45 



THE POSITIONS OF THE SMALL STAR NEAR ? URSA MAJORIS. 



These results appear to prove, that these stars have had no rela- 

 tive motion during the last fifty or sixty years. 



Assuming then that the change in the polar distance of the Pole 

 Star, between 1755 and 1821 has arisen entirely from the luni-solar 

 precession, we can compute the quantity of the luni-solar preces- 

 sion in longitude is as follows : D, L, I and O representing the de- 

 clination, longitude and latitude of the Pole Star and obliquity 

 of the ecliptic in 1 755, and AL and AD, representing the luni-solar 

 variation of longitude and variation of declination between 1755 

 and 1821, 



sin. D = cos O sin /+ sin O cos I sin. L, 



sin. (Z)+ aD)= cos. O sin. /+ sin cos.l sin(L4- aD), 



whence 



sin. ^ A ^ = 



sin. ^ aD cos. (D + ^ a JP) 



cos. i sin. Ocos. (L+^aD) 



From the preceding place of the Pole Star in 1755, and the ob- 

 liquity of the ecliptic =23° 28' 15",3, we deduce 



