98'' On the observations of Comets. 



For the first observation we have 



True R. A. True Declin. 



Arcturus, 211° 51' 36" 20° 7' 41" 



a Lyra, 277 42 50 38 37 25 



To correct the distances, it is necessary to know the alti- 

 tude of the comet. This may be found, first by the globe, 

 and afterwards when the Right Ascension and Dechnation 

 are ascertained, the altitude may be calculated correctly, 

 which, if very different from the assumed, the distances 

 should be corrected again with it. We will suppose, then, 

 the apparent altitude of the comet 5° 19'. 



The latitude of the place of observation was 39° 52' 30" 

 N. With this, the altitudes of the stars corresponding to 

 the time, will be found by calculation. 



Apparent altitude of Arcturus, 48° 57 



Apparent altitude of » Lyra, 71 45 



With these data we find for the first distance dD=& 58" 

 and for the second f?D=9' 8". Therefore the true distances 

 will be 



True distance to Arcturus, 82° 13' 28" 



True distance to » Lyra, 90 41 38 



Let c (fig. 1 .) be the comet, a Arcturus, and 6 the other 

 star. In the triangle pa6, the side ab will be found equal to 

 59° 0' 44", and the angle 'pah=5&' 15' 46". In the triangle 

 c«6, the three sides being given, the angle cah will be found 

 = 95° 31' 27" from which subtracting the angle pah, it will 

 remain cap =39° 15' 41". Now, in the triangle pea, know- 

 ing the sides pa and ca, and the angle cap, the side cp will 

 be found = 39° 5b' 41", and the angle cpa= 102° 19' \&". 

 Subtracting cp from 90°, and cpa from the Right Ascension 

 of Arcturus, we shall have ; 



R. A. of the comet. Declin. of the comet. 

 July 10th, at 2^ 39' 48" 109° 32' 20" 50° 4' 19" N. 



' Supposing 1' of error in each of the distances observed, 

 formula 1 gives dx=M" 8, which being substituted in formu- 

 las 2 and 3, these give dv=^50" 6 and dw=-Ab" 2. 



