56 



elusions I had deduced, and it becomes of importance to endeavour 

 to investigate more minutely the existence or non-existence of proper 

 motion in this Star. Assuming the fixedness of the three Stars, 

 Rigel, a Orionis and a. Cygni, vre may investigate the proper motion 

 of Polaris (if any) and that without any knowledge of the preces- 

 sion of the Equinoxes. 



We may conceive a spherical triangle formed by Polaris in 

 1755, Rigel and « Cygni, and another formed by the Pole in 1821, 

 Rigel and a Cygni. — We can compute the distance of the 

 vertices of these triangles, or the distance of the jilace of the Pole 

 Star in 1755 from the Pole in 1821, and comparing this distance 

 with the observed polar distance of the Pole Star in 1821, we have 

 the proper motion of the Pole Star in polar distance, and also by a 

 small additional computation, the proper motion in right ascension. 

 We may instead of Rigel use a Orionis. Also instead of a Cygni 

 we may use a, Aquilae, if we correct for its proper motion, and then 

 use it as a fixed Star. Thus, we have four determinations : — the 

 mean of the four gives .S^S for the proper motion of the Polar Star 

 in declination, by which quantity it has increased its distance from 

 the Pole in 66 years.— This is much greater than could have 

 been expected under the circumstances that have been previously 

 stated, and makes a considerable change in the former conclusion 

 respecting the luni-solar precession. It was therefore desirable to 

 enquire into the accuracy of the result, by as many independent 

 operations as possible. 



.'! . The variation of the declination of the Stars near the Equinoctial 

 Colure, provided they were without proper motion, would separately 

 give with exactness the quantity of luni-solar precession, by com- 

 paring the N. P. distances in 1755 and 1821. But as several of 

 tliem have considerable proper motions, it is necessary to investigate 

 it for each, previously to applying them to investigate the luni-solar 

 precession. 



