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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 (N. 184). Hence it appears 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 power.
Bodies, whether luminous or not, are only visible by the rays which proceed from them. 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 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 (N. 186). 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 Ptolemy 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 (N. 187). Near the earth's surface the path of the ray may be supposed to be circular; and the angle at the center of the earth corresponding to this path 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 point 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, increased 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. 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. The looming also or elevation of coasts, mountains, and ships, when viewed across the sea, arises from unusual refraction. A friend of the author, while standing 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 so 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 on land. In 1818, Captain Scoresby, whose observations on the phenomena of the polar seas are so valuable, recognized his father's ship by its inverted image in the air, although the vessel itself was below the horizon. He afterward 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 (N. 188). 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 (N. 189).
Many of the phenomena that have been ascribed to extraordinary refraction seem to be occasioned by a partial or total reflection of the rays of light at the surfaces of strata of different densities (N. 184). It is well known that when light falls obliquely upon the external surface of a transparent medium, as on a plate of glass or 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 travelers 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 this 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 which he was standing, a windmill, his own figure and that of a friend, depicted immediately opposite to him on the sea. This appearance lasted about ten minutes, till the sun had risen nearly his own diameter above the surface of the waves. The whole then seemed to be elevated into the air and successively vanished. The rays of the sun fell upon the cliff at an incidence of 73° from the perpendicular, and the sea was covered with a dense fog many yards in height which gradually receded before the rising sun. When extraordinary refraction takes place laterally, the strata of variable density are perpendicular to the horizon, and if combined with vertical refraction, the objects are magnified as when seen through a telescope. From this cause, on the 26th of July, 1798, the cliffs of France, fifty miles off, were seen as distinctly from Hastings as if they had been close at hand; and even Dieppe was said to have been visible in the afternoon.
The stratum of air in the horizon is so much thicker and more dense than the stratum in the vertical, that the sun's light is diminished 1300 times in passing through it, which enables us to look at him when setting without being dazzled. The loss of light and consequently of heat by the absorbing power of the atmosphere, increases with the obliquity of incidence. Of ten thousand rays falling on its surface, 8123 arrive at a
given point of the earth if they fall perpendicularly; 7024 arrive, if the angle of direction be fifty degrees; 2831, if it be seven degrees; and only five rays will arrive through a horizontal stratum. Since so great a quantity of light is lost in passing through the atmosphere, many celestial objects may be altogether invisible from the plain, which may be seen from elevated situations. Diminished splendor, and the false estimate we make of distance from the number of intervening objects, lead us to suppose the sun and moon to be much larger when in the horizon than at any other altitude, though their apparent diameters are then somewhat less. Instead of the sudden transitions of light and darkness, the reflective power of the air adorns nature with the rosy and golden hues of the Aurora and twilight. Even when the sun is eighteen degrees below the horizon, a sufficient portion of light remains to show, that at the height of thirty miles it is still dense enough to reflect light. The atmosphere scatters the sun's rays, and gives all the beautiful tints and cheerfulness of day. It transmits the blue light in greatest abundance; the higher we ascend, the sky assumes a deeper hue; but in the expanse of space, the sun and stars must appear like brilliant specks in profound blackness.
Constitution of Light according to Sir Isaac Newton-Absorption of Light -Colors of Bodies-Constitution of Light according to Sir David Brewster-New Colors in the Solar Spectrum-Fraunhofer's Dark LinesDispersion of Light-The Achromatic Telescope-Homogeneous LightAccidental and Complementary Colors-M. Plateau's Experiments and Theory of Accidental Colors.
Ir is impossible thus to trace the path of a sunbeam through our atmosphere without feeling a desire to know its nature, by what power it traverses the immensity of space, and the various modifications it undergoes at the surfaces and in the interior of terrestrial substances.
Sir Isaac Newton proved the compound nature of white light as emitted from the sun, by passing a sunbeam through a glass prism (N. 190), which separating