20 
For a point located in a corner of the image where the coordinates are 
assumed to be 
c 
and for the same s 0 =2,5 microns the formulas give the results 
s a ^16 cc or 5" 
15 cc or 5" 
The slight decrease of the standard error is naturally due to the use of one 
average value for the standard error of unit weight all over the plate. 
The standard errors of the directions derived here depend on a definition 
of the camera axis as the straight line between the (inner) perspective center 
of the lens and the principal point. The geometrical quality of the direction 
in space of this axis is of course important for the determination of the geo 
metrical quality of the oriented directions reconstructed from the photograph. 
It is evident that the relation between the camera axis and some fixed direc 
tions, for example the circles of a theodolite with which the camera is joined, 
in general are determined with the aid of measurements in photographs and 
readings of the circles. Consequently, the standard error of the determination 
of the absolute horizontal and vertical directions of the camera axis can be 
expected to be of the same order of magnitude as the relative direction of a 
ray with respect to the camera axis. The geometrical quality of the circles of 
the theodolite will, however, be of great importance in this case. 
Conclusions 
The investigations have shown that the determination of directions of rays 
from photographs with the aid of interpolation principles can be accomplished 
with considerably higher geometrical quality than with the aid of the elements 
of the interior orientation. 
The great importance of a well defined procedure for the determination of 
the elements of the interior orientation of the camera (or photographs) and the 
non-projective regular errors of the image coordinates has been emphasized. 
The calibration must be made under actual operational conditions as well as 
from specific tests of the lens under laboratory conditions. The test points 
should be chosen so that the elements of the interior orientation can be deter 
mined from point combinations in circles around the principal point, partic 
ularly because the basic geometrical quality of the image coordinates can be 
compared for different radial distances from the center. Preliminary tests have