2. 
36. The analytical work was designed to approximate instrumental methods as 
closely as ppssible, except that all common geodetic control points in each 
model were used to eliminate y parallax by a least squares solution. The six 
classical locations of relative orientation were not used. 
Research Procedure - After the instrumental triangulations, the research 
work was carried out. 
1. Photographic coordinates - On all 37 photographs, the x and y 
photographic coordinates of the geodetic points were measured using the A7 as 
a stereocomparator. These coordinates served as the raw material for the 
analytical work which followed . 
2. Spatial resection - An analytical spatial resection was performed 
for each photograph using all geodetic points on the photograph and an iterated 
least squares solution. The resection was performed without any correction for 
systematic radial distortion, as were all the triangulations. Residual standard 
errors in photographic x and y after the resection varied among the photographs 
from ±0.006 mm. to ±0.027 mm.; for all points on all photographs the values 
were ±0.012 mm. in x and in y. 
The orientation elements were obtained explicitly from the resection. The 
weight numbers for the orientation elements were used to compute the standard 
error in determining each orientation element. The mean standard errors of 
determination were ±46" in tO, ±51" in^, ±17" inj^, ±1.8 m. in X^, ±1.6 m. in 
Yl, and ±0.6 m. in Zl, where Xl, Yl, and Zl are the exposure station coordi 
nates in the geodetic control plane coordinate system. 
3. Orientation error determination - The orientation elements obtained 
from the spatial resection were subtracted from the elements determined by the 
several instrumental triangulations to give the orientation errors of each photo 
graph for each triangulation. These errors are shown in Figures 1 through 6. 
The values are not completely correct, of course, differing from the true errors 
by; (1) the orientation errors in the spatial resection, and (2) the amounts by 
which the counters and dials of the A7 fail to represent the physical orientation 
elements of the triangulation. I have already given the spatial resection 
standard errors. 
To find the counter errors of the A7, additional analytical resections were 
performed. In this work, the triangulation strip coordinates instead of the 
measured photographic coordinates were oriented to the geodetic ground coordi 
nates. In this way,the triangulated strip is positioned, model by model, to the 
geodetic points on the ground. The orientation elements obtained by this work 
were as close to their A7 counter values as could be expected from the errors 
inherent in the resection. In triangulation 2, for example, the triangulation 
elements by resection differ from the A7 elements by standard error values of 
±2.5 m. in X L and Yl, ±1.8 m. in Zl, ±52" in^, ±39" in^, and ±40" in 1£, 
The orientation errors in Figures 1 through 6 show changes in consecutive 
errors far greater than can be explained by errors of the spatial resection and the 
A7 counters. Notice that the changes in consecutive errors can be nearly as 
great as the mean change for the entire strip. 
Notice also the general similarity of the error patterns among the different 
triangulations. We know that repeated triangulation of the same strip gives 
little improvement in results. Obviously the repetition of the orientation errors 
is the main reason for this. All triangulations were performed by relative