(2 dX)2 + (S d¥) 2 
4 
{dX 1 — dX 2 + dX 3 — dX 4 )2 + (rfFj. — dY 2 + dY 3 — dY 4 ) 2 
i/F 3 ) — — i/X 4 )}2 + 
dX 3 )j i ^b[dY 1 ~ dY 4 )\ 2 
2 («2 + ¿2) 
The weight and correlation numbers are 
0 % = <2r 0 K 0 = 1/2, Q aa = 1/2(02 + 6*), 
Qw =A 2 M Q o, w = ¿ 2 /& 4 
Qcc = ¿7 2(02 + £2), Q^x 0 = - A/2o2, 0 w Y o = 6/2^2. 
Accordingly the equivalent principal distance of plotting is 
c = h + dc 
and the coordinates of the principal point are approximately 
X j 4 ' = dX0 — c d\p, y jj' d\ q T c do) 
when the rotations are small. 
Evaluation. 
When evaluating a photograph with disturbed inner orientation, the 
correction can be made in different ways. 1) The photograph can be 
graphically transformed into the plane of the frame by rectification, 
using the fiducial marks as control points. 2) The transformation can 
be done analytically by using the corresponding correction formulas. 
3) The corrected data of the actual inner orientation can be used with 
the distrubed image with necessary further correction for dtp and d<&. 
Example. 
Six plates were exposed in the Heyde phototheodolite to determine 
the coordinates of the fiducial marks. The fiducial marks were mea 
sured in a Wild comparator (No 824). The coordinates measured in 
each plate were transformed (Helmert) to have the marks as well 
located on the axes as possible. The means of the transformed coordi 
nates of the six plates were regarded as the given coordinates of the 
fiducial marks of the frame. The value of their standard deviation was 
computed as s x>y = 3.44 ¡xm. From the same data the standard devia 
tion of one determination was computed to be s Xt y = 8.43 /xm. 
472