insteuctio:ns for making pilot balloon observations 51 



Special formulas used in computation. — Even with the most care- 

 fully selected base line, instances will arise in which the movement 

 of the balloon will be in a nearly vertical plane through the base line. 

 In such cases the azimuth angles cannot be read with sufficient ac-i 

 curacy to avoid appreciable errors in the calculation, and more accur- 

 ate results are obtained by using the triangle in the vertical plane. 

 See figures 14, 15, 16, and 17 for the plan of triangulation. 



FORMULAS USED WHEN THE TWO STATIONS ARE AT APPROXIMATELY 

 THE SAME ELEVATION 



Figure 14, in triangle ABP, angle APB=(e—e'), then 



AP 



and 



sin e' sin {e — e') 

 d=AP cos e 



h=AP sin e 



sin {e—e') 



(5) 

 (6) 



^55^^\ 



Figure 14. — Plan of triangulation of two-theodolite observations where balloon, P, is in a vertical plane 

 through base line, the stations being at the same elevation. 



Figure 15, in triangle ABP, angle ^BP=180°-(e+e'); 

 Since sin 180°— (e + g')=sin ie-^e'), then 



AP 



b . r> 6 sin e' 



7T or AP= 



sin e' sin (e + e') sin {e-\-e'] 



b sin e' cos e 



d=AP cos g= 

 h=AP sin e 



sin (e + e') 

 b sin e' sin e 



sin {e-\-e') 



(7) 

 (8) 



