The rainbow assumes a _semicircular_ appearance, because it is only at certain angles that the refracted rays are visible to our eyes, as is evident from the experiment of the glass globe formerly alluded to, which will refract the rays only in a certain position. We have already stated that the red rays make an angle of 42° 2´, and the violet an angle of 40° 17´. Now, if a line be drawn horizontally from the spectator’s eye, it is evident that angles formed with this line, of a certain dimension, in every direction, will produce a circle, as will appear by attaching a cord of a given length to a certain point, round which it may turn as round its axis; and, in every point will describe an angle with the horizontal line of a certain and determinate extent. Sometimes it happens that _three_ or more bows are visible, though with different degrees of distinctness. I have more than once observed this phenomenon, particularly in Edinburgh, in the month of August, 1825, when three rainbows were distinctly seen in the same quarter of the sky; and, if I recollect right, a fragment of a fourth made its appearance. This happens when the rays suffer a third or fourth reflection; but, on account of the light lost by so many reflections, such bows are, for the most part, altogether imperceptible. If there were no ground to intercept the rain and the view of the observer, the rainbow would form a _complete circle_, the centre of which is diametrically opposite to the sun. Such circles are sometimes seen in the spray of the sea or of a cascade, or from the tops of lofty mountains, when the showers happen in the vales below. Rainbows of various descriptions are frequently observed rising amidst the spray and exhalations of waterfalls, and among the waves of the sea whose tops are blown by the wind into small drops. There is one regularly seen, when the sun is shining, and the spectator in a proper position, at the fall of Staubbach, in the bosom of the Alps; one near Schaffhausen; one at the cascade of Lauffen; and one at the cataract of Niagara in North America. A still more beautiful one is said to be seen at Terni, where the whole current of the river Velino, rushing from a steep precipice of nearly 200 feet high, presents to the spectator below, a variegated circle, over-arching the fall, and two other bows suddenly reflected on the right and left. Don Ulloa, in the account of his journeys in South America, relates that circular rainbows are frequently seen on the mountains above Quito in Peru. It is said that a rainbow was once seen near London, caused by the exhalations of that city, after the sun had been below the horizon more than twenty minutes.[14] A naval friend, says Mr. Bucke, informed me, that, as he was one day watching the sun’s effect upon the exhalations near Juan Fernandez, he saw upwards of five-and-twenty _ires marinæ_ animate the sea at the same time. In these marine bows the concave sides were