18 
Then we find the weight numbers of the corrections after application of 
the general law of error propagation to the expressions 
dx=dx 0 + cd(p and dz=dz 0 +cdco 
For the expressions (17), (20), and (21) we find the weight numbers of the 
corrections to be 
Qxx—J— Qzz 
(52) 
Assuming weight numbers for the measurements in the preliminary principal 
point of 1 in each direction with the same weight number for the measure 
ments in the photographic plate we obtain the total weight number of the 
coordinates of the principal points as Q XOXo =Q zozo =i and the standard errors 
of the position of the principal point for use in the equations (49) and (50) are 
]/To 
2 
(53) 
S x 0 S zo s 0 
It should be noted that the weight number of the radial distortion from circle 
combinations of four points is 
Qdrdr 4 
(54) 
and consequently that the standard error of the radial distortion is 
(55) 
S dr~2 S 0 
The correction for radial distortion in jc and z depends upon the location of 
the points, however. The maximum standard error of the radial distortion 
correction is therefore given by (55). 
If corrections are applied to the image coordinates for other circumstances, 
such as tangential distortion or affine deformation, the corresponding stand 
ard error should be computed and taken into account. From differentiation 
of formulas (49) and (50) there is found, for x 0 and z 0 near zero: 
c(dx — dx 0 ) — xdc 
(56) 
z{xdx — xdx 0 + cdc 
dp = 
dz — dz 0 — 
(57) 
2 , 2 
X +C 
For the study of error propagation with these expressions it should be noted 
that the differentials dx 0 , dz 0 and dc refer to the calibration procedure while 
the differentials dx and dz refer to the measurements in the photograph from 
which the rays will be reconstructed. Provided that the calibration is made 
under operational conditions the same average value of the standard error of