The author observes that opinions differ as to the elevation of the Aurora Borealis above the surface of the earth, and that this is a point which can be determined only by a series of concurring observations. The appearance of a phenomenon of this kind on the 29th of March, 1826, assuming the form of a regular arch at right angles to the magnetic meridian, and marked by peculiar features, continuing for above an hour in the same position, afforded a most favourable opportunity for obtaining the data requisite for the solution of this problem; and the author accordingly took great pains to collect as many authentic accounts as possible of the apparent position of this luminous arch with reference to the stars, when seen from various places where it had been observed in England and in Scotland. It appears to have been actually seen in places 170 miles distant from one another, in a north and south direction, and 45 miles distant from east to west, thus comprising an area of 7000 or 8000 square miles; but it must have been visible over a much greater extent. Accounts were received of its having been seen as far north as Edinburgh, and as far south as Manchester and Doncaster, and at most of the intermediate towns; and from the exact; correspondence of the descriptions from all these places, it was impossible to doubt that they referred to the same luminous appearance. In proceeding from north to south, the apparent altitude of the arch continually increased, still keeping to the south of the zenith till we come to Kendal, at which place it very nearly crossed the zenith; at Warrington, which is further south, the culminating point of the arch was north of the zenith. Wherever seen, the arch always seemed to terminate nearly in the magnetic, east and west, at two opposite points of the horizon. The observations, in which the author places the greatest confidence for determining the height of this aurora, were those made at Whitehaven and at Warrington, places which are distant 83 miles from one another, and situated nearly on the same magnetic meridian. Calculating from the data they afford, he finds the height of the arch very nearly 100 miles above the surface of the earth, and immediately over the towns of Kendal and of Kirkby-Stephen. This conclusion is corroborated by observations at Jedburgh; but if the former be compared with those at Edinburgh, the height will come out to be 150 or 160 miles, and the position vertical about Carlisle: but he thinks the former result more entitled to confidence. Assuming the height to be 100 miles, it will follow that the breadth of the arch would be 8 or 9 miles, and its visible length in an east and west direction from any one place would be about 550 miles. The author then proceeds to take a comparative view of the results of inquiries on the height and position of other auroræ which have at different times appeared, and are recorded in the Philosophical Transactions and other scientific journals. He also gives an account of a luminous arch seen both at Kendal and at Manchester on the 27th of December last, which appeared in the zenith at the former place, and was elevated 53° from the north at the latter place; whence its height is deduced to be 100 miles. From the general agreement of this series of observations, the author infers that these luminous arches of the aurora, which are occasionally seen stretching from east to west, are all nearly of the same height; namely, about 100 miles. Observations are still wanting for the determination of the length of beams parallel to the dipping-needle, which constitute the more ordinary forms of the aurora borealis; neither can it be determined whether these beams arise above the arches, as from a base, or whether they descend below, as if appended to the arches. It is remarkable that the arches and beams are rarely, if ever, seen connected together, or in juxta-position; but always in parts of the heavens at a considerable distance from each other.
Analysis of shape uses local apparent position rather than physical position
