54 INSTRUCTIONS FOR MAKING PILOT BALLOON OBSERVATIONS 



The same rules apply to the use of the sign between e' and B, as 

 apply to the sign before h" cot e' in equations (9) and (10). 



168. It will be noted that the d and h formulas (5), (6), and (7), 

 (8), are identical except the plus sign between e and e' is used in the 

 latter, where the balloon is between the stations. 



Formulas (9) and (10), used where there is appreciable difference in 

 elevation of the stations, are also similar to (5), (6), and (7), (8), 

 except for the increase or decrease in length of base line, 6, by h" 

 cot e' . The following rules govern the sign of U" cot e': 



If elevation of A station is less than B station, use plus sign if 

 balloon is on A station side or between the stations; when on B 

 station side use minus sign. 



The reverse is true if the elevation of A station is greater than B 

 station. 



The value of h" cot e' may be found by slide rule, and the correct 

 value for h substituted in the formulas. 



169. In actual practice, the angles as read at the A and B stations 

 are recorded on Form No. 1110-Aer., "Pilot Balloon Ascension Re- 

 port." Upon completion of the observation, the angles recorded at 

 the B station are copied upon the form used at the A station, and the 

 C angles (a— jS) determined for the observation. See figure 5. 



170. Computation. — The first minute of the observation shown on 

 this form (table 2) was computed from the B station by formula (4), 

 as the azimuth angle /3 for this minute is beyond the range of the sine 

 scale of the slide rule. The remainder of the observation is computed 

 from the A station by formula (3). 



The computation for the first minute is accomplished by the special 

 slide rule, as follows: 



1. Set right end of slide on 6=4949 m., on A scale. 



2. Move runner to sin 169.90° = cos 79.90°, that is to red 79.90° on 

 S scale. 



3. Move slide to bring sin 9.59 under runner; that is, bring black 

 9.59° on S scale under runner. (The horizontal distance, 5209 m., is 

 indicated on A scale by end of slide.) 



4. Moverunner to tan 3.35°; that is, to black 3.35° on T scale. The 

 height, 305 m., is indicated on A scale by runner line. 



The remainder of the observation is computed from the A station; 

 therefore, angles /3 and e are used instead of a and e' . 



171. In practice it is found advantageous to complete the four 

 steps of the computation and take both height and distance off the 

 rule at the same time, rather than to record distance at the end of the 

 third step and the height at the end of the fourth. 



172. The method of computation described for slide rule is used 

 with similar advantage when the computation is accomplished by 

 logarithms or computing machine. The above example is computed 

 by logarithms, as follows: 



log 4949 = 3. 69452 



log cos 79.90 = 9. 24395 — 10 



colog sin 9 . 59 = . 77833 



log d' =13. 71680 - 10^/' = 5,209 m. 



log tan 3. 35 = 8. 76742 - 10 



log h' =22. 48422 - 20/(/ = 305 m. 



