26 ANALYTICAL AERIAL TRIANGULATION, DISCUSSION 
refrain from putting all of our thinking on an- 
alytical triangulation in the framework of the 
old instrumental method; by that I mean the 
instrumental method of necessity was restricted 
to building up a photo for one model, subse- 
quently adding another photo, and the process 
was repeated to give what we call cantilever 
extension. 
The analytical method does not need to be 
restricted to this thinking. We should think in 
terms of larger groups of a simultaneous solution 
of a whole strip or of a block, so that the errors 
of propagation which derive from cantilever 
extension will be eliminated. The method by Dr 
Schmid does this very well. One item to be con- 
sidered there — I am sorry he did not have time 
to explain it further — is that weighting factors 
must be applied. The methods of solution will be 
determined by how you wish to apply your 
weighting factors. For instance, in the Cornell 
method the direct geodetic restraint method, we 
have predetermined that a point on the ground 
is a known control point in horizontal, or a 
known bench mark the vertical control point 
and hence that the rays from a pair of photos 
must intersect at a particular elevation or a 
particular horizontal position on the ground. 
This predetermines the type of equation and 
thus we will have more types of equations, but 
less actual computation. 
Prof. P. WISER: Je remercie Monsieur 
MeNair d’avoir terminé si promptement son 
exposé et je déclare la séance levée. 
Continuation of the Discussion in the Meeting Held on Thursday, 8th September 
(Chairman: Prof L. SOLAINI. See page 44) 
Mr G. H. Scuur: Mr President, Ladies and 
Gentlemen, I am glad to have an opportunity to 
make some remarks on two points raised yester- 
day during the discussion on analytical aerial 
triangulation. Professor Thompson advocated 
the advantage of setting up the linear equations 
for the iteration procedure once for all and in- 
verting them, as against the use of modified 
coefficients at each iteration. The Ordnance 
Survey have a large amount of experience with 
this procedure and I understand that I was mis- 
taken yesterday in supposing that they are going 
to abandon it. They are going to retain this 
feature but change some others, and it will be 
interesting to see what their experience is as 
regards the economy of this procedure. 
At the National Research Council of Canada 
we now have a fair amount of experience with 
the use of modified coefficients. We have found 
that in practice two iterations of the relative 
orientation are nearly always sufficient to obtain 
convergence of the rotational elements to within 
the computing accuracy of our programme 
which is within a few decimal seconds. 
For the first iteration we use five points and 
for the second iteration we use all designated 
points. Thus the coefficients must be computed 
twice for five points in each model only and 
only once for the other points. A slight saving 
could be achieved by using a pre-solved solu- 
tion for the first iteration on five, or maybe six 
points. However, for the second, which is the 
final iteration, I think it is better to compute 
the coefficients using the actual positions of the 
points. Doing this, one has the advantage of 
remaining free in choosing the position of points 
in best possible locations in each model. 
It may require more computation time, but 
with ever-increasing speeds of electronic com- 
puters this is not a serious disadvantage. The 
pre-solved solution would still be used for those 
models where the points can be chosen in 
standard locations and not for the other models. 
However, this complicates the operation of the 
computer and it is not advisable for that reason. 
Therefore, it seems to me that a pre-solved 
solution is advisable only if the computer one 
uses has too small a memory to store the pro- 
gramme for the computation and solution of 
the correction equations. 
Dr Inghilleri remarks that he does not agree 
with me when I say that Dr Herget's correction 
equation which I understand he uses is not 
sound. I would like to answer this. Herget's 
correction equation does not truly represent the 
position of intersection, not even in the case of 
differential rotations. It has been shown in 
detail in my paper. This circumstance makes it 
rather difficult to put up an argument in favour 
of it and as yet I have not heard any. 
Also, how are we going to weight the equa- 
tions? It has been done here by multiplying each 
correction equation by the sine of the angle 
between corresponding rays. This has the con- 
venient result of eliminating an awkward factor, 
but it has never been proved that it follows from 
any assumption concerning weight and correla- 
tion of the observations. 
On top of this, we obtain a correction equa- 
tion that is considerably more complicated than 
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