of Aberration and Nutation. 281 



— (15",3958 sin £3 + 1",2255 sin 2© +0", 1846 sin 2 ]) ) x 



(1 +tan M. sin M. tan D) 



— (8",9771 cos S3 + -5799 00520 +-0874cos2D — -08'77cos2S2) 



X (cos M.. tan D). 

 And that, in the case of declinations, we have only to change 

 the right hand factors for (tan w, cos M) and ( — sin M) respec- 

 tively. 



Whilst this subject was under our consideration, (and after 

 I had entei'ed on the computation of the tables, as a specimen 

 of the plan,) the fourth number of M. Schumacher's Astrono- 

 viischc Nachrichten appeared : in which M. Bessel has pursued 

 nearly the same coin'se of investigation as that to which I have 

 just alluded : with this additional improvement, however, that 

 the correction for the precession of the eqidnoxes is introduced 

 without causing any additional trouble to the computer. And 

 my object, in now making this communication, is to call the 

 attention of the public to this new plan, which possesses many 

 gjilvantages over those which have hitherto been in general 

 use: and which, by the further labours of M. Bessel (to which 

 I shall presently allude) are rendered of very extensive appli- 

 cation. M. Bessel's corrections are as follow : * 

 Right Ascension. 

 H- (46",01 75 -f 20",0436 tan D. sin M) t 



— (15",3958 + 6",6821 tan D. sin M.) sin hi 



— ( 1",2255 + 0",5319 tan D. sin'.iR) sin 2 O 



— ( 8",9771 cos S t) tan D. cos M 



— ( 0",5799 cos 20) tan D. cos A\ 



— (18",5837 cos O) cos M. sec D . 



— (20",2550 sin ©) sin iR. sec D,. 



Declination. 

 -l-20",04-36 cos M.t 



— 6",6821 sin 83 . cos M 



— 0",5319 sin 2©. cos ill 

 + 8",9771 cos St- sin AK 

 + 0",5799 cos 2©. sin A\ 



— (18",5837 cos ©) x(tan w. cos D— sin M.. sin D) 



— (20"-2550 sin ©) cos A\. sin D. 



The first line in each of these expressions denotes tlie pre- 

 cession of the equinoxes, where t is equal to the time elapsed 



• Some of the co-efficients here R'vcn differ, in a small degree, from 

 those given hy M. Hessel ; there beinf; evidently an error in his coniinita- 

 tions; as 1 have more particularly remarked in my " Astioiiomical Tables, 

 &c. for \KZ'Zr 



f M. Uessel lias here introduced the c|uantity (•087G(^ cos 268): hut I 

 have rejected it from this view of the subject, as too small to be of any im- 

 pfjrtance. 



Vol. GO. No. 291. Oct. 1822. N n from 



