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SIGN CONVENTIONS IN PHOTOGRAMMETRY, DISCUSSION 
      
  
Discussion 
Prof W. ScHERMERHORN: This is a nice sub- 
ject on which we could have discussion for some 
time. If there is anyone who is strongly opposed 
to this and believes that he could not be happy 
with such a system, he is invited to speak now. 
[ am entirely in favour of this proposal. 
Mr G. H. Scuvur: I am not strongly opposed 
to this but there are some remarks I should like 
to make on the question of the base components. 
If you do not object to my doing that, I should 
like to do so. 
As regards the other things, it is just as you 
have said; we have used them up to now and we 
are quite satisfied that they represent a con- 
venient and logical solution. 
However, I should like to refer to this point 
of base components and vector analysis. Vector 
analysis is becoming more and more used in 
photogrammetry. Here it is customary to iden- 
tify the component of the vector by indices, 
either by lower indices or, if a distinction must 
be made, by covariant or contravariant, by lower 
and higher indices. 
In photogrammetric derivations we should 
remain in accordance with this practice for two 
reasons: first, because it is customary in an 
established mathematical discipline; and, sec- 
ondly, if you write the indices x, y and z at the 
same height as the 5, then each base component 
will in vector analysis look like a product of two 
scalars. Therefore, if we use vector analysis, we 
will in practice derive components of all vectors 
except the vectors which represent a base with 
indices. We will only make an exception for this 
base in the components of this base. This is 
rather awkward, and the only logical solution 
from this point of view is to accept lower indices. 
Since the base components are components with 
respect to the X, Y, Z system, which is written 
in capitals, we should also have capitals for 
x, y and z. 
I should like to know whether there are 
equally strong arguments in favour of the 
present proposal. If so, I am quite ready to 
accept the six proposals as a whole just in order 
to obtain the necessary uniformity in the choice 
of positive directions and rotations. 
Prof W. SCHERMERHORN: I should like to ask 
for the answer to this from the floor. Is there 
one of you who could answer this? 
Mr B. HALLERT: I think it is most important 
that we try to educate our students so that they 
are able to adjust themselves to all possible 
systems. This is most important, I think, be- 
cause as Professor Schermerhorn has said the 
instrument factories will go their own way. 
Prof W. SCHERMERHORN: That is all that is 
behind it. It is mainly a question of how we 
teach, and that the literature and publications 
are on a uniform basis so that people will under- 
stand them straightaway. 
There is something in what Mr Schut has 
said. I do not know whether he is entirely right. 
He said that in future vectorial algebra will be 
the main, or a very important, method which 
will be applied to photogrammetric processes. 
I do not believe that entirely. Anyhow, it is not 
necessary. 
I should just like to add another word in 
this respect speaking as a teacher: we must avoid 
using complicated methods of notations and 
systems if problems can be solved by means of 
classical methods, such as classical algebra 
and geometry, which are understood by most 
people. We darken a lot of good things by using 
mathematical systems unknown to the majority 
of the people in photogrammetry. I would ask 
you not to forget that we have a lot of people 
who are not primarily mathematicians or who 
have not spent a considerable part of their lives 
studying mathematical methods. That is one of 
the reasons why you will never find these com- 
plicated methods in the Delft publications ex- 
cept where it is impossible to reach a solution 
other than by these complicated means which I 
find very difficult. In just the same way as I said 
to the artist concerning the piece of modern art 
which we have at the front of our building, "I 
want to get something which I can understand 
without instructions", I feel the same about the 
mathematical tools in my house: if I do not 
understand them, then there are more people 
who do not understand them.