X y z 



N^cos,^, N,(l - e')sin(?!)i 



N2 cosc^j COS A A NjCos (^2 sin A A Nj (1 - e^) sin 02 

 



= 



(AA= A,-A.) 



which when expanded reduces to 



Ax + By - Cz = 0, 



A = ( 1 - e^) tan j sin A A 



B = (1 - e^) (tan 02 ~ t^" j cos A A) 



C = sin A A 

 Since equation (11) was developed for generalized coefficients A, B, C we have only to 

 substitute the values of A, B, C from (14) in (11) to obtain after some algebraic manipulation. 



(14) 



cot a^g = (1 - e^) — - 



Nj^ (tan J cos A A - tan 02) cos 0^ 



AA 



(15) 



By symmetrical interchange of subscripts and replacing A A by — A A , we obtain cot a^\ from 

 (15) as 



N,^ (tan 0j- tan 02 cos A A) cos 02 



:ot agy^ = (1 - e^) 



AA 



(16) 



Equations (15) and (16) represent the azimuths of the great elliptic section as shown in 

 Figure 14. 



NORMAL SECTION AND GREAT ELLIPTIC SECTION AZIMUTHS IN TERMS OF PARAMETRIC 



LATITUDE d 



I N 



From the transformation equations tan = (1 — e^)'/^ tan 0, cos Q = — cos 0, 



sin e = lLl£!l'^' N sin 0, (1 - e^ cos^ 0)'/^= ii^I-^' ' N 

 a a 



applied to equations (12), (13), (15), 16) we have the normal section and great elliptic section 



azimuths in terms of parametric latitude. 



Normal Section Azimuths in terms of Q. 



sin 6( cos A A — cos Q^ tan Q^ + e^ (sin Q^ ~ ^i" ^1 ^ '^^^ ^1 ^^^ ^2 



cot aAD = +■ 



AB 



cot a 



BA 



d-e' cos^ej'/'sinAA (^7) 



sin 02 cos AA - cos 62 tan 0^ + e^ (sin 6^ — sin d^) cos 02 sec 6^ 

 (1 -e'cos'02)'^' sin A A 



47 



