THE FORM OF AN AIRPEANE LOOP 
209 
has results for the azimuth and elevation of the same point on 
the airplane’s path as measured from the plate of the other 
camera. Call these angles and a', respectively. 
We have now to find the co-ordinates of the point of the path 
of the airplane from these four angles, and the length of the 
base line. In figure 42, let L be the length of the base line (in 
our work, about one-half mile) between the two piers A and B. 
Let the line K to pier A be the projection of the axis of camera 
Ay and Q to pier By be the projection of the axis of camera B, 
Let the angle b be the azimuth of the ray in question from camera 
A, referred to the base line, and the azimuth determined from 
camera B. Then 
b ^ A + c. (4) 
y = 180° — R + c' (5) 
where the angles A and B have previously been accurately sur- 
veyed. We have given then (see Fig. 43) the angles a, b, and 
y, and the length L of the base line. S is the point to be de- 
termined, and X, Y, and ' Z referred for convenience to pier 
A as origin, its co-ordinates. Then 
X = R cos b X — R' cos b' A- L 
Y = R sin h Y ~ R' sin 
Z — R tan a Z — R' tan a' 
and if we eliminate R and R' from these equations, we obtain, 
cos & sin 6' 
^ “ sin (y — by 
F = Z tan 6 (7) 
tan a 
cos & ^ ^ 
