2′ and 40° 17' or 1° 45'; a quantity nearly equal to three and a half times the apparent breadth of the sun. This space is occupied by the remaining five colored arches, and, as each is 32' in width, (Art. 421,) they necessarily overlap one another, and cause, by their mutual blending, an indistinctness in the boundary of the several hues. The two half-breadths of the red and violet arches added to 1° 45' give the whole width of the bow, which is equal to 20 17, or about four and a half times the apparent diameter of the sun. 429. The breadth of the exterior bow, from the middle of the red to that of the violet, is found in like manner to be 3o 10'-the difference between 54° 9′ and 50° 59. To this quantity 32' must be added to obtain the entire breadth. The interval between the bows, computing from the red of the primary to that of the secondary, is 8° 57'. All these results, deduced theoretically, precisely agree with those obtained by actual measurement. 430. POSITION AND SIZE OF THE RAINBOW. Since the centre of the rainbow is in the direction of the line imagined to be drawn from the sun through the eye of the spectator, its position will evidently vary with that of the spectator, and its size with the altitude of the sun. If this luminary is 42° 2' above the horizon, the top of the inner bow will be just visible; but if upon the horizon, the bow will be a semicircle, having an elevation of 42° 2. If the observer, in the latter case, were upon the summit of a mountain, the arch would be somewhat greater than a semicircle; since the line of direction. from the sun through his eye, would strike the sky opposite, at a point above the horizon. Should a person happen to be upon a mountain, when the sun is high in the heavens, and a shower at the same time occur in the vale below, he will sometimes perceive a rainbow forming a complete circle. State what is said in regard to the breadth of the bows. Such are said by Ulloa to be frequently seen on the mountains of Peru above Quito. The foaming waters of cataracts are often spanned by richly tinted bows, caused by the rising spray. They are regularly seen at the falls of Schaffhausen, on the Rhine, and at the cataract of Niagara. At Terni, in Italy, where the river Velino rushes over a precipice 200 feet high, a bow of rare beauty is beheld. It appears, to a spectator below, arching the falls with its glowing tints, while two other bows are reflected on the right and left. 431. RAINBOWS IN THE NORTH. Rainbows are sometimes seen at mid-day. On the 13th of Dec. 1847, at one o'clock, P. M., Prof. Olmstead beheld at Yale College an entire bow in the north. During the same week, the writer observed at Hartford a similar bow at nearly the same hour of the day. Such a phenomenon can never arise, in the case of the primary bow, unless the sun's altitude at the time is considerably less than 42°, which only happens in the winter. 432. EXTRAORDI NARY BOWS. When the light of the sun is held, while walking on the walls of Chester, by the river Dee, a rainbow of the form represented in figure 24., where A B C is the primary bow, DE F the secondary, and AHGC the extraordinary bow, cutting the secondary at H and G. Its colors were arranged like those of the primary. Give the instances of rainbows over cataracts. When can rainbows appear in the north? Explain from figure 24. the extraordinary bow seen by Halley. 433. The sun was shining c.early upon the calm surface of the river, and Dr. Halley discovered that the extraordinary bow was nothing more than the rest of the circle of which the primary was a part, bent upwards by reflection from the water. A similar rainbow, formed by reflection from the river Eure, was beheld at Chartres, in 1665; when a faint arch was seen crossing the primary at its summit. 434. SUPERNUMERARY Bows. Arches of prismatic colors are sometimes seen, both within the primary, and without the secondary bows, to which the name of supernumerary or supplementary bows is given. 435. On the 5th of July, 1828, Dr. Brewster saw three supernumerary bows within the primary, each composed of green and red arches. Outside of the secondary a red arch was clearly seen, and beyond this a faint green one. At Montreal, in September, 1823, three supplementary bows were noticed by Prof. Twining, within the primary; exhibiting however, only a single color, which was violet or rather a dull red. At Hartford, Ct., on the 5th of August, 1847, at sunset, two supernumerary bows were seen by the writer, within the primary, extending throughout the whole semicircle. The first, in contact with the primary, consisted of green and red arches, and the second of a single band of pale red light. The most remarkable phenomenon of this kind, was that observed by the Rev. Mr. Fisher, in Dumfrieshire, and related by Dr. Brewster, at a meeting of the British Association, in 1840. In this case the primary was attended by five supernumerary bows, and the secondary by three. Kaemtz remarks, that it is not easy to account for these supplementary bows in a satisfactory manner; hut according to Young, Arago, and others they arise om the action of the rays of light upon each other: the xplanation however, is too abstruse to be here introduced. 436. LUNAR Bows. Rainbows are sometimes pro Relate the cases given of supernumerary bows. duced by the light of the moon; their occurrence, however, is extremely rare, and their tints so very faint as to be scarcely perceptible. One of the most brilliant ever beheld, was seen by Mr. Tunstall, at Gretna Bridge, in Yorkshire, on the night of the 18th of October, 1782. It became visible about nine o'clock, and continued, with varying degrees of brightness, till past two. At first it appeared as a distinct bow without colors, but afterwards the tints were very conspicuous and vivid, preserving the same order as in the solar bow, though paler; the red, violet, and green being the brightest. At twelve o'clock it attained its greatest splendor. This phenomenon occurred three days before the moon was full; during its continuance, the wind was very high, and a drizzling rain fell for most of the time. Another bow was seen by the same observer, on the 27th of February, in the same year. The colors were tolerably distinct, but the orange appeared to predominate. A lunar bow with colors, was also noticed near Chesterfield, about Christmas, in the year 1710, and is described by Thoresby in the Philosophical Transactions. CHAPTER III. OF MIRAGE. 437. When a ray of light, proceeding from any object, passes obliquely out of one medium into another of a different density, it is refracted, or bent from its course, (C. 704,) and when it reaches the eye, the object is seen in the direction of the last refracted ray. Relate the several instances of lunar bows. What is the subject of chapter third? In what direction is an object seen, when the rays that come from it to the eye first pass through media of different densities? 8* 438. Thus, if E represents the earth, and 1-2, 2-3, 3-4, different strata of the atmosphere, decreasing in density from 1 to 4, a ray of light proceeding from the star S, and meeting the exterior stratum of the atmosphere at 4, will be successively refracted in the directions 4-3, 3-2, and 2-1; so that a spectator at 1 will not see the star S in its real position, but in the direction of 1-2 S'. For this reason all celestial objects, (unless in the zenith, where there is no refraction,) appear above their true position. (C. 703.) Thus, the sun and moon, for instance, at their apparent rising and setting are actually below the horizon. 439. The variations in the density of the atmosphere near the earth, produced by local changes in temperature, occasion a similar displacement of terrestrial objects; this is ordinarily seen in the slight elevation of coasts and ships, when viewed across the sea, and is then called looming; but to the more extraordinary phenomenon of this nature, the name of mirage has been given. When this phenomenon occurs, images of ships erect and inverted are seen in the air, delightful visions of tranquil lakes and verdant fields delude the fainting traveler of the desert, and sometimes, as in the case of Reggio, a noble city with all its splendid panorama of towers and arches, stately palaces and terraced heights, appears like a fairy scene upon the slumbering waters of the sea. What is mirage? |