58 INSTRUCTIONS FOR MAKING PILOT BALLOON OBSERVATIONS 



VII. THE TAIL METHOD 



181. The trigonometry of the tail method. — The weakness of the 

 single-theodohte method is the necessity for assuming a fixed rate of 

 ascent of the balloon. The tail method — a modification of the single- 

 theodolite method — overcomes this weakness to a certain extent. 

 It consists in observing the apparent length of a tail attached to the 

 balloon as seen through the telescope of the theodolite. It is useful 

 when the wind is fairly strong so that the elevation of the balloon 

 does not exceed about 40°, but is not applicable when the elevation 

 is large. 



Fio. 19. 



182. In Fig. 19, let be the observer, B the balloon, BC the vertical 

 line, OC a horizontal line, and T the end of the tail of the balloon. 

 Join OT and OB and draw TM perpendicular to OB. 



Let be the circular measure of the angle TOM. 



TM 

 Then, since d is small, tttT/^^ (approx.). 



Let BT~l and C05=£'= angle of elevation of balloon. 



Then Z MTB=90°- ZMTB= ZCOB=E, so that MT=l cos E. 



I cos E 

 Hence 0M= — ^—f or since MB is small, we may write 



OB- 



l cos E 



Hence CB 



I cos E 



sin £"= height of balloon, 



and 



^^ I cos E -r^ 

 0C= 7. — cos E= 



= horizontal displacement. 



The tail thus enables the height of the balloon to be calculated 

 without making any assumptions about the rate of ascent of the bal- 

 loon. The computation for wind velocity and direction follows as in 

 the foregoing method. 



