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ANALYTICAL AERIAL TRIANGULATION, SCHUT 17 
three rotations are small it will certainly increase the required number of iterations. It 
cannot be an economical procedure if the linear equations are set up and solved in each 
iteration. 
12. The Herget Method has been developed for the third triangulation procedure and 
applied to the second one. The condition of intersection is linearized not by differentia- 
tion but by computing the effect of a small rotation and shift applied to the vector Vii 
which is the vector from the projection centre of photograph i+1 to the end of the vector 
of minimum distance. 
A. differential rotation JR changes the vector V;+1 by a vector óR X V, , ,. A shift 
changes the base vector B by a vector óB. Herget's linear equation specifies that by this 
rotation and shift the component of the vector sum B + V; 41 0n an axis in the direction 
of the present vector of minimum distance must be reduced to zero. In our notation 
OR XV, C+ (B+ 0B): €^ — 0 
in which 
OR = oi + a,j + ask, 
1 
Vui (B X Vo,- Ce) Vo 
1+1 sin I 
( 2 Vo. X vo 
sino ^ 
and the superscript " now denotes a unit vector. 
In other words, the linear equation specifies only that after rotation and shift the 
head of the vector V;,, must lie somewhere in the plane which contains V, and is parallel 
to V;,, before its rotation. This is not sufficient to make corresponding rays intersect. 
Therefore the linearization is not based upon sound mathematical reasoning. 
As a result the linear equation differs from the one which would have been obtained 
by differentiation of Herget’s condition equation and the orientation procedure can be 
expected to converge a little slower than in the author's and Schmid's methods. 
The linear equation has the additional disadvantage of being considerably more 
complicated than the one in paragraph 6. 
The linear equations obtained are “weigthed” by multiplication by sin 0. This weight- 
ing is not properly based on weight and correlation of the observations and is therefore 
not proper either. It only makes the linear equation a little less complicated. 
It has been argued here that the Herget method fails to meet the specifications for 
a sound method from the theoretical point of view on a total of three counts. Besides, in 
its applications the second triangulation procedure is employed with its unfortunate 
consequence. 
This does not imply that the Herget method will always give inferior results. Indeed, 
if no redundant observations are used in the orientation, this method will give the same 
results as any other method which uses the same triangulation procedure provided of 
course that in each method the iteration is continued until it converges and that the 
computations are performed with the required accuracy. 
i41, 
On the computation of map coordinates. 
13. If the strip triangulation is performed by the third of the aforementioned proce- 
dures, that is by simultaneous computation of the orientation elements of all photo- 
graphs, condition equations referring to the measured ground control points can be in- 
cluded in the computation. In this way the strip is automatically adjusted to ground 
control and strip coordinates are immediately obtained in the coordinate system employed 
for the ground control points. 
If one of the first two procedures is chosen it is always possible to perform the