metres long made in a 10-metre length of film, 
that the mean irregular error was 12 microns. 
A film of good quality was used there. Such lar- 
ge errors which by their very nature cannot be 
eliminated have an undesirable effect in large- 
scale plotting and point evaluation. Ultra-flat 
plates are preferable for such purposes. 
The errors caused by film shrinkage are 
large by comparison with those remaining after 
correction of distortion, and photogrammetrists 
should undertake everything in order to get the 
film without shrinkage. 
On camera port glass I say the same as on 
filters, and coming to the end, I say something 
on refraction and earth curvature. With high 
photographic flights refraction becomes appre- 
ciable in that the oblique rays are curved. In 
vertical photography the effect of refraction is 
symmetrical and results in a positive distortion. 
Although this is not a linear function of the 
picture radius, it can be compensated for by a 
small change of the principal distance for a mean 
flight height. For higher flights, the refraction 
should be corrected for in the interests of 
greater accuracy. 
54 GEOMETRISCHE EIGENSCHAFTEN DES BILDES, DISCUSSION 
The curvature of the earth exercises a much 
greater influence than does refraction. Basically 
this influence is no distortion, since if the model 
is made from pictures which are free of all er- 
rors a true model of the terrain including its 
curvature will be obtained. Nevertheless, the 
photogrammetrist requires a model which is 
referred to a flat surface. This can be achieved 
by treating the differences in height between 
the curved earth and a plane tangential to it 
as radial distortion in the picture. The “dis- 
tortion" is negative, proportional to the flight 
height, and increases as the third power of the 
picture radius. It is also rotationally symmetri- 
cal in the case of vertical photography, and for 
this reason can be corrected for, together with 
lens distortion, by the use of correction plates 
during plotting. For practical purposes both re- 
fraction and earth curvature are taken together 
in computing the distortion. 
The deviations arising from earth curvature 
and refraction are of the order of 10 to 100 mi- 
crons. Unless they are corrected for during plot- 
ting there is no purpose in asking for survey 
lenses with accuracies of a few microns. 
Discussion 
Professor B. HALLERT: In his paper Dr David 
has presented an excellent review of actual 
problems, particularly concerning the various 
sources of errors affecting the centre of pro- 
jection of the photographs and from the stand- 
point of the manufacture of lenses and cameras. 
Here a few remarks will be made, especially 
from the standpoint of the photogrammetrists 
and regarding the possibility of the experimental 
determination of irregular errors of the centre of 
projections of the photographs, and estimation 
of the irregular errors of photographs in photo- 
grammetric practice. These two concepts, 
*regular errors of the centre of projection" and 
*remaining irregular errors off the centre of 
projection" seem to me to be of basic impor- 
tance for all discussion on accuracy of photo- 
graphs from a geometrical standpoint. 
First I will mention the agreed method which 
has been applied to check photographs from 
high towers and from the air, from aeroplanes, 
in both cases, after photography of very accura- 
tely determined check-points on the ground 
which have formed a grid. The shape of the 
grid is very simple according to the method of 
the relief squares if we have the point regularly 
located like that. The results of rather com- 
prehensive tests have been published at this 
Congress in my paper, “Results of Practical In- 
vestigations into the Accuracy of Aerial and 
Terrestrial Photographs”. 
Exactly the same principles have been ap- 
plied to x-ray photographs, micro photographs 
and all kinds of photographs from terrestrial 
cameras. Many more similar tests than have 
been published at this Congress have been per- 
formed. I had a few slides, but unfortunately 
they have disappeared, and instead I have here 
a number of papers which can be distributed 
later on to those who are interested. 
It should also be mentioned that a clear 
white distribution in the photographs has been 
determined, in other words the standard errors 
of points located far from the centre is larger 
than the standard error of points in the centre. 
This means that we should take into account 
the weight deviations within the photographs at 
least in our computations of a theoretical na- 
ture. 
Another method, (we call it the Y-parallax 
method), has also been applied for routine tests 
of models under actual plotting. Good results 
have been obtained with this method under 
normal circumstances. Here I will refer to the 
report of Sub-Commission IV—4, in particular 
to the investigations of material from Sub- 
      
  
  
   
  
  
  
  
   
   
   
  
   
  
    
  
   
   
    
  
   
    
  
    
  
   
  
  
  
  
  
  
   
  
  
  
  
  
   
  
  
  
  
   
   
  
  
   
  
  
  
   
   
  
   
   
  
     
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