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ANALYTICAL AERIAL TRIANGULATION, AUTHOR'S PRESENTATION 9 
although it is an extremely useful and original 
idea on photogrammetry. 
I regard that as a very powerful method in 
photogrammetry, for reasons which I have given 
in my paper. One of which is that it makes the 
computations more flexible in that one can 
determine whether one's observations are good 
or not, before embarking upon the adjustment 
and computation of a whole block. 
The next point I raise is the matter of condi- 
tion equations where I agree with Mr Schut in 
saying that what one wants to consider in the 
condition equations is the basic condition for 
relative orientation, which is coplanarity of the 
rays and not whether some particular function 
such as the Y-parallax shall vanish. If you 
consider the problem from its fundamental as- 
pect, which is coplanarity of pairs of rays, then 
I think there is always a possibility of simplifica- 
tion. 
In that same paragraph I raise the question 
of what unknowns are best chosen, and the con- 
clusion I have come to is that the standard 
method which is used with plotting instruments 
of keeping one photo projector fixed and putting 
all the variations on the second one turns out to 
be the best choice of unknowns in the analytical 
relative orientation. At least it is the method I 
have found best and leads to the least amount 
of arithmetic, as I have pointed out here. But 
there are, of course, other methods. There is 
the method of putting rotations on both photo- 
graphs, using the air base as your X-axis of 
co-ordinates. There are indeed other methods; 
for example, a very interesting disposition of the 
unknowns is shown in an instrument which 
Messrs Kern are showing at this exhibition, in 
which two rotations are put on one photo, two 
on the second photo and the fifth unknown, 
the Z-base component, and this has led to a 
very interesting instrument which you can see in 
the exhibition. I have had a look at it and I do 
not think that choice of unknowns leads to any 
simplification in the computation method. 
Then in paragraph five I draw attention to 
the possible use of an intermediate stereographic 
projection for the computation of orientation. 
So far as I can see I do not think it will lead to 
any great simplification. 
Finally, I make a point on the iteration 
process. All these methods of solving non-linear 
equations are bound to be iterative. There are 
two, I suppose, basic methods of iteration. One 
is known as a first order process and the other 
one is a second order process. I suppose there 
are third and fourth order processes but they 
are usually too complicated. 
In the first order process one sets up a linear 
equation in effect, and one does not vary the 
co-efficients of this linear equation even though 
you could get better co-efficients for subsequent 
approximations. You keep these co-efficients 
fixed and this results in more iterations. The 
alternative method, the second order process, 
is the one which most of you have learnt at 
school in Newton's method for solving quadratic 
and higher order equations in which the co- 
efficient of the linear equation is successfully 
altered, as you get better approximation so you 
get a better linear equation, and this is the 
second order process which Mr Schut in effect 
advises. I do not think it is necessary because it 
results in a far greater complication in the 
arithmetic, although of course it results in fewer 
iterations; but a high speed computor really does 
not mind how many iterations it does. What it 
really likes is to hàve a relatively simple process 
to work on and iterate many times on that. 
Therefore, I would advise a first order process 
rather than a second order one. 
Prof P. WisER: Merci, Professeur Thomp- 
son, je vous remercie pour cette extrémement 
intéressante mise en route des problémes ac- 
tuels, et je vais tout de suite passer . . . 
Prof G. CASSINIS: Vous permettez un mo- 
ment — je voulais, si vous le permettez, remer- 
cier moi aussi Monsieur Thompson. Comme 
vous le savez, il a été malade dernièrement mais 
nous l’avons vu aujourd’hui avec une belle mine 
et nous lui souhaitons une parfaite guérison et 
une reprise complète de ses activités.