The errors of the image coordinates can also be expressed as func- 
tions of the elements of the orientation of the camera according to the 
well known differential formulae, see for instance reference [8] 
  
  
  
  
= sin C cos e)? x! x/’2 c2 
dx! dx’, E (S SD eun C Cos ey dx, + de — i de + 
ch c c 
xy (x' cos © + C sin x'sin q — C COS 9 
+ XN due y'de + - ? e) ( ? e) dh 
C ch 
(55) 
"sin : 
dy’ = dy’, + ym e (x'sin e — c cos g) dx, — 
ch 
x'sin e — C COS , xy 
n scu dy, a de 4- 
h C C 
/2 + c2 "cos 
+ Y eros do + x’de + > ? (x'sin e — c cos e) dh 
  
c ch 
(56) 
dx', and dy', are small translations of the image coordinates, dx , dy, 
and dh are small translations of the entire camera, dc is a change of the 
principal distance of the camera, de, de and dx are small changes in the 
angles of the external orientation. 
From the expressions (55) and (56) correction working equations 
can be established and then normal equations, Some of the elements of 
orientation are completely correlated, however, and therefore the nor- 
mal equation system cannot be solved. Some of the elements of orien- 
tation must therefore be excluded. From direct mesurements in connec- 
tion with the photography, h and x, can be determined conveniently and 
with high precision. These elements are therefore excluded and the rests 
of the expressions (55) and (56) are used for further computations. 
Hence we find the working correction equations: 
, ro 9 I 
x x2 4 c2 x'y 
y. um —À dec di, — y'de — zr de + — do — dx' (57) 
z c c c 
Pal 
x y 
v, = x de + dy’, + x’dk — — de + 
. C c 
72 + 2 ; sin 
Y lC dee(x cot y) e dy, dy’: (58) 
C 
46 
+