84 F. H. Bigelow — Solution of the Aurora Problem. 



The methods of obtaining the heights of auroras hitherto 

 given have afforded very discordant results, and a brief inspec- 

 tion shows that one or more terms of the problem have been 

 assumed, which of course implies the discordant results men- 

 tioned. In my analysis there is one assumption at the begin- 

 ning, but it is checked by the measurements, so that we resort 

 in effect to a solution by trial and error. Auroral heights have 

 been treated in several ways, (1) by parallax from two stations 

 near the same meridian, the distance between the stations 

 being known ; (2) by observing a distinguishing point from 

 two stations on different meridians, to determine the height 

 and the azimuth of the point of vision ; (3) by certain meas- 

 ures from one station ; (4) by comparing with the height of 

 neighboring objects. The results for height range from 75 km 

 to 1600 km , in fact from the ground to the limits of the atmo- 

 sphere. One general criticism applies to all these methods, 

 that observers are not sure of seeing the same point continu- 

 ously at one station, or of seeing the same point at all from 

 different stations. M. Biese and M. Petrelius, near Sodankyla, 

 were stationed 4-5 miles apart in the same meridian, being con- 

 nected by a telephone line. Having arranged to observe the 

 same object simultaneously, Biese sent this message, " fix the 

 line where the red ray is found ;" at the other station no red 

 ray could be seen. 



Nordenskiold's solution rests upon an hypothesis regarding 

 the position of the center of the visible auroral circle above 

 the surface of the earth. He measures the apparent altitude 

 of the center of the arch (j), the amplitude of the arch on the 

 horizon (2/9), and assumes the angle at the center of the earth 

 between the station and the radius to the center of the visible 

 circle. Hornstein assumes the angle at the center of the earth 

 between the radius to one of two stations on the same meridian, 

 and the radius extending to the point of measurement, which, 

 as in the former case, is the same as assuming the distance 

 from the observer to the given point. Newton assumes the 

 distance from the observer to the center of curvature of the 

 nearest part of the belt of the maximum number of auroras, 

 which amounts to referring the phenomenon seen to the mag- 

 netic system of the earth. His solution relates only to the 

 arches, but I shall show how with an assumption similar to his 

 we may utilize the streamers, as distinguished from the arches, 

 supposing those to lie in the lines of the magnetic field sur- 

 rounding the earth. 



The observations required consist in measuring the angle of 

 inclination of a streamer to the vertical plane passing. through 

 the station, together with the azimuth of the ray, prolonged if 

 necessary, at the point of its springing from the horizon. An 



