On Practical Geodesy. 41 



we can find the angles of depression a , a^^, by means of 

 (109), and then find the azimuths from 



. R,, cos l„ cos <o 



sin A, = 



sin A„ = 



k • cos a, 

 R, cos I, cos 0) 



k ' cos a,, 



When A^ or A^^ is found to be nearly 90°, it cannot 

 be accurately obtained by means of the usual tables of 

 logarithms ; so that, in such case, it is necessary to proceed 

 as indicated in the works on trigonometry. Thus, putting 

 A for the angle to be found, and N for the value of the 

 function to which sin A is equated (which is nearly equal to 

 1), we have — 



sin (45° -J A) = "yA 



N 



^^' tan (45° — J A) = Y-l 



— N 



+ N 

 from which to compute the value of the angle A. 



And when, in the sequel, an angle is to be found from an 

 expression for its sine which is nearly equal to unity ; then, 

 putting N to represent such expression, we should proceed 

 to find the angle by these formulae. 



OthervAse. 

 (When the stations are not more than 40 miles asunder.) 

 From the spherical triangle S^PS^^ we have the formulae — 



tan I (A, + A..) = -°^ I ;;:-;; -cot I . 



sin r sin w sin I" sin co 

 sm V = — , — = : — 



sin A„3 sm A^ 



Then to find the azimuths we have — 



. R,, sin I" 



tan X = 



R^ sin r 



tan 1 (A, — A,) = tan J (A, + A,,) tan (x — 45°) 

 ' J (A, + AJ = i (A, + A,,) 



