17 
tation points. Consequently, after determination of the standard errors of 
these linear functions according to the laws of error propagation, tolerances 
can be determined on a specific level, using the ¿-distribution as discussed 
above. 
The mean value of the standard error of a residual y-parallax in arbitrary 
model points after an adjustment of the relative orientation according to the 
method of least squares is about 1.35 0 , where s 0 is the standard error of unit 
weight. For 4 degrees of freedom in the determination of s 0 , the tolerance of a 
residual y-parallax becomes about 2.8 times the standard error on the five 
percent level. For .y 0 = 6 microns the residual j-parallaxes should not exceed 
22 microns under the assumptions made here. 
In order to determine tolerances of model coordinates or elevations after 
the absolute orientation as functions of the relative orientation the compensat 
ing effects of the absolute orientation and the measurements in the model 
have to be taken into account, see Hallert-Ottoson-Ternryd 1960. 
I: 1.3 Root Mean Square Values of Standard Errors 
Particularly in photogrammetry, the accuracy of the entire procedure is 
frequently checked from a comparison between the final photogrammetric 
coordinates and the corresponding geodetic data. The geodetic coordinates 
are in general assumed to be of such high geometrical quality that they can be 
regarded as errorless in comparison with the photogrammetric coordinates. 
The discrepancies obtained from the comparison can therefore be regarded 
as true values and the root mean square value is an expression for the true 
standard error of the photogrammetric coordinates. If the corresponding 
value has been determined from the estimated errors of the fundamental 
operations and the relevant laws of error propagation, a comparison between 
the two determinations of the final accuracy is of great interest. The deviation 
which is to be expected and which usually is obtained should not exceed specific 
tolerances. Therefore it is of considerable interest to determine them. Examples 
of this problem have been treated in Haller t-Ottoson-Ternryd 1960. 
The confidence limits were computed according to the cA/ 2 -distribution. 
For 10 redundant observations (degrees of freedom) and on the 5 percent 
level, the confidence limits are 0.75 0 —l-8^o where s 0 is an estimation of the 
basic standard error of unit weight of the fundamental operations (primarily 
the relative orientation). If the root mean square value of the discrepancies 
between geodetic and photogrammetric coordinates were found to fall within 
the limits, the theoretical derivation of the error propagation was not disproved. 
In Hallert-Ottoson-Ternryd 1960 and Hallert-Ottoson-Ohlin 1964 all tests 
indicated that the applied theory could be accepted.