INSTRUCTIONS FOR MAKING PILOT BALLOON OBSERVATIONS 49 



follows: The A scale is double and above, and the D scale is below 

 the slide. The sine and tangent scales are on the same side of the 

 slide, and both refer to the double A scale. They are graduated in 

 degrees and tenths to agree with the graduations on the theodolites. 

 The sine scale ranges from 0.57° to 90°, and the tangent scale from 

 0.57° to 45°. Cof unctions are numbered in red. This slide rule 

 may be purchased from one of the leading slide-rule manufacturers. 

 160. Theodolite setting. — The theodolite at station A is set with 

 0° azimuth on station B, and the theodolite at station B with 180° 

 azimuth on station A; thereby both instruments point in the same 

 direction in the vertical plane of the base line when set on 0° azimuth. 

 Computation is simplified by this method or orientation, as the angle 

 C of the horizontal triangle is obtained by merely subtracting the 

 smaller azimuth angle from the larger. See figure 13. 



-'-y^ 



Figure 13. Plan of triangulation in two-theodolite observation, showing position of balloon, P, and azi- 

 muth angles a and /3, and elevation angles e and e' , read from the theodolites at A and B station 

 lespectively. 



161. General jormula used in computation. — See figure 13 for general 

 plan of triangulation. In the triangle ABC, angle ACB=a—j3. 

 Since sin A = oi, and sin 5= sin /3, then 



and 



then 



and 



or d- 



b sin (8 



oxd'- 



sin (a— jS) 

 b sin a 



sin a sin (a— /3) ^^ "* sin (a— iS) 

 b sin /3 tan e 



h=d tan e= 

 h' = d' tan e' 



sin (a— (8) 



b sin a tan e' 



sin {a—fi) 



(1) 

 (2) 

 (3) 

 (4) 



