32 Mr Potter on the Aurora Burealis 



Manchester. These being corrected for the curvature of the 

 earth, give the real elevation as from 197 to 21 8 English miles. 



If we examine the arch of the 12th December by the for- 

 mula for a small circle around the magnetic pole, — as the 

 eastern end was observed to cut the horizon near the Lion's neck, 

 and a Aquilae was in its upper edge in the western horizon, — 

 it must have had an extent in azimuth of about 115° for its 

 under edge, and its altitude was found for the same edge to 

 be 10°. On these data we find the value of x to be 350.56 

 English miles, and that of a? to be 421.67, and R — r, or its 

 height 77 miles, taking the magnetic polar distance of Man- 

 chester at 41°, which it appears to be nearly, calculating 

 from Captain Parry's observations on the position of the 

 Pole. Then for the upper edge we have to add the 

 breadth of the arch, which we find to be 31 miles, and the 

 height is 77. + 31 1=08 miles, — a quantity agreeing as well with 

 the trigonometrical computations as we can expect, when we 

 see that the data are furnished only in round numbers. The 

 arches seen on the 25th December were too diffuse on their 

 eastern ends for noticing the stars they passed near ; but, cal- 

 culating from the magnetic north to their western end, I see 

 that they had less proportional extent in azimuth to their alti- 

 tude than the one calculated above, and so venture to predict, 

 that, if sufficient observations have been made for trigonome- 

 trical computations, that aurora will be found to have been at 

 a higher elevation than the one of the 12th December. 



These confirm the former calculations of Mr Dalton and 

 others, by assigning a great elevation to this meteor ; but I 

 consider this as a secondary consideration to that of proving, 

 when we have correct measurements with divided instruments, 

 the extent of conformity with small circles (or say rather cy- 

 lindrical rings,) round the pole, or the extent of the deviation 

 from them. This involves the important subject of the mag- 

 netic variation and dip, which we should leave no means of in- 

 vestigating unexplored. 



It will be seen that we are not tied to the angles of the points 

 where the arch cuts the horizon, but may take them at any 

 other elevations with proper instruments ; and by substituting, 

 in place of the equation of the tangent plane, that of any other 

 given plane passing through the place of observation, we shall 



