F. H. Bigelow — Solution of the Aurora Problem. 85 



instrument can be readily constructed for this purpose, 

 horizontal circle for azimuth, 1. 



levelled, the zero reading be- 

 ing set to the North geographic 

 pole, carries a vertical arc 

 graduated d= 90° ; the zero 

 being at the top. At the 

 center of this semicircle swings 

 a bar having one edge straight, 

 marked off with a linear scale. 

 The sight line is on the diam- 

 eter of the azimuth circle that 

 pierces the center of the ver- 

 tical semicircle, and may be 

 simply a couple of diaphragms. 

 The observation is made by 

 turning the straight edge into 

 such a position that it will lie 

 parallel to the axis of a ray, 

 or any other line to be meas- 

 ured, reading the top and bot- 

 tom of the visible ray on the 

 divisions of the linear scale, 

 which gives the angular dis- 

 tance of the same from the for measuring the 

 point of disappearance of the the vertlcal 

 ray as it passes the horizon ; also reading the angle on the 

 semicircle at which the arm is inclined from the vertical ; and 

 the azimuth on the horizontal circle of the point at which the 

 ray touches the horizon. Such an observation can be made 

 very quickly, even so as to take the rapid flashes of the vibrat- 

 ing auroras. The more inclined the rays from the vertical 

 the more valuable the observation, and if the ends of the arch 

 show streamers also visible at the horizon, they will be those 

 especially desirable to secure. 



In the following solution we shall utilize the equation, cotan 

 1= 2 cot 6 =-- 2 tanm, which was explained in my paper on the 

 Corona (this Journal, Nov., 1890), the notation being, r, d, the 

 coordinates of any point on the curve whose equation is, 



N — — . ; I the angle that the line of force makes with 



3 r ' " 



the radius to the point, and m the angle that the circle-tangent 



makes with the polar axis of reference. We take as the polar 



axis the radius that passes through the magnetic poles, which 



would be accurate if the potential were uniformly distributed 



in the earth considered as a magnet, but actually to that point 



of the surface to which the ray really belongs, as referred to 



Fig. 1. — General plan of an apparatus 

 inclination of a ray to 



