40 On Practical Geodesy. 



find the azimuths and the angles D^, D^^, by means of the 

 formulae — 



tanHA.+D.)= :-|g;:;;:; .coti. 



- Hi>, + A„) = £2^11;^). cot i. 



To find a^, a^^, % z^, z^^, and s, we may proceed as follows: — 

 First we find 8„ 8,,, from 



^, = JJ — V 



h„ =. r — L" 

 Then from the triangles S ID , S^^ID^^, we have, to find IS , 



ID, IS, ID- ; 



tani(is.+iD.)^ :;:;g;+t:i -^-i^- 



tani(IS.-ID.)^ -|g;+t:i '^-i^- 

 tani(IS. + m.)^ ;-|[t- + g| tani3. 



tan i (IS. - ID.) = ^^^f(f- + ^-) • tan ^ K 

 cosi(A. — D.) 



Then— a, = 90° — IS, 



a, = IS. — 90° 



^ = «/ + «/; 



s, = ID. — IS, 

 0. = IS. — ID, 

 s = 0, • K, • sin 1" = 2. • R. • sin 1" 

 But we can find k and s otherwise, thus — 



7 _ R, cos I, sin (0 R,, cos l„ sin w 



sin A. cos a. sin A, cos a, 



^^^.^•sinr 

 2 • sin A ^ 

 Or having found k, in terms of the given data, from 

 A^ = (R, cos /,)^ +. (R. cos l,^f — 2 • R, • R,, cos Z, cos Z. cos <o 



+ (1 — ey • (R, sin ^, -- R. sin Z.)^ 



