turned upwards, the drops of water rising from below, and not falling from above, as in the instances of the aerial arches. Rainbows are also occasionally seen on the grass, in the morning dew, and likewise when the hoar-frost is descending. Dr. Langwith once saw a bow lying on the ground, the colours of which were almost as lively as those of a common rainbow. It was not round but oblong, and was extended several hundred yards. The colours took up less space, and were much more lively in those parts of the bow which were near him than in those which were at a distance. When M. Labillardiere was on Mount Teneriffe, he saw the contours of his body traced on the clouds beneath him in all the colours of the solar bow. He had previously witnessed this phenomenon on the Kesrouan in Asia Minor. The rainbows of Greenland are said to be frequently of a pale white, fringed with a brownish yellow, arising from the rays of the sun being reflected from a frozen cloud. The following is a summary view of the principal facts which have been ascertained respecting the rainbow:--1. The rainbow can only be seen when it rains, and in that point of the heavens which is opposite to the sun. 2. Both the primary and secondary bows are variegated with all the prismatic colours--the red being the highest colour in the primary, or brightest bow, and the violet the highest in the exterior. 3. The primary rainbow can never be a greater arc than a semicircle; and when the sun is set, no bow, in ordinary circumstances, can be seen. 4. The breadth of the inner or primary bow--supposing the sun but a point--is 1° 45´; and the breadth of the exterior bow 3° 12´, which is nearly twice as great as that of the other; and the distance between the bows is 8° 55´. But since the body of the sun subtends an angle of about half a degree, by so much will each bow be increased, and their distance diminished; and therefore the breadth of the interior bow will be 2° 15´, and that of the exterior, 3° 42´, and their distance 8° 25´. The greatest semidiameter of the interior bow, on the same grounds, will be 42° 17´, and the least of the exterior bow 50° 43´. 5. When the sun is in the horizon, either in the morning or evening, the bows will appear complete semicircles. On the other hand, when the sun’s altitude is equal to 42° 2´ or to 54° 10´, the summits of the bows will be depressed below the horizon. Hence, during the days of summer, within a certain interval each day, no visible rainbows can be formed, on account of the sun’s high altitude above the horizon. 6. The altitude of the bows above the horizon, or surface of the earth, varies, according to the elevation of the sun. The altitude, at any time, may be taken by a common quadrant, or other angular instrument; but, if the sun’s altitude at any particular time be known, the height of the summit of any of the bows may be found, by subtracting the sun’s altitude from 42° 2´ for the inner bow, and from 54° 10´, for the outer.