The Sun's co-ordinates, referred to the same equinox and equator as the 

 heliocentric ones, are : 



X = R COS (0 -\- aberration -\- nutation -|- precession) 



Y =Rsin ((g) + " " " ) C0S.0 



Z = Y tan CO 



tan A„ - j^^ 



Z+ z 

 tan Do = i — V cos A 



A = (z -(- Z) cosec D 



A = A„ +y [—0.17 X dv, —{A X x — QAl) V ] 

 rf Ao 



D = D„ + y' 



7 



This mode of computing (with a constant term for aberration) for the mean 

 equinox, and reducing to the apparent, in the case of Neptune, saves the neces- 

 sity, unless for the sake of extreme minuteness, of noticing the variable part 

 of aberration in Right Ascension and Declination. 



The Ephemerides of 1848 and 1849 have, however, been referred at once to 

 the apparent equinox and equator, by leaving out this constant term, and inter- 

 polating from the primitive Ephemeris the daily geocentric motions. The for- 

 mulae used are the following : 



X = a {r -\- & r) sin {A! -\- v -\- h v) 



y = 6 (r + « r) sin (B' + ?) -|- S v) 



z = c {r -\- h r) sm{C' -\- V -\- h v) 

 Log a = 9.9998770 -|- 0.0000000,0 x d SI -\- 0.0000000,0 X d c. 

 Log b = 9.9662367 -(- 0.0000000,2 x d Q, — 0.0000008,8 X d <^ 

 Log c = 9.5800353 — 0.0000001,3 X d Q, + 0.0000051,1 X ^ " 



o I II II II 



A> = 137 14 14.90 -I- 1.000 x d Q, -\- 0.000 X d c^ 

 B' = 47 47 49.20 -f 0.991 X d Q, -{- 0.0.30 X d o> 

 C = 43 55 2.06 -f 1.045 X d Q, -\- Q.IQI X d ^ 

 S V = the perturbations of the elliptic true longitude v. 

 8 7-= the perturbations of the elliptic true radius vector r 

 d t = the aberration time in parts of a day. 

 J2' = the apparent longitude of the node. 

 J =: the apparent obliquity of the ecliptic. 

 d^ ^Sl'— 130° 5' 40" 

 d a = J — 23° 27' 23" 



