46 



Z, = 85 8 26,3; ^ = 66 42 20,8, also aD = 21 82,7. 



Hence the above formula gives 



t II 



aL = 55 25,13, or if 

 aD =: 21 32,7 + «, 

 aI. = 55 25,13 + 2,30 u. 



u may represent the error, if any, occasioned both by supposing 

 the Pole Star without proper motion in declination, and by sup- 

 posing the declinations in 1755 and 1821 exact. It is probable, 

 from the extreme exactness with which the declination of the Pole 

 Star can be obtained, that as far as the latter source of error is 

 concerned u does not exceed a fraction of a second. This will 

 appear more evident when we compare the declinations obtained 

 by computation from those in 1755 and 1821 with the observed. 



The above value of Ah gives the annual luni-solar precession in 

 longitude = 50",38l + ,035 u. Therefore the formula for luni- 

 solar precession in NPD, in 1 788, of any star 



— 20,063 7 .p 

 = „ ^, . c COS. AR. 



— O.Ol* u 3 



To obtain the declination of the Pole Star at any time, it is con- 

 venient on account of its proximity to the Pole to have recourse to 

 the formula 



. sin. i aZ,. COS./. sin O. COS. (L + t aI.) 

 ""•*^-^= COS. (D + i^D) ' 



or in the present position of the Pole Star 



_ A L, COS. I sin O COS. L 



aZ> = ^ — r, 



COS. D 



r being a small correction, which may, for one hundred years pos- 

 terior to 1 755, be tal(eu from the following 



