THE AURORA BOREALIS.--There have been seven exhibitions of the aurora borealis during the year 1849, two of which were sufficiently remarkable to merit something more than a passing notice. The first occurred on the evening of January 14th. At 10 P.M., a well-defined auroral arch, about 5° in width, extended from NNE. to W., its highest part reaching nearly to Arided in Cygnus. At 11h there was one complete arch, and segments of two other arches, all brilliant, crossing each other in the NW., and throwing off intensely bright streamers, some of which reached the altitude of the Pointers. The aurora was now exceedingly beautiful, and emitted considerable light. The streamers appeared to have a duplex lateral motion, running along the upper edge of the arch from west to north, and then backwards from north to west. The clear sky beneath the arches was almost black, from contrast. At 11h 30m the arches had broken up, and the streamers appeared to emanate from the horizon. _February 18._--At 9 P.M. there was a brilliant band of auroral light in the east about 6° in width, which shot upwards towards the zenith, throwing off short lateral streamers. At times, a complete arch of varying width extended from the eastern to the western horizon; at others, it was broken up into two or more detached portions. At 9h 45m, a magnificent rainbow-like arch about 2° in width, spanned the heavens from ENE. to WSW. The altitude of the centre was apparently about 75°; the lower edge, at or near the highest point of the arch, was bounded by the star Castor. The arch was beautifully defined, and of perfectly even width throughout its entire extent; it disappeared in a few minutes after my attention was called to it, and soon after the sky became overcast. But for the absence of the moon, it might easily have been mistaken for a lunar rainbow. A precisely similar arch made its appearance here on the evening of the 21st of March 1833, and as far as my observation goes, these perfect rainbow-like arches are of exceedingly rare occurrence. The following phenomenon though unconnected with auroræ, is probably of electric origin; and, as an unusual atmospheric appearance, is worthy of being placed on record:--_September 16._--The sky was mostly overcast throughout the day, except a segment extending from WSW. to ENE., which was bright and clear to an altitude of about 15°. The upper boundary of the clear blue space was an elliptical segment formed by a sheet of white cloud, which was partially illuminated towards the western extremity, and somewhat resembled an auroral arch. I first noticed this blue arch about 3 P.M., and from that time until it disappeared, about six o'clock, there was not the slightest apparent change, either in its altitude or position. It was observed as early as 7 o'clock in the morning, when it was, nearer to the horizon.