3. 
orientation at the classical six points in the model. Therefore, I thought that 
small errors may have existed in the areas of each model where the relative 
orientation points are commonly chosen. These errors could cause the similarity 
of orientation error patterns that I found for the different triangulations. 
4. Analytical triangulation - To test this hypothesis, I performed the 
analytical triangulation that I mentioned earlier. I designed this method of 
analytical triangulation to be very similar to instrumental triangulation. However, 
in the analytical method the y parallaxes in each model were eliminated simulta 
neously from all common geodetic points by a least squares solution. In this way 
each available model point helped to determine all orientation elements. The 
standard residual y parallax for 306 point intersections in the 30 model strip was 
±0.007 mm. 
The orientation errors of the analytical triangulation - in which parallax was 
removed at essentially random points in the model - show the same error pattern 
that occurs in the classical instrumental work. Therefore, small errors at the 
classical six points do not explain the error pattern similarity. 
In the resection work the x and y photographic coordinates of points on the 
entier photograph are used to determine the orientation. In instrumental aerial 
triangulation, only y ditierences from the preceding photograph's common points 
are used. Perhaps the error pattern' similarities are caused by this failure of the 
y parallax methods to use all possible information in triangulation. Further 
research must be performed to answer this question. 
5. Fictitious triangulation - Of course, because of correlation the 
errors of the triangulation strip coordinates propagate more smoothly than the 
errors of the individual orientation elements. I have devised a simple analytical 
method for showing the coordinate error propagation that is caused only by 
orientation errors. This method involves the following steps: 
a. Transform the ground coordinates of fictitious geodetic points to 
their photographic coordinates, using the true elements of 
orientation determined from the spatial resections; 
b. Use the incorrect orientation elements of an instrumental triangu 
lation to intersect the fictitious photographic coordinates back to 
the ground, model by model, as in a triangulation with aerial 
polygons; 
c. Adjust the points as for a normal triangulation. 
I selected the fictitious points so that in each model they lie at the 
classical six points of relative orientation. The false orientation elements used 
were those for triangulation 2 . 
The resulting raw triangulation strip coordinate errors are shown in Figure 7. 
Some systematic errors have been removed by polynomials in X to show the 
deviations from smooth curves more clearly. 
6. Strip adjustment - All triangulations except number 6 were adjusted 
nonconformally to least squares polynomials with the following forms: 
X = a Q + ajx + a£X^ + + a4y + a5xy 
Y = c Q + c\x + C2X^ + C3y + c^xy + c^x^y 
Z = d Q + d]X + d2x2 + d0X^ + d4y + dsxy + dgX^y . 
All triangulations bu numbers 3 and fictitious 2 then were adjusted for the effects