OP ARTS AND SCIENCES. 211 



The same is true in a greater or less degree of the stars whose an- 

 nual proper motions are less than 0".l. If these are Bradley's stars, 

 the new reduction by Professor Auwers, and redeterminations at 

 Pulcova and Greenwich, will be sufficient for the present ; but, if not, 

 60 wide a field for minute criticism is thus opened, that I suspect the 

 only cases at present worth testing will be those in which special 

 accuracy is to be expected ; as in the vicinity of the north pole, where 

 the early observations of W. Struve afford the best possible means of 

 comparison, in addition to the standard places of Groombridge. 



In what follows, I give first the precession-constants and formulae ; 

 and next an auxiliary table for the computation of the relations be- 

 tween the star's proper motion and the solar motion supposed directed 

 to the point whose AR. is 259°50'.8 and Decl. + 32°29'.l. 



The computation of the most probable proper motion involves : first, 

 the reduction of all observations with proper systematic corrections to 

 a fixed epoch by precession, next the assignment of weights and estab- 

 lishment of conditional equations, and lastly their solution ; but when 

 the proper motion is large, or the star near the pole, either the geomet- 

 rical formulae must be used, or a preliminary proper motion employed 

 to compute the terms of secular variation depending on it. In volume 

 IV. Part I. of the Annals of Harvard College Observatory (also 

 included in Volume VIII. of the Memoirs of this Academy, New 

 Series), I have given some examples of a still more rigid treatment 

 of such cases. 



PRECESSION-CONSTANTS AND FORMULA. 



Fundamenta Astronomiae, p. 297 (Bessel, I.). 



For 1750 + f 



m = 45".99592 + t 0".0003086450 

 n =20 .05039 — t .0000970204 



Annales de I'Observatoire Imperiale (Memoires, II. 209). 

 For 1850 + t^ 



m (ji) = 46".05912 + 0".00028372 t^ 

 n {v) = 20 .05197 — .00008663 t^ 



Tabulae Regiomontanse (Bessel II.). 



For 1750"+ < 



m = 46".02824 + t 0".0003086450 

 n = 20 .06442 — t .0000970204 



