19 
unit weight of the image coordinates can be used. It is, however, important 
to check possible correlation between the errors of the principal point {dx Q , dz Q ) 
on one hand and the error of the principal distance (dc) on the other. For this 
purpose the expressions for the corrections of the principal point and of the 
principal distance in terms of the observed errors can be computed from (8), 
(9), (10), (12), and (13). 
We find the correction of the preliminary values of the principal point 
to be 
dx p = — \(dx i + dx 2 + dx: 3 + dx 4 +dz { — dz 2 +dz 2 —dz 4 ) 
dz p = — \{dz^ + dz 2 + dz 3 + dz 4 +dx l — dx 2 +dx 2 — dx 4 ) 
(58) 
(59) 
The correction of the principal distance is 
The correlation numbers between these three expressions, defined as the sums 
of the products of the coefficients of identical observations, become zero, 
which indicates that the correlation can be neglected in the error propagation 
from the expressions (56) and (57). 
Therefore the special law of error propagation can be applied and we find 
(61) 
jV+^l/ 
x 2 + z 2 + c 2 \ 
,2 
(62) 
s, 
'P 
Assuming the same average standard error of unit weight of the image coordi 
nate measurements s 0 an d use °f expressions (51) through (55) the follow 
ing simplified expressions are obtained with some minor, evident approxima 
tions 
(63) 
(64) 
Assuming $0=2,5 micron and x=z—0 we find for c— 150 mm 
s a =Sp&20 cc (centesimal seconds) or about 6" (sexagesimal seconds)