On Practical Geodesy. 49 



sin V sin w 



sin D„ = 



sin z, 



sin A (r — 0.) ,^ . 



^^■^ * ^' = sin\\v+z) ■ «°* * (D" - -) 



K,, • 2 * cos /^ sin 0) 



sin A,, = -. — ^ 



" 5 • sm 2 



cos ^ (A, + A,, + <o) , „ 



'-^ i'" = - cos ! (A, I aI I j • °°^ i ^' 



And similarly when ^.^ is given instead of ?,. 



Pkoblem 8. 



Given the azimuth A^, the diiference of longitude w, and 

 the length s and circular measure 2 of the arc between the 

 stations ; to find the latitudes, &;c. 



ruttins: — G = -• ^77 — • — n. 



° sin w 2, • sin 1 



We easily find, from 62 — 



" V (a + eG) • (a — eG) 

 And now we can find the other entities as in problems 6 

 and 7. 



Problem 9. 



Given the two latitudes l^, l^^, and the length s and circular 

 measure ^ of the arc between the stations; to find the 

 azimuths A^, A^^, &c. 



To find U, U', 0^, z^^y we have — 

 H sin I 



R sin I 



R, • sin 1" 



R,, • sin 1" 

 Then from the spherical triangles S^PD^^, S^^PD , we have 

 —putting p = h(l' + z^ + LO, q=i (^ + 0, + L'),— 



sin {p — g,) sin {p — V) 



tan ^ A, = ; -. — 7 ^r^TT — 



^ ' sin p sin y? — W) 



H 



