On Practical Geodesy. 43 



<^^ = 1 (<^^^ 4- ^ ) -j. 1 ((^^ — ^^)j there can be no appreciable 

 difference whether we use | 2 or ct^. 



Find the chord k by means of the usual formula — 

 7 _ 2 • 5 • sin i ^ 

 2 • sin 1" 



Then, to find the difference of longitude w, and the angle 

 </>,^ by means of the plane triangle p.C^p^^, we have — 



, , -o 7 ■ 7 ^ • sin A, cos i S 



tan h, — K, cos I, ; tan h,, = ^ 2 — 



sin <f)^ 



h {^. + 0,) = 90° - i ^, 

 tanH<A.--) = ^^{|^J-cotl<^^ 



Then to find the azimuth A^^ and latitude l^^, we have — 



. sin <4,, . . 



sin A,, = — — ^-^ • sm A, 

 sin <^, 



tan hi" =- '''tff^^f^^^i • «ot i V 

 2 cos J (A, + A,, — (u) 2 



^p" If instead of l^, A^, we were given l^^, \^, we should 

 first proceed to find the angle ^^, by means of — 



and then proceed in an analogous manner to find <^,, w, A„ 

 and l^^. 



Otherwise (Case 1st). 

 Given Z^, A^, s ; to find w, Z^^, and A.^^ (see foot-note). 

 To find z^y D^, (0, and L'', we have — 



s 



R, sin 1" 



tan I (L" _ = ^!°i(,t'~^"^ • tan J ., 

 Sin J (A, + D^) 



. -r ,, sin V sin A, 



sm L" = ^-— - — '- ' 



sinD,, 



