Mr. Dalton, from an observation of the luminous arches on a base of 22 miles, found the altitude of the Aurora to be about 150 miles (Dalton’s ‘Meteorological Observations and Essays,’ 1793, pp. 54, 153). [Sidenote: Dr. Thompson assumes considerable height. His table. Average of 31 observations, 500 miles.] Dr. Thompson, ‘Annals of Philosophy,’ vol. iv. p. 429 (1814), assumes that the height of the beams above the surface of the earth was much greater than that of most other meteorological appearances, and gives (p. 430) a table of Auroræ, mainly taken from Bergman, Opusc. v. p. 291, of 31 Auroræ observed in the years 1621 to 1793, with heights in English miles. The lowest is, 23rd February, 1784, London (Cavendish), 62 miles; the highest, 23rd October, 1751, Fournerius, 1006 miles! The average of the 31 estimated observations gives a height of about 500 miles. It is not stated how these observations were obtained, though methods are mentioned how they might be. [Sidenote: Prof. Heis’s instrument for determining height of Auroræ.] Prof. Heis, of Münster, exhibited at the recent Scientific Loan Collection at South Kensington (‘Official Catalogue,’ 3rd edit. p. 296, No. 1231) an instrument for the determination of the position of the point of convergence of the rays of the Aurora, and for determining the height of the Aurora. A ball resting in a pan was to be brought into position, so that several diverging pencils of Aurora, when properly viewed, were covered by the rod which passed through the centre of the ball. The point of the rod (which could be moved up and down in the ball), when the instrument was set to the astronomical meridian, showed the azimuth and altitude of the converging point of the pencils of light. This point of convergence does not coincide with the point to which the inclination-needle directs. From the deviation of the two points, the height of the Aurora could be calculated. [Sidenote: Professor Newton’s method of calculating height.] Professor H. A. Newton (Sil. Journ. of Science, 2nd ser. vol. xxix. p. 286) has proposed a method of calculating the height of Auroræ by one observation of altitude and amplitude of an arch. It assumes that the auroral arches are arcs of circles, of which the centre is the magnetic axis of the earth, or at least that they are nearly parallel to the earth’s surface, and probably also to the narrow belt or ring surrounding the magnetic and astronomical poles. Professor Newton finds that, _d_ being the distance from the observer to the centre of curvature of the nearest part of this belt (for England, situated about 75° N. lat., 50° W. long.), _h_ the apparent altitude of the arch, 2_a_ its amplitude on the horizon, _x_ its height, R the earth’s radius, and _c_ the distance of the observer from the ends of the arch:— sin φ = sin _d_ cos _a_ cosec(_d_ + _h_) (1) tan _c_ = _z_ sin _h_ sin φ sec ²φ (2) _x_ = R - (sec _c_ - 1) (3)