LATITUDE DETERMINATION. 27 



Following the determination of the constants of the instrument used, 

 the next step is to obtain the apparent declinations of the stars used. When- 

 ever possible, these should be taken from the Nautical Almanac or the 

 Berliner Jahrbuch. In other cases they must be computed. The positions 

 of stars are given in Safford's Catalogue, for the epoch 1875.0, together with 

 the annua] precession and proper motion. The declinations there given 

 should be revised by the aid of more recent catalogues, particularly with 

 reference to stars of class C. The annual precession and proper motion 

 multiplied by the number of years which have elapsed and applied, together 

 with the effect of secular variation in precession, give the declination at the 

 beginning of the year. Further corrections to bring the positions down to 

 the date of observation are expressed by the svmbols A.a', Bb', Cc', Ddf. 

 Logarithms of a', b', c', d' are given in Safford's Catalogue, and A, B, C, and 

 D are given in the Nautical Almanac. A slight additional correction, also, 

 is to be made for proper motion, for the elapsed portion of the year. This 

 reduction is illustrated below. 



LATITUDE DETERMINATION. 



Example of reduction. Compulation of apparent declination of star 1539. 

 [From Safford's Catalogue, p. 40.] 



log a' = 1. 2757 log IV = 9. MM log c' = 9. 7307 log A' = 9. 8273 

 N T ov. 0. log A = 9. 0900 log B = 0. 3649a log C = 1. 1000 log D = 1. 1796 



0.9723 9.8943,, 0.8373 I 0069 



Aa' = + 9.38 Bb=_0. 78 Co' = + 6. 88 Dd'=+10. 1G 



With all this preliminary work done, the reduction proper of latitude 

 observations is comparatively a simple matter. Grouping the observations 

 by pairs, the mean declination of each pair is obtained, the corrections for 



