OP THE AURORA BOREALES, ETC. 325 



The altitudes of the summits of tlie arch being observed 25° at Dent and 7° at Heron Court, 

 correcting these for refraction, we find the distance of the arch from Dent to have been 136.33 

 miles, and its height above the earth's surface 59.4 miles. 



I some years ago shewed, in the Edinburgh Journal of Science, that the locality of an 

 arch of an Aurora Borealis might be determined from observations at one place, by the help 

 of the hypothesis that tiie arch is a small circle round the magnetic axis. This hypothesis 

 cannot be accurate, from the change of the variation on the earth's surface, and we must con- 

 clude that, strictly, the regular arches are only perpendicular to a series of magnetic meridians; 

 which for localities exterior to the earth's atmosphere, may be found, when the meteor has 

 been more accurately observed, to differ from any assignable series on the earth's surface. 



As an approximation this method gives the height sufficiently in accordance with the 

 trigonometrical method, to induce us to attempt more accurate observations, when the theory 

 of terrestrial magnetism shall be sufficiently advanced to enable us to profit by them. 



The required observations are the altitude of the summit of the arch, and its extent on 

 any given plane perpendicular to the magnetic meridian. 



When the given plane is the horizon, the formula takes the following simple form: 



where r = earth's radius, 



R = distance of the arch from the earth's centre, 



e = trig. tang, of altitude of the summit, 



m = (secant same angle)^, 



/ = (secant -^ extent on horizon)^, 



p = 1 + eg, where g = trig. tang, of magnetic polar distance of the place of observation. 



In the Aurora of the 17th September, I obtained the following observation with the view 

 to its being used with the above formula. 



" s"". iOl™. Arch 38° or 39° high, and extending about 160° on the horizon." 



Taking the altitude 39°, and r = 3954 miles, the formula gives R = 4007.9 miles ; whence 

 R - r = height above the earth's surface = 53 . 9 miles. 



We saw that the height of the under edge was 56 miles, and of the upper edge 71 miles 

 at 8''.24"'. 



From the preceeding results, we must conclude that the meteor occurs immediately beyond 

 the ordinary limits assigned to the earth's atmosphere, and from that to very great altitudes ; 

 which is in accordance with the results of many previous calculations. 



I shall conclude my paper with expressing my conviction that the Aurora Borealis will, 

 in some future time, from its connection with the earth's magnetism, be subjected to much 

 more accurate methods of observation than have hitherto been attempted. 



R. POTTER. 



