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ANALYTICAL AERIAL TRIANGULATION, SCHUT 11 
will not obtain a sound method from the mathematical point of view but only a practical 
application, or an impractical one, as the case may be. 
On procedures of strip triangulation. 
2. Analytical aerial triangulation is performed by three different procedures which 
in the presence of redundant observations will lead to slightly different results because 
of differences in error propagation. 
In two procedures the triangulation is performed in steps: each photograph of a 
strip is oriented in turn with respect to the preceding one. In the first of these the pro- 
cedure on first order plotters is simulated in so far as the five elements of relative 
orientation are computed first. These elements are computed by means of a condition 
which expresses in some form that corresponding rays must intersect. Then, without af- 
fecting the relative orientation, the resulting model is scaled by means in common with 
the preceding model. In the presence of redundant observations, e.g. more than five 
points measured in each model and more than one common point in two successive mo- 
dels, relative orientation and scale are adjusted independently. 
In the second procedure all six orientation elements of the photograph are computed 
simultaneously and, in the presence of redundant observations, adjusted simultaneously. 
This means that for rays to points which are common with the preceding model, the 
condition of intersection with the corresponding ray from the first photograph in that 
model is used for the adjustment of all orientation elements. 
In the third procedure the triangulation is performed in one step: all available 
conditions are employed to compute the orientation elements of all photographs simul- 
taneously. 
3. In each procedure model deformation will be caused if distortion of the photo- 
graphs is not properly corrected and if measuring errors or identification errors occur. 
Using the second procedure and more than one common point between models, model 
deformation will cause deformation of the next model because the position of the 
common points will be used in the determination of all orientation elements of the next 
photograph. Deformation of the new model in turn cause deformation of the next and 
of all following models. Therefore only in the initial model of a strip is model deforma- 
tion independent of errors in other models. Consequently the result of a triangulation 
depends on the choice of the initial model and especially different results must be ex- 
pected from two triangulations employing the same measurements but starting at 
opposite ends of a strip. 
It seems possible to practically eliminate this anomaly in the following way. First 
the relative orientation of each two successive photographs is computed from measure- 
ments of corresponding points in the model alone. Then the effect of the common points 
on the relative orientation is computed for each two successive models. Finally these 
effects are distributed equally over the models concerned. In this way the second proce- 
dure would become considerably more cumbersome than the first but it would at least 
become a logical procedure and the computations would still be much simpler than the 
simultaneous solution of all equations in the third procedure. 
On condition equations. 
4. The specifications of paragraph 1 will now be employed to investigate four methods 
which have actually been coded for use on electronic computers. 
These methods make use of the condition that corresponding rays must intersect. 
They express this condition by different equations. 
a. The method developed by the author at the National Research Council of Canada 
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