216 Mr Potter on the Aurora Borcali.s. 



Then knowing R, r and the angle eaO in the triangle eaO, 

 we find the distance, or the side a e, by the ordinary trigono- 

 metrical rule. 



When we take the extent of the arch, on any other plane 

 than that of the horizon, the formula for the value of R be- 

 comes less simple ; by following the same plan as before, we 

 find this formula, viz. 



(e~ I o- p 2 -\-j- m o- p 2 — ej m o 5 p — ej lop 3 1 \ 

 (//}- — mo 2 )" 2 '' + 4/ 



And when we know R, we easily find the distance as in the 

 other case. 



I have not yet been able to make observations for any other 

 plane than that of the horizon, but if the aurora shall occur as 

 frequently next winter as it did the last, I hope it will not pass 

 over without some observations being obtained which will tend 

 finally to settle the question of the height of the meteor above 

 the surface of the earth. I propose keeping a vigilant look 

 out for displays of it on which I may myself make observa- 

 tions with such an instrument as I have. But I should be glad 

 to hear that others, with better instruments, may feel suffi- 

 cient interest in the inquiry to seek opportunities of observing. 

 For the o-uidance of such friends of science, I will take the li- 

 berty to suggest, that it will generally be found best to take 

 the measurements for the under or inner edge of the arch, 

 when it is not a very high one, above the horizon ; for in this 

 case the under edge is almost always well defined, whilst its 

 upper one is frequently so diffuse that two observers would 

 seldom agree to less than 30' of a degree where it ended. When 

 the arch passes at an altitude approaching the zenith, it will 

 o-enerally be immaterial on which edge the observation is made. 



I have not yet met with an observation which would en- 

 able me to calculate the arch of the 25th December last, by 

 the parallactic method, but I hope some observer will yet ap- 

 pear who has recorded an observation of it sufficient for the 

 purpose. In the meantime, I give the height and distance as 

 brought out by the analytical formula?. 



The lower arch of the aurora had an altitude of 20° for its 

 under edge in the magnetic north, and it cut the horizon about 

 (51° west of this point for the same edge. 



