INSTRUCTIONS FOR MAKING PILOT BALLOON OBSERVATIONS 35 



107. Elevation angles below ^5°.— To compute the value d from the 



formula, tan «=^, where e is less than 45°, the runner of the sUde 



rule, is set at h, in meters, on the D scale of slide rule, and then central 

 slide is moved until the elevation, angle e (for the same minute) on 

 scale T is brought under the hair line of runner. The value of d is 

 then read from the D scale of slide rule under the index of the central 

 slide. In some instances this will be the right index and at other 

 times it will be the left index. With reference to data sheet for single- 

 theodoUte observation, table 1, to compute the distance out for the 

 first minute, set the runner of slide rule on 216 of the D scale then 

 adjust the central slide until 27.6 (the elevation angle for the same 

 minute) on the tangent scale is placed under the hair line of runner and 

 coincident with 216 on the D scale. Under the right index of slide and 

 on the D scale read 413 meters. Notice that the subdivisions on the 

 T scale for angles less than 20° are equivalent to 5 minutes of arc and 

 those subdivisions from 20° to 45° are equivalent to 10 minutes of arc, 

 while the divisions of angles as read from the theodoUte are in degrees 

 and tenths of degrees. Therefore, it will be necessary to convert the 

 tenths of degrees to minutes in order to make the settings of T scale 

 accurate. This is a simple mental operation accomplished by multi- 

 plying the tenths of the angle by 6 the resulting product being the 

 fractional part of the angle converted to minutes. 



108. Elevation angles above 45°. — When the elevation angle is above 

 45°, set the index of the T scale over h found on D scale, set the hair 

 line of the runner over the elevation angle found on T scale, and read 

 the value d under the hair hne of runner on D scale. This value is the 

 quantity sought, and is to be recorded in the corresponding space on 

 Form No. lllOA-Aer. As an example, suppose the elevation angle is 

 54°. 9 and the altitude of the balloon in 600 meters. To compute the 

 value of d for this case we would set the index of central slide over 600 

 on the D scale, then on the T scale of the central slide we would find 

 the angle 54.9° and place the hair line of the runner thereon. Under 

 the hair line and on the D scale we would read off the value of d, or 

 422 meters. It will be noticed that the T scale provided only for 

 angles of 45° or less, and since the function of an angle is equal to the 

 cofunction of the complementary angle, the operation involves a 

 reversal of the method when an angle of more than 45° is recorded. 

 To simplify the settings when the angles are greater than 45°, let the 5° 

 divisions of the tangent scale be re-marked beginning at the 40° 

 division which Avill be designated as 50° ; 30° will be 60°, etc. It these 

 divisions are marked upon the celluloid surface of the rule in red ink, 

 it will be found to assist greatly in the settings for angles greater than 

 45°. Let it be noticed and used as a check that the results of all slide- 

 rule computations made on angles of elevation less than 45° will be 

 greater than the h value on which the computation was made. Simi- 

 larly, the results of all slide-rule computations made on angles of 

 elevation greater than 45° will be less than the corresponding h factor. 



109. It will be noted that the T scale does not contain angles below 

 6°. In computations involving elevation angles below 6° and above 

 84° the sine scale may be used instead of the tanget scale, since the 

 natural sines and tangents of angles up to approximately 6° are equal 

 to at least the third decimal place. It must be remembered, however. 



