50 On Practical Geodesy, 



^ " Sin q sm (q — L ) 



tan^ . „ = ^in (?. - L") Bin (p - O 

 sm ^ sin [p — z/) 



'^ Sin 2' sin (g' — z^) 



In this method of solution we have not made use of %. 

 In the following method we shall not make use of s, but of 

 5; and it is applicable to any two stations on the earth's 

 spheroidal surface, as weU as to mutually visible stations. 



Otherwise, 

 Find the angles a^^, a^, of depression of the chord by means 



of- 



tan X = ~ 



tan J (a,, — a,) = tan (x — 45°) • tan J !§ 

 1 (a, + a,) = J :S 

 To find the azimuths we have the equations — 

 cos a^ COS l^ cos A.-f-cos a^^ cos l^^ COS A,^ = sin a, sin ^^4- sin a,^ sin l^, 

 1 — cos^ A, _ (R,, cos a,, cos l,y 

 1 — cos^ A^^ (R, .cos a, cos l,y 



By putting 

 M, = cos a, cos I/, M,, = cos a,^ cos I,/, Q = sin a, sin ^, + sin a,, sin l,^ 

 we easily find — 



cosA - Q • ^\- ^/(Q^R/R.r-(R^-R^.) • (M^/ R^ -mvr^) 



M,/(R^— R^,) 



Since cos A^ must be positive when the angle A^ is acute, 

 .*. it is evident that in all cases it is the + sign which must 

 precede the radical in the above expression for cos A^. It 

 is evident that in the expression for cos A^^, it is the — ■ sign 

 only which should precede the radical. 



When l^ = l^^ ; then a^^ — a/, R^ = R^, ; M^ = M^^ ; 

 and the above expressions can be written in the forms — 



cos A = QR. (R.-RJ _ 



' m; (r; + r^,):(r;- r J 



