50 INSTRUCTIONS FOR MAKING PILOT BALLOON OBSERVATIONS 



Wherein ^= primary station. 

 5= secondary station. 



6= base line. 



^ = angle of triangle at A. 

 ^= angle of triangle at B. 

 C= angle of triangle at C. 

 a = azimuth angle read at station A. 



/3 = azimuth angle read at station B. 

 c?= horizontal distance of balloon from station A. 

 rf'=horizontal distance of balloon from station B. 

 h = altitude of balloon above station A. 

 A,' = altitude of balloon above station B. 

 /i,"= difference in elevation of stations A and B. 



e= elevation angle at station A. 

 e'= elevation angle at station B. 



162. It will be noticed that the azimuth angles are used in the form- 

 ula instead of the smaller interior angles, A and B, of the horizontal 

 triangle. With a little practice, and by taking advantage of the 

 following trigonometric relations, the larger angles are readily set 

 on the slide rule: Angles from 0° to 90° are considered as x; from 90° 

 to 180° as 90° + x; from 180° to 270° as 180°+a^; and from 270° to 

 360° as 270°4a:. Therefore, sin (90°+a;)=-cos x; sin (180°+a:) = 

 sin x; =— sin x; sin 270°+a:=— cos x. That is, to obtain the sine of 

 angles between 90° and 180°, subtract 90° and use the cosine of the 

 result; between 180° and 270°, subtract 180° and use the sine and 

 between 270° and 360°, subtract 270° and use the cosine. This 

 device is employed to avoid the tedious process of subtracting the 

 angles from 180° and 360°, as would otherwise be necessary. 



163. By substituting the first two digits of the azimuth angles by 

 their sum, the mechanical process of the above subtraction is eliminated 

 and the required angle is obtained at a glance. For example, in angle 

 113.38°. substitute 2 for 11, the result^ 23.38°, is the angle required; 

 hence sin 113.38° = cos 23.38°; in angle 213.18°, substitute 3 for 21, 

 hence sin 213.18°=sin 33.18°; and, in angle 347.48°, substitute 7 for 

 34, hence sin 347.48° = cos 77.48°. This device holds true excej)t for 

 angles just above 90°, 180°, and 270°, where the subtraction is made 

 without mental effort. Moreover, when the sum of the first two 

 digits of the angle is 10 or 11 a second addition of these digits must 

 be made, i. e., use 1 or 2 respectively. 



164. Obviously, the methods used in preparing the angles for slide 

 rule are great time savers in computation. The only mechanical 

 work required is in obtahiing a— /3, and this subtraction is done for 

 the entire observation in advance of the computation. 



165. If the stations are at the same elevation, h and h' should agree 

 closely; otherwise, they will differ by an amount equal to the difference 

 in the elevation of the stations above sea level. A comparison of 

 h and h' enables the computer to check his results with more or less 

 accuracy. Ordinarily the computation is done from the A station 

 only, the height, h' being computed from B station, say every fifth 

 or tenth minute as a check. 



