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make a surface perfectly flat and it is also not possible to measure the 
flatness exactly. Some points of view concerning the determination of 
the flatness of surfaces in comparison with a control plane have been 
given in reference [5]. The microscope method for the measurements 
has also been described in the same paper. According to practical ex- 
perience the mean square value of the standard error of the final ele- 
vations of a surface due to the measurements only, is of the magnitude 
0.005 mm under normal circumstances. Evidently the influence of this 
error upon the image coordinates will vary with the location of the 
actual image points. In the principal point there is no influence but in 
the corners of a wide angle photographs the radial displacement is 
approximately of the same magnitude as the deflections from the ideal 
plane, to which the camera constant (calibrated focal length) is referr- 
ed. The deflections can evidently be interpreted as changes dc in the 
camera constant for each actual point. 
The analytical expression of the displacements can be written 
dr’ = — de (1) 
where dr” is the radial displacement at the radius r^ from the principal 
point and dc is the change in the camera constant c. 
Using the statistical expressions s, ands, we find 
8, = dig (2) 
[n a certain camera with the camera constant c and the standard error 
s, the standard error s, of the radial distance evidently will become 
proportional to the radii r’. 
The influence upon the image coordinates x” and y' can evidently be 
written 
X A. 
Sur — TT Se (3) 
C 
J 
y : 
S, = = s. (4) 
; C 
One important task of the actual investigations is to prove if this 
theoretical assumption is in agreement with practice. If this is the case 
the image coordinates evidently will have different weights due to the 
lacking flatness of the image and depending upon the location of the 
points in question. Up to now the image coordinates have been treated 
as equal in weight. Of course, the projection method is important.