



EPHEMERIDES AND AUXILIARY TABLES. 



and transforming to oblique coordinates x l and y l parallel to the hour and declination circles, 



o a a 2 . 



Xl = d ' C SP ' Vl ~ W ' Sm P ' 



or eliminating ocf and a/' by the equation of the ellipse a 2 6 2 = i 2 a? + a 2 y 5 



xf =2 a? cos 2 p -\- b 2 sin 2 p. 

 yf = a 2 sin* p + 6 2 cos 2 p. 



in which the substitution of the values a =z r, b = cos (8 -\- E) give 



o>i = rVl sin 2 j5 sin 2 (# + E) 

 y l = rV I cos s p sin 8 (S + E) 



which, being subtracted from the semidiameter, give the defect of illumination 

 da cos 3 = r x t = r (1 VI sin 2 ^ sin 2 (S + E), 

 48=r y l = r (I V I cos 2 p sin 2 (S + E), 

 For the preliminary correction in parallax we have, as usual, 



/ IT p COS Iff ia -v 



a a = _ 2 C - L. sm(0 a) 

 A cos 8 



. . 



A sin C 



in which a' and # denote the geocentric places, and ^ is the auxiliary angle 



tan tan iff sec (0 a) 

 The second equation may be written, 



ff o ^? p sin iff (sin 5 cotg cos d) =. | p cos ^' sin 8 cos (0 ) ^> sin ^' cos 8 > 



x cos 8 x 1 sin <? xo 



. - - cos (a a) 



- 



A A 



It is very convenient to make use of auxiliary tables for these values, at least in the case of 

 series so extended as the Santiago observations ; we, therefore, write 



' = A sin (0 ) 

 8 8 1 = D + E cos (0 a) 



and construct tables of A = - - -; D =: - ; E= - and for meridian observa- 



A cos 8 A A 



tions D +E= - sin (yf 8) 



