Here dm is a difference in scale between the x and y directions, and dp is a 
lack of orthogonality between the x and y-axes. From formulas 5.4.11 and 
5.4.12 we obtain 
d = ± 1¡dm 2 + dp 2 5.4.13 
1 dp 
a — arctan 5.4.14 
2 dm 
Here a is in the intervaland the sign of d is the same as that of dm. 
Affine film shrinkage is thus included in the mathematical model by adding 
the terms in formula 5.4.10 to those of formula 5.1.2. 
For acetate emulsion bases we get regular shrinkage of higher degrees and 
as shown by Talts [25] these can be determined and corrected for from measu 
rements on the fiducial marks, which have to be sufficient in number and sui 
tably located. The aerial cameras from Jena are now equipped with scales along 
the sides of the picture that makes it possible to determine two different scales 
on the photograph. The reseau cameras produced by several companies are 
very well suited to investigations of film shrinkage. 
5.5. LINEAR FORMULAS 
The calculation procedure in the following is based on the method of least 
squares. The expressions 5.1.1 and 5.1.2 must then be linearized. They are 
expanded in a Taylor series. If a), cp and ^ are small, we obtain after neglecting 
terms of higher order: 
x —"b c 
X-X 0 
Z-Z 0 
+ 
X—X 0 
dxo + —^^ dc — 
Z-Zo ~ Z-Z 0 
(X-X 0 ) (Y-Yo) 
c X—X 0 
dXo + ^ c dZ 0 
(Z-Z 0 y 
(X-X 0 ) 
Y-Yr 
(Z—Z 0 ) 2 
, y - y ° , 
y=y 0 + c z _ z - + 
cito + jl + (2—Z„) 2 f cd(p + Z—Z c 
• c dx 
5.5.1 
Y-Yo 
dy 0 + dc 
Zj—Zn 
Z—Z f 
Y-Y 0 
dY 0 + ^ 2 yL c dZo 
, (V-ro) 2 l , , (X-X 0 ) (Y-Yo) , 
1 + ~ 7T7Z ! c doj H — C dtp 
(Z—ZqY 
(Z-Z o) 2 
X—X( 
Z-Zo 
c dx 
5.5.2 
18