dx 
The meaning of the coefficients of the expressions (1) and (2) can 
easily be determined from a comparison with the expressions (5) and 
(6). The expressions (5) and (6) were first derived by v. GRUBER 1930. 
A considerably simplified and generalized derivation was performed 
by HALLERT 1954— 1955. 
The complete differential formulae of the expressions (5) and (6) 
are of great importance for several purposes, in particular for the 
theory of errors and for investigations into error propagation. In 
v. GRUBER 1930 certain types of differential formulae of the expres- 
sions (5) and (6) are presented but since several substitutions are 
necessary for the practical application the formulae cannot be regarded 
as general. They further refer to the projection case only. 
In a general shape the differential formula of (5) can be written: 
ÔX 0 
. d ÔX 2» ox 2 x a ÔX 1 Sa 
p oT + oy’ y te er art óg egt 
( ox 
oa 
Ox 2 
v 
  
- deo + - 
) 
= or oh 
The z'- and $y'-eoordinates, however, are determined in a coordinate 
system the origin of which is located in the principal point of the image. 
The quantities dx' and dy' therefore can also be caused by the errors 
-da, and -dy, in the position of the principal point. In the formulae 
below dx’ and dy’ can be substituted by -dz, and -dy, respectively if 
the influence of the errors of the position of the principal point are to 
be studied. 
In a similar way the differential formulae of the expression (6) can 
be discussed. 
The numerators of the expressions (5) and (6) are below denoted 
N, and N, respectively. The denominator is denoted D. After 
differentiation of (5) and (6) the following formulae are found: 
h 
daz p: ty sin c 4- e eos o cos x) dx’ + 
h , . . , 
-- p (— x Sin o -- e eos o sin x) dy' + 
h , , - 
-+- De {— eos o (x' cos x 4- y sin 2) dc + 
Va à 
t AD + 
“I