48 On Practical Geodesy. 



tan i (L" - z,) = ^!'^f<f'-'°) • tan i I' 



sm i (A, + w) 



. Tx sin Z' • sin A, sin I' • sin w 



sm D,, = , — ^^ '- = -. 



sm L ' sin z, 



tan i (A, - D„) = ^j^^ * j^I ~ l\ ' <=°H <- 



sm ^ (ii + ^ ) 



Then we can find S,, by 83 or any of the formulae 88, and 

 the azimuth A,, by means of any of the formulae 94. 



Then, Z, = 90° — (L" + 8 J. fee, &c. 



When instead of I,, A„ we are given I,,, A,^, the analogous 

 methods of proceeding are evident. 



Pkoblem 6. 



Given the azimuth A,, the latitude l,„ and the length s 

 and circular measure 5 of the arc between the stations ; to 

 find A,,, l^, o), &c. 



To find 0), 0,,, D,, A,,, and I,, we have — 

 s * sin ^ • sin A, 



sm 0) 



cos l^, -sin r 



5 



sin D, 



K,, • sin 1" 



cos l„ ' sin w 



sm z, 



tan 1 A, = s"^ i i^'' — ^') . cot J (D, — to) 



tan i Z' = - cos j (K + A, + <o) . ^ ^. 

 cos i (A, + A, - a>) 



If A,,, I,, were given instead of A,, l,„ the method of solu- 

 tion is analogous, and requires no particular elucidation. 



Pkoblem 7. 



Given the latitude l^, the difference of longitude w, and the 

 length s and circular measure ^ of the arc between the 

 stations ; to find the azimuths A^, A^^, the latitude l^^, &c. 



To find , D,,, A^, A,,, l^,, we have — 



Pv, • sin 1" 



