OF ARTS AND SCIENCES. 213" 



Menten has tabulated the values of A and A', and the logarithms of 

 the other quantities for every minute of right ascension. These ex- 

 pressions do not include the effect either of precession in changing the 

 apparent amount of projier motion, or of proper motion in changing the 

 precession ; in other words, they are geometrical secular variations only. 

 The secular variation of the whole motion, omitting terras of the order 

 of the squares and products of the proper motions, is obtained by 

 adding to MentenV formula the terms, — 



«' 

 0.01944 [« tan d cos « 4- — sec 5^ sin a] 

 '15 -" 



— 0.01944. 15 fi sin a 



in right ascension and declination respectively ; where /w and ft' are 

 the annual proper motions, ix expressed in time, fi' in arc of a great 

 circle. 



o 



Argelander in his Abo catalogue gives secular variations of preces- 

 sion only, and includes one half of these terms. Thus for a Draconis, 

 the geometrical secular variations for 1830, computed by Menten's 

 formula3 (without allowing for the trifling secular change in the 

 table), are, — 



— o!o3622 and — 0".0299. 



The proper -motion terms in the secular variation of the whole 

 motion, according to the previous formulae, are, — 



+ o!oi921 4- 0".0254. 



Hence the secular variation of the total motion is, for 1830, — 



— 0.01701 and — 0".004o, 

 not including squares and products of proper motion. 



o 



The Abo Catalogue has, — 



— 0.0265 and — 0".017; 



that is, one half the proper-motion terms in the secular variation of 

 the whole motion, or, in other words, the whole effect of proper motion 

 in changing the precession, is included. 



^Sometimes it is necessary to employ the geometrical formulae : they 

 are these, according to Carrington, using Bessel's constants, for the 

 reduction from 1750 -j- t to 1750 -|- t'. 



