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, 2a 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) |
Gave a height from 33 to 281 miles, and a mean of 130 miles.
This method with 28 Auroræ gave a height from 33 to 281 miles and a mean of 130 miles.
Galle has suggested (Pogg. Ann. cxlvi. p. 133) that the height of Auroræ might be calculated from the amount of divergence between the apparent altitude of the auroral corona and that indicated by the dipping-needle, a principle which has been adopted in Prof. Heis’s apparatus before described. The results do not differ materially from Professor Newton’s.
The conclusions to be arrived at from the foregoing instances and opinions are certainly very puzzling. The terrestrial character of some Auroræ seems well established. The height to which these phenomena may ascend is left almost a matter of conjecture, and further observations are very desirable.
Phosphorescence.
Phosphorescence. Phosphorescent bands. Storm-clouds which threw out cirri. Shone with a sort of phosphorescence. Storm-cloud surrounded by glories of a phosphorescent whiteness.