214 Mr Potter on the Aurora Borealis. 



of the plane of the horizon, that of any other plane passing 

 through the place of observation. 



The most general way of treating the problem is to take 

 the plane at right angles to the magnetic meridian, but making 

 any angle with the vertical line. Thus we arrive at a general 

 formula, which will be discussed below, and from which we 

 deduce that for the plane of the horizon as a particular case, 

 and it is the simplest one. 



But it will not be without service to make observations for 

 planes of different elevations on the same arch. For if, as 

 some philosophers maintain, thei'e are more virtual magnetic 

 poles than two on the earth's surface, we ought to find con- 

 siderable deviation from a circle in the direction of the symme- 

 trical rings or arches. But if we find a close coincidence, be- 

 tween the results furnished by the different points on a high 

 and extensive arch, we must consider that there is only one 

 such pole for each hemisphere ; and if the electrical theory 

 shall be established, which, from recent experiments, there is 

 reason to expect, we must allow the irregularity in the direc- 

 tion of the magnetic tendency on the earth's surface, to arise 

 from partial and local causes, such as the situation of places 

 with respect to large continents and the diurnal rotation, or 

 the effects of prevailing winds, &c. 



To proceed to the general problem, let Fig. 6, Plate II. re- 

 present a view of an auroral arch, the plane A E X being in the 

 magnetic meridian, and the line A X being its intersection with 

 the horizon. The data required for the solution of the pro- 

 blem, are the angle E A X, or the elevation of the arch, the 

 angle D A X, or the inclination of the plane D A F, with that 

 of the horizon, and the angle D A F. 



Then if a be the place of observation in Fig. 1, a M ss a 

 portion of the earth's surface, M O the magnetic axis, and ef 

 a portion of an auroral arch, we may take the centre O as the 

 origin of the co-ordinates, and put e = the trig. tang, of the 

 angle c a~X, J ; '— the trig. tang, of the angle daj\ i being = 

 the trig, secant, and J — trig. tang, of the angle of inclination 

 rf«X, and g — the trig, contangent of the magnetic polar dis- 

 tance of the place of observation, or = the trig. tang, of the 

 angle M O oc. 



