284 APPENDIX. 



For a first approximation the terms depending on the square and third power 

 of T T may be neglected, and the value of T T O thus found can be corrected 

 so as to exactly satisfy the equation. 



If v exceeds 169, the formula 



r = [1.9149336] tan i v -f- [1.4378123] tan 8 } v 



may be used instead of the table. 

 Thus, for v = 169 50 44&quot;.28, 



log tan i. .1.0513610 

 1.9149336 



925.33 2.9662946 



log tan 3 iy. .3.1540830 



1.4378123 



39074.67 4.5918953 



7 = 40000.00 



This method will often be found more convenient than the table, even where 

 v is less than 169. 



35. 



Table Va contains BESSEL S table here referred to, in a slightly modified 

 form ; and also a similar table by POSSELT, for the coefficients v and v&quot; in the 

 formula of article 34, 



to = v + d v -4- dd v&quot; + d 3 v &quot; -f etc., 



it is taken from ENCKE S edition of OLBERS Abhandlung iiber die IcicMcste und bcquemste 

 Mdhodc die Bahn cities Cometen zu berechnen (Weimar, 1847). The following 

 explanation of its construction and use is taken from the same work, with 

 such changes as are needed to adapt it to the notation of the preceding 

 articles : 

 If we put 



# = tan ^ w 

 t = tan i v 



