750 
ent pictures, the differential formula is 
(see for instance[2], [3] or [4]) : 
Pv = — xdki + (x -— b)dko — = dei 
1 
y? 
J 
HE qu = (1 + 2) hdws. (1) 
h h? 
If only one projector is used for the relative 
orientation (dependent pictures), the for- 
mula is 
bum (= Be oh eV ds 
7 
y y m 
—([14-—] Ados 4- dbys — — dbzs. (2) 
A? 7 , h 
The coordinate system in which the coeffi- 
cients are determined is shown in Figure 1. 
The corresponding formulas for conver- 
gent pictures are of fundamental impor- 
tance for the investigations. For instru- 
ments with the ¢ axis of the projector 
primary, as in the Multiplex or the Kelsh- 
plotter, the derived formulasare as follows: 
For independent pictures: 
2 ) 
jy — i^ COS $1— À sin $i (1+ = jan 
2 
2 
+ | (x— b) cos $»— À sin d» (1+ =) L 
1 
xy (x—b)y 
—— dé dep 
% ®1+ % b 
  
(r5) . y 
-j ; sin a+ (1425) c05 du ids (3) 
1 
and for dependent pictures: 
2 
p | (x— b) cos $»— A sin (14%) fax 
/ 
(x—b)y 
a CR 
Je) 
  
2 
sin $»4- ( 142) COS $» t hide», 
4 
y dia 
-Fdby,— x dbz». (4) 
h 
The formulas have been derived from the 
expressions (15b) by v. Gruber in [2]. The 
signs of the orientation elements are chosen 
to agree with formulas (1) and (2). For 
oı=2=0 formulas (3) and (4) of course 
reduce to (1) and (2). In Figure 2 the nor- 
mal positions of the orientation points are 
shown. The coordinate system is selected 
with its origin in the nadir-point of the left 
projector, and the positive directions of the 
axes are as shown. Of course, other posi- 
  
   
   
  
    
   
  
   
  
  
    
  
  
  
   
  
   
  
   
   
    
  
  
  
  
  
  
  
    
     
   
   
   
   
   
   
   
   
   
  
   
    
   
PHOTOGRAMMETRIC ENGINEERING 
  
  
Fıc. 1. The geometric condition for relative 
orientation of near vertical pictures. Normally 
the points 1-6 are used for the correction of 
y-parallaxes. 
tions for the orientation points could be 
chosen. 
The differential formulas (3) and (4) are 
used for the derivation of error or correc- 
tion equations. For an arbitrary point the 
general correction equation for dependent 
pictures is 
Y= — dbys 
1.2 
v (x,— b) cos $»— À sin $» (140) Ls 
, 
y Cy — b ^v 
eh hy 
h h 
(x,— b) . y»? 
+ | — —- sin 4»-- ( 1+ ay COS d» hdw; 
h h? 
= Puy. ©) 
The correction equations for the points 1-6 
are found by inserting the coordinates of 
the orientation points in this general cor- 
rection equation. The coordinates of the 
orientation points and the coefficients for 
these equations are given in Table 1. 
From the correction-equations, normal 
equations can be set up and solved. The 
solution gives the corrections to the ele- 
ments of the relative orientation, the 
weight and correlation-numbers and the 
square sum of the residual y-parallaxes in 
the orientation points (the square sum 
[v9]). The error propagation in functions of 
the adjusted quantities can be studied 
either by direct use of the normal equa- 
tions, or by the aid of the general law of 
error propagation in which the weight and 
correlation-numbers found from the nor- 
mal equations are used. 
It may also be shown directly from the 
error equations that the condition for the 
relative orientation can be expressed in