GEODESIC INVESTIGATIONS. l7l 



Then, in the triangle S, PD,„ we have the angle F = ca, the side SJD^, = «„ 

 and the side PS' = Z^ = 90° — I'. Hence, to find the azimuth A' we have — 



T~, sin ?, sin w 

 sm V = / 



sm 2^ 



To find the azimuth A" we have — 



2 • sin ca ■ R' cos V 



sin A = : — = 



s • sm 2 



And to find the latitude I", we have either of the following : — 

 tan - Z = (^tan- ^ + "j j • g^^F^ -^3 



™°» ^" — ~co3i(^'4-^" — co) cot 2 f. 

 The other entities can now be found as in problem 1. 



ProMem 8. 



Given the azimuth A', the difference of longitude co, and the length s and 

 circular measure 2 of the geodesic arc between the stations : to find — the 

 latitudes of the stations, the azimuth A", and all other entities. 



Formula 20 gives us — 



-n nil s • sin 2 sin A' 



a,, cos r = : — 



2 sm o) 



.•. if we find G such that 



s sin 2 sin A' 

 G = 



2 ■ sin 0) 

 We have — 



a^ cos^ I" 



= a^ 



\' L" 

 smZ = 1^ 



e^sin^Z" 



(a -t- 6?) • (a — G) 



■\- eG) ■ {a — eG)j 



from which to find the latitude I". 



We can now find the arc S^^D^ or z^, as in problem 6, or from — 



cos I" sin o) 



sm z = . . j^ 



i (sin A' — tan i 2 cos I" sin w)^ -|- (cos I" . sin oo)'^ > ^ 



and the azimuth A" from formulae — 



_ sin I,, sin a> cos J- 2 • ^/ 



sm D, = '^ = -, , ,. ■ em ^ 



' sm z^, cos [z^^ — ^ 2) 



sin i (I — z^,) 

 *^^ * ^ = sin i {l„ + .„) • '^"^ (^' - "> • 

 smd then the latitude I' from — 



tan i ^, = — — 1 y >/ — -, — 777 r ■ cot i Z,, 



' cos i {A -f- ^ — c") 



The other entities can now be found as in problem 1. 



