction is about the fourteenth part of the horizontal angle.

Some very singular appearances occur from the accidental expansion or condensation of the strata of the atmosphere contiguous to the surface of the earth, by which distant objects, instead of being elevated, are depressed; and sometimes, being at once both elevated and depressed, they appear double, one of the images being direct, and the other inverted. In consequence of the upper edges of the sun and moon being less refracted than the lower, they


often appear to be oval when near the horizon. looming also, or elevation of coasts, mountains and ships, when viewed across the sea, arises from unusual refrac tion. A friend of the author's, on the plains of Hindostan, saw the whole upper chain of the Himalaya mountains start into view, from a sudden change in the density of the air, occasioned by a heavy shower after a very long course of dry and hot weather. Single and double images of objects at sea, arising from sudden changes of temperature, which are not soon communicated to the water on account of its density as to the air, occur more rarely, and are of shorter duration than similar appearances of land. In 1818, Captain Scoresby, whose observations on the phenomena of the polar seas are so valuable, recognised his father's ship by its inverted image in the air, although the vessel itself was below the horizon. He afterwards found that she was seventeen miles beyond the horizon, and thirty miles distant. Two images are sometimes seen suspended in the air over a ship, one direct and the other inverted, with their topmasts or their hulls meeting, according as the inverted image is above or below the direct image. Dr. Wollaston has proved that these appearances are owing to the refraction of the rays through media of different densities, by the very simple experiment of looking along a red hot poker at a distant object. Two images are seen, one direct and another inverted, in consequence of the change induced by the heat in the density of the adjacent air. He produced the same effect by a saline or saccharine solution with water and spirit of wine floating upon it.

Many of the phenomena that have been ascribed to extraordinary refraction seem to be occasioned by a particl

or total reflection of the rays of light at the surfaces of strata of different densities. It is well known that when light falls obliquely upon the external surface of a transparent medium, as on a plate of glass, or a stratum of air, one portion is reflected and the other transmitted, but when light falls very obliquely upon the internal surface, the whole is reflected and not a ray is transmitted; in all cases the angles made by the incident and reflected rays with a perpendicular to the surface being equal. As the brightness of the reflected image depends on the quantity of light, those arising from total reflection must be by far the most vivid. The delusive appearance of water, so well known to African travellers, and to the Arab of the desert, as the Lake of the Gazelles, is ascribed to the reflection which takes place between strata of air of different densities, owing to radiation of heat from the arid sandy plains. The mirage described by Captain Mundy, in his Journal of a Tour in India, probably arises from this cause. A deep precipitous valley below us, at the bottom of which I had seen one or two miserable villages in the morning, bore in the evening a complete resemblance to a beautiful lake; the vapor, which played the part of water, ascending nearly half way up the sides of the vale, and on its bright surface, trees and rocks being distinctly reflected. I had not been long contemplating the phenomenon, before a sudden storm came on and dropped a curtain of clouds over the scene.'

An occurrence which happened on the 18th of November, 1804, was probably produced by reflection. Dr. Buchan, while watching the rising sun from the cliff about a mile to the east of Brighton, at the instant the solar disc emerged from the surface of the ocean, saw the cliff on

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