APPENDIX. 



295 



The angle u is to be taken between and 180 when b is positive, and be 

 tween 180 and 360 when b is negative. When b = 0, the body is in one of the 

 nodes of its orbit, in the ascending node when sin (L /) and sin (I a) have 

 the same sign ; and in the descending node when they have opposite signs. 



It is immaterial in which of the two quadrants that give the same tangent, 

 the auxiliary angles A , B , C, etc., are taken. In the following examples they 

 are always taken between -4- 90 and 90. 



II. 



III. 



13. 

 14. 

 15. 



r sin M sm t 

 sin b 



sin (I! a)s&amp;gt;n_ ficosEs\n(L a sn . A 

 ~ sin ( ^) sin (Z Q ) cos i 



sin (i, E) sin b 



7? cos .Fsin (Z/ Q) tan i _ Z^ sin .fsin (L a) sin U Q) _ ./ 

 sin (&amp;gt; J) ^ sin (-f 6) 



Other expressions for // may be obtained by combining 13 with all the 

 formulas II. 



Examples : 



Given, a= 8059 12&quot;.07, z7=281l 34&quot;.99, ^=:53 23 2&quot;.46, = 1037 9&quot;.55, 

 5 = 3 6 33&quot;.561, log Z?= 9.9926158. 



