sin 



' '= cos S sin 9^ , (7) 



tan S tan S 



tan ( Ac- A') = ■ = , (8) 



sin(JL -Oo) cos 6>o 



2 



tan { — -da) f 



tan a = ^ = (9) 



sin S ^™ S 



sin0'= cot ( Ap - A') cot a ' or 



tan a'sin l9'tan (Ac - A') = 1 (10) 



From the oblique spherical triangle PQiQj find 



cos ( Aj - Aj) = - cos (77 - Oj) cos a ,+ sin (n- - Oj) sin a 1 cos (S, - S2) or 

 cos (A2 - Aj) = cos a-i, cos Oj + sin a^ sin 02 cos (S,— S,). (10.1) 



Computations from the formulae 



First compute \, and Q^ from (3) and (4). 



tan Q^ cos Aj- tan ^j cos A 2 



tan Ao = 



tan ^1 sin Aj— tan Q2 sin A, 



cot ^0 = cot J cos ( Aq - Ai ) = cot ^2 cos ( Aq- A2) 

 Next compute a^ and Oj from (5), 



cos 00 cos 00 



sin a, = 



cos (9i cos 02 



Then Si and 83 from (6) 



tan S, = cos Ci cot 0i , tan S 2 = cos a j cot 02 

 The computations for aj, a^, Sj and S2 are checked by (10.1) 



cos (A2 - Ai) = cos Oi cos Oj + sin a, sin a^ cos (Sj — Sj). 



Now for equally spaced intervals along the great circle track, for instance in 100 nautical 

 mile intervals, let S = Sj ± 100k. 



k= 1, 2, 3, N. 



With these values of S one computes successively corresponding values of 0', A' and a' 



from equations (7), (8), and (9) 



tan S ^ cot 00 



sin 0'= sin 0o cos S, tan (Ao - A') = , tan a = — ; 



cos 00 sin S 



These last computations are checked by (10) 



sin 0' • tan ( Ao - A') • tan a'= 1. 



25 



