The arc of the aurora borealis is a portion of a luminous ring, the different points of which are sensibly at equal distances from the earth, and which centres upon the boreal magnetic pole, so as to cut at right angles all the magnetic meridians that converge towards this pole. Such a ring, seen by an observer placed at the surface of the earth, evidently presents to him the known arc of the aurora; and its _apparent_ summit is always necessarily situated in the magnetic meridian of the place.
The diameter of the luminous ring is greater in proportion as the magnetic pole is more distant from the surface of the earth, since this pole must be situated upon the intersection of the plane of the ring with the axis of the terrestrial globe; if we could determine rigorously the position of the aurora borealis, we should then have the means of knowing exactly that of the pole itself.
Each observer sees the summit of the auroral arc at his magnetic meridian; it is, therefore, only those who are on the same magnetic meridian who see the same summit, and who are able by simultaneous observations to take its height.
If the summit of the arc pass beyond the zenith of the observer, the latter is surrounded by the matter of the aurora borealis. This matter is nothing else than aqueous vapors traversed by the discharges, and which are in general luminous only at a certain height from the ground, either because the air is there more rarefied, or because they are themselves congealed, and more capable, consequently, of liberating their electric light. Then it is, that, from being nearer to the spot where the phenomenon is taking place, the observer hears the crepitation, or whizzing, of which we have spoken, especially if he be in an open country and in a quiet place. But if the arc do not attain to his zenith, he is situated beyond the region in which the meeting of the electric currents takes place; he sees only an arc a little more elevated to the north or the south, according as he is situated in one hemisphere or the other; and he hears no noise, on account of his too great distance. The crepitation is the result of the action of a powerful magnetic pole upon luminous electric jets in its immediate neighborhood. With regard to the sulphurous odor which some observers have perceived, it arises, as does that which accompanies the fall of lightning, from the conversion into ozone of the oxygen of the air, by the passage of electric discharges.