4IO 



NA TURE 



[Feb. 28, 1 1 



in natural science. There are, of course, not wanting 

 estimates and observations relating to this question, 

 but the general results of these, particularly of the earlier 

 ones, are very contradictory. There seems, however, to 

 be every probability of this problem being very soon 

 solved. 



As a basis for the measurements of the aurora we have 

 generally selected the arcs or the more pronounced solitary 

 streamers, when they have been clearly and simultaneously 

 observed from two points situated some distance from 

 each other, the apparent height or position in each place 

 having been determined by comparisons with, and mea- 

 surements of, stars. In consequence, however, of the 

 rapid shifting both of appearance and position of the 

 aurorse, this method is difficult and unsatisfactory, and 

 these drawbacks may to a great extent explain the very 

 divergent results which have been obtained by the 

 same. 



In order to give an idea of the manner and principle of 

 measuring the aurorse in their simplest form I ven- 

 ture to describe the method I have been in the habit of 

 following. 



On March 17, 1880, a great aurora was observed at the 

 145 stations which I had established over the southern 

 part of Norway, the west coast of Southern Sweden, and 

 in Denmark. One of the characteristics of this pheno- 

 menon was a large broad arc, or, perhaps more correctly, 

 band, which for a long time spanned the sky from east to 

 west. In Bergen (Norway), where my own observatory 

 was established, it remained for some time in the zenith, 

 then moving a little to the south, but at the stations lying 

 further north it was seen in the south, while at those south 

 of Bergen it was seen in the north. 



By its characteristic internal repose and slow motion 

 this remarkable band was especially suited to establish 

 the identity of this aurora at the various stations and to 

 serve as a basis for its measurement. It had apparently, 

 when in its most southern position, no connection with 

 the types which appeared simultaneously in the north, 

 the latter being streamers which it was impossible, from 

 their rapid change of form and appearance to observe 

 connectedly at the various stations. 



If the various reports of this auroral phenomenon be 

 examined, not the slightest doubt will remain of the 

 object seen being the same, i.e. that the same arc was 

 observed at the most southern as well as the most northern 

 stations. The further we move southwards however — 

 away from the same — the more the apparently observed 

 height diminishes, until we find that at the most southern 

 points it was seen merely as an ordinary low-lying arc. 

 In Bergen no trace of an auroral phenomenon was seen 

 south of the band in question, and the reports from the 

 stations south of this place all agree that neither was any 

 seen there. From this we may conclude with certainty 

 that the auroral arc observed in the zenith of the horizon 

 of Bergen was the identical one seen at all the southern 

 stations, and that the line of demarcation of the pheno- 

 menon seen from that place was the absolute southern 

 extension of the band. 



Before it is possible, however, from the observations 

 before us to measure the height of the arc, it is necessary 

 to ascertain its direction and its position in space rela- 

 tively to the localities on the surface of the earth from 

 which it was seen. In the main the point of culmination 

 of ordinary auroral arcs is in the direction of the magnetic 

 north of the place of observation, and the arcs themselves 

 follow approximately the magnetic parallels. I found, 

 however, from caret ul calculations that the apex of this 

 arc deviated some lo" west from the magnetic meridian, 

 and that its course or strike was at an angle of about 25^ 

 With the geographical parallel circles. 



The calculation of the height of the arc rests on the 

 following principle. If in Fig. i S and S' denote points 

 of observation, c the centrum of the earth, and P tv/o 



points in the aurora borealis situated in the same perpen- 

 dicular plane through s and s', whose angles above the 

 horizon /; and h' have been determined at each station, 

 and the longitude and latitude of each place is known, it 

 is possible (by a well-known trigonometrical formula, viz. 

 cos d = cos (/ — /'; cos b cos b' + sin b sin /', where / and 

 /' indicate the longitude and b and b' the latitude of the 

 two places, and li the distance or great circle between the 

 two) to find the arc S S', which is equal to .s c s'. From 

 this again s S' (| s s' = sin i s c s') is found. Further, 

 i- X = .r-' = I s C s'. One knows, therefore, in the triangle 

 s P s', the side s s' and the angles p S s' and p s' s, so that 

 its other parts, as for instance P s, may be ascertained by 

 means of some simple trigonometrical calculations. If 

 P S is known, we further obtain, in the triangle P s C, S C, 

 which is equal to the radius of the earth, and the angle 

 P S C = 90° + /'• From this P C is found, and, subtracting 

 S C, the perpendicular height of P above the earth's surface 

 is determined. Finally, if i. PC s is ascertained, the point 

 on the earth above which P is situated perpendicularly is 

 found. 



In practice the matter is, however, not quite so simple. 

 The method presupposes thus that P lies in the same 



vertical plane as both points of observation, which would 

 rarely occur, but still it retains its adaptability, even if P 

 only indicates a point in the upper or lower edge of the 

 auroral arc, the culminating point of which has been de- 

 termined in both places, provided that these lie in the 

 same plane perpendicularly in the longitudinal axis of the 

 circle, or may at all events be referred to such a common 

 plane. 



It is, however, far more difficult to overcome another 

 drawback. Provided that the arc has a perceptible thick- 

 ness in relation to its horizontal breadth, those parts of 

 the upper or lower edge of the arc which present them- 

 selves to the various observers cannot always be referred 

 to the same parts of the arc, in consequence of the cir- 

 cumstance that the apparent breadth, particularly with 

 the lower arcs, is due to a combination of both the real 

 breadth and thickness of the arc. 



If (f, b, i; dm Fig. 2 represent the circumference of a 

 circle observed from the points a, i;, c, assuming that the 

 Inie of demarcation of the arc north and south is parallel 

 with the inclination needle, the point a will denote the 

 upper (southern) edge for a and b, for C on the other 

 hand b; and, in a similar manner, the lower (northern) 

 edge is determined by the point d for A and li, c for C, &c. 



