Formula for calculating the Places of Stars. 267 



which may be regarded as a general formula for the integra- 

 tion of functions of all kinds. 



32, St. Andrew-square, Edinburgh, Edwaud SaNG. 



August 7, 1829. 



XXXIX. Formulce and Tables for calculating the Apparent 



Places of Fixed Stars, as given by Professor Bessel. 



{Frovi Prof. Encke's Ephemeris for 1830, p. 158-198.) 



General precession 50"*231 



A =t— 0-02652 sin 2© —0-33316 sin S +0-00401 sin 2 S 

 6= - 0"-580 cos20-8"-977 cos £8 +0"-088 cos 2 Q 

 C = —20-255 cos s cos 

 D = —20-255 sin © 



a — 4.6"-053 + 20"-057 tg 8 sin a 

 i = tg 8 cos a. 

 c = sec 8 cos u 

 d = sec 8 sin « 



a' = 20"-057 cos a. 



V ■=. — sin a 



c' = tg e cos 6 — sin 8 sin a 



d! = sin 8 cos « 



m proper motion right in ascension. 

 7?i' pi'oper motion in declination. 



t days from the beginning of the year expressed in parts of 

 the year. 



App. Al = iR 1830 



+ Aa + B6 + Cc + Df/ + i^m 



App. Decl. = Decl. 1830 



+ Aa' + B6' + Cc* + D^' + tvi 

 If we assume 

 A 20"-057 = ^' cos G D = h cos H 



B = ^r sin G C = /^ sin H 



A 46"-053 = / C tg e = z 



We shall have 

 App. A\. = A11830 + / + / 7?< 



+ g sin (G + a) tg 8 + A sin (11 + «) sec 8. 

 App. Decl. = Decl. 1830 + i cos S + im^ 



+ ^cos(G + «) + Zs cos (H + «) sin8 



The following Tables contain the values of a and 8 lor the 

 beginning of the year, together with the values of the constants 

 liere introduced, or their logarithms, for every 10th day of 

 the year : 



2 M 2 Mean 



