INSTRUCTIONS FOR MAKING PILOT BALLOON OBSERVATIONS 55 



Unless metric tables of trigonometric functions are available, it 

 will be necessary to multiply the decimal part of the angle by 6 in 

 order to covert it into minutes. 



173. Constructing the horizontal projection of two-theodolite ohs'.rva- 

 tion. — The horizontal projection of a two-theodolite observation is 

 constructed in exactly the same manner as that of the single. (See 

 pars. 112 and 113.) The azimuth angle and the computed distance 

 from the A station are usually plotted, although the same data from 

 the B station may be plotted if desired. 



174. Obtaining wind data from horizontal 'projection oj two-theodolite 

 observation. — Whether the horizontal projection be of a single- or a 

 double-theodolite observation, the same method of determining the 

 wind direction and velocity is used, except in obtaining the wind 

 direction from a double-theodolite plot, the bearing of the base line 

 must be taken into consideration. In order to do this, instead of 

 reading the direction in the usual manner at the initial line, it is read 

 at a point whose bearing clockwise from the initial line is equal to the 

 bearing of the base line, plus or minus 180°. A simple method of 

 locating the point at which the desired protractor reading is to be 

 made is to set the 180° line of the protractor on the initial line and 

 mark a point on the board where the protractor reads an angle equal 

 to the bearing of the base line from north. 



175. The effects of the curvature of the earth upon two-theodolite 

 observations. — In common practice, the baseline is the horizontal dis- 

 tance between the stations. The theodolites are set up on either end 

 of the baseline with their primary axes having the direction of gravity, 

 and forming an angle at the center of the earth, which becomes greater 

 as the distance between the stations increases. When this divergence 

 angle is small as is usually the case in two-theodolite work, its mag- 

 nitude in degrees is found by dividing the length of the baseline by the 

 circumference of the earth and multiplying the result by 360. The 

 divergence angle is given by the equation: 



where d is the divergence angle in degrees; b, the baseline; and R, 

 the radius of the earth in kilometers (from American Ephemeris). 



176. In the case of a baseline of 5 km. in length, the divergence 

 angle is found to be: 



40092 



X 360 = 0.045 



degree, which is significant since the angles are usually read to minutes 

 or to hundredths of a degree. 



Therefore, with a comparatively long baseline, in order for the 

 altitudes of the balloon computed from the B station to be comparable 

 to those computed from the A station, it is necessary to apply a cor- 

 rection to the vertical angles at the B station. The vertical angle is 

 corrected by subtracting the product of the divergence angle and the 



