PROFESSOR POTTER, ON THE HEIGHT OF THE AURORvE BOREALES, ETC. 321 



The Conspectus for the 1 2th October, furnishes more sets of contemporaneous observations, 

 namely, Cambridge and York at 7*. 55" Greenwich time; Guisborough and Heron Court at 

 8''.20™; Dent and Manchester at 8*. 55"; Armagh and Manchester at 9''.0"'; and about 12 to 

 14 minutes later; Dent and Heron Court at lo''.40". Observations at Dent and Armagh, might 

 have been taken, but with a much diminished base line ; and Armagh is situated on so distant 

 a magnetic meridian from that of Dent or Manchester, that the calculations have a greater 

 value with respect to the law of terrestrial magnetism, than as giving very accurately the height 

 of the Aurora. 



The regular and perfect arches have their highest points so nearly in the magnetic meri- 

 dian, that if there be any determinable deviation from this, more accurate methods of observation 

 must be employed in order to measure it. If two places be situated on the 

 same magnetic meridian, the point in the arch which has the greatest altitude 

 above the horizon at the one place, will be the same as the point which has tiie 

 greatest altitude at the other. If the places are not situated on the same magnetic 

 meridian, this will not be the case ; and in order to calculate the height of the 

 arch above the earth's surface, from observations of the altitudes of the highest 

 points, we must obtain our base by projecting the places on an intermediate 

 magnetic meridian. 



Let A and B be the two places, draw Aa, Bb perpendiculars on the magnetic 

 meridian, then ab will be the base to be used in the trigonometrical calculations; 

 and putting v = the magnetic variation, we have the formula in English miles, 



(lb = ^difference of latitudes in degrees x cos w ± difference of longitudes in 

 degrees x cos latitude x sin v \ 69. 



The lower sign to be used when the place having the greater latitude, has 

 the less West longitude. The arc of the magnetic meridian thus found and 

 its chord, will not sensibly differ for any two of the places of observation ; but 

 the observed altitudes will require correction for the curvature of the meridian, in order to reduce 

 the calculation to the case of a rectilineal triangle. a 



If C be the centre of the earth, A the point of the arch 

 supposed to be observed at a and b, the projections as in the 

 last figure. Then to solve the triangle Aab, we increase the 

 observed altitude at a by half the angle aCh, and diminish the 

 observed altitude at 6 by the same quantity, for the angles Abb', 

 and Aab. Having found the distance Ab, we find the distance 

 of A from the earth's centime by solving the triangle .^6C ; and 

 therefore know the height above the earth's surface. 



In this way I have calculated the following observations: 



When the altitude of the arch was referred to a given star, I have calculated the altitude 

 of the star from the Right Ascension and Declination given in the Nautical Almanac, for 1833. 



In sucii case there was no correction for refraction to be applied, as the star and arcli 

 were equally affected. 



In the observations on the 17th September, we have the following: the time in all cases 

 being Greenwich time. 



From Professor Airy's observations at Cambridge. "8''.2.')"'. — The Aurora appeared in the 

 form of a large bright cloud, bounded on the lower side by the iiorizon, atui on the upper 

 »ide by an arch of a small circle (not differing much from a great circle). The extremities 

 of the arch were in the N. li. and W. N. W. or nearly W. The upper boundary was lower 

 than /3 Ursa; Majoris by ^ x distance from o Ursa? Majoris to /3 Ursa; Majoris," &c. 

 Vol. VIII. Pakt III. T t 



