52 INSTRUCTIONS TOR MAKING PILOT BALLOON OBSERVATIONS 



FORMULAS USED WHEN THE TWO STATIONS ARE NOT AT THE SAME 



ELEVATION 



166. First method (fig. 16).— In triangle B'DB, A" = difference in 

 elevation of stations; angle B'DB = e', elevation angle at B station. 

 In triangle ADP, angle APD=e—e' or lSO°—(e-\-e'); the latter 

 being when balloon is between stations, then 



AP 



AD 



otAP= 



AD sin e' 



sin e' sin {e±e') "^ ^"^"^ sin \e±e') 

 Since AD=AB'-^B'D, AB'--=h, and B'D=h" cot e' , then, 



FiGURE 15.— Plan of triangulntion of two-theodolite observations where balloon, P, is in vertical plane 

 through baseline, between stations, the stations being at the same elevation. 



AD=bdih" cot e' (the sign of h" cot e' depends upon position of 

 balloon and relative height of stations), therefore 



AP 



then 



and 



ib ±h" cot e') sin e' 



sin {e±e') 



{b±h" cot e') sin e' cos e 



AP COS e 



h=AP sin e 



sin (e±e') 



{h±h" cot e') sin e' sin e 



sin {e±e') 



(9), 



(10) 



167. Second method. — Another method of computation may be 

 employed where the length of the hypotenuse (shortest distance) 

 between the stations is used as the base instead of the horizontal 

 distance. 



Figure 17. — In triangle ABB', /i" = the difference of elevation 

 between stations, 6 = base line; = angle of elevation of station B 

 above base line 6. 



